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@@ -0,0 +1,1970 @@
+1
+00:00:05,690 --> 00:00:08,810
+تمام يا بنات، هنبدأ اليوم إن شاء الله بالـ chapter
+
+2
+00:00:08,810 --> 00:00:15,810
+الثالث اللي بيحكي عن الـ vectors والـ scalars لما
+
+3
+00:00:15,810 --> 00:00:20,570
+حكينا في الـ chapter الماضي عن الـ distance والـ
+
+4
+00:00:20,570 --> 00:00:24,050
+displacement قلنا إن الـ displacement كـ vector
+
+5
+00:00:24,050 --> 00:00:29,130
+quantity لها جزء كامل هنأجله لـ chapter 3 وهو
+
+6
+00:00:29,130 --> 00:00:33,990
+أي chapter 3 اللي هنشرح قبل  احتياط الـ vectors
+
+7
+00:00:33,990 --> 00:00:37,850
+هنشرح الـ coordinates axis أو الـ coordinate systems
+
+8
+00:00:37,850 --> 00:00:44,050
+اللي هم أنظمة المحاور الكارتزية وما شابه، ثم
+
+9
+00:00:44,050 --> 00:00:47,810
+هنخش في تعريف الـ vector وإيش بيميزه عن الـ scalars
+
+10
+00:00:47,810 --> 00:00:53,890
+ثم هنتعلم كيف نجمع وكيف نطرح الـ vectors، ثم هناخد
+
+11
+00:00:53,890 --> 00:00:59,920
+حاجة نسميها مركبات الـ vector، مركباته، وبعدين
+
+12
+00:00:59,920 --> 00:01:04,100
+هناخد ضرب الـ vectors، والضرب عبارة عن ثلاثة أنواع
+
+13
+00:01:04,100 --> 00:01:09,180
+نوع في هذا الـ chapter، ونوع موجود في chapter 7، و
+
+14
+00:01:09,180 --> 00:01:13,080
+نوع موجود في chapter 11، هناخد تبع 7 وتبع 11، و
+
+15
+00:01:13,080 --> 00:01:17,220
+نجمعهم هنا، وناخد كل ما يتعلق بالـ vectors بهذا الـ
+
+16
+00:01:17,220 --> 00:01:20,820
+chapter، عشان كده لو شفتوا أنتم الـ problems اللي
+
+17
+00:01:20,820 --> 00:01:25,660
+مطلوبة منا في بعض الأسئلة مكتوب من chapter 7 وفي
+
+18
+00:01:25,660 --> 00:01:29,440
+بعض الـ problems موجودة من chapter 11، أحنا هنشرحهم
+
+19
+00:01:29,440 --> 00:01:35,320
+كلهم ونخلص منه الكتاب، فلسفته إن الشغل اللي بتلزمنا
+
+20
+00:01:35,320 --> 00:01:38,440
+في chapter 7 أجيلة لـ chapter 7، والشغل اللي بتلزمنا في
+
+21
+00:01:38,440 --> 00:01:42,760
+chapter 11 أجيلة لـ chapter 11، احنا قلنا لأ، من هالجهة، ناخد
+
+22
+00:01:42,760 --> 00:01:48,240
+كل حاجة بتتعلق بالـ vectors ونخلص منها، فهذه الـ problems
+
+23
+00:01:48,240 --> 00:01:53,320
+من chapter 7: سبعة، وتسعة، واثنا عشر، وثلاثة عشر من chapter 7، وواحد، وثلاثة، وسبعة
+
+24
+00:01:53,320 --> 00:01:59,680
+وعشرة من chapter 11، طبعا حسب الكتاب، يلا نبدأ coordinate
+
+25
+00:01:59,680 --> 00:02:04,760
+systems، أنظمة الإحداثيات، coordinates، محاور أو
+
+26
+00:02:04,760 --> 00:02:09,960
+إحداثيات، تمام، احنا حكينا يا بنات لما قلنا بنحدد
+
+27
+00:02:09,960 --> 00:02:14,000
+موضع أي جسم، مش قلنا ما ينفعش تقولي موضعه خمسة أمتار، و
+
+28
+00:02:14,000 --> 00:02:19,040
+بس، لازم تقولي مرجعية، هذه المرجعية بدل ما تقولي
+
+29
+00:02:19,040 --> 00:02:23,680
+والله الطيران، وتقولي عزجولة، وتقولي المفترق
+
+30
+00:02:23,680 --> 00:02:30,180
+الشجاعية، بدي شغلات عامة مالهاش خصوصية، هذه الشغلة
+
+31
+00:02:30,180 --> 00:02:36,180
+العامية سميناها محاور، هذه المحاور لها عدة
+
+32
+00:02:36,180 --> 00:02:41,040
+أنواع، أول نوع اللي أنتم اخذتو، المشهور، المحاور
+
+33
+00:02:41,040 --> 00:02:44,920
+الكارتزية، أو الإحداثية الكارتزية، مش أخذناها اللي
+
+34
+00:02:44,920 --> 00:02:51,520
+هي عبارة عن إيش؟ عبارة عن محور سيني ومحور صادى، هدول
+
+35
+00:02:51,520 --> 00:02:54,200
+لازم يكونوا متعامدين ولا لأ؟ هدول لازم يكونوا
+
+36
+00:02:54,200 --> 00:02:58,600
+متعامدين، إذا بيقول لي: In physics it is important to
+
+37
+00:02:58,600 --> 00:03:02,260
+define the position of a point in space، بتحدد أي
+
+38
+00:03:02,260 --> 00:03:07,780
+نقطة وين بالضبط موضحها، In doing so we need a
+
+39
+00:03:07,780 --> 00:03:11,180
+coordinate system، أول coordinate هناخده هو الـ
+
+40
+00:03:11,180 --> 00:03:14,800
+Cartesian coordinates، الشيخ كارتيزيان، كاردياس ده هم
+
+41
+00:03:14,800 --> 00:03:19,960
+X و Y، من إيش بتستفيد؟ قال لي عشان لما بدي أديك
+
+42
+00:03:20,490 --> 00:03:25,450
+رقمين، واحد صادى وواحد سيني، ولازم  ممكن إلا تحدد
+
+43
+00:03:25,450 --> 00:03:27,570
+موضع النقطة، صح ولا لأ؟
+
+44
+00:03:57,100 --> 00:04:07,550
+تسعين درجة، تتقاطع، تتقاطع، تتقاطع في نقطة، هذه النقطة
+
+45
+00:04:07,550 --> 00:04:13,330
+بسميها نقطة الأصل، إذا: intersect at a point called
+
+46
+00:04:13,330 --> 00:04:19,970
+the origin، تسمى نقطة الأصل، حلو، To get any point in
+
+47
+00:04:19,970 --> 00:04:24,840
+a plane، في مستوى، is assigned to numerical values،
+
+48
+00:04:24,840 --> 00:04:29,140
+بديها رقمين، numerical values، رقمين، إيش هم؟
+
+49
+00:04:29,140 --> 00:04:33,580
+الرقمين دول، وحدة بسميها الـ X value، وواحدة الـ Y
+
+50
+00:04:33,580 --> 00:04:37,700
+value، هجيت هذه شايفينها خمسة وثلاثة، إيش يعني؟
+
+51
+00:04:37,700 --> 00:04:41,820
+بقول له ع السيني خمسة، وع الصادي ثلاثة، لما أقول لك
+
+52
+00:04:41,820 --> 00:04:45,620
+خمسة وثلاثة، في أي بنت بتحط نقطة غير هذه النقطة؟
+
+53
+00:04:45,620 --> 00:04:50,360
+إذا بهدول الرقمين بكون حددت تماما موضع النقطة،
+
+54
+00:04:50,360 --> 00:04:55,280
+ولا لأ؟ خلاص، إذا أنا بيلزمني رقمين عشان أَحدد موضع
+
+55
+00:04:55,280 --> 00:05:01,940
+أي نقطة، رقمين، sorry، رقمين سيني وصادي، تمام، هاي
+
+56
+00:05:01,940 --> 00:05:05,580
+نسميها الإحداثي السيني اللي هي الخمسة، والثلاثة هو
+
+57
+00:05:05,580 --> 00:05:09,500
+الإحداثي الصادي، أصلاً أخذنا هذه الشغلات مظبوط ولا لأ؟
+
+58
+00:05:09,500 --> 00:05:14,150
+تمام، ده طيب لما يكون في عندي فراغ بقول له بدي محور
+
+59
+00:05:14,150 --> 00:05:19,310
+ثالث، صح ولا لأ؟ المحور الثالث اللي هو Z أو اللي
+
+60
+00:05:19,310 --> 00:05:23,410
+احنا عندنا Z، لازم يكون عمودي على الاثنين، ذاكرين
+
+61
+00:05:23,410 --> 00:05:30,340
+هدول؟ وين أخذناهم؟ في المجال المغناطيسي، ذاكرينها؟
+
+62
+00:05:30,340 --> 00:05:35,460
+هدول،  بقولوا X، Y، و Z، هذول ثلاثة متعامدين، X، Y، و Z
+
+63
+00:05:35,460 --> 00:05:41,020
+لأنهم يكونوا متعامدين، وذاكرين هدول؟ برضه X، Y، و Z
+
+64
+00:05:41,020 --> 00:05:46,260
+طبعاً، إذن هذا كله عشان المحور الثالث صعب الواحد
+
+65
+00:05:46,260 --> 00:05:50,540
+يرسمه على اللوح، فراحوا جابوا كيف تتعامل معاه، طبعاً،
+
+66
+00:05:50,540 --> 00:05:54,200
+إذن بيقول لي: For three dimensional case، لأن كان عندك
+
+67
+00:05:54,200 --> 00:05:58,790
+بُعد ثالث، فيه فرق، There is a third axis، في عندك
+
+68
+00:05:58,790 --> 00:06:02,650
+محور ثالث اللي بتسميه Z axis، perpendicular to the
+
+69
+00:06:02,650 --> 00:06:06,630
+XY plane، لازم يكون عمودي على الاثنين، تمام، and
+
+70
+00:06:06,630 --> 00:06:09,530
+passing through the origin، واحنا بنرسمه هيك، و
+
+71
+00:06:09,530 --> 00:06:13,910
+رائع عليكم، هذا المحور الثالث، طبعاً لو بدرسوا على
+
+72
+00:06:13,910 --> 00:06:17,750
+لوح برسموه هيك، لكن بتتخيلوا إن هذا مش على لوح، طالع
+
+73
+00:06:17,750 --> 00:06:22,850
+على برا، تمام، and passing through the origin، the
+
+74
+00:06:22,850 --> 00:06:25,130
+Cartesian coordinates، هذه الـ Cartesian Coordinates
+
+75
+00:06:25,130 --> 00:06:28,830
+لها اسم ثاني بيسموها rectangular coordinates،
+
+76
+00:06:28,830 --> 00:06:34,670
+rectangle يعني مستطيل، تمام، مش مشكلة المسميات، تمام،
+
+77
+00:06:35,940 --> 00:06:38,560
+بس عندنا Cartesian Coordinates، قال لي لأ، محاور
+
+78
+00:06:38,560 --> 00:06:43,180
+كتيرة، احنا بدنا ناخد نوعين من أنواع المحاور، هذا
+
+79
+00:06:43,180 --> 00:06:47,800
+نوع ثاني بيسموه Polar Coordinates، المحاور القطبية،
+
+80
+00:06:47,800 --> 00:06:54,300
+قطبية، قطب، Pol، Polar، قطبي، قال له أنت في الـ Cartesian
+
+81
+00:06:54,300 --> 00:06:58,760
+Coordinates إيش بيهتمك؟ بقول له لما تديني معلومات بدي
+
+82
+00:06:58,760 --> 00:07:02,940
+أقدر أَحدد موضع النقطة، مش هي المهمة، هي مهمة الـ
+
+83
+00:07:02,940 --> 00:07:07,440
+coordinates، قال طب أنا بدي أديك رقمين بس مش
+
+84
+00:07:07,440 --> 00:07:13,400
+سيني وصادي، بدي أديك رقمين كالتالي: بدي بعد النقطة عن
+
+85
+00:07:13,400 --> 00:07:17,780
+الـ origin، وبَدي الزاوية اللي بيعملها البعد مع الـ X
+
+86
+00:07:17,780 --> 00:07:21,620
+Axis، بيكفيني هدول الرقمين ولا بيكفونيش؟ خلّيني أشوف
+
+87
+00:07:21,620 --> 00:07:26,660
+يا بنات، هجيت هاي هدر؟ ها دي نقطة، أنت قلت لي الـ C
+
+88
+00:07:26,660 --> 00:07:31,260
+نقطة بحددها، لو أقول لك ها دي خمسة أمتار، وها دي الزاوية
+
+89
+00:07:31,260 --> 00:07:36,170
+45، بتبدأ تحددها ولا لأ؟ خلاص، طب ليش أنا بغير عدة
+
+90
+00:07:36,170 --> 00:07:41,070
+نقول، ليش بنغير؟ إذا بيقول لي: Sometime، أحياناً بيلزمك
+
+91
+00:07:41,070 --> 00:07:46,750
+تكون عندك بدائل غير الـ Cartesian Coordinates، It is
+
+92
+00:07:46,750 --> 00:07:48,970
+convenient... convenient يعني ماعنده، suitable...
+
+93
+00:07:48,970 --> 00:07:52,720
+إيش معنى suitable؟ مناسب، فـ convenient هي suitable،
+
+94
+00:07:52,720 --> 00:07:57,300
+يعني مناسب، أحياناً أفضل مناسبة، يعني: To specify a
+
+95
+00:07:57,300 --> 00:08:01,760
+point in space by its distance from the origin،
+
+96
+00:08:01,760 --> 00:08:06,780
+المسافة بين النقطة والـ origin، وهذا بَديها الرمز R،
+
+97
+00:08:06,780 --> 00:08:12,030
+الرمز إيش هو؟ الـ Radius اللي هو نصف القطر، مظبوط،
+
+98
+00:08:12,030 --> 00:08:18,450
+تمام، and a value θ، value θ، ليش بالرمز، للزاوية،
+
+99
+00:08:18,450 --> 00:08:23,690
+تمام، denote the angle between the X-axis and R، هذه
+
+100
+00:08:23,690 --> 00:08:29,670
+R تعمل زاوية مع الـ X-axis، حدد لي إياها، وبكفيني إني
+
+101
+00:08:29,670 --> 00:08:34,370
+أحدد النقطة، يعني لو كان اللي أنت بتحكيه، هاي محاور
+
+102
+00:08:34,370 --> 00:08:43,150
+أقول لك ثلاثة أمتار وعشرين درجة، تقدر تصورها؟ طيب، خمسة
+
+103
+00:08:43,150 --> 00:08:49,160
+أمتار وصفراً درجة، وين النقطة؟ المحور السيني، هيك
+
+104
+00:08:49,160 --> 00:08:53,780
+حددتوها، برافو عليكم، لو أقول ثلاثة أمتار وتسعين درجة،
+
+105
+00:08:53,780 --> 00:08:58,360
+وين؟ أين؟ عليكم؟ إذا بيكفيني ولا بيكفونيش؟ بيكفيني،
+
+106
+00:08:58,360 --> 00:09:02,800
+خلاص، لو إنك أنت، هذه النقطة وهذه النقطة، إيه
+
+107
+00:09:02,800 --> 00:09:08,120
+باختلِفوا على بعض؟ بنقارن البعد عن الـ origin، لكن
+
+108
+00:09:08,120 --> 00:09:12,340
+زاوية واحدة ولا لأ؟ ونفس العملية، هذه النقطة وهذه
+
+109
+00:09:12,340 --> 00:09:15,840
+النقطة، إشبه في قياس الزاوية، هذه زاوية ثلاثين وهذه
+
+110
+00:09:15,840 --> 00:09:19,860
+ستين، وهكذا، إذا هذين النقطتين بيكفوني، طب ليش أنت
+
+111
+00:09:19,860 --> 00:09:25,300
+بتغير ده؟ ليه بغير؟ للتسهيل، أنت كل الـ
+
+112
+00:09:25,300 --> 00:09:28,440
+coordinates عشان أسهل حلي، يكون في عندي مرجعية ولا
+
+113
+00:09:28,440 --> 00:09:32,960
+لأ؟ نقدر ننتقل للفصل الجاي أو الـ chapter الجاي، بدنا
+
+114
+00:09:32,960 --> 00:09:37,250
+نحكي عن الحركة في مستوى، والحركة في مستوى أشهرها
+
+115
+00:09:37,250 --> 00:09:42,570
+حركة المقذوفات، المقذوفات بتمشي سيني أو صادى، زي
+
+116
+00:09:42,570 --> 00:09:46,270
+السقوط الحر، فيها سيني وفيها صادي، إذا إيش هو اللي
+
+117
+00:09:46,270 --> 00:09:50,090
+بتغير؟ قال لي بتغير سيني وبتغير صادي، تمام؟ طبعاً لما
+
+118
+00:09:50,090 --> 00:09:54,370
+يكون عندك متغيرين، أصعب مما لو كان عندك متغير واحد،
+
+119
+00:09:54,370 --> 00:09:57,690
+ولا لأ؟ أطول على الأقل، بلاش أقول أصعب، قال لي طب
+
+120
+00:09:57,690 --> 00:10:03,600
+الحركة الدائرية، حركة مستوية ولا بخط مستقيم؟ دائرية،
+
+121
+00:10:03,600 --> 00:10:09,380
+في حد بيعرف يرسم دائرة على خط واحد؟ لأ، إذا برضه حركة
+
+122
+00:10:09,380 --> 00:10:13,980
+مستوية، قال لي إذا إيش متغيراتك؟ بقول له سيني وصادي، قال
+
+123
+00:10:13,980 --> 00:10:18,100
+لي: اه، لو استخدمت الـ polar coordinates، هيكون عندك
+
+124
+00:10:18,100 --> 00:10:22,950
+بس متغير واحد، كيف؟ بقول له: اه، ثابتة، إيش المتغير
+
+125
+00:10:22,950 --> 00:10:28,990
+الواحد؟ ثيتا، إذا استخدمت كارتيزيان coordinates، X
+
+126
+00:10:28,990 --> 00:10:32,870
+وY متغيرين، استخدم البولر، ما ضلّش عندي إلا ثيتا
+
+127
+00:10:32,870 --> 00:10:38,310
+متغير، إذا مرات تغيير الـ coordinates بيسهّل عليّ
+
+128
+00:10:38,310 --> 00:10:42,010
+الحل، في التونسيين، ما زال نفسي هدف متحقق إني بقدر
+
+129
+00:10:42,010 --> 00:10:46,370
+أحدد النقطة، إيه هو؟ بإنشاء R وثيتا، طبعاً في أنظمة
+
+130
+00:10:46,370 --> 00:10:49,810
+مختلفة واحنا لسه شوية شوية، زي ما بنحكي ده ده ده
+
+131
+00:10:49,810 --> 00:10:53,250
+ده، بناخد العلم السنة الجاية، بتاخدوا حاجة بيسموها
+
+132
+00:10:53,250 --> 00:10:59,070
+الإحداثيات الكروية والأسطوانية، وفي عدة أنواع بس
+
+133
+00:10:59,070 --> 00:11:05,740
+حبة حبة، تمام، إذا ده اللي، طيب الكارتيزيان الـ
+
+134
+00:11:05,740 --> 00:11:08,620
+coordinates هدفها تحديد نقطة، والـ polar
+
+135
+00:11:08,620 --> 00:11:12,100
+coordinates هدفها تحديد نقطة، إذا لازم يكون بينهم
+
+136
+00:11:12,100 --> 00:11:15,740
+علاقة ولا لأ؟ لازم يكون بينهم علاقة، قلت له طيب، هي
+
+137
+00:11:15,740 --> 00:11:21,730
+النقطة، هادي المسافة X ولا لأ؟ هادي المسافة Y، وهادي
+
+138
+00:11:21,730 --> 00:11:26,430
+R، وهادي ثيتا، طيب حبيبي في فيثاغورس سمعته فيه، بقدر
+
+139
+00:11:26,430 --> 00:11:30,270
+أجيب R بدلالة X وY ولا لأ؟ إذا R هي جذر تربيع لـ
+
+140
+00:11:30,270 --> 00:11:34,090
+X تربيع زائد Y تربيع، يعني بمعنى آخر لو أتتني X وY
+
+141
+00:11:34,090 --> 00:11:39,680
+صعب أجيب R؟ لأ، طب والزاوية؟ ده ليه سهل؟ أخذنا حساب
+
+142
+00:11:39,680 --> 00:11:43,760
+المثلثات في المدرسة، قال لي: جا الزاوية، في الثانوية،
+
+143
+00:11:43,760 --> 00:11:50,340
+مقابل على وتر، أمين؟ والمقابل Y، والوتر R، جيب
+
+144
+00:11:50,340 --> 00:11:57,200
+الزاوية أو جا الزاوية Y على R، طب وجتا الزاوية؟ X
+
+145
+00:11:57,200 --> 00:12:01,500
+على R، إذن هذه هي العلاقات، إذن بيقول لي هدول،
+
+146
+00:12:01,500 --> 00:12:07,260
+كلهم يعرفهم ولا لأ؟ Cos الزاوية بتساوي X على R، Sin
+
+147
+00:12:07,260 --> 00:12:11,800
+الزاوية بتساوي Y على R، هادي حبيبنا فيثاغورس، وهادي
+
+148
+00:12:11,800 --> 00:12:16,040
+جتا الزاوية بتساوي مقابل على مجاور، إذن اعطيني
+
+149
+00:12:16,040 --> 00:12:18,540
+Cartesian Coordinates بحوّلها لك لـ R، اعطيني R
+
+150
+00:12:18,540 --> 00:12:22,740
+بحوّلها لك لـ Cartesian، لأن كله بيؤدي نفس الهدف، وهو
+
+151
+00:12:22,740 --> 00:12:29,340
+تحديد موضع نقطة ما، تمام... نشوف... نشوف المثال،
+
+152
+00:12:29,340 --> 00:12:34,420
+بيقول لي: أنا بدي أعطيك Cartesian Coordinates لنقطة، و
+
+153
+00:12:34,420 --> 00:12:39,540
+بعد كده بدي أطلب منك إحداثياتها القطبية، إيش يعني
+
+154
+00:12:39,540 --> 00:12:43,500
+إحداثيات القطبية؟ بدي R وثيتا، مش هيك مظبوط؟ تمام،
+
+155
+00:12:43,500 --> 00:12:47,520
+قال لي: The Cartesian Coordinates of a point in the
+
+156
+00:12:47,520 --> 00:12:51,520
+XY plane are، سالب ثلاثة ونصف وسالب اثنين ونصف،
+
+157
+00:12:51,520 --> 00:12:59,120
+اتخيلتوها النقطة وين؟ في أي ربع؟ برافو عليكم، إذا
+
+158
+00:12:59,120 --> 00:13:02,620
+تشوفوا الإحداثيات خلتني أتوقع إنه نقطة ولا لأ، و
+
+159
+00:13:02,620 --> 00:13:06,020
+أتخيلها، وهذا الهدف من الإحداثيات، قال لي: هذه هي
+
+160
+00:13:06,020 --> 00:13:11,340
+النقطة، صح ولا لأ؟ تمام، هجيت، إيش بدك؟ قال لي بدي الـ
+
+161
+00:13:11,340 --> 00:13:14,920
+polar coordinates، يعني إيش؟ يعني بدي من هون لهون،
+
+162
+00:13:15,520 --> 00:13:18,900
+وبدي زاوية، هذه كلها ولا لأ؟ وبدي هذه الزاوية...
+
+163
+00:13:18,900 --> 00:13:23,000
+هذه الزاوية اللي أنت رسمتها، منفعة تكون أقل من 180؟
+
+164
+00:13:23,000 --> 00:13:27,380
+لأ، أكبر... أكبر من 180... بين الرسم... تمام...
+
+165
+00:13:27,380 --> 00:13:33,090
+قلّي: اه... حبيبنا فيثاغورس بقول: هاي... اه، بتساوي
+
+166
+00:13:33,090 --> 00:13:3
+
+223
+00:17:59,900 --> 00:18:04,960
+معرفة الكثافة؟ كتلة على حجم كتلة على حجم كتلة على
+
+224
+00:18:04,960 --> 00:18:08,060
+حجم كتلة على حجم كتلة على حجم كتلة على حجم
+
+225
+00:18:08,060 --> 00:18:08,940
+على حجم كتلة على حجم كتلة على حجم كتلة على حجم
+
+226
+00:18:08,940 --> 00:18:09,060
+كتلة على حجم كتلة على حجم كتلة على حجم كتلة على
+
+227
+00:18:09,060 --> 00:18:09,860
+حجم كتلة على حجم كتلة على حجم كتلة على حجم كتلة
+
+228
+00:18:09,860 --> 00:18:20,080
+على حجم كتلة على حجم كتلة على حجم كتلة على حجم
+
+229
+00:18:20,080 --> 00:18:20,700
+كتلة على حجم كتلة على حجم كتلة على حجم كتلة على
+
+230
+00:18:20,700 --> 00:18:30,900
+على حجم كتلة على حجم كتلة على حجم كتلة على حجم
+
+231
+00:18:32,060 --> 00:18:36,460
+واتفقنا المرة الماضية لما واحد يقول لك انزاح الجسم خمسة
+
+232
+00:18:36,460 --> 00:18:41,760
+متر، بقول لك  وراح ينزاح شرقا ولا غربا ولا لفوق
+
+233
+00:18:41,760 --> 00:18:45,920
+ولا لتحت؟ مظبوط،  لا غير لما تقولي مسافة بين حيطة
+
+234
+00:18:45,920 --> 00:18:50,040
+وحيطة خمسة، بين حيطة وهذه الحيطة وهذه الحيطة
+
+235
+00:18:50,040 --> 00:18:54,320
+ولا هذه وهذه بتفرق؟ ما تفرقش، مسافة أما تقولي انزاح
+
+236
+00:18:54,320 --> 00:18:59,500
+بمقدار معين في اتجاه معين، إذا  is the physical quantity that
+
+237
+00:18:59,500 --> 00:19:04,160
+has both magnitude and direction، إذا الـ vector
+
+238
+00:19:04,160 --> 00:19:11,490
+أهم شغلة إيه؟ magnitude و direction، حلو، إيش الأمثلة
+
+239
+00:19:11,490 --> 00:19:15,310
+اليوم دي كتير، هم الأمثلة اللي في الفيزياء كتير
+
+240
+00:19:15,310 --> 00:19:20,190
+velocity مش speed،  در بالكم، acceleration،
+
+241
+00:19:20,190 --> 00:19:28,690
+displacement، force، area، مساحة، واحنا المساحة عشان
+
+242
+00:19:28,690 --> 00:19:32,910
+مرات بتحتاج نجيبها في الأسئلة، نفترض أن نقول والله
+
+243
+00:19:32,910 --> 00:19:35,970
+من هالكميات منها vector بنحط
+
+244
+00:19:38,150 --> 00:19:42,690
+Time، كتلة، area، none of them، عشان واحد يحط لي none
+
+245
+00:19:42,690 --> 00:19:47,230
+of them، تمام، وهي الـ area نكتبها، الـ area is a
+
+246
+00:19:47,230 --> 00:19:51,150
+vector، وهنجيبها ونشرحها، وهنثبتها ونؤكد عليها، و
+
+247
+00:19:51,150 --> 00:19:55,510
+هتبقى لها تكرر، معلومة متواترة، الـ area is a
+
+248
+00:19:55,510 --> 00:20:00,850
+vector quantity، المساحة، أوه أوه، عشان كده بجيبها في
+
+249
+00:20:00,850 --> 00:20:04,870
+الـ quiz عشان تتخربطوا، المساحة عبارة عن vector
+
+250
+00:20:04,870 --> 00:20:10,770
+واتجاهها دائما عمودي على السطح، عمودي
+
+251
+00:20:10,770 --> 00:20:14,050
+على السطح، ده ده ده، لسه شوية شوية، ما تستغربوش
+
+252
+00:20:14,050 --> 00:20:19,490
+تكشروش، هنجيبها تمام، هنثبت لكم معاها بس لسه
+
+253
+00:20:19,490 --> 00:20:25,580
+ما وصلناش، عشان القاعدة اللي فاتت، تمام، جالي، امنت
+
+254
+00:20:25,580 --> 00:20:29,980
+الكميات الفيزيائية إما vector أو scalar، طب جيت أنا
+
+255
+00:20:29,980 --> 00:20:35,080
+بدي أكتب مرة سرعة ومرة كتلة، السرعة vector والـ
+
+256
+00:20:35,080 --> 00:20:41,320
+الكتلة scalar، طب كيف أميز بينهم؟ طب عرفتها من إيه؟ M
+
+257
+00:20:41,320 --> 00:20:45,880
+و هادي V، مظبوط ولا لأ؟ في عندي كمية، بأول ما أشوفها
+
+258
+00:20:45,880 --> 00:20:50,380
+بيقول هذا يعني vector، إذا أنا بدي أتفق أنا وياك
+
+259
+00:20:50,380 --> 00:20:55,560
+كل العالم إنك لما تشوف رمز تقول هذا يمثل كمية
+
+260
+00:20:55,560 --> 00:21:01,500
+متجهة، كيف؟ أول ما بدأوا يقولوا كانوا بسهولة يعملوا هيك
+
+261
+00:21:01,500 --> 00:21:08,610
+ويحطوا سهم،  سهل، إذاً هذه إيش؟ متجهة، طبعا زمان لما نقول زمان
+
+262
+00:21:08,610 --> 00:21:12,130
+زمان، قبل ما تنولدوا يعني قبل ما تنولدوا بكثير، لما
+
+263
+00:21:12,130 --> 00:21:14,770
+جوا يشتغلوا قالوا كان فيه computers، قالوا لأ
+
+264
+00:21:14,770 --> 00:21:19,770
+ما كانش فيه computers، كيف كانوا يطبعوا؟ يكتبوا، و
+
+265
+00:21:19,770 --> 00:21:24,190
+بعد كده جاءت ماكينة الطباعة، تمام؟ في ماكينة الطباعة
+
+266
+00:21:24,190 --> 00:21:30,760
+يا بنات، حطوا سهم فوق الحرف يوريني اتجاهه، قصة تمام؟
+
+267
+00:21:30,760 --> 00:21:33,760
+قالوا فكرتنا شغل غير، هذا السهم سهل على
+
+268
+00:21:33,760 --> 00:21:37,320
+السكرتيرة والسكرتير، المغلبين اللي بدهم يطبعوا وراك
+
+269
+00:21:37,320 --> 00:21:43,280
+قالوا بسيطة، في في الطباعة حاجة اسمها bold، غامق
+
+270
+00:21:43,280 --> 00:21:48,060
+قالوا الرمز الغامق بدنا نعتمد هو رمز الكمية
+
+271
+00:21:48,060 --> 00:21:53,000
+المتجهة، ههه، سهلت علينا شوية، والرمز العادي بدون غامق
+
+272
+00:21:53,000 --> 00:21:58,970
+هو scalar، إذا بيقول لي in the book، في كتابك القيمة
+
+273
+00:21:58,970 --> 00:22:06,750
+الكتورية ستميزها من القيمة العددية بكتابتها
+
+274
+00:22:06,750 --> 00:22:12,750
+بكتابة، بيكتبها، بكتابة
+
+275
+00:22:12,750 --> 00:22:17,930
+بيكتبها، بكتابة، بيكتبها، بكتابة، بيكتبها، بكتابة
+
+276
+00:22:17,930 --> 00:22:17,990
+بيكتبها، بكتابة، بيكتبها، بكتابة، بيكتبها، بكتابة
+
+277
+00:22:17,990 --> 00:22:18,370
+بيكتبها، بكتابة، بيكتبها، بكتابة، بيكتبها، بكتابة
+
+278
+00:22:18,370 --> 00:22:22,830
+بيكتبها، بكتابة، بيكتبها، بكتابة، بيكتبها، will be
+
+279
+00:22:22,830 --> 00:22:27,590
+typing it in boldface، وأحيانا بيحطوا كمان الـ arrow
+
+280
+00:22:27,590 --> 00:22:32,690
+فوق الحرف، طبعا في الـ computer سهل شوية مش زي طباعة
+
+281
+00:22:32,690 --> 00:22:37,300
+زمان، تم، بيحطوها هيك، أو في كتب بس بيقول لك أنا بصراحة
+
+282
+00:22:37,300 --> 00:22:42,340
+مغلب، ما بديش إياه، بس هنا شايفين الـ a زي هذا الحرف
+
+283
+00:22:42,340 --> 00:22:46,640
+ولا أغمق، أغمق، تم، قال هو الـ vector إيش له
+
+284
+00:22:46,640 --> 00:22:51,300
+magnitude و direction، طب أنا بدي بس الـ magnitude
+
+285
+00:22:51,300 --> 00:22:55,580
+كيف أميز أني أنا بدي بس الـ magnitude؟ قال، حط اللي
+
+286
+00:22:55,580 --> 00:23:02,920
+يا في إشارة بتعرفوها في الرياضيات، القيمة المطلقة، طب
+
+287
+00:23:02,920 --> 00:23:06,480
+وهي القيمة المطلقة بتيجي للمقدار، قال لي اه لأن
+
+288
+00:23:06,480 --> 00:23:09,820
+المقدار ممنوع يكون سالب، إيش هي القيمة المطلقة؟ لأن
+
+289
+00:23:09,820 --> 00:23:14,620
+ناقص خمسة، خمسة، ليش مشركم الدعوة في السالب؟ قال لي
+
+290
+00:23:14,620 --> 00:23:18,420
+لأن السالب اتعلمت أنه بتعني direction، ولما
+
+291
+00:23:18,420 --> 00:23:20,560
+تقول لي  أو دي دي الـ magnitude، إيه دعوة في الـ
+
+292
+00:23:20,560 --> 00:23:24,580
+direction؟ إذا السالب ما كانش له دعوة فيه، فبالتالي كيف
+
+293
+00:23:24,580 --> 00:23:28,840
+أنا جاهز؟ قال، هاي الـ vector رمز وحطيته بين إشارة
+
+294
+00:23:28,840 --> 00:23:33,930
+المطلقة، absolute، احنا بنسميها، أخذتوها جربتوها بالـ
+
+295
+00:23:33,930 --> 00:23:38,630
+calculus، وصلتوا الحمد لله، تم، إذا الـ absolute أو
+
+296
+00:23:38,630 --> 00:23:42,910
+قال لي هادي برضه الرمز، مرات في صعب تعمله، طبعا في
+
+297
+00:23:42,910 --> 00:23:46,270
+الـ word، إيه طريقة تعملوها؟ قال لي إيش أعمله؟ قال لي
+
+298
+00:23:46,270 --> 00:23:50,850
+شوف الحرف إيه، لابد، ونحط سهم وميله، أعمله إيتاليك، هذه
+
+299
+00:23:50,850 --> 00:23:54,920
+معناته أنا إيش بدي من الـ vector؟ الـ magnitude، فهمتوا
+
+300
+00:23:54,920 --> 00:23:59,220
+يا بنات؟ احنا قاعدين بنشرح لسه الرموز عشان نفهم
+
+301
+00:23:59,220 --> 00:24:04,840
+معاكم فيها، تمام، the magnitude of a vector is
+
+302
+00:24:04,840 --> 00:24:09,140
+always positive، ما ينفعش تحط negative، لأن الـ
+
+303
+00:24:09,140 --> 00:24:12,660
+negative معناته direction، ممنوع تقولي الـ
+
+304
+00:24:12,660 --> 00:24:17,080
+magnitude ناقص ثلاثة، وش هالشغل؟ بينفع الـ speed تكون
+
+305
+00:24:17,080 --> 00:24:24,400
+سلبية؟  نسبية، هو احنا خلينا نرجع لـ speed، هي الـ
+
+306
+00:24:24,400 --> 00:24:28,480
+magnitude بتاعت الـ velocity، مظبوط؟ هذه معلومة
+
+307
+00:24:28,480 --> 00:24:32,660
+حكيتها، الـ speed هي الـ magnitude، الـ magnitude مسموحة
+
+308
+00:24:32,660 --> 00:24:36,560
+تكون سالبة؟ لأ، إذا مسموحة الـ speed تكون سالبة؟ لأ
+
+309
+00:24:36,560 --> 00:24:40,600
+الفلسفية، اه الفلسفية، اه، نهدى أكتر، سالب يعني شرق أو
+
+310
+00:24:40,600 --> 00:24:47,150
+غرب، شمال أو جنوب، ده ما؟ جالي، طيب الرمز اتفقت أنا و
+
+311
+00:24:47,150 --> 00:24:51,950
+اياك عليه، بتحط bold، معناته بيديك الـ vector، حطيت
+
+312
+00:24:51,950 --> 00:24:55,270
+إيتاليك، معناته بيديك مقدار الـ vector، طب كيف بيتعامل
+
+313
+00:24:55,270 --> 00:25:00,110
+معاه؟ قال، أنا كيف بدي أقول الـ vector هذا له مقدار و
+
+314
+00:25:00,110 --> 00:25:08,130
+اتجاه؟ قاله لو عملت لك هيك، بيني
+
+315
+00:25:08,130 --> 00:25:13,230
+اتجاهه هيك، من إيش عرفته؟ من السهم، حلو، كل الناس
+
+316
+00:25:13,230 --> 00:25:18,230
+بتلاقي في السهم، إذا طيب هادي كم اتجاه؟ واحد، طب و
+
+317
+00:25:18,230 --> 00:25:28,310
+هادي؟ زي بعض، اتجاه واحد لكن نفس الطول، تقدر تقول أن هادي
+
+318
+00:25:28,310 --> 00:25:32,650
+أكبر من هادي ولا لا، إذا بدك تمثل الـ vector، السهم
+
+319
+00:25:32,650 --> 00:25:37,050
+اتفهمنا أنا وياك عليه، طب الطول، قال لي الطول بدي
+
+320
+00:25:37,050 --> 00:25:42,460
+يتناسب مع المقدار، الطول بدي يتناسب مع المقدار، إذاً
+
+321
+00:25:42,460 --> 00:25:46,380
+geometrically، يعني هندسيا، تمام؟ أنتم عارفين علم
+
+322
+00:25:46,380 --> 00:25:50,600
+الهندسة، تمام؟ if the vector quantity is
+
+323
+00:25:50,600 --> 00:25:57,630
+represented، هتمثل، by a straight line، خط مستقيم، هاي
+
+324
+00:25:57,630 --> 00:26:02,850
+هم خطوط مستقيمة، تمام، and and a row at one end of
+
+325
+00:26:02,850 --> 00:26:08,190
+the line، مع سهم عند أحد أطراف الخط، طول السهم عشان
+
+326
+00:26:08,190 --> 00:26:13,150
+يدل على الاتجاه، والطول عشان يحسسك قد ايش مقدار
+
+327
+00:26:13,150 --> 00:26:19,980
+الكمية، تمام، هو بيقول الـ length of the line، طول الـ
+
+328
+00:26:19,980 --> 00:26:23,360
+line represent the magnitude of the vector، and
+
+329
+00:26:23,360 --> 00:26:26,780
+الـ arrow points to the direction of the vector، و
+
+330
+00:26:26,780 --> 00:26:32,080
+الـ arrow بيوجه أو يشير الى نحو الاتجاه، تمام، هذا
+
+331
+00:26:32,080 --> 00:26:39,140
+vector، شايفينه؟ هذا بنسميه طرف... بنسميه ذيل وطرف
+
+332
+00:26:39,140 --> 00:26:44,160
+بنسميه رأس، صعب، هاي الراس الكبير، والذيل مهم، باين
+
+333
+00:26:44,160 --> 00:26:48,620
+دي سهلة، دائما الـ ... الرموز بتيجي من شغلات مألوفة
+
+334
+00:26:48,620 --> 00:26:54,580
+للناس، عشان الحفظ هيكون سهل، والتعامل معها سهل، حلو
+
+335
+00:26:56,070 --> 00:27:00,170
+أمين، هل جيت بنا... قال ليه؟ بنا نخش على صفات الـ
+
+336
+00:27:00,170 --> 00:27:04,490
+vectors، دالًا، two vectors بدي أقول عنهم متساويين
+
+337
+00:27:04,490 --> 00:27:09,310
+بينفع أقول واحد خمسة وواحد تاني خمسة بس واحد شرق
+
+338
+00:27:09,310 --> 00:27:13,230
+وواحد غرب بيساوي بعض؟ واحد شرق وواحد شمال بيساوي
+
+339
+00:27:13,230 --> 00:27:17,970
+بعض؟ ما بينفعش يساوي بعض، وانت عشان تقول يساوي، ذاكرين
+
+340
+00:27:17,970 --> 00:27:20,670
+لما قلنا يساوي لازم يكون اللي هان يساوي هان في كل
+
+341
+00:27:20,670 --> 00:27:26,050
+شيء؟ طب إذا لازم يكون الاثنين له نفس المقدار ونفس
+
+342
+00:27:26,050 --> 00:27:30,630
+الاتجاه، إذا بقول يا بنات، equality of two vectors
+
+343
+00:27:30,630 --> 00:27:34,870
+مساواة الـ vectors، any two vectors are said to be
+
+344
+00:27:34,870 --> 00:27:42,630
+equal، يقال عنهم متساويين، if، عندي شرط، they have the
+
+345
+00:27:42,630 --> 00:27:46,210
+same magnitude، إذا لازم يكونوا يكونوا نفس المقدار
+
+346
+00:27:46,210 --> 00:27:52,330
+and point، ويشيروا، in the same direction، regardless
+
+347
+00:27:52,330 --> 00:27:56,890
+of its location، بغض النظر عن الموقع، مش مش ضروري
+
+348
+00:27:56,890 --> 00:28:00,530
+يكونوا الاثنين بدأوا من نفس النقطة، لأ، المهم يكونوا
+
+349
+00:28:00,530 --> 00:28:02,450
+يكونوا يكونوا يكونوا نفس الطول، ويكونوا يكونوا
+
+350
+00:28:02,450 --> 00:28:05,130
+يكونوا يكونوا نفس الاتجاه، قال، يشوف هدول الأربعة
+
+351
+00:28:06,150 --> 00:28:09,890
+كلهم من نفس النقطة انطلقوا، جيس، بالمسطرة، ده اللي نفس
+
+352
+00:28:09,890 --> 00:28:14,010
+الطول، تطلع عليهم والله متوازيين، متوازيين يعني نفس
+
+353
+00:28:14,010 --> 00:28:19,310
+الاتجاه ولا لا؟ بقول هدول الأربعة عبارة عن vectors
+
+354
+00:28:19,310 --> 00:28:25,550
+متساوية، ماشية يا بنات لحد الآن ماشية الأمور، هاي الـ
+
+355
+00:28:25,550 --> 00:28:30,360
+vector، بمشي جاعل ولا ممشيش؟ اتغير إيش فيه؟ اتغير
+
+356
+00:28:30,360 --> 00:28:34,800
+موقعه؟ اتغير اتجاهه؟ إذا بصحيح اللي تحركه ولا لأ؟
+
+357
+00:28:34,800 --> 00:28:40,130
+بصحيح اللي اتحركه بشرط يحافظ على مقداره واتجاهه، بينفع
+
+358
+00:28:40,130 --> 00:28:45,310
+إتميله، ممنوع إذا مياله غيرت اتجاهه، عشان كده هذه
+
+359
+00:28:45,310 --> 00:28:48,590
+الحركة، عشان بيقول regardless of their location
+
+360
+00:28:48,590 --> 00:28:54,630
+ما كانش عاثر باتجاهه، وبالتالي الحركة تفرقش معاه، الـ
+
+361
+00:28:54,630 --> 00:28:58,990
+vector، vector،  دلوقت إيه إيه، ما تغيرش حاجة، ماصارش فيه
+
+362
+00:28:58,990 --> 00:29:03,050
+أي تغيير، حلو
+
+363
+00:29:04,600 --> 00:29:09,440
+كلنا خلصنا روضة، صح ولا لأ؟ تم، وفي الروضة علمونا
+
+364
+00:29:09,440 --> 00:29:13,680
+اثنين وثلاثة خمسة، إذا جيت مني اتعلم اثنين وثلاثة
+
+365
+00:29:13,680 --> 00:29:19,120
+ممكن ما يكونوش خمسة حسب الاتجاه، صح؟ إذا اثنين و
+
+366
+00:29:19,120 --> 00:29:25,260
+ثلاثة ممكن يكون واحد، وممكن يكون شغل أكثر، صحيح؟
+
+367
+00:29:25,260 --> 00:29:29,260
+حسب الاتجاه، ده إيش يعني؟ بقول يعني جمع الـ vectors
+
+368
+00:29:29,260 --> 00:29:30,580
+غير عن جمع الروضة
+
+369
+00:29:33,170 --> 00:29:37,230
+قال لي هاي في طريقة بنسميها طريقة المثلث، الـ
+
+370
+00:29:37,230 --> 00:29:40,890
+triangle method، ما أنتم عارفين إيش معاها method؟ قال لي
+
+371
+00:29:40,890 --> 00:29:47,310
+هدول vectors، شايفينهم؟ هينقل واحد، خط واتجاهه معروف
+
+372
+00:29:47,310 --> 00:29:52,630
+من الرسمة ولا لأ؟ تطلع يا حكاية، دي الراس، مبين أن دي
+
+373
+00:29:52,630 --> 00:29:57,490
+الـ B، عند رأس الـ A، صح؟ جالي، إيش جمعهم؟ أو المحصلة
+
+374
+00:29:57,490 --> 00:30:02,090
+نسميها الـ resultant، جالي، أجيب خط من دي الأولى لراس
+
+375
+00:30:02,090 --> 00:30:08,610
+الثاني، تصورته وين؟ جالي هذه هي المحصلة، جامعة، طب
+
+376
+00:30:08,610 --> 00:30:13,230
+تطلع يا بنات لو جيتوا بالمسطرة، بالمسطرة هذا ثلاثة
+
+377
+00:30:13,230 --> 00:30:17,870
+ وهذا أربعة، بتطلع هذا سبعة؟ ولا ممكن ولا يطلع
+
+378
+00:30:17,870 --> 00:30:23,470
+خمسة؟ ما يطلعش خمسة، بيطلع خمسة لو كانوا متعامدين، اه، هنا
+
+379
+00:30:23,470 --> 00:30:28,170
+في الزوايا مش شغال، لكن لا بيطلع... لا... ما يطلعش لا
+
+380
+00:30:28,170 --> 00:30:32,210
+سبعة ولا حاجة، تمام، ولا خمسة، من الجهة بس بيطلع رقم
+
+381
+00:30:32,210 --> 00:30:36,510
+أقل من سبعة، إذا واحد ثلاثة، واحد أربعة، حاجة  حلاجة
+
+382
+00:30:36,510 --> 00:30:39,330
+أقل من سبعة، بيقول إيه؟ ضحكوا علينا في الروضة؟ لأ
+
+383
+00:30:39,330 --> 00:30:45,610
+ما ضحكوش عليكم، كانوا بيجمعوا scalars، تمام، حلو، طيب
+
+384
+00:30:45,610 --> 00:30:50,930
+قال لي طب هذا الـ vector إيه؟ حركليه وما تغيرش فيه لا
+
+385
+00:30:50,930 --> 00:31:02,190
+مقدار ولا اتجاه، نفس الطول؟ عملتيش إيه؟ جالي، وبي؟
+
+386
+00:31:02,190 --> 00:31:07,390
+قال لي اجمع لي، جيت مش a
+
+445
+00:36:08,530 --> 00:36:13,710
+تكون الـ vector؟ جمع من دين الأول لرأس الثاني طب
+
+446
+00:36:13,710 --> 00:36:18,140
+بدي أطرح قال يجب أن تطرح جيبني ناقص B مظبوط أو لا؟
+
+447
+00:36:18,140 --> 00:36:21,100
+أول بدأ دي بنقص بيه، بعدين إيش عمل؟ إيش عمل فيه
+
+448
+00:36:21,100 --> 00:36:26,620
+بيه؟ اه كيسه هد نقص بيه ولا لا؟ هجيت بدي أطرح
+
+449
+00:36:26,620 --> 00:36:32,520
+نقص بيه هذا الـ vector ولا لا؟ شايفين مثلها؟ هاي
+
+450
+00:36:32,520 --> 00:36:37,620
+نقص بيه سهل لحد تلقاه، وهد مانجيش في امتحانات لحد
+
+451
+00:36:37,620 --> 00:36:41,960
+تلقاه، ولا شيء راح ثقافة اه ما هو احنا مانينا نقعد
+
+452
+00:36:41,960 --> 00:36:47,200
+هاجد بدي أجمع two vectors بدي أجيب معايا منجلة و
+
+453
+00:36:47,200 --> 00:36:52,400
+بيكار و مصطرة و أجيس و وجود اكس جثة واش هتشغلها
+
+454
+00:36:52,400 --> 00:36:55,980
+دي الروضة أسهلنا ما هيتعلمنا في الروضة كيف نجمعه
+
+455
+00:36:55,980 --> 00:36:58,820
+على إيدينا و علمونا نحط في مخكم مش عارف أيه شو
+
+456
+00:36:58,820 --> 00:37:02,460
+سهلة بدي طريقة زي تاعة الروضة أجمع فيها الـ vectors
+
+457
+00:37:03,700 --> 00:37:08,400
+الآن بدنا نتفق على طريقة ما كي دعو بالرسم أنت
+
+458
+00:37:08,400 --> 00:37:10,860
+الرسم كيف كنت .. ليش كنت ترسم؟ أقوله عشان أشوف
+
+459
+00:37:10,860 --> 00:37:14,480
+الاتجاه صح ولا لأ أشوف الاتجاه أول ما أرسم هي ده
+
+460
+00:37:14,480 --> 00:37:19,800
+أقولت الاتجاه هو معروف لو رسمته هي اتجاهه بعرفه طب
+
+461
+00:37:19,800 --> 00:37:25,120
+أنا بدي أديك أرقام منها تعرف المقدار والاتجاه ما
+
+462
+00:37:25,120 --> 00:37:30,340
+كي دعو بالرسم تتخيله على طول من رقم معين تمام
+
+463
+00:37:32,300 --> 00:37:36,040
+أول نعمل الـ quizات و بعدين نرجع عشان نكسر الكلام
+
+464
+00:37:36,040 --> 00:37:42,060
+لكتير فنشوف إيش حكينا صيني و إيش حكينا عربي تمه
+
+465
+00:37:42,060 --> 00:37:47,760
+بيقول لي عندك two vectors واحد نقدره إثنا عشر و الثاني
+
+466
+00:37:47,760 --> 00:37:52,300
+نقدره ثمانية أداني للاتجاهات؟ لأ جالي الاتجاهات
+
+467
+00:37:52,300 --> 00:37:57,060
+عشوائية ممكن احتمالات كتيرة عندك تمه بيقول لي بدي
+
+468
+00:37:57,060 --> 00:38:06,190
+أديك رقمين بدي لو جمعتهم أكبر قدر ممكن جدّيش و أقل
+
+469
+00:38:06,190 --> 00:38:10,930
+قدر ممكن جدّيش يعني أكبر قيمة للجمع و أقل قيمة
+
+470
+00:38:10,930 --> 00:38:13,990
+للجمع the magnitude of two vectors a and b are
+
+471
+00:38:13,990 --> 00:38:17,670
+twelve and eight units which pair of numbers إيش
+
+472
+00:38:17,670 --> 00:38:21,890
+من الأزواج الأرقام اللي أديك إياها represents the
+
+473
+00:38:21,890 --> 00:38:25,830
+largest and the smallest possible values for the
+
+474
+00:38:25,830 --> 00:38:29,190
+magnitude of the resultant vector بدي أجمع يطلع
+
+475
+00:38:31,280 --> 00:38:40,560
+أكبر جمع ممكن يكون 14.4؟ لأ 14 من هنا جت؟ اه بقولك
+
+476
+00:38:40,560 --> 00:38:43,740
+من هنا جت لو معاكي calculator شوفي في الـ calculator يطلع لك
+
+477
+00:38:43,740 --> 00:38:48,410
+الرقم هذا عرفت منين أصله؟ ده غالبا الخيارات بتكون
+
+478
+00:38:48,410 --> 00:38:52,630
+إلها معنى يا بنات حتى لو غلط بحط إلها معنى ليش؟
+
+479
+00:38:52,630 --> 00:38:57,030
+لأنه فلسفة الـ multiple choice بقولك الطالب وين ما
+
+480
+00:38:57,030 --> 00:39:02,110
+يفكر يجيله جواب مشلج مشلجش مش مشكلة المهم ما يتغلبش
+
+481
+00:39:02,110 --> 00:39:06,430
+يقعد يبحث في السؤال مش هو ده يطلع الجواب لأ يطلع
+
+482
+00:39:06,430 --> 00:39:11,870
+الجواب يخلص وصح ولا غلط مش مشكلة فعرفت منين أصله؟
+
+483
+00:39:11,870 --> 00:39:17,570
+تمام إثنا عشر و ثمانية طبعا ده حلوة طلع الشمال مجلهو
+
+484
+00:39:17,570 --> 00:39:22,090
+خطر زي ما هو مريح ايوة حطبطوا والله منطقين هذول
+
+485
+00:39:22,090 --> 00:39:29,210
+هاي أقلهم أصل صح؟ تمام إيش رأيكم في هذول؟ طيب
+
+486
+00:39:29,210 --> 00:39:32,650
+وقتيش بيكونوا عشرين لما يكونوا في نفس الاتجاه و
+
+487
+00:39:32,650 --> 00:39:37,570
+وقتيش بيكونوا أربعة عالين عليكم إذا لو جيت سألت
+
+488
+00:39:37,570 --> 00:39:41,830
+وبدأ ترجم و أحط في مخي أكبر مقدار للجامع لما
+
+489
+00:39:41,830 --> 00:39:46,020
+يكونوا في نفس الاتجاه صح؟ اه و أقل المقدار لجمع لما
+
+490
+00:39:46,020 --> 00:39:52,380
+يكون عكس بعيد داخلك المعلومة اه none of them هذي
+
+491
+00:39:52,380 --> 00:39:59,860
+برضه منطقيا تمام حلو إذا هذول هما العشرين هي أكبر
+
+492
+00:39:59,860 --> 00:40:05,120
+قيمة والأربعة أقل قيمة ممكنة صحيح ولا لا؟ حلو؟ كمان
+
+493
+00:40:05,120 --> 00:40:11,530
+كويس بيقول under what condition تحت أي شرط أو ظرف
+
+494
+00:40:11,530 --> 00:40:16,050
+does the resultant vector A زائد B resultant يعني
+
+495
+00:40:16,050 --> 00:40:19,630
+محصلة الـ vector يعني مجموع A زائد B ما هو بيطلع
+
+496
+00:40:19,630 --> 00:40:23,150
+vector نسميه resultant vector المحصلة have a
+
+497
+00:40:23,150 --> 00:40:27,630
+magnitude equal to A زائد B مجموعته تبعه بيساوي
+
+498
+00:40:27,630 --> 00:40:31,190
+مجموع two magnitudes زي ثوّل عشرين وانتوا جاوبته
+
+499
+00:40:31,190 --> 00:40:35,830
+السؤال هذا وقتي إيش؟ انتوا طبعا جاوبته تطلعوا إيش
+
+500
+00:40:35,830 --> 00:40:36,670
+الخيارات؟
+
+501
+00:40:39,160 --> 00:40:42,220
+are parallel and in the same direction are
+
+502
+00:40:42,220 --> 00:40:45,060
+parallel and in the same direction ولا parallel
+
+503
+00:40:45,060 --> 00:40:49,280
+and in opposite direction هذي بتطلع أربعة تمام are
+
+504
+00:40:49,280 --> 00:40:53,780
+perpendicular عش اسم كل انت اللي تاو حاجاتي زينا
+
+505
+00:40:53,780 --> 00:40:58,480
+زينا شايفة لما يكون perpendicular تطلع 14.4 بالصفر
+
+506
+00:40:58,480 --> 00:41:00,600
+في الـ calculator الشغل تمام حلو
+
+507
+00:41:03,140 --> 00:41:09,040
+طيب اتفجنا بدي أرمي المسطرة والمنجلة والبيكار و
+
+508
+00:41:09,040 --> 00:41:14,400
+الرسم وبدي أتعلم طريقة أجمع بدون هالشغل كله لا
+
+509
+00:41:14,400 --> 00:41:18,420
+طريقة مثلث ولا طريقة متوازي الأضلاع احنا أخذنا من
+
+510
+00:41:18,420 --> 00:41:21,160
+كلمة مثلث متوازي الأضلاع بالإضافة إلى الطريقة
+
+511
+00:41:21,160 --> 00:41:24,800
+المشهورة إيش معنات مثلث إيش معنات Parallelogram
+
+512
+00:41:24,800 --> 00:41:30,180
+مظبوط ولا لأ؟ بكفي تمه؟ جلني الآن شوفني هالـ vector
+
+513
+00:41:33,600 --> 00:41:37,420
+بدي أعرف حاجة اسمها unit vector احنا اتفقنا الـ
+
+514
+00:41:37,420 --> 00:41:42,400
+vector إيش بدك تديني؟ شغلتين مقدار واتجاه جيني
+
+515
+00:41:42,400 --> 00:41:47,080
+الاتجاه بدي أعرفه بشغلة بدي اسميها unit vector هل
+
+516
+00:41:47,080 --> 00:41:50,840
+جيت لكل مسمى من اسمه نصيب؟ مش بالواطن لأ الواحد
+
+517
+00:41:50,840 --> 00:41:55,220
+بعد ما يسمي بخير بيسموه إيش كريم تمام؟ و أمير لو
+
+518
+00:41:55,220 --> 00:42:00,320
+أحد شطوعه لم يسميه إيش أمير بعد ما يعرفه unit vector
+
+519
+00:42:00,320 --> 00:42:04,560
+أنا سميته vector معناته عادي scalar هو vector
+
+520
+00:42:04,560 --> 00:42:09,680
+مظبوط ليه سميته unit جالي عشان مقداره واحد إذا
+
+521
+00:42:09,680 --> 00:42:13,760
+اتجاه الوحدة إذا unit vector هو vector جدّيش مقداره
+
+522
+00:42:13,760 --> 00:42:16,680
+بكرة نجيه السؤال إيش مقدار الـ unit vector وفيه
+
+523
+00:42:16,680 --> 00:42:20,700
+عقدر تتفكروا إيش إيه إيش بيساوي مقداره واحد اصلا من
+
+524
+00:42:20,700 --> 00:42:25,100
+اسمه إيجابا إذن a unit vector is a vector .. إيش جابت
+
+525
+00:42:25,100 --> 00:42:28,240
+من ضربك؟ ما أنت بتقول لي vector .. is a vector with
+
+526
+00:42:28,240 --> 00:42:30,960
+a specific direction .. إله اتجاه معين .. الآن دي
+
+527
+00:42:30,960 --> 00:42:35,860
+بنقول عنه .. having a magnitude of one without any
+
+528
+00:42:35,860 --> 00:42:39,020
+units or dimensions .. لا إله dimensions ولا وحدات
+
+529
+00:42:39,020 --> 00:42:42,140
+.. ليش؟ قال عشان تضربوا في الكمية الفيزيائية ما
+
+530
+00:42:42,140 --> 00:42:46,810
+تتغير شمقدار الواحد لما تضربه الواحد بتغير المقدار؟
+
+531
+00:42:46,810 --> 00:42:50,510
+لأ ومالوش dimension  اتغير الكمية الفيزيائية ولا
+
+532
+00:42:50,510 --> 00:42:54,050
+ينص زي ما هي إذا هذا إيش مهمته؟ جالي الـ specific
+
+533
+00:42:54,050 --> 00:42:58,490
+direction بس يشوفوا ليه الاتجاه تمام جالي إيه الشم
+
+534
+00:42:58,490 --> 00:43:02,330
+هذول الـ specific direction؟ جالي نعطاه يا علماء
+
+535
+00:43:02,330 --> 00:43:06,130
+بدنا نكفج احنا وياكم على رموز أول ما البني آدم
+
+536
+00:43:06,130 --> 00:43:10,570
+يشوف يقول هذا باتجاه المحور السيني والرمز الثاني
+
+537
+00:43:10,570 --> 00:43:14,290
+أول ما يشوفوه يقول هاي باتجاه المحور الصادي وواحد
+
+538
+00:43:14,290 --> 00:43:17,890
+باتجاه المحور العينّي تمام يا بنات؟ إيش هم الرموز
+
+539
+00:43:17,890 --> 00:43:21,430
+اللي اتفقوا عليهم وإن كان بعد كده غيّروهم بس أول ما
+
+540
+00:43:21,430 --> 00:43:24,290
+اتفقوا قالوا هاي الـ Cartesian Coordinates في عندك
+
+541
+00:43:24,290 --> 00:43:31,870
+الرمز I  بتعرفوه؟ حط فوقه hat أو تديّة ثمانية هذا
+
+542
+00:43:31,870 --> 00:43:36,300
+معناته unit vector ده دي إيش مقداره؟ واحد كيف اتجاهه
+
+543
+00:43:36,300 --> 00:43:40,860
+الـ I ده اللي هدا متجه باتجاه المحور السيني الموجب
+
+544
+00:43:40,860 --> 00:43:46,980
+عرفته وين السيني الموجب طيب يا بنات حلو طلعوا عليها
+
+545
+00:43:46,980 --> 00:43:51,160
+هاي vector خمسة
+
+546
+00:43:51,160 --> 00:43:57,620
+و I اتخيلتوا باللزام
+
+547
+00:43:57,620 --> 00:44:02,040
+ارسمه خدش أشيلك في رسمة أنا أديتك معلومة كاملة ولا
+
+548
+00:44:02,040 --> 00:44:03,960
+لأ خمسة مقدار و الـ I
+
+549
+00:44:06,990 --> 00:44:13,870
+TB بيساوي سالب تلاتة I السالب إيش معناته؟ شرق ولا
+
+550
+00:44:13,870 --> 00:44:18,790
+غرب؟ غرب، ومقداره؟ تلاتة إذا بيزن راسه؟ من غير
+
+551
+00:44:18,790 --> 00:44:23,050
+unit؟ بعدي إنه غير unit، هو لو .. لو في .. لو هذه
+
+552
+00:44:23,050 --> 00:44:26,250
+سرعة، بدي أقول لك متر برساكن، بس أنا بقول A و B، أحكي
+
+553
+00:44:28,440 --> 00:44:32,300
+أيوة برأي عليك ليه؟ استخدمت إيش؟ الملاحظة التي
+
+554
+00:44:32,300 --> 00:44:35,600
+حكيتها الشرط السالب لما تفوت على الـ vector إيش
+
+555
+00:44:35,600 --> 00:44:42,540
+بتسوي فيه؟ تعكس اتجاهه تمام؟ أحكي كيف طلعت مالهاش
+
+556
+00:44:42,540 --> 00:44:45,520
+اتجاه من اتجاه المحدد و مش اتجاهك؟ الـ I مالهاش
+
+557
+00:44:45,520 --> 00:44:53,000
+اتجاه الـ I هجيت هادي .. الها اتجاه؟ مش اتجاه، الها
+
+558
+00:44:53,000 --> 00:44:58,020
+dimension هذه الخمسة نفترض أنها بتحكي عن قوة بقول لك
+
+559
+00:44:58,020 --> 00:45:03,020
+هذه نيوتن منفع هذه تكون لها كمان وحدة؟ مانفعش إذا
+
+560
+00:45:03,020 --> 00:45:06,540
+هذه الـ direction و بس مالهاش وحدات ولا لها
+
+561
+00:45:06,540 --> 00:45:10,680
+dimension أه هذه معناها Tunis و dimension فهمت
+
+562
+00:45:10,680 --> 00:45:16,160
+عليها؟ تم لأ أنا حكيتها قلوا طيب قالوا يا علم
+
+563
+00:45:16,160 --> 00:45:20,820
+ما تفجع على الـ J أول ما تشوف الـ J وين رايحة؟ تجاه
+
+564
+00:45:20,820 --> 00:45:29,590
+الصادي يعني هاي vector بتساوي اتنين J يا عصمو لفوق
+
+565
+00:45:29,590 --> 00:45:34,750
+إذا شوفوا الكتابة كيف بتسافر علينا خلص قدّينا
+
+566
+00:45:34,750 --> 00:45:39,810
+الغرض ولا لا بحكاية الـ unit vectors تمه و لو أقول
+
+567
+00:45:39,810 --> 00:45:46,470
+B بتساوي سالب تلاتة J  عرفته ولا لا لتحت حلو
+
+568
+00:45:46,470 --> 00:45:51,290
+جالي حلو و الـ K طبعا بتعرفوا انتوا الذد الموجة
+
+569
+00:45:51,290 --> 00:45:56,000
+بيقول رايح عليكم إذا لما يقول لي زائد بقوله على
+
+570
+00:45:56,000 --> 00:46:02,320
+طالع برا ذاكرين هذول الرموز اضطرت و قالها هادي و
+
+571
+00:46:02,320 --> 00:46:10,480
+هادي هادي K و هادي سالب K مظبوط ولا لأ حلو تمه
+
+572
+00:46:13,370 --> 00:46:18,150
+بيقول لي this means that if a vector A is directed
+
+573
+00:46:18,150 --> 00:46:22,410
+along the positive x axis عندك vector وما أعرف
+
+574
+00:46:22,410 --> 00:46:26,310
+اتجاهه باتجاه المحور السيني الموجب والمقدار تبعه A
+
+575
+00:46:26,310 --> 00:46:30,910
+هيو إيتاليك كيف تكتبه قال لي هيك بكتبه صحّيك ولا لأ
+
+576
+00:46:30,910 --> 00:46:37,870
+إذا كل القصة هذه اختزلت بهذا الرقم A بتساوي هاي
+
+577
+00:46:37,870 --> 00:46:42,090
+المقدار وهذا الاتجاه السيني الموجب أمين يا بنات؟
+
+578
+00:46:42,090 --> 00:46:47,470
+حلو إذا صار في عندي شغلة بيسموها متجهات الوحدة
+
+579
+00:46:47,470 --> 00:46:52,450
+متجهة الوحدة ليش سموه متجهة وحدة عشان مقداره؟ هجيت
+
+580
+00:46:52,450 --> 00:46:56,450
+في عندي اتجاهات مختلفة لكن ثابتة واحد ملزق بالسين
+
+581
+00:46:56,450 --> 00:47:02,350
+اللي هو I واحد ملزق بالصاد J واحد ملزق بالعين خلاص
+
+582
+00:47:02,350 --> 00:47:08,900
+طبوالـ minus sign اللي توّي سألت في .. إيه إيش
+
+583
+00:47:08,900 --> 00:47:14,260
+معناته؟ السالب مظبوط ولا لأ؟ حلو هل جيت بيقول لي
+
+584
+00:47:14,260 --> 00:47:18,780
+مركبات؟ إيش يعني مركبات بالعربي؟ يعني لو عندك
+
+585
+00:47:18,780 --> 00:47:21,820
+محلول يقول لك إيش مركبات يعني مش متكون ولا لأ؟
+
+586
+00:47:21,820 --> 00:47:27,880
+مكونات طيب، ده نشوف لهذا الـ vector يلا يا بناتي
+
+587
+00:47:27,880 --> 00:47:33,180
+أحط I ولا J على هذا؟ بس عنيه وياه؟ I ولا J؟
+
+588
+00:48:03,680 --> 00:48:05,080
+هههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+589
+00:48:07,690 --> 00:48:13,030
+هي مكونات إذا هل الـ vector a مكوناته واحد بتجاه
+
+590
+00:48:13,030 --> 00:48:16,870
+السيني واحد بتجاه الصادي صح ولا لأ لأنه لو جمعت
+
+591
+00:48:16,870 --> 00:48:20,470
+التنين السيني والصادي بتطلع الم غلبك أنا إيه
+
+592
+00:48:20,470 --> 00:48:25,030
+ماعرفش أكتبه لا سين ولا صاد صح ولا لأ بقول خلاص
+
+593
+00:48:25,030 --> 00:48:31,420
+حلّله زي لما أقول والله حلّلي الخمسة كرقم بقول اتنين
+
+594
+00:48:31,420 --> 00:48:35,600
+و تلاتة و أربعة و واحد يعني أنت ليش لما تحلله لما
+
+595
+00:48:35,600 --> 00:48:41,180
+تجمعهم بتطلع الخمسة كما وهي مكوناته حطهم بتطلع
+
+596
+00:48:41,180 --> 00:48:49,280
+الكامل ممكن تكتب هيك صحّيكوا ولا لأ هجيت شايفة إيه
+
+597
+00:48:49,280 --> 00:48:53,300
+اشتغلت فيه لا هو سيني ولا هو صادي هيك وهيك اتنين
+
+598
+00:48:53,990 --> 00:48:58,970
+إذا بيقول لي it is clear that the vector a can be
+
+599
+00:48:58,970 --> 00:49:03,890
+represented by the sum هو عبارة عن مجموع sum of
+
+600
+00:49:03,890 --> 00:49:08,550
+two vectors واحد سيني واحد صادي أمين ولا لأ؟ إذا
+
+601
+00:49:08,550 --> 00:49:12,290
+هذول عبارة عن sum of two vectors one parallel to
+
+602
+00:49:12,290 --> 00:49:16,150
+the x-axis ومزاد parallel to the x-axis وحط جنبه I
+
+603
+00:49:17,080 --> 00:49:21,460
+صح؟ و one parallel to the y axis حُط جنبه J فصار
+
+604
+00:49:21,460 --> 00:49:26,940
+إيه بتسوي هيك زي إيد هيك قلت له حلو هذه أحد مركبات
+
+605
+00:49:26,940 --> 00:49:31,080
+هذه ولا لأ إيش هسميه مركبة السينية لأنه باتجاه
+
+606
+00:49:31,080 --> 00:49:35,340
+السيني وإيش هسمي هذه مركبة الصادية فهمته إيش
+
+607
+00:49:35,340 --> 00:49:39,020
+معناه مركبات تمام نكمل بعدين تمام يا سامي
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/1noCDAkxHwg_raw.json b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/1noCDAkxHwg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..bf1caf90ea2a160a45181f35772817822b3a9169
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/1noCDAkxHwg_raw.json
@@ -0,0 +1 @@
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المagnitude مسموحة تكون سالبة؟ لأ اذا مسموحة ال speed تكون سالبة؟ لأ الفلسفية اه الفلسفية اه نهد اكتر سالب يعني شرق او قرض شمال او جنوب ده ما؟", "tokens": [3224, 2407, 1975, 5016, 8315, 16490, 1211, 11703, 9957, 1829, 8717, 47341, 3615, 5296, 35457, 25708, 39896, 2423, 15668, 6055, 3555, 34268, 2423, 9269, 3714, 19913, 3555, 2407, 9566, 22807, 29538, 20449, 1211, 20498, 3660, 11331, 4117, 36081, 11296, 2423, 3073, 39896, 2423, 15668, 9673, 4535, 4377, 3714, 38251, 2407, 5016, 3660, 6055, 30544, 8608, 6027, 49401, 22807, 5296, 10721, 1975, 15730, 3714, 38251, 2407, 5016, 3660, 2423, 3073, 6055, 30544, 8608, 6027, 49401, 22807, 5296, 10721, 27188, 1211, 3794, 5172, 10632, 1975, 3224, 27188, 1211, 3794, 5172, 10632, 1975, 3224, 8717, 3224, 3215, 1975, 4117, 2655, 2288, 8608, 6027, 3555, 37495, 22653, 13412, 2288, 4587, 1975, 2407, 12174, 43042, 13412, 2304, 6027, 1975, 2407, 10874, 1863, 37746, 11778, 3224, 19446, 22807], "avg_logprob": -0.30614838222178015, "compression_ratio": 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1538.29, "text": "من ايش عرفته؟ من الساهم حلو كل الناس بتلقى في الساهم اذا طيب هدى كام اتجاه؟ هت طب و هدى؟ زى بعض كاتجاه لكن نفس الطول تقدر تقول ان هدى اكبر من هدى ولا لا اذا بدك تمثل ال vector الساهم اتفهمنا انا وياك عليه طب الطول قال لي الطول بدى يتناسب مع المقدر", "tokens": [27842, 1975, 1829, 8592, 6225, 28480, 47395, 22807, 9154, 21136, 995, 16095, 11331, 1211, 2407, 28242, 2423, 8315, 3794, 39894, 1211, 4587, 7578, 8978, 21136, 995, 16095, 1975, 15730, 23032, 1829, 3555, 8032, 3215, 7578, 9122, 10943, 1975, 2655, 7435, 40294, 22807, 8032, 2655, 23032, 3555, 4032, 8032, 3215, 7578, 22807, 30767, 7578, 45030, 11242, 9122, 9307, 7435, 40294, 44381, 8717, 36178, 41950, 12610, 6055, 28543, 2288, 6055, 39648, 16472, 8032, 3215, 7578, 1975, 4117, 26890, 9154, 8032, 3215, 7578, 49429, 20193, 1975, 15730, 47525, 4117, 46811, 12984, 1211, 2423, 8062, 21136, 995, 16095, 1975, 2655, 5172, 16095, 8315, 1975, 8315, 4032, 25528, 4117, 47356, 23032, 3555, 41950, 12610, 50239, 32239, 41950, 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"end": 1534.87, "word": " طب", "probability": 0.823974609375}, {"start": 1534.87, "end": 1535.71, "word": " الطول", "probability": 0.897216796875}, {"start": 1535.71, "end": 1536.17, "word": " قال", "probability": 0.556640625}, {"start": 1536.17, "end": 1536.29, "word": " لي", "probability": 0.365966796875}, {"start": 1536.29, "end": 1536.77, "word": " الطول", "probability": 0.94384765625}, {"start": 1536.77, "end": 1537.05, "word": " بدى", "probability": 0.588623046875}, {"start": 1537.05, "end": 1537.53, "word": " يتناسب", "probability": 0.944091796875}, {"start": 1537.53, "end": 1537.69, "word": " مع", "probability": 0.990234375}, {"start": 1537.69, "end": 1538.29, "word": " المقدر", "probability": 0.89453125}], "temperature": 1.0}, {"id": 70, "seek": 155274, "start": 1539.12, "end": 1552.74, "text": "الطول بدى تتناسب مع المقدار إذاً geometrically يعني هندسيا تمام؟ انتوا عارفوا علم الهندسة تمام؟ if the vector quantity is represented هتمثل", "tokens": [6027, 9566, 12610, 47525, 7578, 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geometrically", "probability": 0.6084798177083334}, {"start": 1543.38, "end": 1543.72, "word": " يعني", "probability": 0.8271484375}, {"start": 1543.72, "end": 1544.54, "word": " هندسيا", "probability": 0.964599609375}, {"start": 1544.54, "end": 1545.56, "word": " تمام؟", "probability": 0.6255696614583334}, {"start": 1545.56, "end": 1545.94, "word": " انتوا", "probability": 0.547119140625}, {"start": 1545.94, "end": 1546.16, "word": " عارفوا", "probability": 0.8330078125}, {"start": 1546.16, "end": 1546.38, "word": " علم", "probability": 0.8515625}, {"start": 1546.38, "end": 1547.18, "word": " الهندسة", "probability": 0.99208984375}, {"start": 1547.18, "end": 1548.58, "word": " تمام؟", "probability": 0.7975260416666666}, {"start": 1548.58, "end": 1548.76, "word": " if", "probability": 0.261962890625}, {"start": 1548.76, "end": 1549.1, "word": " the", "probability": 0.8193359375}, {"start": 1549.1, "end": 1549.46, "word": " vector", "probability": 0.9345703125}, {"start": 1549.46, "end": 1550.28, "word": " quantity", "probability": 0.98779296875}, {"start": 1550.28, "end": 1550.6, "word": " is", "probability": 0.953125}, {"start": 1550.6, "end": 1551.52, "word": " represented", "probability": 0.80810546875}, {"start": 1551.52, "end": 1552.74, "word": " هتمثل", "probability": 0.8154296875}], "temperature": 1.0}, {"id": 71, "seek": 157553, "start": 1553.65, "end": 1575.53, "text": "by a straight line خط مستقيم هاي هم خطوط مستقيمة تمام and and a row at one end of the line مع سهم عند أحد أطراف الخط طول السهم عشان يدل عليهش الاتجاه والطول عشان يحسسك جديش مقدار الكمية تمام", "tokens": [2322, 257, 2997, 1622, 16490, 9566, 3714, 14851, 4587, 32640, 8032, 47302, 8032, 2304, 16490, 9566, 2407, 9566, 3714, 14851, 4587, 32640, 3660, 46811, 10943, 293, 293, 257, 5386, 412, 472, 917, 295, 264, 1622, 20449, 8608, 16095, 43242, 5551, 24401, 5551, 9566, 23557, 5172, 33962, 9566, 23032, 12610, 21136, 16095, 6225, 8592, 7649, 7251, 3215, 1211, 47356, 8592, 2423, 9307, 7435, 40294, 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"probability": 0.5859375}, {"start": 1584.78, "end": 1585.0, "word": " to", "probability": 0.9423828125}, {"start": 1585.0, "end": 1585.14, "word": " the", "probability": 0.82470703125}, {"start": 1585.14, "end": 1585.64, "word": " direction", "probability": 0.9599609375}, {"start": 1585.64, "end": 1585.86, "word": " of", "probability": 0.9560546875}, {"start": 1585.86, "end": 1586.0, "word": " the", "probability": 0.8779296875}, {"start": 1586.0, "end": 1586.38, "word": " vector", "probability": 0.98095703125}, {"start": 1586.38, "end": 1586.78, "word": " و", "probability": 0.2135009765625}, {"start": 1586.78, "end": 1587.42, "word": " الاروة", "probability": 0.914306640625}, {"start": 1587.42, "end": 1588.16, "word": " بيوجه", "probability": 0.9456787109375}, {"start": 1588.16, "end": 1588.64, "word": " او", "probability": 0.6815185546875}, {"start": 1588.64, "end": 1589.04, "word": " يشير", "probability": 0.9557291666666666}, {"start": 1589.04, "end": 1589.3, "word": " الى", "probability": 0.81396484375}, {"start": 1589.3, "end": 1589.54, "word": " نحو", "probability": 0.9532877604166666}, {"start": 1589.54, "end": 1590.22, "word": " الاتجاه", "probability": 0.9013671875}, {"start": 1590.22, "end": 1591.08, "word": " تمام", "probability": 0.952392578125}, {"start": 1591.08, "end": 1592.08, "word": " هذا", "probability": 0.7236328125}, {"start": 1592.08, "end": 1592.48, "word": " vector", "probability": 0.36474609375}, {"start": 1592.48, "end": 1593.14, "word": " شايفينه", "probability": 0.88193359375}, {"start": 1593.14, "end": 1594.64, "word": " هذا", "probability": 0.402587890625}, {"start": 1594.64, "end": 1595.62, "word": " بنسميه", "probability": 0.76214599609375}], "temperature": 1.0}, {"id": 73, "seek": 161458, "start": 1596.34, "end": 1614.58, "text": "طرف .. بنسميه ديل وطرف بنسميه راس صعب هاي الراس الكبير و الديل مهم باين دي سهل دايما ال .. الرموز بتيجي من شغلات مألوفة للناس عشان الحفظ هيكون سهل والتعامل معها سهل حلو", "tokens": [9566, 28480, 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" ديل", "probability": 0.498046875}, {"start": 1598.38, "end": 1599.14, "word": " وطرف", "probability": 0.81005859375}, {"start": 1599.14, "end": 1600.2, "word": " بنسميه", "probability": 0.92431640625}, {"start": 1600.2, "end": 1600.54, "word": " راس", "probability": 0.768798828125}, {"start": 1600.54, "end": 1601.02, "word": " صعب", "probability": 0.8147786458333334}, {"start": 1601.02, "end": 1601.56, "word": " هاي", "probability": 0.5108642578125}, {"start": 1601.56, "end": 1601.8, "word": " الراس", "probability": 0.82861328125}, {"start": 1601.8, "end": 1602.32, "word": " الكبير", "probability": 0.9724934895833334}, {"start": 1602.32, "end": 1603.02, "word": " و", "probability": 0.51708984375}, {"start": 1603.02, "end": 1603.42, "word": " الديل", "probability": 0.58056640625}, {"start": 1603.42, "end": 1603.78, "word": " مهم", "probability": 0.652099609375}, {"start": 1603.78, "end": 1604.16, "word": " باين", "probability": 0.8846028645833334}, {"start": 1604.16, "end": 1604.38, 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{"start": 2077.0, "end": 2077.1, "word": " ولا", "probability": 0.482421875}, {"start": 2077.1, "end": 2077.82, "word": " اللي", "probability": 0.929931640625}, {"start": 2077.82, "end": 2078.12, "word": " بدكم", "probability": 0.893310546875}, {"start": 2078.12, "end": 2078.4, "word": " ايه", "probability": 0.5927734375}, {"start": 2078.4, "end": 2079.34, "word": " تعنى", "probability": 0.5412190755208334}, {"start": 2079.34, "end": 2083.9, "word": " negative", "probability": 0.68310546875}, {"start": 2083.9, "end": 2084.1, "word": " ايش", "probability": 0.7687174479166666}, {"start": 2084.1, "end": 2084.3, "word": " يعني", "probability": 0.904296875}, {"start": 2084.3, "end": 2084.72, "word": " negative", "probability": 0.90087890625}], "temperature": 1.0}, {"id": 93, "seek": 209429, "start": 2085.61, "end": 2094.29, "text": "سالب احنا بنا لغة سالب ايش معناه تسالب في ال victors جالب يعكس اتجاهه بس", "tokens": [3794, 6027, 3555, 1975, 5016, 8315, 4724, 8315, 5296, 17082, 3660, 8608, 6027, 3555, 1975, 1829, 8592, 20449, 8315, 3224, 6055, 3794, 6027, 3555, 8978, 2423, 4403, 830, 10874, 6027, 3555, 37495, 4117, 3794, 1975, 2655, 7435, 40294, 3224, 4724, 3794], "avg_logprob": -0.23772322031713666, "compression_ratio": 1.3225806451612903, "no_speech_prob": 0.0, "words": [{"start": 2085.61, "end": 2086.11, "word": "سالب", "probability": 0.79541015625}, {"start": 2086.11, "end": 2086.87, "word": " احنا", "probability": 0.8525390625}, {"start": 2086.87, "end": 2087.09, "word": " بنا", "probability": 0.4912109375}, {"start": 2087.09, "end": 2087.59, "word": " لغة", "probability": 0.9169921875}, {"start": 2087.59, "end": 2088.73, "word": " سالب", "probability": 0.9441731770833334}, {"start": 2088.73, "end": 2089.63, "word": " ايش", "probability": 0.7488606770833334}, {"start": 2089.63, "end": 2090.01, "word": " معناه", "probability": 0.8610026041666666}, {"start": 2090.01, "end": 2090.55, "word": " تسالب", "probability": 0.86669921875}, {"start": 2090.55, "end": 2090.69, 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مركبات تمام نكمل بعدين تمام يا سامي", "tokens": [9381, 5016, 22807, 4032, 472, 8952, 281, 264, 288, 10298, 11331, 10859, 9566, 10874, 1863, 3555, 3224, 10874, 1829, 3224, 6156, 9381, 9640, 1975, 1829, 3224, 39894, 3794, 45865, 39896, 4117, 30767, 1829, 1975, 25708, 39896, 4117, 12174, 1211, 2655, 43761, 11331, 1211, 2407, 29538, 1975, 24401, 3714, 31747, 3555, 9307, 29538, 49429, 5296, 10721, 1975, 1829, 8592, 8032, 38251, 1829, 3224, 3714, 31747, 49401, 31767, 9957, 10632, 5296, 33456, 3224, 4724, 9307, 7435, 40294, 31767, 9957, 1829, 4032, 1975, 1829, 8592, 8032, 38251, 1829, 29538, 3714, 31747, 49401, 31767, 18513, 10632, 1975, 5172, 16095, 47395, 1975, 1829, 8592, 20449, 8315, 3224, 3714, 31747, 3555, 9307, 46811, 10943, 8717, 24793, 1211, 39182, 9957, 46811, 10943, 35186, 8608, 10943, 1829], "avg_logprob": -0.269531257947286, "compression_ratio": 1.7991071428571428, "no_speech_prob": 9.59634780883789e-06, "words": [{"start": 2957.0800000000004, "end": 2957.8, "word": "صح؟", 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" هذه", "probability": 0.56396484375}, {"start": 2972.76, "end": 2973.78, "word": " مركبة", "probability": 0.9596354166666666}, {"start": 2973.78, "end": 2974.46, "word": " الصادية", "probability": 0.7020670572916666}, {"start": 2974.46, "end": 2975.24, "word": " افهمته", "probability": 0.81365966796875}, {"start": 2975.24, "end": 2975.34, "word": " ايش", "probability": 0.8401692708333334}, {"start": 2975.34, "end": 2975.54, "word": " معناه", "probability": 0.7568359375}, {"start": 2975.54, "end": 2976.3, "word": " مركبات", "probability": 0.959228515625}, {"start": 2976.3, "end": 2977.3, "word": " تمام", "probability": 0.85009765625}, {"start": 2977.3, "end": 2977.94, "word": " نكمل", "probability": 0.7111409505208334}, {"start": 2977.94, "end": 2978.28, "word": " بعدين", "probability": 0.5625}, {"start": 2978.28, "end": 2978.58, "word": " تمام", "probability": 0.960205078125}, {"start": 2978.58, "end": 2978.76, "word": " يا", "probability": 0.85546875}, {"start": 2978.76, "end": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/4GxkJ1fxBBI.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/4GxkJ1fxBBI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..25f9ce8565d4b6b555910c00541f84e699867953
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/4GxkJ1fxBBI.srt
@@ -0,0 +1,1882 @@
+1
+00:00:05,090 --> 00:00:10,410
+تمام يا بنات نستأنف اللي بدنا، chapter رقم أربعة و
+
+2
+00:00:10,410 --> 00:00:14,150
+اللي قلنا تقريباً معلومات chapter اثنين بدنا نعيدها
+
+3
+00:00:14,150 --> 00:00:20,950
+بس على two copies، واحدة أفقية وواحدة رأسية، حكينا
+
+4
+00:00:20,950 --> 00:00:27,430
+أن الحركة باتجاهين أو الحركة المستوية نتعامل معها
+
+5
+00:00:27,430 --> 00:00:34,090
+على أنها حركة أفقية X motion و
+
+6
+00:00:34,090 --> 00:00:34,730
+Y motion
+
+7
+00:00:38,680 --> 00:00:43,200
+وحكينا لو كانت التسارع ثابت، معناته التسارع
+
+8
+00:00:43,200 --> 00:00:48,040
+بمركبتين، تبعاته الأفقية والرأسية، ثوابت، وبالتالي
+
+9
+00:00:48,040 --> 00:00:54,860
+بيصير في عندي قوانين VX final بتساوي VX initial
+
+10
+00:00:54,860 --> 00:01:01,230
+زائد aX في الـT، مظبوط ولا لأ؟ وفي عندي X final ناقص X
+
+11
+00:01:01,230 --> 00:01:07,630
+initial بتساوي vx initial في t زائد نصف aX في t تربيع
+
+12
+00:01:07,630 --> 00:01:14,190
+وكما في قانون عندي vx final تربيع بتساوي vx initial
+
+13
+00:01:14,190 --> 00:01:20,830
+تربيع زائد 2aX (X final ناقص X initial)، نفس
+
+14
+00:01:20,830 --> 00:01:25,370
+القوانين اللي بكتبهم للحركة الرأسية، إذا بتكون في
+
+15
+00:01:25,370 --> 00:01:30,230
+عندي حركتين، أفقية ورأسية، وكل سؤال عبارة عن سؤالين
+
+16
+00:01:30,230 --> 00:01:36,980
+أفقي ورأسي، مين المشترك بين الاثنتين؟ الزمن، مش هيك؟
+
+17
+00:01:36,980 --> 00:01:42,160
+اتفقنا؟ بدنا نيجي الآن، إيش في أمثلة طبيعية لحركة
+
+18
+00:01:42,160 --> 00:01:46,280
+مستوية؟ قال لي حركة المقذوفات، إذا  نproject الـ
+
+19
+00:01:46,280 --> 00:01:52,000
+motion، هجيت إيش تعريف حركة المقذوفات؟ بنقول أي جسم
+
+20
+00:01:52,000 --> 00:01:59,590
+بتقذفه وبتفلته، لما تفلته مين بده يتحكم فيه غير
+
+21
+00:01:59,590 --> 00:02:03,350
+الجاذبية الأرضية، مش فيه غير الجاذبية الأرضية، إذن
+
+22
+00:02:03,350 --> 00:02:07,670
+هذه بنسميها حركة المقذوفات. لو نيجي نتذكر ما هو
+
+23
+00:02:07,670 --> 00:02:13,810
+تعريف السقوط الحر، هو جسم مين بيأثر فيه فقط؟ برضه
+
+24
+00:02:13,810 --> 00:02:18,050
+تسارع الجاذبية الأرضية، إذن تعريف السقوط الحر و
+
+25
+00:02:18,050 --> 00:02:22,560
+تعريف الprojectile motion نفس الشيء. طب إيش الفرق
+
+26
+00:02:22,560 --> 00:02:27,100
+عن بعض؟ قال في السقوط الحر كنت أنا  أشترط أن تكون
+
+27
+00:02:27,100 --> 00:02:31,940
+السرعة الابتدائية إما لأعلى وإما لأسفل، بس ممنوع
+
+28
+00:02:31,940 --> 00:02:38,380
+تكون بزاوية معينة، بمعنى آخر السرعة الابتدائية إذا
+
+29
+00:02:38,380 --> 00:02:42,750
+إلها مركبة أفقية، بقول هذا projectile motion، إذا
+
+30
+00:02:42,750 --> 00:02:48,010
+مركبتها الأفقية صفر، بقول سقوط حر، بمعنى آخر السقوط
+
+31
+00:02:48,010 --> 00:02:52,090
+الحر هو projectile motion بس حالة خاصة، إذا الـ
+
+32
+00:02:52,090 --> 00:02:57,470
+projectile motion هو يحتوي تلقائياً على السقوط الحر
+
+33
+00:02:57,470 --> 00:03:02,760
+نيجي نشوف إيش التعريف، بقول if a particle is given an
+
+34
+00:03:02,760 --> 00:03:07,460
+initial velocity، اعترض سرعة ابتدائية، and then
+
+35
+00:03:07,460 --> 00:03:13,360
+follows a path، اتبعت مسار، هذا المسار مين بتحتكم فيه؟
+
+36
+00:03:13,360 --> 00:03:17,740
+determined only by gravity، يحدده فقط الجاذبية
+
+37
+00:03:17,740 --> 00:03:22,780
+الأرضية، we have projected motion، تمام، نذكر chapter
+
+38
+00:03:22,780 --> 00:03:30,690
+2، تسارع الجاذبية الأرضية، كيف اتجاهه؟ لأسفل، أفقي ولا
+
+39
+00:03:30,690 --> 00:03:37,730
+رأسي؟ رأسي، إذا معناته في حركة المقذوفات، التسارع
+
+40
+00:03:37,730 --> 00:03:45,770
+تبعه فقط رأسي ولا لأ؟ مش هيك؟ ليش حتى السالب؟ لأنه
+
+41
+00:03:45,770 --> 00:03:52,430
+لأسفل، وحطيت g لأنه عمودي، لو إجتمعنا الآن من هذه
+
+42
+00:03:52,430 --> 00:03:58,350
+المعلومات، جدّيش aX لحركة المقذوف؟ فعلاً يا عيني عليكم
+
+43
+00:04:00,640 --> 00:04:06,900
+إذن حركة المقذوفات هي عبارة عن حركتين، أفقية
+
+44
+00:04:06,900 --> 00:04:11,560
+بتسارع صفر، ورأسية بتسارع الجاذبية الأرضية، ولا لأ؟
+
+45
+00:04:11,560 --> 00:04:17,400
+كمان، يعني معناته هذه القوانين سارية المفعول، إيش بده
+
+46
+00:04:17,400 --> 00:04:24,280
+يحط محل aX؟ صفر، إذن هذه راحت صح؟ وهذه aX راحت،
+
+47
+00:04:24,280 --> 00:04:32,660
+وهذه aX راحت،  إيش يتطلع؟ هذه وهذه إخوة، هذه VX
+
+48
+00:04:32,660 --> 00:04:36,220
+final بتساوي VX initial،  ربعة حقاً، كأنه، إذا هذا
+
+49
+00:04:36,220 --> 00:04:38,780
+القانون هو نفسه هذا القانون، هذا ما بش لازم يعمل
+
+50
+00:04:38,780 --> 00:04:43,700
+مرة، ليش؟ نقول إيش ده بيقول؟ بيقول لما تقول لي
+
+51
+00:04:43,700 --> 00:04:46,840
+السرعة الابتدائية الأفقية هي نفسها النهائية، يعني
+
+52
+00:04:46,840 --> 00:04:51,560
+السرعة الأفقية بتتغير؟ ثابتة، سرعة الأفقية ليش؟ قال
+
+53
+00:04:51,560 --> 00:04:56,920
+لي،  أصل ما فيش تسارع أفقي، والتسارع يعني تغير سرعة،
+
+54
+00:04:56,920 --> 00:05:01,940
+إذا السرعة ما تغيرت فهي ثابتة، وإذا ما فيش تسارع
+
+55
+00:05:01,940 --> 00:05:07,780
+مسموح للسرعة تتغير؟ لأ، إذا السرعة الأفقية ثابتة،
+
+56
+00:05:07,780 --> 00:05:11,040
+هذا القانون أخذناه في الصف الرابع ابتدائي، المسافة
+
+57
+00:05:11,040 --> 00:05:13,940
+بتساوي سرعة في زمن، وهذا القانون صار المفعول طول
+
+58
+00:05:13,940 --> 00:05:19,270
+ما فيش تسارع، وهو سارٍ المفعول، مسافة بتساوي سرعة في زمن، بس
+
+59
+00:05:19,270 --> 00:05:24,510
+أفقي أفقي، قال الصبورة قالت وين في ay حط محلها سالب
+
+60
+00:05:24,510 --> 00:05:29,290
+g، مظبوط؟  لا نجرى القوانين المناظرة يا بنات، بقوله
+
+61
+00:05:29,290 --> 00:05:37,230
+هنا Vy final بتساوي Vy initial زائد ay، بيصير
+
+62
+00:05:37,230 --> 00:05:44,780
+سالب g، وهنا بدي Y final ناقص Y
+
+63
+00:05:44,780 --> 00:05:50,880
+initial بتساوي Vy initial في T ناقص نصف GT تربيع، و
+
+64
+00:05:50,880 --> 00:05:58,220
+Vy final تربيع بتساوي Vy initial تربيع ناقص 2G(Y
+
+65
+00:05:58,220 --> 00:06:03,320
+final ناقص Y initial)، هذه حركة المقذوفات، إذا حركة
+
+66
+00:06:03,320 --> 00:06:08,060
+المقذوفات هي مجموعة حركتين، حركة أفقية بسرعة ثابتة
+
+67
+00:06:08,700 --> 00:06:14,340
+وحركة رأسية سقوط حر بتسارع الجاذبية الأرضية، يعني
+
+68
+00:06:14,340 --> 00:06:19,500
+سقوط حر، تمام؟ تمام، إذا إيش بيقول لي؟ بيقول لي as
+
+69
+00:06:19,500 --> 00:06:23,420
+the acceleration of gravity is always straight
+
+70
+00:06:23,420 --> 00:06:27,340
+downward، وهذه معلومة كنا بنعرفها، تمام؟ with a
+
+71
+00:06:27,340 --> 00:06:31,700
+magnitude of g، the acceleration of a projectile
+
+72
+00:06:31,700 --> 00:06:39,430
+كتبت هذا، بيعني أنه، هذا يعني أن حركة المقذوف يمكن
+
+73
+00:06:39,430 --> 00:06:47,790
+أن تكون مجموح حركتين، حركة رأسية،
+
+74
+00:06:47,790 --> 00:06:51,990
+تسارعها  يساوي سالب g، وعارفين ليش حطينا السالب؟
+
+75
+00:06:51,990 --> 00:06:55,470
+عشان أنا كل حاجة لأعلى positive وكل حاجة لأسفل
+
+76
+00:06:55,470 --> 00:07:01,150
+سالبة، and a horizontal motion with no acceleration
+
+77
+00:07:01,150 --> 00:07:05,610
+no acceleration بتعني constant velocity، ولا لأ؟ تمام،
+
+78
+00:07:05,610 --> 00:07:08,370
+قال لي لو اعتبرت هدول القوانين اللي أنا كتبتهم
+
+79
+00:07:08,370 --> 00:07:11,790
+هيكتبهم على اعتبار أن هو اعتبر هنا x initial و y
+
+80
+00:07:11,790 --> 00:07:17,450
+initial صفر، تمام، هدول القوانين عرفناهم، هو بنفسه
+
+81
+00:07:17,450 --> 00:07:22,470
+هذا وهذا، ما أصلاً مش قانون، هذه معلومة، أنه ما فيش
+
+82
+00:07:22,470 --> 00:07:26,510
+تسارع أفقي، بتعني أن السرعة الأفقية ابتدائية ولا
+
+83
+00:07:26,510 --> 00:07:29,910
+نهائية بتفرق؟ لأ، وهذا القانون الوحيد اللي موجود
+
+84
+00:07:29,910 --> 00:07:36,690
+مسافة بتساوي سرعة في زمن، ده ما بيقول لي
+
+85
+00:07:36,690 --> 00:07:42,990
+لو إيدي أطلعت هذه، شايفين القانون، بدي آخذ الزمن
+
+86
+00:07:42,990 --> 00:07:49,810
+منه، أقدر أقول T بتساوي X final ناقص X initial على VX
+
+87
+00:07:49,810 --> 00:07:56,790
+initial، صح ولا لأ؟ قال خذ لي هذا وعوضه هنا، هتجيب لك
+
+88
+00:07:56,790 --> 00:08:03,230
+معادلة بين Y و X، صح؟ لأنه بدّل T، إيش بده يجيب؟ X
+
+89
+00:08:03,230 --> 00:08:08,670
+قال لي لو إجيت عوضت ال T من هذه المعادلة وحطيتها
+
+90
+00:08:08,670 --> 00:08:15,030
+في هذه المعادلة، هتطلع هكذا معادلة، قال لي هذه الطلاب
+
+91
+00:08:15,030 --> 00:08:18,210
+قالوا أخذناها، والطالبات قالوا ما أخذناش لسه، أنا
+
+92
+00:08:18,210 --> 00:08:21,690
+شوف الطالبات التانيات إيش بيقولوا، معادلة زي هذه، Y
+
+93
+00:08:21,690 --> 00:08:30,970
+بتساوي AX ناقص BX تربيع، معادلة إيش هذه؟ اللي هي قطع
+
+94
+00:08:30,970 --> 00:08:38,020
+مكافئة، بسموه parabola، سمعتوا كلمة parabola؟ parabola
+
+95
+00:08:38,020 --> 00:08:44,420
+ما أخذتوها في القلب، كل لحظة جديدة، طيب أذكركم فيها، هذه
+
+96
+00:08:44,420 --> 00:08:51,760
+أو هذه، طبعاً ممكن هذه وهذه نسميها parabola، قطعة
+
+97
+00:08:51,760 --> 00:08:56,580
+مكافئة، بيسموها، تمام، قال لي معناته إيش بيقول؟ بيقول هذه
+
+98
+00:08:56,580 --> 00:08:58,660
+أنت إيش بتجيب؟ قلت له أنا هذه، بجيب لك حركة
+
+99
+00:08:58,660 --> 00:09:03,880
+المقذوفات، قال لي معناته المقذوفات تتبع مسار شكله هيك
+
+100
+00:09:03,880 --> 00:09:10,380
+يعني كل جسم يقذف لازم يتبع parabola، مش عشوائي هكذا
+
+101
+00:09:10,380 --> 00:09:14,480
+المعادلة جابت رياضيات احنا ما بدنا، ما بدنا صفات
+
+102
+00:09:14,480 --> 00:09:18,960
+لا parabola ولا حاجة، بس بدنا نحط في مخنا كلمة parabola
+
+103
+00:09:18,960 --> 00:09:22,620
+معناها قطعة مكافئة، هتاخذوها في الـcalculus، هتاخذوها
+
+104
+00:09:22,620 --> 00:09:28,680
+هؤلاء الشباب، هاخدها قبلكم؟ معاكم؟ أخذتوها؟ المهم
+
+105
+00:09:28,680 --> 00:09:34,860
+هي شكلها، يعني أي جسم بأقذفه يا بنات، أي جسم بأقذفه،
+
+106
+00:09:34,860 --> 00:09:38,300
+مش اللي بده يحدد مساره الجاذبية الأرضية، معناته
+
+107
+00:09:38,300 --> 00:09:43,640
+مساره هيه، منحنى، شايفينه؟ هذا هو المسار، خلّيني
+
+108
+00:09:43,640 --> 00:09:47,820
+أقول جزء من دائرة، هيك بده يكون مساره، من هنا
+
+109
+00:09:47,820 --> 00:09:54,220
+أطلقته، هذه النقطة أقصى ارتفاع ولا لأ؟ وصل هنا
+
+110
+00:09:54,220 --> 00:09:59,600
+اتطلعوا، قذفته بزاوية معينة، هجيت أنا هاي قذفته
+
+111
+00:09:59,600 --> 00:10:03,280
+بزاوية معطاة، المعطيات بتقدروا هذه الصورة الابتدائية
+
+112
+00:10:03,280 --> 00:10:07,900
+تجيب لي مركبتيها، الأفقية والرأسية، هاي مركبة
+
+113
+00:10:07,900 --> 00:10:10,900
+الأفقية، وهي الرأسية، هجيت هذه المركبة الأفقية
+
+114
+00:10:10,900 --> 00:10:17,710
+مسموح إنها تتغير؟ لأ، طب حلو،  مساؤكم، أنتم قلتوا ممنوع
+
+115
+00:10:17,710 --> 00:10:22,790
+تتغير، عند أقصى ارتفاع في حركة المقذوفات، كده السرعة
+
+116
+00:10:22,790 --> 00:10:27,430
+الـY صفر، بس الـX ثابت، بيه، هنا اللي قال صفر غلط،
+
+117
+00:10:27,430 --> 00:10:32,850
+ثابت ليش؟ لأن المركبة الأفقية موجودة، إذا الـY صفر
+
+118
+00:10:33,440 --> 00:10:39,200
+والأفقية موجودة، بمعنى آخر، لو أديكم في الquiz عند
+
+119
+00:10:39,200 --> 00:10:43,000
+أقصى ارتفاع في حركة المقذوفات، أول خيار بيقول Zero
+
+120
+00:10:43,000 --> 00:10:46,060
+عشان تتعلموا عليه وتقولوا غلط، الـY هو Zero، إذن هو
+
+121
+00:10:46,060 --> 00:10:50,480
+مش Zero، طب بيجي سؤال ثاني بيقول لك السرعة الابتدائية
+
+122
+00:10:50,480 --> 00:10:54,700
+في حركة المقذوفات وكتب لك هذه العلاقة، V initial
+
+123
+00:10:54,700 --> 00:11:00,040
+وحط هيك، بتساوي 5i زائد 3j متر per second،
+
+124
+00:11:01,110 --> 00:11:04,050
+هذه حركة، هذه حركة المقذوفات، وهذه السرعة
+
+125
+00:11:04,050 --> 00:11:08,450
+الابتدائية، بدي أسأل، عند أقصى ارتفاع كده السرعة؟
+
+126
+00:11:08,450 --> 00:11:11,750
+أيش؟ ليش؟
+
+127
+00:11:11,750 --> 00:11:18,670
+صح؟ لأنه بس الأفقية، طب كده الأفقية؟ 5، بتتغير؟
+
+128
+00:11:18,670 --> 00:11:23,870
+لأ، إذا في بداية أو عند أقصى ارتفاع أو نهاية، كده؟
+
+129
+00:11:23,870 --> 00:11:28,870
+5، أبسط،  تحكي فعلاً صح؟ كأن في مجتمع الجبل لو كان
+
+130
+00:11:28,870 --> 00:11:32,220
+، لو كان صفر، فالاسم يكون المركبات اللي بيبقى
+
+131
+00:11:32,220 --> 00:11:36,220
+واضحة؟ هذا لو كان صفر، وما جاك صفر؟ وأنا بقول لك عند
+
+132
+00:11:36,220 --> 00:11:41,280
+أقصى ارتفاع، جدّيش السرعة؟ إذا جلت صفر، بقول لي غلط، مش
+
+133
+00:11:41,280 --> 00:11:46,740
+صفر، إذا اللي عند أقصى ارتفاع جدّيش السرعة؟ مش صفر، مش
+
+134
+00:11:46,740 --> 00:11:50,340
+صفر، إيش جاوبنا؟ 5، جاوبنا 5، ما جاوبنا
+
+135
+00:11:50,340 --> 00:11:58,820
+الصفر؟ ممنوع تقولي صفر، ولا مرة، ولا مرة، ولا مرة،
+
+136
+00:11:58,820 --> 00:12:05,520
+ولا مرة، ولا مرة، ولا مرة، ولا مرة، ولا مرة،
+
+137
+00:12:05,520 --> 00:12:05,560
+ولا مرة، ولا مرة، ولا مرة، ولا مرة، ولا مرة،
+
+138
+00:12:05,560 --> 00:12:05,960
+ولا مرة، ولا مرة، ولا مرة، ولا مرة، ولا مرة،
+
+139
+00:12:05,960 --> 00:12:06,160
+ولا مرة، ولا مرة، ولا مرة، ولا مرة، ولا مرة،
+
+140
+00:12:06,160 --> 00:12:07,180
+ولا مرة، ولا مرة، ولا مرة، ولا مرة، ولا مرة،
+
+141
+00:12:07,180 --> 00:12:10,880
+ولا مرة، ولا مرة، ولا مرة، ولا مرة، ولا مرة،
+
+142
+00:12:10,880 --> 00:12:16,040
+ولا مرة، ولا مرة،
+
+143
+00:12:16,040 --> 00:12:22,740
+ولا مرة، ولا مرة، ولا مرة، ولا مرة، ولا مرة،
+
+144
+00:12:23,540 --> 00:12:26,480
+لأ، مش هلق، هو في بس اللي هو المحور السيني اللي هو
+
+145
+00:12:26,480 --> 00:12:34,500
+الـg، الـg،  أفقي، طلع، لكن كلها أفقي، لأ، الرأسية، عشان كده
+
+146
+00:12:34,500 --> 00:12:38,740
+لما حكيت لك هنا، طلع، هتجيب على هذه السرعة الرأسية،
+
+147
+00:12:38,740 --> 00:12:43,120
+هنضع أقصى ارتفاع، هذه بصير صفر، لكن هذه ما بتغيرش، إذا
+
+148
+00:12:43,120 --> 00:12:45,980
+جدّيش السرعة عند أقصى ارتفاع؟ بقوله 5، ضلت الأفقية،
+
+149
+00:12:45,980 --> 00:12:51,340
+الرأسية راحت، عشان كده تطلع هي السهم، شايفينه؟ هجيت
+
+150
+00:12:51,340 --> 00:12:55,780
+هذا، هيهو من أطول هذا ولا هذا؟ مش هذا أطول، معناته
+
+151
+00:12:55,780 --> 00:13:00,570
+الرأسية، الأفقية زي ما هو، طلع أنت من النقطة الرأسية
+
+152
+00:13:00,570 --> 00:13:05,650
+ضلت، روح الرأسية، الأفقية زي ما هو، الأفقية زي ما هو،
+
+153
+00:13:05,650 --> 00:13:10,250
+الأفقية زي ما هو، الرأسية قاعد بتغير، لأنه في تسارع
+
+154
+00:13:10,250 --> 00:13:14,930
+رأسي، والتسارع الرأسي بيعني تغير السرعة الرأسية، و
+
+155
+00:13:14,930 --> 00:13:19,750
+عدم وجود التسارع الأفقي بيعني أن المركبة الأفقية
+
+156
+00:13:19,750 --> 00:13:29,400
+ممنوعة تتغير، تمام يا بنات؟ أي استفسار؟ تمام؟ الآن
+
+157
+00:13:29,400 --> 00:13:33,680
+العنوان إيش بيقول؟ horizontal range and maximum
+
+158
+00:13:33,680 --> 00:13:37,660
+height of a projectile، بدنا نشتغل قانونين، ممنوع
+
+159
+00:13:37,660 --> 00:13:42,360
+نحفظهم، مش مطلوب منا نحفظهم، وأنا بقول مش مطلوب، مش
+
+160
+00:13:42,360 --> 00:13:47,420
+مطلوب، ممنوع نحفظهم، أقوى من أنه مش مطلوب، بمعنى آخر
+
+161
+00:13:47,420 --> 00:13:51,260
+لو واحد قال الrange، ورحت أنا بصير حافظ القانون
+
+162
+00:13:51,260 --> 00:13:57,070
+وحطيته وعوضت، بجيب له،  لكن يشتقوا من أولهم، محطوطين
+
+163
+00:13:57,070 --> 00:14:06,550
+قوانين، لكن ممنوع تحفظهم، تمام؟ نرجع للرسمة، هل جيت أنا
+
+164
+00:14:06,550 --> 00:14:10,430
+واتفقت، أي حاجة في حركة المقذوفات، بدي أجسمها
+
+165
+00:14:10,430 --> 00:14:17,010
+لنصين، صح؟ أفقي ورأسي، كل المعطيات بدك تعرف لها
+
+166
+00:14:17,010 --> 00:14:21,850
+أفقية ولا رأسية، والمطلوب بت
+
+223
+00:18:55,230 --> 00:18:59,210
+نفترض الـ R عشرة، بقول عشرة و صفر، و0R و 0
+
+224
+00:18:59,210 --> 00:19:03,030
+ولا لأ؟ إذا هذه إحداثية عشرة و صفر، نركز على
+
+225
+00:19:03,030 --> 00:19:06,930
+الإحداثية الصفرية، الإحداثي الصفر لهذه كده، وهذه
+
+226
+00:19:06,930 --> 00:19:12,190
+صفر و صفر، زي الصفر، إذا لما بدي أعود هنا صفر، نأخذ
+
+227
+00:19:12,190 --> 00:19:19,450
+صفر صح؟ ولا تحكي صيني، تمام. أنت قلت  نبدا نشرح
+
+228
+00:19:19,450 --> 00:19:26,080
+الزمن منها صح؟ وبالتالي من العودة، ماذا يسمى الـ y
+
+229
+00:19:26,080 --> 00:19:34,060
+final؟ صفر، y initial صفر، بتساوي v، وهنا أنا، وهذه
+
+230
+00:19:34,060 --> 00:19:43,700
+y، إذا v initial sin θ في t ناقص نص g في t تربيع، صح؟ في حد
+
+231
+00:19:43,700 --> 00:19:48,240
+ما يعرفش يجيب الـ t؟ هل جيت؟ جسم المعادلة على t عشان
+
+232
+00:19:48,240 --> 00:19:55,170
+أطير هذه، وأطير هذه، أطلع الـ T، إذا الـ T اللي بتدور
+
+233
+00:19:55,170 --> 00:20:00,810
+عليها صفر، المقال صفر صفر، اه، يحصل بعدين 2V
+
+234
+00:20:00,810 --> 00:20:07,130
+initial Sine of θ على g، الزمن اللي أنغلبك جبته
+
+235
+00:20:07,130 --> 00:20:13,290
+ولا ما جبتهوش؟ الآن، بتجيب الـ X final هي R، الـ
+
+236
+00:20:13,290 --> 00:20:20,790
+range، X initial صفر صح؟ بتساوي V initial Cosine of
+
+237
+00:20:20,790 --> 00:20:30,490
+θ، بدي الـ T هيا مظبوط؟  نحط 2V initial sin
+
+238
+00:20:30,490 --> 00:20:36,930
+θ على V initial في V initial، اذا بيساوي V initial
+
+239
+00:20:36,930 --> 00:20:41,350
+تربيع، 2 sin θ cos θ، ايش القدرة في مخهم؟
+
+240
+00:20:41,350 --> 00:20:48,050
+sin 2θ، إذا هذه sin 2θ على g، هاي الـ
+
+241
+00:20:48,050 --> 00:20:54,850
+range اللي بتدور عليه، وبرضه ممنوع نحفظها، اتفجنا بس
+
+242
+00:20:54,850 --> 00:20:59,970
+برضه مسموح نتطلع عليه، ما هي أكبر قيمة لل range لما
+
+243
+00:20:59,970 --> 00:21:06,150
+sin 2θ تساوي 1، اللي هي V initial تربيع على g، طب هي
+
+244
+00:21:06,150 --> 00:21:11,570
+sin 2θ، واحنا بنعرف أن الـ θ sin 90 هو الواحد
+
+245
+00:21:11,570 --> 00:21:15,690
+إذا لازم θ تكون 45، ولا لأ؟ عشان كده بيقول لي ايش
+
+246
+00:21:15,690 --> 00:21:20,520
+بيقول لي يا ترى لو بدك أكبر range، كيف تحط الزاوية؟
+
+247
+00:21:20,520 --> 00:21:25,920
+بقول له 45 وأنت مغمض، صح ولا لأ؟ إذا أنت نشن على زاوية
+
+248
+00:21:25,920 --> 00:21:32,900
+45، بتحصل على أكبر range ممكن، صحيح ولا لأ؟ تمام، طبعا
+
+249
+00:21:32,900 --> 00:21:35,640
+أنتم زمان أخذتم في الرياضيات، في التفاضل، و
+
+250
+00:21:35,640 --> 00:21:39,120
+التكامل، في توجيهي، لما تجيبوا الشغل، عشان تكون الـ
+
+251
+00:21:39,120 --> 00:21:43,600
+function أكبر أو أصغر، ذاكرين؟ هو تطبيقات التفاضل
+
+252
+00:21:43,600 --> 00:21:47,880
+ما أخذتوهاش في توجيهي، لما
+
+253
+00:21:47,880 --> 00:21:56,410
+يكون عندكم، خليني أكتب y، ما بدي أكتب صاد، y بتساوي 2x
+
+254
+00:21:56,410 --> 00:22:01,790
+تربيع، زي 3x، ولو سألكم ماهي قيمة x اللي بتخلي y
+
+255
+00:22:01,790 --> 00:22:06,630
+أكبر ما يمكن، أو أصغر ما يمكن، ايش كنتوا تسووا؟ كنتوا
+
+256
+00:22:06,630 --> 00:22:11,010
+تشتقوا وتساويها بصفر، قال يعني لو هدى اشتقتوا بالنسبة
+
+257
+00:22:11,010 --> 00:22:16,550
+لـ θ وسويتوها بصفر، هيطلع عندك θ 45، قصب عنك صح؟
+
+258
+00:22:17,310 --> 00:22:25,070
+لكن هذا كله كلكلس خلصناه تبع توجيهي، تمام، حلو. إذا الـ
+
+259
+00:22:25,070 --> 00:22:30,730
+maximum height، أول حاجة عملتها حللت السرعة
+
+260
+00:22:30,730 --> 00:22:34,930
+الابتدائية إلى سينية وصادية، ولا لأ؟ بقت كده، بقول له at
+
+261
+00:22:34,930 --> 00:22:41,170
+the maximum height، الشيء هو صفر، السرعة الصادية هي
+
+262
+00:22:41,170 --> 00:22:48,790
+صفر، بقول using the equation، حطيت، طلعت هذه، الـ
+
+263
+00:22:48,790 --> 00:22:52,810
+range، قال لي to find the range we need the time
+
+264
+00:22:52,810 --> 00:22:55,970
+لأنه قال لي هذه المعادلة بتجيب الـ range فيها زمن،
+
+265
+00:22:55,970 --> 00:23:00,330
+بتجيب زمن، we need the time of flight، زمن
+
+266
+00:23:00,330 --> 00:23:04,410
+الطيران، يعني زمن الكل، تمام، nothing that for the
+
+267
+00:23:04,410 --> 00:23:07,590
+total time of flight، while finally بتساوي صفر
+
+268
+00:23:07,590 --> 00:23:12,290
+ذكّريني، الرسم اللي راحت صفر، صفر كان هنا وصار هنا
+
+269
+00:23:12,290 --> 00:23:17,010
+برغم أنه تحرك، لكن تحرك مسافة أفقية، مسافة عمودية
+
+270
+00:23:17,010 --> 00:23:17,550
+لا، احكي
+
+271
+00:23:20,200 --> 00:23:23,620
+في الـ .. مش هيك Vy اصلا؟ ايوه Vy، في وين الـ صفر الـ y؟
+
+272
+00:23:23,620 --> 00:23:28,460
+صفر كمان؟ صفر الـ y صفر؟ لأ، أنت حسبتها لأ وين؟
+
+273
+00:23:28,460 --> 00:23:32,020
+مش عندها أقصر طريقة؟ ومين جالك هدى؟ عندها أقصر طريقة
+
+274
+00:23:32,020 --> 00:23:36,540
+هدى
+
+275
+00:23:36,540 --> 00:23:42,900
+وين هدى؟ لمّا كان عوضت هدى، هدى عوضت على صفر، هدى هدى
+
+276
+00:23:42,900 --> 00:23:48,770
+عوضت على صفر، هنا عوضت مع الـ wifi من الديل، اتف اي
+
+277
+00:23:48,770 --> 00:23:50,690
+وين؟ وين؟ وين؟ وين؟ وين؟ وين؟ وين؟ وين؟ وين؟ وين؟
+
+278
+00:23:50,690 --> 00:23:51,030
+وين؟ وين؟ وين؟ وين؟ وين؟ وين؟ وين؟ وين؟ وين؟
+
+279
+00:23:51,030 --> 00:23:51,450
+وين؟ وين؟ وين؟ وين؟ وين؟ وين؟ وين؟ وين؟
+
+280
+00:23:51,450 --> 00:23:51,610
+وين؟ وين؟ وين؟ وين؟ وين؟
+
+281
+00:23:51,610 --> 00:23:56,150
+وين؟ وين؟ وين؟ وين؟ وين؟ وين؟ وين؟
+
+282
+00:23:56,150 --> 00:23:56,250
+وين؟ وين؟ وين؟
+
+283
+00:23:56,250 --> 00:24:02,190
+وين؟ وين؟ وين؟ وين؟ وين؟
+
+284
+00:24:02,190 --> 00:24:12,910
+وين؟ وين؟ وين؟ وين؟ وين؟
+
+285
+00:24:12,910 --> 00:24:17,150
+وين؟  يا نكون جنبها ايه؟ لو أنا بدي أحطهم جنب بعض
+
+286
+00:24:17,150 --> 00:24:22,550
+تمام؟ حلو. احكي ليش لما جينا للزمن، ما عوضش في
+
+287
+00:24:22,550 --> 00:24:28,230
+القانون الأول ها؟ هو أنت ايش بدك؟ تمام. أنت جيبت
+
+288
+00:24:28,230 --> 00:24:34,690
+الزمن من ها، ايش مطلوب؟ x ولا v؟ y؟ ايش مطلوب منك؟
+
+289
+00:24:34,690 --> 00:24:41,130
+ال range، ايش هو؟ الـ x، ليش ما عرفتها؟ ما نجيبها من ها
+
+290
+00:24:41,130 --> 00:24:47,800
+مدى، حل، بتعرفي هادي؟ كده ش؟ من جده كان أقصى ارتفاع؟
+
+291
+00:24:47,800 --> 00:24:52,820
+أنا بدي زمن الكل، مش أنا بدي زمن الكل؟ هل السرعة
+
+292
+00:24:52,820 --> 00:24:56,440
+النهائية لما وصل الأرض، عرفتها أنت؟ عشان كده ما عرفتش
+
+293
+00:24:56,440 --> 00:25:02,240
+آخذها، لأنه الـ Vy final، يا بنتي هادي ما عرفتهاش، واحد
+
+294
+00:25:02,240 --> 00:25:04,760
+يقول طب جاب بيه أقصى ارتفاع، وضروف، اثنين مش دائما
+
+295
+00:25:06,130 --> 00:25:11,210
+صح؟ أنا مدي الـ range من نقطة البداية للنهاية، صح؟
+
+296
+00:25:11,210 --> 00:25:14,990
+معطى، بدي الزمن من نقطة البداية للنهاية، بعرف
+
+297
+00:25:14,990 --> 00:25:19,250
+السرعة الصادية عند النهاية؟ ما بعرفش، إذا نهايتها
+
+298
+00:25:19,250 --> 00:25:23,590
+تخدمني المعادلة، ما تخدمناش، ما بقدرش أجيب منها، لأنه في
+
+299
+00:25:23,590 --> 00:25:32,450
+شغلات مجهولة غير الزمن، عرفتي ليش؟ غيرها، لأ،
+
+300
+00:25:32,450 --> 00:25:37,720
+ذاكرة لما قلت لكم أن هو القانون هذا،  من مخكم؟ لأ،
+
+301
+00:25:37,720 --> 00:25:43,560
+ممكن يدرسوكم هذه حالة خاصة .. هذه حالة خاصة زمن
+
+302
+00:25:43,560 --> 00:25:48,420
+السقوط لا يساوي زمن الهبوط، وقلنا على أيام الشباب
+
+303
+00:25:48,420 --> 00:25:54,600
+قلت لكم امحوا هذا القانون من مخكم، وأنا قلت لكم هذا مش
+
+304
+00:25:54,600 --> 00:26:01,790
+قانون، تمام. إذا جبت الـ T من هذا القول، لأن كله بعرفه
+
+305
+00:26:01,790 --> 00:26:05,370
+إلا الـ T، لكن عايز قانون ثاني في شغلات ثانية مش
+
+306
+00:26:05,370 --> 00:26:11,150
+معروفة، طلعت الـ T، ومنها طلعت الـ range، وقلنا كنا
+
+307
+00:26:11,150 --> 00:26:19,330
+بنعرف أن sin θ بتساوي 1 لما θ تساوي 90 درجة، عند 2θ
+
+308
+00:26:19,330 --> 00:26:25,090
+يعني θ تكون 45 درجة، تمام. This is because the
+
+309
+00:26:25,090 --> 00:26:30,250
+maximum value of sin 2θ is 1، And this occurs لما
+
+310
+00:26:30,250 --> 00:26:37,770
+2θ تساوي 90، أو تساوي 45، اه، لحد الآن ماشية الأمور؟
+
+311
+00:26:37,770 --> 00:26:44,330
+ماشي الأمور، شوفها لك، وزاد قال لي شوف لي خمس حجارة
+
+312
+00:26:44,330 --> 00:26:51,450
+بدي أضربهم بنفس الـ speed، لكن بـ directions مختلفة
+
+313
+00:26:51,450 --> 00:26:57,980
+شايفين الزوايا؟ كل واحد له زاوية خاصة به، تمام؟ ايش
+
+314
+00:26:57,980 --> 00:27:02,160
+بده؟ بيقول لي a projectile launched، أطلقات from the
+
+315
+00:27:02,160 --> 00:27:05,140
+origin، كلهم، هايهم الخمسة، طالعين من النقطة نفسها
+
+316
+00:27:05,140 --> 00:27:09,540
+صحيح؟ واحد، اثنين، ثلاثة، أربعة، خمسة، from the
+
+317
+00:27:09,540 --> 00:27:14,560
+origin with the same initial speed، بصحيح اللي يقول
+
+318
+00:27:14,560 --> 00:27:20,410
+ليه؟ with the same initial velocity؟ ليش؟ لأنه
+
+319
+00:27:20,410 --> 00:27:25,610
+اتجاهات مختلفة، إذا جالي speed بصحح له، لأنه نفترض
+
+320
+00:27:25,610 --> 00:27:29,030
+خمسة، كلهم خمسة، بس واحد بيعمل زي 15، وواحد
+
+321
+00:27:29,030 --> 00:27:32,430
+بيعمل زي 75، وواحد 45، فبسمح له
+
+322
+00:27:32,430 --> 00:27:35,310
+يقول لي initial speed، لكن ممنوع يقول لي initial
+
+323
+00:27:35,310 --> 00:27:38,090
+velocity، لأنه لو جالي initial velocity، بقول له الراس
+
+324
+00:27:38,090 --> 00:27:42,610
+ما بتقولش هيك، الراس ما بتقولش هيك، صح ولا لأ؟ طيب
+
+325
+00:27:42,610 --> 00:27:47,190
+initial speed but at various angles، زوايا مختلفة
+
+326
+00:27:47,190 --> 00:27:51,540
+زي ما تشوفون، For which of the launch angles the
+
+327
+00:27:51,540 --> 00:27:55,060
+time of flight is the largest؟ قال، لمين من هدول
+
+328
+00:27:55,060 --> 00:27:58,740
+هياخذ أكبر زمن عشان يصل للأرض؟ شفت الزمن، شفته؟
+
+329
+00:27:58,740 --> 00:28:00,360
+ايوه، واحنا قاعدين نتطلع
+
+330
+00:28:03,110 --> 00:28:06,870
+معناته بيعتمد على θ، ولا لأ؟ كل ما θ كبرت، كل ما
+
+331
+00:28:06,870 --> 00:28:10,750
+الزمن كبر، وأكثر حد لما يصير 90، إذا بتتوقعوا
+
+332
+00:28:10,750 --> 00:28:15,230
+مين أكبر واحد؟ الـ 75، حسب هذا القانون اللي
+
+333
+00:28:15,230 --> 00:28:20,230
+by chance جبناه احنا وياكم، إذا بيقول لي حتكون الـ 75
+
+334
+00:28:20,230 --> 00:28:23,310
+ولا الـ 45؟ الـ 45 الأكبر، ايه؟
+
+335
+00:28:23,310 --> 00:28:29,030
+تدري، ببالكم، مش أكبر زمن ولا 75 ولا كلهم
+
+336
+00:28:29,030 --> 00:28:34,670
+مضيع، ولا واحدة منهم 75، خمسة وسبعين، صح؟ شيلشي، وبرافو
+
+337
+00:28:34,670 --> 00:28:37,290
+عليك، يعني هيجيكم سؤال، عالمودي مرة أكبر شيء، ومرة
+
+338
+00:28:37,290 --> 00:28:42,450
+أقل شيء، لأنه احنا بنكرر السؤال بتغيير صيغة بسيطة
+
+339
+00:28:42,450 --> 00:28:47,770
+صحين يا بنات؟ تمام، بيجينا نشوف هالكوزين وراء بعض
+
+340
+00:28:47,770 --> 00:28:52,490
+نشوفهم صحين ولا لأ، بيقول لي in a projectile motion
+
+341
+00:28:52,490 --> 00:28:57,170
+projectile motion، حركة مقذوفات، صح ولا لأ؟ كيف
+
+342
+00:28:57,170 --> 00:29:02,730
+تصرفات تجاهه؟ عمودي لأسفل، في حد مش عارف المعلومة
+
+343
+00:29:02,730 --> 00:29:07,330
+دي؟ ده، ما تشوفش السؤال، بيقول in a projectile motion
+
+344
+00:29:07,330 --> 00:29:11,870
+at what point، عند أي نقطة أثناء الحركة، along the
+
+345
+00:29:11,870 --> 00:29:15,870
+path، أثناء مسار تبع الحركة، اللي هو برضه، اتفقنا
+
+346
+00:29:15,870 --> 00:29:20,990
+ذاكرين؟ are the velocity and the acceleration
+
+347
+00:29:20,990 --> 00:29:25,390
+vectors are perpendicular to each other، ايش عن الـ
+
+348
+00:29:25,390 --> 00:29:30,950
+perpendicular؟ حلو، أولًا، نروح تسارع، في حدا مختلف
+
+349
+00:29:30,950 --> 00:29:36,230
+عليه؟ كيف اتجاهه؟ لأسفل، لأسفل، بدي عند أي نقطة
+
+350
+00:29:36,230 --> 00:29:42,590
+السرعة بتكون أفقية، عند أقصى الارتفاع، لأن هذا صادق
+
+351
+00:29:42,590 --> 00:29:45,150
+بيقول لي بدي السرعة تكون عمودية على الصادي، ايش
+
+352
+00:29:45,150 --> 00:29:49,110
+يعني؟ سينية، يعني السرعة تكون بس سينية، بس سينية
+
+353
+00:29:49,110 --> 00:29:51,630
+بيقول لي عند أقصى الارتفاع، لأنه في مركبة صادية
+
+354
+00:29:51,630 --> 00:29:55,390
+للسرعة عند أقصى الارتفاع، إذن مين بدي يكون؟ هذا هو
+
+355
+00:30:01,720 --> 00:30:04,600
+مش معاكم الـ z، وبعدين project of motion، بيصيب الـ z
+
+356
+00:30:04,600 --> 00:30:08,340
+في fireworks، فما تتغلبيش حالك، ما بدنا نخش في التفاصيل
+
+357
+00:30:10,060 --> 00:30:14,340
+هل the launch point، يعني نقطة البداية الانطلاق، ولا
+
+358
+00:30:14,340 --> 00:30:18,320
+هي نقطة الـ landing point، landing يعني هبوط، نقطة
+
+359
+00:30:18,320 --> 00:30:21,500
+الهبوط، ولا the highest point، ولا، ولا، فيه نقطة الـ
+
+360
+00:30:21,500 --> 00:30:26,000
+highest point، تمام. شوف السؤال، بدي أكرره، أغير كلمة
+
+361
+00:30:26,000 --> 00:30:30,200
+في السؤال، بدل كلمة perpendicular، بدي أحط parallel
+
+362
+00:30:30,200 --> 00:30:36,980
+أطلع السؤال، ايش بيصير؟ واين السرعة بتكون فقط
+
+363
+00:30:36,980 --> 00:30:39,600
+صادية؟ وين؟
+
+364
+00:30:41,010 --> 00:30:45,210
+فكر منيح، ولا
+
+365
+00:30:45,210 --> 00:30:51,430
+مرة، ولا في نقطة، عند نقطة البداية، بتكون عند أقصى
+
+366
+00:30:51,430 --> 00:30:54,490
+ارتفاع، بيكونوا، مش اتفقنا بـ Urban Declar، وعند
+
+367
+00:30:54,490 --> 00:30:59,330
+اللي هو Note، برضه بيكون الناس في زاوية مظبوط هيك
+
+368
+00:30:59,330 --> 00:31:03,310
+ولا لأ؟ هاي الرسمة، ها نتذكر مع بعض بعين الله
+
+369
+00:31:03,310 --> 00:31:07,990
+هادي الرسمة، هي، نعيدها، وين ها أجدها؟
+
+370
+00:31:11,330 --> 00:31:19,090
+هل السرعة صادية؟ لأ، السرعة صادية؟ السرعة صادية؟ إذا
+
+371
+00:31:19,090 --> 00:31:21,410
+هذه النقطة، ولا هذه النقطة، ولا هذه النقطة؟ ولا
+
+372
+00:31:21,410 --> 00:31:27,070
+واحدة، إذا nowhere، إذا الجواب الصح، عرفتم كيف
+
+373
+00:31:27,070 --> 00:31:30,770
+السؤال طلع ايش غيرنا؟ كل ما غيرنا في السؤال صار
+
+374
+00:31:30,770 --> 00:31:38,130
+الجواب nowhere، كله
+
+375
+00:31:38,130 --> 00:31:40,090
+سامع عربي ولا في حد سامع صيني؟
+
+376
+00:31:43,200 --> 00:31:49,530
+عربي؟ تمه .. نشوف أي أسئلة. جالي هذا example 4.3
+
+377
+00:31:49,530 --> 00:31:55,050
+الكتاب مغلبنا، جايب السؤال صعب في البداية، أنا أروح
+
+378
+00:31:55,050 --> 00:31:59,310
+على 4.4 أولًا، بعدين ارجع لـ 4.3، تمام، خلينا نبدأ
+
+379
+00:31:59,310 --> 00:32:04,390
+بالسهل هذا، بعدين نجيب هذا، سؤال زي الشرط والسيارة
+
+380
+00:32:04,390 --> 00:32:08,870
+ذاكرينهم؟ هذا مشهور، بعدين نجيب قصة حياته من أول جديد، وأنا حليته بطريقتين، بعدين نشوفه، كل هذا عدي
+
+381
+00:32:08,870 --> 00:32:12,270
+رجعت له، نيجي هذا السؤال، هذا حلو، برافو عليكي، بشبه
+
+382
+00:32:12,270 --> 00:32:16,740
+السؤال أخذناه، ذاكرين المبنى؟ أبو خمسة عشر طابق، ولا
+
+383
+00:32:16,740 --> 00:32:21,540
+خليتوه ثلاثة طوابق اللي بينهم، ذاكرينه؟ تمام. هذا نفس
+
+384
+00:32:21,540 --> 00:32:25,580
+المبنى، 45 متر، المرة هيك، هذه الحجر خبطناها مظبوط؟
+
+385
+00:32:25,580 --> 00:32:31,400
+خبطناها هيك، المرة هذه بده يخبِطه بزاوية، صار الـ
+
+386
+00:32:31,400 --> 00:32:34,280
+projectile in motion، إذا بيقول لي a stone، نفس الحجر is
+
+387
+00:32:34,
+
+445
+00:37:07,800 --> 00:37:14,070
+ناقص 4A C ع 2A ده كان أنا سمحت لك تنسيه، أنا سامع حاجة
+
+446
+00:37:14,070 --> 00:37:18,770
+تنسيها، بس بتعرفش A و B و C؟ A معامل X تربيع، أو B
+
+447
+00:37:18,770 --> 00:37:24,070
+معامل X و C ثابت؟ مظلومة لأ؟ إذا إيش ما يكون يكون،
+
+448
+00:37:24,070 --> 00:37:27,130
+إن شاء الله يكون جذر، القول العام بيجيبه، ثمانية
+
+449
+00:37:27,130 --> 00:37:31,750
+بنتين؟ حلو، طلعت لك T، أي أول مقلوب، إيش بده
+
+450
+00:37:31,750 --> 00:37:38,150
+الكيماء؟ What is the speed of the stone? just
+
+451
+00:37:38,150 --> 00:37:41,430
+before it strikes the ground قبل ما يضرب الأرض
+
+452
+00:37:41,430 --> 00:37:47,950
+مباشرة سرعة النهائية، طيب، اتطلع وإيش كاتب what is
+
+453
+00:37:47,950 --> 00:37:53,010
+the speed، لو جالك what is the velocity، تفرج إيه
+
+454
+00:37:53,010 --> 00:37:58,870
+معناه speed، أيوة، إذا إنك بتفرج، لو رحنا أقوم وأقول
+
+455
+00:37:58,870 --> 00:38:01,110
+إيش معناه speed، أقوم وأقول سرعة، إيش معناه
+
+456
+00:38:01,110 --> 00:38:04,410
+velocity، سرعة، لكن إحنا من أساسياتنا إتعلمنا إن الـ
+
+457
+00:38:04,410 --> 00:38:08,920
+speed والسرعة والـ velocity، ماذا يختلف؟ طيب .. منفع
+
+458
+00:38:08,920 --> 00:38:13,040
+أجيب الـ speed بدون معرفة الـ velocity؟ لأ، لأن الـ
+
+459
+00:38:13,040 --> 00:38:17,320
+speed مقدار الـ velocity، زي ما تقولي بدي مقدار
+
+460
+00:38:17,320 --> 00:38:21,140
+vector، بقول لك بدي مقدار الـ vector، صح ولا لأ؟ إذا أنا
+
+461
+00:38:21,140 --> 00:38:25,480
+بدي أول حاجة أجيب الـ velocity، هي الـ velocity كم
+
+462
+00:38:25,480 --> 00:38:28,800
+مركبة، بتتوقع تنتهي .. تنتهي .. تنتهي .. تنتهي ..
+
+463
+00:38:28,800 --> 00:38:29,320
+تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي
+
+464
+00:38:29,320 --> 00:38:30,060
+.. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي ..
+
+465
+00:38:30,060 --> 00:38:33,420
+تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي
+
+466
+00:38:33,420 --> 00:38:33,700
+.. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي ..
+
+467
+00:38:33,700 --> 00:38:41,530
+تنتهي .. بنقول له V X Final، إيش علاقتها بالـ X
+
+468
+00:38:41,530 --> 00:38:51,030
+initial، نفسها، طموحيها يوردين أسعابها، وأنا لو
+
+469
+00:38:51,030 --> 00:38:55,050
+كتبتها دي كمان مرة، إيه علامات، بقول له اه اليك
+
+470
+00:38:55,050 --> 00:38:59,950
+علامة، أحكي الجزء لما تكون V X Final نزلت من نفس
+
+471
+00:38:59,950 --> 00:39:08,810
+الزاوية، لأنك بيه sign كتابة، طيب، نزلت من .. وين هذه
+
+472
+00:39:08,810 --> 00:39:12,950
+أنا عارفة إيش عوضت، اه
+
+473
+00:39:12,950 --> 00:39:23,410
+اه، حسب، وين، مش بالضرورة، مش بالضرورة، أنا إيش عوضت
+
+474
+00:39:23,410 --> 00:39:29,590
+قلت هي جت هذه 17.3، فأنت بتاخد الـ cosine، مش رقم، طيب
+
+475
+00:39:29,590 --> 00:39:35,210
+هذا رقم، هذه 720 دقيقة ثانية، مسموح تتغير؟ عادة
+
+476
+00:39:35,210 --> 00:39:42,150
+للأولى، اه اه، لأ، رقم الـ V لحالة تمام، هي عيب الدرع
+
+477
+00:39:42,150 --> 00:39:46,130
+زي مهينة، فتكمل الـ theta بتختلف حسب الـ theta الجديدة
+
+478
+00:39:46,130 --> 00:39:52,530
+هجيت هادي، ما عملتش عشان أجيبها، ولا أنا بس نَجّلت، جولت
+
+479
+00:39:52,530 --> 00:39:56,050
+بس مجرد، ليش أنا بديك علامات عليها؟ عشانك بتأكد لي
+
+480
+00:39:56,050 --> 00:40:00,400
+معلومة فيزيائية، إن الصراع الصيني لا تتغير، صح؟ إنه
+
+481
+00:40:00,400 --> 00:40:03,000
+نهائية ولا ابتدائية، ضي بعض ولا لأ؟ هذه معلومة
+
+482
+00:40:03,000 --> 00:40:07,640
+فيزيائية، بَتُبَلِّيها، واخد عليها علامات، إيه ضال؟ بتدي
+
+483
+00:40:07,640 --> 00:40:12,280
+الصادية النهائية، الصادية النهائية، هيها، مش أنت
+
+484
+00:40:12,280 --> 00:40:18,500
+جبتيها توي، وقلت 4.22، إذا بقدر أقول VY final بتساوي
+
+485
+00:40:18,500 --> 00:40:24,060
+VY initial ناقص G في T، اللي بتساوي هذه عشرة ناقص تسعة
+
+486
+00:40:24,060 --> 00:40:29,170
+point ثمانية في أربعة point two two، جدش طلعت بالسالب
+
+487
+00:40:29,170 --> 00:40:33,910
+جدش، نجلوني واحد تلاتين point تلاتة meter per
+
+488
+00:40:33,910 --> 00:40:41,050
+second، طلعت سالب، لها معنى ولا ما لهاش معنى؟ إنّه لا
+
+489
+00:40:41,050 --> 00:40:45,630
+أسفل، اه، لأن واحد يقول لأ، إحنا إتعلمنا السالب نرفضه
+
+490
+00:40:45,630 --> 00:40:49,370
+هذا الزمن، صح أو لأ؟ هذه لأ، بالعكس، لو طلعت موجبة
+
+491
+00:40:49,370 --> 00:40:55,270
+برُفضها، لأنه نازلة، لأنه نازلة، هذه جبتها، وهذه جبتها
+
+492
+00:40:55,270 --> 00:41:03,030
+بقل، رجول V final، طالعة، متساوي 17.3 I ناقص 31.3 J
+
+493
+00:41:03,030 --> 00:41:08,370
+meter per second ولا لأ؟ لو جالي أودي دي الـ velocity
+
+494
+00:41:08,370 --> 00:41:14,330
+بقول له خلص السؤال صح، لو جالي velocity خلص، لكن بده
+
+495
+00:41:14,330 --> 00:41:17,830
+يُثبِت هذا، بده بالـ magnitude، لكن لو جالي أودي دي الـ
+
+496
+00:41:17,830 --> 00:41:21,400
+velocity، بقول له يعطيني العافية، خلص السؤال صحيح، يكفي ولا
+
+497
+00:41:21,400 --> 00:41:26,580
+لأ؟ بدي الـ magnitude .. إيه؟ سهل، جذر .. هذا ربي
+
+498
+00:41:26,580 --> 00:41:30,800
+تربيع، وهذا تربيع، وبشتغله حتى لو كان في عشرة
+
+499
+00:41:30,800 --> 00:41:34,980
+بالرب، ع ولا لأ؟ وهذي نفس العملية، بقدر أجيب الـ
+
+500
+00:41:34,980 --> 00:41:37,820
+velocity من القانون الثالث، بس يجب أن أحط سالب، مني
+
+501
+00:41:37,820 --> 00:41:43,180
+أنا هنا؟ هذه قصدك؟ اه، يجب أن أحط السالب، أنا؟ براو
+
+502
+00:41:43,180 --> 00:41:51,390
+عليك، تمام، حلو، إذا معناته طلعت أنا الزمن، ورحت جبت
+
+503
+00:41:51,390 --> 00:41:55,710
+الصادية، وقلت له السالب يعني down، وقلت له الـ X هذا
+
+504
+00:41:55,710 --> 00:42:02,970
+هي هي هي، جيب لي speed، سؤال سهل، خلصنا
+
+505
+00:42:02,970 --> 00:42:07,750
+أي صفر، صار نرجع
+
+506
+00:42:12,970 --> 00:42:16,090
+طبعاً أنا ما بعرفش أنتم عندكم محلول مرة واحدة، أظنني
+
+507
+00:42:16,090 --> 00:42:20,170
+هذا المثال، أنا هنا محلول مرتين، واتفقت مع الشباب
+
+508
+00:42:20,170 --> 00:42:23,190
+إنّه هذا الحل الثاني، عشان مش مكتوب بعينكم، هحطه على
+
+509
+00:42:23,190 --> 00:42:27,790
+مجموعة الواتس، عشان ما يقعدوش يصوروا يعني، وتتعبوا
+
+510
+00:42:27,790 --> 00:42:31,150
+حياتكم، وتكتبوا ورايا، الحل الأولاني هو حل الكتاب
+
+511
+00:42:31,150 --> 00:42:34,230
+اللي بين يديكم، الكتاب هيك، الحالة، أنا عم بدي أحل
+
+512
+00:42:34,230 --> 00:42:39,750
+بطريقة أسهل، إيش أسوي يا بنات؟ طبعاً كان بدي أحله أول
+
+513
+00:42:39,750 --> 00:42:54,760
+أشوف السؤال إيش بيقول، نشوف السؤال، وبعدين نحله، نفض
+
+514
+00:42:54,760 --> 00:43:02,420
+اللوح، عشان الصح، صح، نحنا وياكم، اتطلع
+
+515
+00:43:02,420 --> 00:43:07,100
+يا بنات، واحدة آخر الحياطة، معها برودة، بدها تطخها
+
+516
+00:43:07,100 --> 00:43:12,800
+الجلم، بدها تصيده، أول ما تطلع الرصاصة من البرودة
+
+517
+00:43:12,800 --> 00:43:17,720
+أنا بتفلت الجلم، هجيت، هي بدها تنشن في البداية
+
+518
+00:43:17,720 --> 00:43:21,580
+عشان تصيب الجلم، للواحدة الأولى بتقول لك أنا مديش، هو
+
+519
+00:43:21,580 --> 00:43:24,800
+نشّن على الجلم، بدي أعمل حساب إنّه بدي ينزل، اه
+
+520
+00:43:24,800 --> 00:43:30,360
+بقول لها لأ، هو مين اللي بدّه ينزل الجلم؟ مش أنا، إيه
+
+521
+00:43:30,360 --> 00:43:34,220
+عشان يخليه ينزل، للأعلى، أنا بتفلتّه، تصارع الجاذبية
+
+522
+00:43:34,220 --> 00:43:40,690
+طب، هي البرودة، الرصاصة لما طلعت، الجاذبية بدهاش تأثر
+
+523
+00:43:40,690 --> 00:43:45,450
+عليها، إذا هتنزلها، إذا المعنى تقول إيه بتساوي اللي
+
+524
+00:43:45,450 --> 00:43:52,690
+بعيدة؟ بدها تنشّن على الجلم وهو واقف، وأنا ساعتها
+
+525
+00:43:52,690 --> 00:43:57,390
+بدي أنزل، المسافة العمودية اللي نزلها الجلم،
+
+526
+00:43:57,390 --> 00:44:02,390
+البرودة هتنزله، الرصاصة هتنزله، إذا هيصيبوا بعض،
+
+527
+00:44:02,390 --> 00:44:08,030
+بدون ما تعملوا حسابات نزول الجلم، مش مصدقة زي ما أنت
+
+528
+00:44:08,030 --> 00:44:13,090
+مش مصدقة؟ لأ، بدي أثبت هذا الكلام، بدي أثبت
+
+529
+00:44:13,090 --> 00:44:18,770
+نقرا السؤال أول، بيقول لأ projectile، projectile
+
+530
+00:44:18,770 --> 00:44:21,690
+مقذوفة، في رصاصة، طوي، قلت عنها أنا مش أنا بدي أُقذِفها
+
+531
+00:44:21,690 --> 00:44:25,690
+a projectile is fired at a target، هدف اللي هو
+
+532
+00:44:25,690 --> 00:44:31,860
+القَلم، in such a way that the projectile leaves
+
+533
+00:44:31,860 --> 00:44:35,180
+the gun at the same time the target is dropped
+
+534
+00:44:35,180 --> 00:44:38,640
+from rest، إذا أول ما الرصاصة طلعت من البرودة، أنت
+
+535
+00:44:38,640 --> 00:44:41,900
+بالتزامن، إذا نبدأ الحركة بنفس اللحظة ولا لأ
+
+536
+00:44:41,900 --> 00:44:47,380
+واحد حركته projectile، اللي هي الرصاصة، والجلم لما
+
+537
+00:44:47,380 --> 00:44:53,390
+أنزله، حركة سقوط حر ولا لأ؟ سقوط حر، حلو، show that
+
+538
+00:44:53,390 --> 00:44:58,950
+اثبت that if the gun is initially aimed، إذا
+
+539
+00:44:58,950 --> 00:45:05,170
+الرصاصة وجهتها خطتها في اتجاه aimed at the
+
+540
+00:45:05,170 --> 00:45:09,910
+stationary target، عند القلم لم يكن واقف، أنت وجهتها
+
+541
+00:45:09,910 --> 00:45:15,670
+على القلم وهو واقف، stationary يعني ثابت، target the
+
+542
+00:45:15,670 --> 00:45:18,770
+projectile hits the falling target as shown in the
+
+543
+00:45:18,770 --> 00:45:23,970
+figure، طيب، ليش أنا جربت على السيارة والشرطي
+
+544
+00:45:23,970 --> 00:45:28,070
+ذاكرينهم، لما الشرطي لاحق السيارة، واحد كان في قانون
+
+545
+00:45:28,070 --> 00:45:30,210
+الثاني، الثاني كان في أنصرات، ولا كانوا في نفس
+
+546
+00:45:30,210 --> 00:45:35,650
+الموقع، إذا عشان الرصاصة تخبط الهدف لازم يكونوا في
+
+547
+00:45:35,650 --> 00:45:41,630
+نفس الموقع ولا لأ؟ حلو، جالي هاي، راسمتي، أنا بدي أثبت
+
+548
+00:45:41,630 --> 00:45:47,010
+إني أنا وجهتها هيك، ها، هيها، ما عملتش حساب نزولها،
+
+549
+00:45:47,010 --> 00:45:50,710
+تمام؟ هجيت، وين اتجابلوا؟ قلت له اتجابلوا، ها، هجيت
+
+550
+00:45:50,710 --> 00:45:54,590
+هذا الارتفاع تبع الحمرة اللي هو الـ target ولا تبع
+
+551
+00:45:54,590 --> 00:45:58,750
+الزرقة، بيختلفوا عن بعض، إذن، هي ترك السؤال إن why
+
+552
+00:45:58,750 --> 00:46:06,440
+للحمرة، و why للزرقة، واحد، تمام؟ أنا هذا الخط
+
+553
+00:46:06,440 --> 00:46:11,500
+لما جيت، وهذه الخط بتعتبر الزاوية ثيتا، وهذه زاوية
+
+554
+00:46:11,500 --> 00:46:14,060
+الخط Alpha، ده بتثبت لي إن Alpha و Theta زي بعض
+
+555
+00:46:14,060 --> 00:46:19,040
+Alpha و Theta زي بعض، هاي اللي بدي أثبته، كيف كده
+
+556
+00:46:19,040 --> 00:46:22,560
+Alpha و Theta، هجيت Theta الشي هي زاوية انطلاق
+
+557
+00:46:22,560 --> 00:46:27,460
+الرصاصة، Alpha هي الزاوية اللي بيعملها الخط ما بين
+
+558
+00:46:27,460 --> 00:46:33,090
+الرصاصة والـ target وهو واقف، مش أنا هيك عملتها، هجيت
+
+559
+00:46:33,090 --> 00:46:38,410
+أنا هيك .. هيك نشنتها، هجيت هذه الزاوية، إيش هي؟
+
+560
+00:46:38,410 --> 00:46:42,410
+زاوية انطلاق الرصاصة، والزاوية اللي بيعملها الخط
+
+561
+00:46:42,410 --> 00:46:48,990
+هذا مع الـ .. مع الـ X-axis، هي هي، طيب، بنثبت، لكن
+
+562
+00:46:48,990 --> 00:46:52,090
+بتقدروا تقولوا إيه؟ فلتوكوا من project in motion
+
+563
+00:46:52,090 --> 00:46:57,410
+هذا الخط أنا مددته هيك، بتقدر تقولي ثاني، الزاوية
+
+564
+00:46:57,410 --> 00:47:02,130
+بيساوي مقابل على مجاور؟ هذا المقابل بتعتبره H؟
+
+565
+00:47:02,130 --> 00:47:07,890
+بالفعل؟ إذا بتقدر تقولي إنه تان الـ Alpha بيساوي H
+
+566
+00:47:07,890 --> 00:47:13,550
+على XX، هذه المسافة كلها؟ صح ولا لأ؟ تمام، نيجي،
+
+567
+00:47:13,550 --> 00:47:19,390
+هالجيت، فَنْتَقِم الهدف بعدين، ونرجع عليها، هذا اللي هو
+
+568
+00:47:19,390 --> 00:47:26,170
+الـ Target، الهدف، كيف بيمشي؟ سقوط حر؟ صح؟ وهذا الـ
+
+569
+00:47:26,170 --> 00:47:31,270
+projectile، ليه؟ صح، صح، الـ projectile
+
+570
+00:47:31,270 --> 00:47:35,530
+هيك عملنا لما قلنا سيارة، وقلنا trooper، ذاكرين
+
+571
+00:47:35,530 --> 00:47:40,110
+وهذه عملنا نفس العملية، هذا سقوط حر، قلت له في
+
+572
+00:47:40,110 --> 00:47:44,050
+السقوط الحر كان فيه قانون بيقول Y final ناقص Y
+
+573
+00:47:44,050 --> 00:47:49,270
+initial، بتساوي V initial Y، أو بدون هذه حتى، مهمش T
+
+574
+00:47:49,270 --> 00:47:54,840
+تربيع T، ناقص half GT تربيع، تطلع لي على الجلم اللي
+
+575
+00:47:54,840 --> 00:48:01,180
+كان بيدي كده، سرعته الابتدائية؟ صفر، مش أنا بدفلتّه
+
+576
+00:48:01,180 --> 00:48:07,520
+إذا سرعته الابتدائية صفر ولا لأ؟ تمام، هذاك من وين
+
+577
+00:48:07,520 --> 00:48:11,800
+بدأ؟ الجلم بدأ من هذه النقطة ولا لأ؟ إذا Y initial
+
+578
+00:48:11,800 --> 00:48:14,860
+بتساوي H ولا لأ؟ إذا هذا H
+
+579
+00:48:19,310 --> 00:48:27,930
+اللي هو Y، هذه H، وهذه Y بتساوي، هذه كم قلنا؟ صفر ناقص
+
+580
+00:48:27,930 --> 00:48:43,110
+نص GT تربيع، تمام هيك؟ حلو، أي شيء صح، سعيد معايا؟
+
+581
+00:48:45,500 --> 00:48:49,580
+الوعي، إيش اه، أنا اتعكس، طب اه اه اه اه، ناقص اتش
+
+582
+00:48:49,580 --> 00:48:56,460
+صحيح، اه، تمام، تمام
+
+583
+00:48:56,460 --> 00:49:00,040
+يا سامي بقى، الـ menu بنعيده المرة الجاية، ما بديش أزعجك
+
+584
+00:49:00,040 --> 00:49:00,520
+دكتورنا
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/4GxkJ1fxBBI_postprocess.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/4GxkJ1fxBBI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6f86dce4d683a3f7666b4977f4d1112f63b3522d
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/4GxkJ1fxBBI_postprocess.srt
@@ -0,0 +1,2336 @@
+1
+00:00:05,090 --> 00:00:10,410
+تمام يا بنات نستأنف اللي بدناه chapter رقم أربعة و
+
+2
+00:00:10,410 --> 00:00:14,150
+اللي قلنا تقريبا معلومات chapter اتنين بدنا نعيدها
+
+3
+00:00:14,150 --> 00:00:20,950
+بس على two copies واحدة صينية و واحدة صادية حكينا
+
+4
+00:00:20,950 --> 00:00:27,430
+ان الحركة باتجاهين او الحركة المستوية نتعامل معاها
+
+5
+00:00:27,430 --> 00:00:34,090
+على انها حركة صينية X motion و
+
+6
+00:00:34,090 --> 00:00:34,730
+Y motion
+
+7
+00:00:38,680 --> 00:00:43,200
+وحكينا لو كانت التصاروح ثابت معناته التصاروح
+
+8
+00:00:43,200 --> 00:00:48,040
+بمركبتين تبعته الصينية ووساطية ثوابت وبالتالي
+
+9
+00:00:48,040 --> 00:00:54,860
+بيصير في عندي قوانين VX final بتساوي VX initial
+
+10
+00:00:54,860 --> 00:01:01,230
+زاد EX في الـT مظبوط ولا لأ؟وفي عندي x final مخص x
+
+11
+00:01:01,230 --> 00:01:07,630
+initial بتسوي vx initial في t زي نص ax في t تربية
+
+12
+00:01:07,630 --> 00:01:14,190
+وكما في قانون عندي vx final تربية بتسوي vx initial
+
+13
+00:01:14,190 --> 00:01:20,830
+تربية زي اتنين ax x final مخص x initial نفس
+
+14
+00:01:20,830 --> 00:01:25,370
+القوانين اللي بكتبهم للحركة الصادريةاذا بتكون في
+
+15
+00:01:25,370 --> 00:01:30,230
+عندى حركتين ثينية وصاضية وكل سؤال عبارة عن سؤالين
+
+16
+00:01:30,230 --> 00:01:36,980
+ثيني وصاضي مين المشترك بينالتنتين الزمن مش هيك
+
+17
+00:01:36,980 --> 00:01:42,160
+اتفقنا؟ بدي نيجي الأن إيش في أمثلة طبيعية لحركة
+
+18
+00:01:42,160 --> 00:01:46,280
+مستوية قاللي حركة المقظوفات إذا ن project ال
+
+19
+00:01:46,280 --> 00:01:52,000
+motion هجيت إيش تعريف حركة المقظوفات؟ بنقول أي جسم
+
+20
+00:01:52,000 --> 00:01:59,590
+بتقظفه و بتفلطه لما تفلطه مين بده يتحكم فيهغير
+
+21
+00:01:59,590 --> 00:02:03,350
+الجاذبية الأرضية، مش فيه غير الجاذبية الأرضية، إذن
+
+22
+00:02:03,350 --> 00:02:07,670
+هذه بنسميها حركة المغضوفات. لو نيجي نتذكر ما هو
+
+23
+00:02:07,670 --> 00:02:13,810
+تعريف السقوط الحر، هو جسم مين بيأثر فيه فقط، برضه
+
+24
+00:02:13,810 --> 00:02:18,050
+تسارع الجاذبية الأرضية، إذن تعريف السقوط الحر و
+
+25
+00:02:18,050 --> 00:02:22,560
+تعريف ال projectile motion نفس الشيء.طب إيش مفروجة
+
+26
+00:02:22,560 --> 00:02:27,100
+عن بعض؟ جال في السقوط الحر كنت أنا أشتريت أن تكون
+
+27
+00:02:27,100 --> 00:02:31,940
+الصراع الابتدائية لا لا أعلى لا لا أسفل بس ممنوع
+
+28
+00:02:31,940 --> 00:02:38,380
+تكون بزاوية معينة بمعنى آخر الصراع الابتدائية إذا
+
+29
+00:02:38,380 --> 00:02:42,750
+إلها مركبة سينية بقول هذا project in motionإذا
+
+30
+00:02:42,750 --> 00:02:48,010
+مركبتها الصينية سفر بقول سقوط حُر بمعنى آخر السقوط
+
+31
+00:02:48,010 --> 00:02:52,090
+الحُر هو projectile motion بس حالة خاصة إذا ال
+
+32
+00:02:52,090 --> 00:02:57,470
+projectile motion هو بحتوي تلقائيا من السقوط الحُر
+
+33
+00:02:57,470 --> 00:03:02,760
+نجي نشوف إيش بعرفه بقول if a particleGiven an
+
+34
+00:03:02,760 --> 00:03:07,460
+initial velocity اعترطة سرعة ابتدائية and then
+
+35
+00:03:07,460 --> 00:03:13,360
+follows above اتبعت مصار هذا المصار مين بتحتتم فيه
+
+36
+00:03:13,360 --> 00:03:17,740
+determined only by gravity يحدده فقط الجاذبية
+
+37
+00:03:17,740 --> 00:03:22,780
+الأرضية we have projected motion تمام نذكر chapter
+
+38
+00:03:22,780 --> 00:03:30,690
+2 تسارع الجاذبية الأرضيةكيف اتجاهه؟ لأسفل سيني ولا
+
+39
+00:03:30,690 --> 00:03:37,730
+صاضي؟ صاضي إذا معناته في حركة المقذوفات التصارع
+
+40
+00:03:37,730 --> 00:03:45,770
+تبعي فقط صاضي ولا لأ؟ مش هيك؟ ليه حتى السالب؟لأنه
+
+41
+00:03:45,770 --> 00:03:52,430
+لازفر وحطيت J لأنه عمودي لو إجتفالتكم الآن من هذه
+
+42
+00:03:52,430 --> 00:03:58,350
+المعلومات جديش EX لحركة المغضوب فعلا يا عيني عليكم
+
+43
+00:04:00,640 --> 00:04:06,900
+إذاً حركة المغذوفات هي عبارة عن حركتين صينية
+
+44
+00:04:06,900 --> 00:04:11,560
+بتسارع سفر وصادية بتسارع الجاذبية الأرضية ولا لأ
+
+45
+00:04:11,560 --> 00:04:17,400
+كما يعني معناته هذه القوانين سارية المفعول إيش بده
+
+46
+00:04:17,400 --> 00:04:24,280
+يحط محل EX؟ سفر إذاً هذه روحت صح؟ وهذه EX روحت
+
+47
+00:04:24,280 --> 00:04:32,660
+وهذه EX روحتليه يتطلع؟ هذه و هذه إخوة، هذه VX
+
+48
+00:04:32,660 --> 00:04:36,220
+Final بيستوي VX Initial، ربه حقيا كادى، إذا هذا
+
+49
+00:04:36,220 --> 00:04:38,780
+القانون هو نفسه هذا القانون، هذا مابش لازم يعمل
+
+50
+00:04:38,780 --> 00:04:43,700
+مرة، ليه نقول إيش ده بيقول؟ بيقول لما تقوللي
+
+51
+00:04:43,700 --> 00:04:46,840
+الصراعة الإبتدائية الصينية هي نفسها النهائية، يعني
+
+52
+00:04:46,840 --> 00:04:51,560
+الصراعة الصينية بتتغير؟ثابتة سرعة الصينية ليش؟ قال
+
+53
+00:04:51,560 --> 00:04:56,920
+لي أصل مافيش تسارع صيني والتسارع تعني تغير سرعة
+
+54
+00:04:56,920 --> 00:05:01,940
+إذا السرعة ماتغيرتش فهي تسارع وإذا مافيش تسارع
+
+55
+00:05:01,940 --> 00:05:07,780
+مسموح للسرعة تتغير؟ لأ إذا السرعة الصينية ثابتة
+
+56
+00:05:07,780 --> 00:05:11,040
+هذا القانون أخدناه في الصف الرابع ابتدائي المسافة
+
+57
+00:05:11,040 --> 00:05:13,940
+بالسواء سرعة بزمن وهذا القانون صار المفقود طول
+
+58
+00:05:13,940 --> 00:05:19,270
+مافيش تسارعوهيسر المفعول مسافة بساوي سرعة عظمة بس
+
+59
+00:05:19,270 --> 00:05:24,510
+سينى سينى جال الصابر جالي وين في a y حط محلها سالب
+
+60
+00:05:24,510 --> 00:05:29,290
+g مظبوطا لا نجرى القوانين المناظرة يا بنات بقوله
+
+61
+00:05:29,290 --> 00:05:37,230
+هنا v y final بساوي v y initial كان زائد a y بيصيه
+
+62
+00:05:37,230 --> 00:05:44,780
+سالب gوهنا بدّي الـ X تلحق وطوار Y final نقص Y
+
+63
+00:05:44,780 --> 00:05:50,880
+initial بيساوي VY initial في T ناقص نص GT تربيع و
+
+64
+00:05:50,880 --> 00:05:58,220
+VY final تربيع ساوي VY initial تربيع ناقص 2G وY
+
+65
+00:05:58,220 --> 00:06:03,320
+final نقص Y initial هذه حركة المغضوفات إذا حركة
+
+66
+00:06:03,320 --> 00:06:08,060
+المغضوفات هي مجموعة حركتين حركة سينية بسرعة ثابتة
+
+67
+00:06:08,700 --> 00:06:14,340
+وحركة صادية سقوط حُر بتسارع الجاذبية الأرضية يعني
+
+68
+00:06:14,340 --> 00:06:19,500
+سقوط حُر تمام؟ تمام إذا إيش بيقوللي؟ بيقوللي as
+
+69
+00:06:19,500 --> 00:06:23,420
+the acceleration of gravity is always straight
+
+70
+00:06:23,420 --> 00:06:27,340
+downward وهذه معلومة كنا بنعرفها تمام؟ with a
+
+71
+00:06:27,340 --> 00:06:31,700
+magnitude of G the acceleration of a projectile
+
+72
+00:06:31,700 --> 00:06:39,430
+كتبت هذا بيعني أنههذا يعني أن محرك البردكتيل يمكن
+
+73
+00:06:39,430 --> 00:06:47,790
+أن يكون مجموح عركتين من محركة رقميةحركة عمودية
+
+74
+00:06:47,790 --> 00:06:51,990
+تصاروحها بالساوي سالب جي وعارفين ليش حطينا السالب
+
+75
+00:06:51,990 --> 00:06:55,470
+عشان انا كل حاجة الأعلى positive وكل حاجة الأسفل
+
+76
+00:06:55,470 --> 00:07:01,150
+سالبة and a horizontal motion with no acceleration
+
+77
+00:07:01,150 --> 00:07:05,610
+no acceleration بتعني constant velocity ولا لأ تمى
+
+78
+00:07:05,610 --> 00:07:08,370
+جالي لو اعتبرت هدول القوانين اللي انا كتبتهم
+
+79
+00:07:08,370 --> 00:07:11,790
+هيكتبهم على اعتبار ان هو اعتبر هنا x initial و y
+
+80
+00:07:11,790 --> 00:07:17,450
+initial صفر تمىهدول القوانين عرفناهم هو بما نفسه
+
+81
+00:07:17,450 --> 00:07:22,470
+هذا وهذا ما أصلا مش قانون هذه معلومة انه مافيش
+
+82
+00:07:22,470 --> 00:07:26,510
+تصارع صيني بتعني انه الصراع الصينية ابتدائية ولا
+
+83
+00:07:26,510 --> 00:07:29,910
+نهائية بتفرق لأ و هذا القانون الوحيد اللي موجود
+
+84
+00:07:29,910 --> 00:07:36,690
+مسافة بتصارع صراع في زمن ده ما بقوللي
+
+85
+00:07:36,690 --> 00:07:42,990
+لو إيدي اتطلعت هذي شايفين القانون بدي أخد الزمن
+
+86
+00:07:42,990 --> 00:07:49,810
+منهبقدر أقول T بتسوي X Final نقص X Initial على VX
+
+87
+00:07:49,810 --> 00:07:56,790
+Initial صح ولا لأ؟ قال يحملي هذا وعوضه هنا هتجيبلك
+
+88
+00:07:56,790 --> 00:08:03,230
+معادلة بين Y و X صح؟ لإنه بدّل T إيش بده أجيب؟X
+
+89
+00:08:03,230 --> 00:08:08,670
+قاللي لو اتيت عوضت ال T من هذه المعادلة و حطيتها
+
+90
+00:08:08,670 --> 00:08:15,030
+في هذه المعادلة هتطلع هكذا معادلة قاللي هذه الطلاب
+
+91
+00:08:15,030 --> 00:08:18,210
+قالوا أخدناها و الطالبات قالوا ما أخدناش لسه أنا
+
+92
+00:08:18,210 --> 00:08:21,690
+شوف الطالبات التانين إيش بقولوا معادلة زي هذه Y
+
+93
+00:08:21,690 --> 00:08:30,970
+بتساوي AX-BX تربيع معادلة إيش هذه؟ اللي هي قطة
+
+94
+00:08:30,970 --> 00:08:38,020
+مكافئةبسموه بارابولا سمعتوا كلمة بارابولا بارابولا
+
+95
+00:08:38,020 --> 00:08:44,420
+ماخدتوش في القلب كل لحظة جديد طيب اذكركم فيها هذه
+
+96
+00:08:44,420 --> 00:08:51,760
+او هذهطبعا ممكن هادي و هادي نسميها برابولة قطعة
+
+97
+00:08:51,760 --> 00:08:56,580
+مكافئة بيسموها تمام جالي معناته ايش بقول بقول هادي
+
+98
+00:08:56,580 --> 00:08:58,660
+انت ايش بتجيب قولتله انا هادي بجيبلك حركة
+
+99
+00:08:58,660 --> 00:09:03,880
+المقذوفات جالي معناته المقذوفات تتبع مسار شكله هيك
+
+100
+00:09:03,880 --> 00:09:10,380
+يعني كل جسميقدف لازم يتبع بربولا مش عشوائي هكذا
+
+101
+00:09:10,380 --> 00:09:14,480
+المعاجلة جابت رياضيات احنا مابدناش .. مابدناش صفات
+
+102
+00:09:14,480 --> 00:09:18,960
+لا بربولا ولا حاجة بس بدنا نحط في مخنا كلمة بربولا
+
+103
+00:09:18,960 --> 00:09:22,620
+معناط قطعة مكافئة هتاخدوها في ال Calculus هتاخدوها
+
+104
+00:09:22,620 --> 00:09:28,680
+هؤلاء الشباب هاخدوها قبلكم؟ معاكم؟ أخدتوها؟ المهم
+
+105
+00:09:28,680 --> 00:09:34,860
+هي شكلهايعني أي جسم بأقضفه يا بنات، أي جسم بأقضفه،
+
+106
+00:09:34,860 --> 00:09:38,300
+مش اللي بده يحدد مصاره الجاذبية الأرضية، معناته
+
+107
+00:09:38,300 --> 00:09:43,640
+مصاره هيه، نمنجكت، شايفينه؟ هذا هو المصار، خلّيني
+
+108
+00:09:43,640 --> 00:09:47,820
+أقول جزء من دائرة، هيك بده يكون مصاره، من هنا
+
+109
+00:09:47,820 --> 00:09:54,220
+أطلقته، هذه النقطة أقصى ارتفاع ولا لأ؟وصل هنا
+
+110
+00:09:54,220 --> 00:09:59,600
+اتطلعوا قذفته بزاوية معينة هجيت انا هاي قذفته
+
+111
+00:09:59,600 --> 00:10:03,280
+بزاوية معطوه المعطية بتقدروا هذه الصورة الابتدائية
+
+112
+00:10:03,280 --> 00:10:07,900
+تجيبلولي مراكبتينها الصينية والصادية هاي مراكبة
+
+113
+00:10:07,900 --> 00:10:10,900
+الصينية وهي الصادية هجيت هذه المراكبة الصينية
+
+114
+00:10:10,900 --> 00:10:17,710
+مسموح انها تتغير؟ لأطب حلو مصاصحين انت قلتوا ممنوع
+
+115
+00:10:17,710 --> 00:10:22,790
+تتغير عند أقصى ارتفاع في حركة المغلوفات كده السرعة
+
+116
+00:10:22,790 --> 00:10:27,430
+ال Y صفر بس ال X ثابت بيه هنا اللي قال صفر غلط
+
+117
+00:10:27,430 --> 00:10:32,850
+ثابت ليه؟ لأن في مراكبة سنية موجودة اذا ال Y الصفر
+
+118
+00:10:33,440 --> 00:10:39,200
+والصينية موجودة بمعنى آخر لو أديكم في ال quiz عند
+
+119
+00:10:39,200 --> 00:10:43,000
+أقصى ارتفاع في حركة المقضوفات أول خيار بيقول Zero
+
+120
+00:10:43,000 --> 00:10:46,060
+عشان تتعلموا عليه و تقولوا غلط ال Y هو Zero إذن هو
+
+121
+00:10:46,060 --> 00:10:50,480
+مش Zero طب بيجي سؤال تاني بيقولك السرعة الإبتدائية
+
+122
+00:10:50,480 --> 00:10:54,700
+في حركة المقضوفات وكتبلك هذه العلاقة V initial
+
+123
+00:10:54,700 --> 00:11:00,040
+وحطت هيك بتساوي خمسة I زائد تلاتة J متر per second
+
+124
+00:11:01,110 --> 00:11:04,050
+هذه حركة .. هذه حركة المغلوفات وهذه السرعة
+
+125
+00:11:04,050 --> 00:11:08,450
+الأبتدائية بدي أسأل عند أقصى ارتفاع كده السرعة؟
+
+126
+00:11:08,450 --> 00:11:11,750
+أبسط ليش؟
+
+127
+00:11:11,750 --> 00:11:18,670
+صح؟ لأنه بس الصينية طب كده الصينية؟ خمسة بتتغير؟
+
+128
+00:11:18,670 --> 00:11:23,870
+لأ إذا في بداية أو عند أقصى ارتفاع أو نهاية كده؟
+
+129
+00:11:23,870 --> 00:11:28,870
+خمسة أبسط تحكي فجد صح؟ كأن في مجتمع الجبل لو كان
+
+130
+00:11:28,870 --> 00:11:32,220
+..لو كان سفر فالاسم يكون المركبات اللي بيبقى
+
+131
+00:11:32,220 --> 00:11:36,220
+واضحة؟ هذا لو كان سفر ومي جالك سفر؟ وانا بقولك عند
+
+132
+00:11:36,220 --> 00:11:41,280
+أقصى ارتفاع جديش السرعة إذا جلت سفر بقوللي غلط مش
+
+133
+00:11:41,280 --> 00:11:46,740
+سفر إذا اللي عند أقصى ارتفاع جديش السرعة مش سفر مش
+
+134
+00:11:46,740 --> 00:11:50,340
+سفر إيه جالهوا ليه؟ خمسة جالوا خمسة ماجلوايه
+
+135
+00:11:50,340 --> 00:11:58,820
+السفر؟ ممنوع تقولي سفرولا مرة ..ولا مرة ..ولا مرة
+
+136
+00:11:58,820 --> 00:12:05,520
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+137
+00:12:05,520 --> 00:12:05,560
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+138
+00:12:05,560 --> 00:12:05,960
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+139
+00:12:05,960 --> 00:12:06,160
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+140
+00:12:06,160 --> 00:12:07,180
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+141
+00:12:07,180 --> 00:12:10,880
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+142
+00:12:10,880 --> 00:12:16,040
+..ولا مرة ..ولا مرة
+
+143
+00:12:16,040 --> 00:12:22,740
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+144
+00:12:23,540 --> 00:12:26,480
+لأ مش هلأ هو فى بس اللى هو المحور السيني اللى هو
+
+145
+00:12:26,480 --> 00:12:34,500
+الـG الـG سفر طلع لكن كلها سفر لأ الزنية عشان كده
+
+146
+00:12:34,500 --> 00:12:38,740
+لما حكيتلك هنا طلعيهتجيب على هذه السرعة التدعية
+
+147
+00:12:38,740 --> 00:12:43,120
+هنضع أقصى التفاح هذه بصير سفر لكن هذه تتغيرش إذا
+
+148
+00:12:43,120 --> 00:12:45,980
+جدتش سرعة عندها أقصى التفاح بقوله خمسة ضلت الصينية
+
+149
+00:12:45,980 --> 00:12:51,340
+الصادية روحت عشان كده تطلع هي السهم شايفينه هجيت
+
+150
+00:12:51,340 --> 00:12:55,780
+هذا هيجو من أطول هذا ولا هذا مش هذا أطول معناته
+
+151
+00:12:55,780 --> 00:13:00,570
+الصادقال الصيني زي ما هوطلع انت من النقطة الصاضي
+
+152
+00:13:00,570 --> 00:13:05,650
+ضال روح الصاضي الصيني زي ما هو الصيني زي ما هو
+
+153
+00:13:05,650 --> 00:13:10,250
+الصيني زي ما هو الصاضي قاعد بيغير لأنه في تصارع
+
+154
+00:13:10,250 --> 00:13:14,930
+صاضي و التصارع الصاضي بيعني تغير الصراع الصاضية و
+
+155
+00:13:14,930 --> 00:13:19,750
+معدم وجود التصارع الصيني بيعني ان المركبة الصينية
+
+156
+00:13:19,750 --> 00:13:29,400
+ممنوعة تتغير تمام يا بنات؟ أي استفسار؟ تمام؟الان
+
+157
+00:13:29,400 --> 00:13:33,680
+العنوان ايش بيقول horizontal range and maximum
+
+158
+00:13:33,680 --> 00:13:37,660
+height of a projectile بدنا نشتغل قانونين ممنوع
+
+159
+00:13:37,660 --> 00:13:42,360
+نحفظهم مش مطلوب مننا نحفظهم وانا بقول مش مطلوب مش
+
+160
+00:13:42,360 --> 00:13:47,420
+مطلوب ممنوع نحفظهم اقوى من انه مش مطلوب بمعنى اخر
+
+161
+00:13:47,420 --> 00:13:51,260
+لو واحد جال ال range وروحت انا بصين حافظ القانون
+
+162
+00:13:51,260 --> 00:13:57,070
+وحطته وعوضت بجبلهوش لكي يشتقوا من اولهو محطوطين
+
+163
+00:13:57,070 --> 00:14:06,550
+قوانين لكن ممنوع تحفظهم تمى نرجع للرسمة هل جيت انا
+
+164
+00:14:06,550 --> 00:14:10,430
+و اتفقت اي حاجة في حركة المغضب فات بدي اجسمها
+
+165
+00:14:10,430 --> 00:14:17,010
+لنصين صح سيني و صعديكل المعطيات بدك تعرف ليها
+
+166
+00:14:17,010 --> 00:14:21,850
+سينية ولا صادية والمطاليب بتطلع انت ايش طالب سيني
+
+167
+00:14:21,850 --> 00:14:26,230
+ولا صادي اذا انت طالب حاجة سينية باجيها صح ولا لأ
+
+168
+00:14:26,230 --> 00:14:29,930
+واذا انت طالب حاجة صادية باجيها هجيت لما يقوللي
+
+169
+00:14:29,930 --> 00:14:34,190
+maximum height ارتفاع اقولكم سيني ولا صادي why اذا
+
+170
+00:14:34,190 --> 00:14:38,230
+why اذا انت هنا بدوا ال range ال range ايش معناته
+
+171
+00:14:38,230 --> 00:14:42,850
+ال مدى اذا بدوا مسافة سينية ولا لأ اذا انت هنا
+
+172
+00:14:43,510 --> 00:14:48,750
+اتفجنا هيك؟ حلو جالي طيب انت هذه الصراع الابتدائية
+
+173
+00:14:48,750 --> 00:14:54,230
+بدي أعطيك إياها هذي سنية أم صادية؟إذاً بدي أحللها
+
+174
+00:14:54,230 --> 00:14:59,930
+الشغل اللي مش جسمها chapter 3 تعلمتك إياه عشان
+
+175
+00:14:59,930 --> 00:15:04,410
+تعرف كيف تحلل أي vector ولا لأ إذاً أول خطوة بدك
+
+176
+00:15:04,410 --> 00:15:09,810
+تعملها الآن عشان تجيب ال range الصورة الإبتدائية
+
+177
+00:15:09,810 --> 00:15:17,010
+جسم ليها نصين يعني حللها بقوله بسيطة V initial
+
+178
+00:15:17,010 --> 00:15:23,550
+الصينية هي V initial cos θو Vinitial الصعبية
+
+179
+00:15:23,550 --> 00:15:30,330
+Vinitial Sine فيتا مظلوط ولا لأ تم ايش بدك قال لي
+
+180
+00:15:30,330 --> 00:15:33,930
+بدي ال maximum height اول حاجة بدي ال maximum
+
+181
+00:15:33,930 --> 00:15:37,270
+height في الرسم مابينا ال maximum height تو ايه
+
+182
+00:15:37,270 --> 00:15:40,310
+عايش اختلافنا ان عند ال maximum height ايش هو
+
+183
+00:15:40,310 --> 00:15:46,670
+السفر؟الـ VY Final الـ VY مش الـ V ما هو مش السرعة
+
+184
+00:15:46,670 --> 00:15:50,990
+الكلية الـ VY صح ولا .. قللي شوفلي هالقانون الحلو
+
+185
+00:15:50,990 --> 00:15:55,690
+هذا إيش بدك تعوض هنا عند maximum height؟ سفر هذا
+
+186
+00:15:55,690 --> 00:16:00,870
+.. هاي .. بظبط؟ VY Final مقص VY Initial انت بدأت
+
+187
+00:16:00,870 --> 00:16:04,350
+من هنا VY Initial هو سفر و VY Final هو H ال
+
+188
+00:16:04,350 --> 00:16:08,390
+maximum height صح ولا لا؟ إذا يلا نعود أنا وياكم
+
+189
+00:16:08,390 --> 00:16:20,490
+هذه سفرفاح ولا لأ ها دي هيها V initial sin θ كل
+
+190
+00:16:20,490 --> 00:16:26,210
+تربية معقز اتنين G و Y final هي H و Y initial صفر
+
+191
+00:16:26,210 --> 00:16:33,890
+لكل مسح صحيح تمام ايش بده قلتله بدي H بدك احسن من
+
+192
+00:16:33,890 --> 00:16:41,710
+هيك معاجلة تجيبلك H هاي HH بيتساوي V initial تربيع
+
+193
+00:16:41,710 --> 00:16:48,130
+Sine تربيع F تعة 2G صحيك ولا لأ؟ هذا و هي طلعته
+
+194
+00:16:48,130 --> 00:16:54,810
+القانون اللي ممنوع نحفظه و ممنوع نحفظه اتفجنا؟ بنا
+
+195
+00:16:54,810 --> 00:16:59,430
+نتطلع عليه بس، مسموح نتطلع عليه؟ في sign ولا فيش
+
+196
+00:16:59,430 --> 00:17:04,630
+sign؟ جديش أكبر قيمة للـSign؟ واحد، لو جالك أكبر
+
+197
+00:17:04,630 --> 00:17:11,670
+قيمة للـH جديش؟يعني V initial تربيه على 2G صح؟
+
+198
+00:17:11,670 --> 00:17:18,090
+يعني لما هذه تكون واحد هذه sign ايش تزاوية اللي
+
+199
+00:17:18,090 --> 00:17:22,190
+signها واحد تسعين يعني بيقوللي اقصى ارتفاع بيكون
+
+200
+00:17:22,190 --> 00:17:26,170
+لما اتطلعه هيك ولا لأ لما يكون عمودي منطق ولا مش
+
+201
+00:17:26,170 --> 00:17:32,950
+منطق هذا منطق خلصت طبعا تطلعوا انتوا انا واحد
+
+202
+00:17:32,950 --> 00:17:35,970
+بيقوللي طب ليش انت ماروحتش شينماهي why بقوله عشان
+
+203
+00:17:35,970 --> 00:17:39,790
+فيها زمن وزمن ما بعرفوشفبالتالي هذه المعاجلة
+
+204
+00:17:39,790 --> 00:17:45,510
+تخدمني و احد للمعاجلة هذه طب نيجي لل range ال
+
+205
+00:17:45,510 --> 00:17:50,570
+range يعني بده X صح ولا قاللي هيها X هيها مافيش
+
+206
+00:17:50,570 --> 00:17:56,810
+أحلى منها فيها زمن ولا فيش طب أنا بعرفش الزمن طب
+
+207
+00:17:56,810 --> 00:18:01,270
+في معاجلة غيرها هو عشان أروح عليها هنا طلع شوية
+
+208
+00:18:01,270 --> 00:18:05,250
+هنا ماكانش في زمن واحد شوفت معاجلة تانية هنا في
+
+209
+00:18:05,250 --> 00:18:09,770
+الصين اللي كان معاجله فيهفي غيرها؟ إذا غصب من عنك
+
+210
+00:18:09,770 --> 00:18:13,690
+بتكشل لها هذه المعادلة بتخليها تخدمك احكيها الجهة
+
+211
+00:18:13,690 --> 00:18:18,250
+تجيك T من أول معادلة Y؟ الـG عادة ها هجيت الـT غصب
+
+212
+00:18:18,250 --> 00:18:21,850
+من عنك بتدول عليها فأنا عجالة في عندي معلومة بيقول
+
+213
+00:18:21,850 --> 00:18:26,730
+الزمن بيصحلك تشحتها من ال Y منظر ل .. لأن الزمن
+
+214
+00:18:26,730 --> 00:18:33,130
+سيني ولا صاضي؟أذا بإمكاني أخده من الصديق ولا لا؟
+
+215
+00:18:33,130 --> 00:18:37,450
+قاللي تقدر تاخدها من هناك كيف أخدها من هناك؟ بدي و
+
+216
+00:18:37,450 --> 00:18:40,590
+اي final و بدي و اي initial؟ قاللي هنا عند النقطة
+
+217
+00:18:40,590 --> 00:18:43,030
+هذه مين يقولي أشهر اهدافيات النقطة هذه؟ Zero Zero
+
+218
+00:18:43,030 --> 00:18:44,210
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+219
+00:18:44,210 --> 00:18:48,970
+Zero Zero Zero Zero Zero
+
+220
+00:18:48,970 --> 00:18:54,750
+Zero Zero Zero Zero
+
+221
+00:18:54,750 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+222
+00:18:55,110 --> 00:18:55,230
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+223
+00:18:55,230 --> 00:18:59,210
+ZeroR و 0 R و 0 نفترض الـ R عشرة بقول عشرة و صفر
+
+224
+00:18:59,210 --> 00:19:03,030
+ولا لأ اذا هذه إحداثية عشرة و صفر نركز على
+
+225
+00:19:03,030 --> 00:19:06,930
+الإحداثية الصاضية الإحداث الصاضي لهذه كده و هذه
+
+226
+00:19:06,930 --> 00:19:12,190
+صفر و صفر زي الصاضي إذا لما بدي أعود هنا صفر ناخد
+
+227
+00:19:12,190 --> 00:19:19,450
+صفر صح؟ و لا تحكي الصيني تمام انت قلت بدا نشحت
+
+228
+00:19:19,450 --> 00:19:26,080
+الزمن منها صح؟ وبالتالي من العودماذا يسمى الـ y
+
+229
+00:19:26,080 --> 00:19:34,060
+final؟ صفر y initial صفر بتساوي v و هنا أنا و هذه
+
+230
+00:19:34,060 --> 00:19:43,700
+y اذا v initial sin θ في t ناقص نص g صحيك؟ في حد
+
+231
+00:19:43,700 --> 00:19:48,240
+ماعرفش يجيب ال t هلجيت؟ جسم المعادلة على t عشان
+
+232
+00:19:48,240 --> 00:19:55,170
+اطير هذه و اطير هذهطلّع الـ T إذا الـ T اللي بتدور
+
+233
+00:19:55,170 --> 00:20:00,810
+عليها صفر مقال صفر صفر اه يحصل بعدين اتنين V
+
+234
+00:20:00,810 --> 00:20:07,130
+Initial Sine of Theta على Y الزمن اللي انغلبك جبته
+
+235
+00:20:07,130 --> 00:20:13,290
+ولا ماتبتهوش الان بتجيه الجهاد X Final هي R ال
+
+236
+00:20:13,290 --> 00:20:20,790
+range X Initial صفر صح بتسوي V Initial Cosine of
+
+237
+00:20:20,790 --> 00:20:30,490
+Thetaبدي الـ T هيا مظبوط؟ حط اتنين V initial sin
+
+238
+00:20:30,490 --> 00:20:36,930
+فيتا V initial في V initial اذا بيساوي V initial
+
+239
+00:20:36,930 --> 00:20:41,350
+تربية اتنين sin فيتا cos فيتا ايش القدرة في مخهم؟
+
+240
+00:20:41,350 --> 00:20:48,050
+sin اتنين فيتا اذا هذه sin اتنين فيتا على G هاي ال
+
+241
+00:20:48,050 --> 00:20:54,850
+range اللي بتدور عليه وبرضه ممنوعنا نحفظهاتفجنا بس
+
+242
+00:20:54,850 --> 00:20:59,970
+برضه مسموح نتطلع عليه ما هي أكبر قيمة لل range لما
+
+243
+00:20:59,970 --> 00:21:06,150
+sin 2θ تسوى 1 اللي هي V initial تربيع على G طب هي
+
+244
+00:21:06,150 --> 00:21:11,570
+sin 2θ و احنا بنعرف ان ال theta sin 90 هو الواحد
+
+245
+00:21:11,570 --> 00:21:15,690
+اذا لازم θ تكون 45 ولا لأ عشان كده بيقوللي ايش
+
+246
+00:21:15,690 --> 00:21:20,520
+بيقوللي يا ترى لو بدك أكبر rangeكيف تحط الزاوية
+
+247
+00:21:20,520 --> 00:21:25,920
+بقوله 45 وانت مغمض صح ولا لأ اذا انت نشن على زاوية
+
+248
+00:21:25,920 --> 00:21:32,900
+45 بتحصل على اكبر range ممكن صحيح ولا لأ تمام طبعا
+
+249
+00:21:32,900 --> 00:21:35,640
+انتوا زمان اخدتوا في الرياضيات في التفاضل و
+
+250
+00:21:35,640 --> 00:21:39,120
+التكامل في توجيهي لما تجيبوا الشغل عشان تكون ال
+
+251
+00:21:39,120 --> 00:21:43,600
+function اكبر او اصغر ذاكرين هو تطبيقات التفاضل
+
+252
+00:21:43,600 --> 00:21:47,880
+مااخدتوهاش في توجيهي لما
+
+253
+00:21:47,880 --> 00:21:56,410
+يكون عنكمخلّيني اكتب Y بديش اكتب صد Y بيتساوي 2X
+
+254
+00:21:56,410 --> 00:22:01,790
+تربيع زي 3X و لو سألكم ماهي قيمة X اللي بتخلي Y
+
+255
+00:22:01,790 --> 00:22:06,630
+اكبر ما يمكن او اصغر مايمكن ايش كنتوا تسووا كنتوا
+
+256
+00:22:06,630 --> 00:22:11,010
+تشتقوا و تسووا بصفر قال يعني لو هد اشتقتوا بالنسبة
+
+257
+00:22:11,010 --> 00:22:16,550
+للثيتا و سويتوا بصفر هيطلع عندك ثيت 45 قصب عنك صح؟
+
+258
+00:22:17,310 --> 00:22:25,070
+لكن هذا كلكلس خلصناه تبع توجيهي تمام حلو إذا ال
+
+259
+00:22:25,070 --> 00:22:30,730
+maximum height أول حاجة عملتها حللت السرعة
+
+260
+00:22:30,730 --> 00:22:34,930
+الإبتدائية إلى سنية وصادية ولا لأ بقت كده بقوله at
+
+261
+00:22:34,930 --> 00:22:41,170
+the maximum height الشي هو السفر السرعة الصادية هي
+
+262
+00:22:41,170 --> 00:22:48,790
+السفر بقول using the equation حطيت طلعت الهذه ال
+
+263
+00:22:48,790 --> 00:22:52,810
+range قال لي to find the range we need the time
+
+264
+00:22:52,810 --> 00:22:55,970
+لأنه قال لي هذه المعادلة بتجيب ال range فيها زمان
+
+265
+00:22:55,970 --> 00:23:00,330
+بتجيز زمان we need the time of a flight زمان
+
+266
+00:23:00,330 --> 00:23:04,410
+الطيران يعني زمان الكل تمام nothing that for the
+
+267
+00:23:04,410 --> 00:23:07,590
+total time of a flight while finally بتساوي سفر
+
+268
+00:23:07,590 --> 00:23:12,290
+ذكيني الرسم اللي راحت سفر و سفر كان هنا وصار هنا
+
+269
+00:23:12,290 --> 00:23:17,010
+برغم انه اتحرك لكن اتحرك مسافة أفقية مسافة عمودية
+
+270
+00:23:17,010 --> 00:23:17,550
+لا احكي
+
+271
+00:23:20,200 --> 00:23:23,620
+في ال .. مش هيك VY اصلا ايوة VY في وين ال سفر ال Y
+
+272
+00:23:23,620 --> 00:23:28,460
+سفر كمان ال Y سفر ال Y سفر؟ لأ انت حسبتها لأ وين
+
+273
+00:23:28,460 --> 00:23:32,020
+مش عندها اقصر تفهة و مين جالك هدى عندها اقصر تفهة
+
+274
+00:23:32,020 --> 00:23:36,540
+هدى
+
+275
+00:23:36,540 --> 00:23:42,900
+وين هدى لمّا كان عوضت هدى هدى عوضت على سفر هدى هدى
+
+276
+00:23:42,900 --> 00:23:48,770
+عوضت على سفرهنا عوضت مع ال wi-fi من الديل اتف اي
+
+277
+00:23:48,770 --> 00:23:50,690
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+278
+00:23:50,690 --> 00:23:51,030
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+279
+00:23:51,030 --> 00:23:51,450
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+280
+00:23:51,450 --> 00:23:51,610
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+281
+00:23:51,610 --> 00:23:56,150
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+282
+00:23:56,150 --> 00:23:56,250
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+283
+00:23:56,250 --> 00:24:02,190
+وين وين وين وين وين وين وين وين وين
+
+284
+00:24:02,190 --> 00:24:12,910
+وين وين وين وين وين وين وين وين
+
+285
+00:24:12,910 --> 00:24:17,150
+وينطبقايا نكون جنبها ايه لو انا بدي احطهم جنب بعض
+
+286
+00:24:17,150 --> 00:24:22,550
+تمام؟ حلو احكي ليش لما جينا الزمن ماعوضش في
+
+287
+00:24:22,550 --> 00:24:28,230
+القانون الأول ها؟ هو انت ايش بدك؟ تمام انت جيبت
+
+288
+00:24:28,230 --> 00:24:34,690
+الزمن من ها ايش مطلوب؟ X ولا V؟ Y؟ ايش مطلوب منك؟
+
+289
+00:24:34,690 --> 00:24:41,130
+ال range ايش هو؟ ال X ليش ماعرفها؟ ماجيبوا من ها
+
+290
+00:24:41,130 --> 00:24:47,800
+مدذك حلوبتعرفى هادى؟ كدهش؟ من جده كان اقصى ارتفاع؟
+
+291
+00:24:47,800 --> 00:24:52,820
+انا بدي زمان لكله مش انا بدي زمان لكله؟ هل السرعة
+
+292
+00:24:52,820 --> 00:24:56,440
+النهائية لما وصل الارض عرفها انت؟ عشان كده ماعرفتش
+
+293
+00:24:56,440 --> 00:25:02,240
+اخده لإنه the why final يا بنكي هادى ماعرفهاش واحد
+
+294
+00:25:02,240 --> 00:25:04,760
+يقول طب جيه بيه اقصى ارتفاع وضروف اتنين مش دايما
+
+295
+00:25:06,130 --> 00:25:11,210
+صح؟ انا مدي ال rage من نقطة البداية للنهاية صح؟
+
+296
+00:25:11,210 --> 00:25:14,990
+معاتو بدي الزمن من نقطة البداية للنهاية بعرف
+
+297
+00:25:14,990 --> 00:25:19,250
+السرعة الصادية عند النهاية؟ بعرفش، اذا نهاية
+
+298
+00:25:19,250 --> 00:25:23,590
+تخدمني المعادلة، تخدمنيش، بقدرش اجيب منها، لأنه في
+
+299
+00:25:23,590 --> 00:25:32,450
+شغلات مجاهية غير الزمن، عرفتي ليش؟ غيرها، لأ،
+
+300
+00:25:32,450 --> 00:25:37,720
+ذاكرة لما قلتلكم ان هي القانون هادا ع من مخكم؟لأ
+
+301
+00:25:37,720 --> 00:25:43,560
+ممكن تدرسوكوا هذه حالة خاصة .. هذه حالة خاصة زمان
+
+302
+00:25:43,560 --> 00:25:48,420
+السقوط لا يساوي زمان الهبوط وقلنا على أيام الشباب
+
+303
+00:25:48,420 --> 00:25:54,600
+قلتهم امحوا هذا القانون من مخكم وانا قلتلكم هذا مش
+
+304
+00:25:54,600 --> 00:26:01,790
+قانون تمامإذا جبت ال T من هذا القلول لأن كله بعرفه
+
+305
+00:26:01,790 --> 00:26:05,370
+إلا ال T لكن عايز قلون تاني في شغلات تانية مش
+
+306
+00:26:05,370 --> 00:26:11,150
+معروفة طلعت ال T و منها طلعت ال range و قال كلنا
+
+307
+00:26:11,150 --> 00:26:19,330
+بنعرف أن sin θ بتسوى 1 لما θ تسوى 90 درجة عند 2 θ
+
+308
+00:26:19,330 --> 00:26:25,090
+يعني θ تكون 45 درجة تمامThis is because the
+
+309
+00:26:25,090 --> 00:26:30,250
+maximum value of sin 2θ is 1 And this occurs لما
+
+310
+00:26:30,250 --> 00:26:37,770
+2θ تسوى 90 أو تسوى 45 أه، لحد الآن ماشي الأمور؟
+
+311
+00:26:37,770 --> 00:26:44,330
+ماشي الأمور، شوفها لك وزاد قال لي شوفلي خمس حجار
+
+312
+00:26:44,330 --> 00:26:51,450
+بدي أضربهم بنفس ال speed لكن ب directions مختلفة
+
+313
+00:26:51,450 --> 00:26:57,980
+شايفين الزوايا؟كل واحد له زاوية خاصة بيه تمام؟ إيش
+
+314
+00:26:57,980 --> 00:27:02,160
+بده؟ بيقولي أ projectile launched أطلقات from the
+
+315
+00:27:02,160 --> 00:27:05,140
+origin كلهم هايهم الخمسة طالعين من النقطة نفسها
+
+316
+00:27:05,140 --> 00:27:09,540
+صحيح؟ واحد، اتنين، تلاتة، أربعة، خمسة from the
+
+317
+00:27:09,540 --> 00:27:14,560
+origin with the same initial speed بصحيح اللي يقول
+
+318
+00:27:14,560 --> 00:27:20,410
+ليه؟ with the same initial velocity؟ ليش؟لأنه
+
+319
+00:27:20,410 --> 00:27:25,610
+اتجاهات مختلفة إذا جالي speed بصحله لأنه نفترض
+
+320
+00:27:25,610 --> 00:27:29,030
+خمسة كلهم خمسة بس واحد بيعمل زي و تلاتي و واحد
+
+321
+00:27:29,030 --> 00:27:32,430
+بيعمل زي و خمستاشر و واحد خمسة و أربعين فبسمحله
+
+322
+00:27:32,430 --> 00:27:35,310
+يقولي initial speed لكن ممنوع يقولي initial
+
+323
+00:27:35,310 --> 00:27:38,090
+velocity لأنه لو جالي initial velocity بقوله الراص
+
+324
+00:27:38,090 --> 00:27:42,610
+مابتقولش هيك الراص مابتقولش هيك صح ولا لأ طيب
+
+325
+00:27:42,610 --> 00:27:47,190
+initial speed but at various angles زوايا مختلفة
+
+326
+00:27:47,190 --> 00:27:51,540
+زي ما تشايفينFor which of the launch angles the
+
+327
+00:27:51,540 --> 00:27:55,060
+time of flight is the largest؟ قال لمين من هدول
+
+328
+00:27:55,060 --> 00:27:58,740
+هياخد أكبر الزمن عشان يصل للأرض؟ شفين الزمن شفته؟
+
+329
+00:27:58,740 --> 00:28:00,360
+ايوه و احنا قاعدين نتطلع
+
+330
+00:28:03,110 --> 00:28:06,870
+معناته بيعتمد ع فيتا ولا لا كل ما فيتا كبرت كل ما
+
+331
+00:28:06,870 --> 00:28:10,750
+صينها كبر و أكتر حد لما يصير تسعين إذا بتتوقعوا
+
+332
+00:28:10,750 --> 00:28:15,230
+مين أكبر واحد؟ الخمسة وسبعين حسب هذا القانون اللي
+
+333
+00:28:15,230 --> 00:28:20,230
+by chance جيبنا احنا وياكم إذا بيقولي هتكون الخمسة
+
+334
+00:28:20,230 --> 00:28:23,310
+أش ولا الخمسة واربعين الخمسة واربعين الأكبر إيه
+
+335
+00:28:23,310 --> 00:28:29,030
+تدري ببالكم مش أكبر زمان ولا خمسة وسبعين ولا كلهم
+
+336
+00:28:29,030 --> 00:28:34,670
+مزعج ولا واحدة منهم خمسة وسبعينخمس صح شجلشي و براو
+
+337
+00:28:34,670 --> 00:28:37,290
+عليكي يعني هيجيكم سؤال عالمودي مرة أكبر إشي و مرة
+
+338
+00:28:37,290 --> 00:28:42,450
+أقل إشي لأنه احنا بنكرر السؤال بتغيير صيغة بسيطة
+
+339
+00:28:42,450 --> 00:28:47,770
+صحين يا بنات تمام بيجينا نشوف هالكوزين ورا بعض
+
+340
+00:28:47,770 --> 00:28:52,490
+نشوفهم صحين ولا لأ بيقولي in a projectile motion
+
+341
+00:28:52,490 --> 00:28:57,170
+projectile motion حركة مغنوفات صح ولا لأ كيف
+
+342
+00:28:57,170 --> 00:29:02,730
+تصاروحات تجاههعمودي لأسفل في حد مش عارف المعلومة
+
+343
+00:29:02,730 --> 00:29:07,330
+دي ده ما تشوفش السؤال بيقول in a projectile motion
+
+344
+00:29:07,330 --> 00:29:11,870
+at what point عند أي نقطة أثناء الحركة along the
+
+345
+00:29:11,870 --> 00:29:15,870
+path أثناء مسار تبع الحركة اللي هو بربه لتفقنا
+
+346
+00:29:15,870 --> 00:29:20,990
+ذاكرين are the velocity and the acceleration
+
+347
+00:29:20,990 --> 00:29:25,390
+vectors are perpendicular to each other ايش عن ال
+
+348
+00:29:25,390 --> 00:29:30,950
+perpendicular؟ حلوأول نروح تسارع في حدا مختلف
+
+349
+00:29:30,950 --> 00:29:36,230
+عليه؟ كيف اتجاهه؟ لأسفة لأسفة بدي عند أي نقطة
+
+350
+00:29:36,230 --> 00:29:42,590
+السرعة بتكون أفقية عند أقصى الارتفاع لأن هذا صادق
+
+351
+00:29:42,590 --> 00:29:45,150
+بيقول لي بدي السرعة تكون عمودية على الصادق إيش
+
+352
+00:29:45,150 --> 00:29:49,110
+يعني؟ سينية يعني السرعة تكون بس سينية بس سينية
+
+353
+00:29:49,110 --> 00:29:51,630
+بيقولي عند أقصى الارتفاع لأنه في مراكبة صادقة
+
+354
+00:29:51,630 --> 00:29:55,390
+للسرعة عند أقصى الارتفاع أذن مين بدي يكون؟ هذا هو
+
+355
+00:30:01,720 --> 00:30:04,600
+مش معاكم ال z و بعدين project of motion بيصيب ال z
+
+356
+00:30:04,600 --> 00:30:08,340
+في fireworks فاتغلبيش حالك ميدناش نخش في التفاصيل
+
+357
+00:30:10,060 --> 00:30:14,340
+هل the launch point يعني نقطة البداية الانطلاق ولا
+
+358
+00:30:14,340 --> 00:30:18,320
+هي نقطة ال landing point landing يعني هبوط نقطة
+
+359
+00:30:18,320 --> 00:30:21,500
+الهبوط ولا the highest point ولا ولا فيه نقطة ال
+
+360
+00:30:21,500 --> 00:30:26,000
+highest point تمام شوف السؤال بدي أكرره أغير كلمة
+
+361
+00:30:26,000 --> 00:30:30,200
+في السؤال بدي كلمة perpendicular بدي أحط parallel
+
+362
+00:30:30,200 --> 00:30:36,980
+أطلع السؤال إيش بيصير؟ وكتيش السرعة بتكون فقط
+
+363
+00:30:36,980 --> 00:30:39,600
+صادية وين؟
+
+364
+00:30:41,010 --> 00:30:45,210
+فكر منيحا ولا
+
+365
+00:30:45,210 --> 00:30:51,430
+مرة ولا في نقطة عند نقطة البداية بتكون عند أقصى
+
+366
+00:30:51,430 --> 00:30:54,490
+ارتفاع بيكونوا مش اتفاقنا بـ Urban Declar و عند
+
+367
+00:30:54,490 --> 00:30:59,330
+اللي هو Note برضه بيكون الناس في زاوية مظلوط هيك
+
+368
+00:30:59,330 --> 00:31:03,310
+ولا لأ؟ هاي الرسمة ها نتذكر مع بعض بعيننا الله
+
+369
+00:31:03,310 --> 00:31:07,990
+هادى الرسمة هى نعيدها وين هاجد بايدها؟
+
+370
+00:31:11,330 --> 00:31:19,090
+هل السرعة صدية؟ لأ، السرعة صدية؟ السرعة صدية؟ اذا
+
+371
+00:31:19,090 --> 00:31:21,410
+هذه النقطة و لا هذه النقطة و لا هذه النقطة؟ ولا
+
+372
+00:31:21,410 --> 00:31:27,070
+واحدة، اذا nowhere، اذا الجواب الصح عرفتوا كيف
+
+373
+00:31:27,070 --> 00:31:30,770
+السؤال طالع ايش غيرنا؟ كل ما غيرنا في السؤال صار
+
+374
+00:31:30,770 --> 00:31:38,130
+جواب nowhere كله
+
+375
+00:31:38,130 --> 00:31:40,090
+سامع عربي و لا في حد سامع صيني؟
+
+376
+00:31:43,200 --> 00:31:49,530
+عربي؟ تمه .. انشوف اي سئلةجالي هذا example 4.3
+
+377
+00:31:49,530 --> 00:31:55,050
+الكتاب مغلبنا جايب السؤال صائب في البداية انا اروح
+
+378
+00:31:55,050 --> 00:31:59,310
+على 4.4 اول بعدين ارجع ل 4.3 تمام خلينا نبدأ
+
+379
+00:31:59,310 --> 00:32:04,390
+بالسهل هذا بعدين نجيه هذا سؤال زي الشرط والسيارة
+
+380
+00:32:04,390 --> 00:32:08,870
+ذاكرينهم هذا مشبوه بعدين نجيه قصة حياته من أولي
+
+381
+00:32:08,870 --> 00:32:12,270
+جديد وانا هايله بطريقتين بعدين نشوفه كل كل هذا عدي
+
+382
+00:32:12,270 --> 00:32:16,740
+رجعتله نيجي هذا السؤال هذا حلوبراو عليكي بشبيه
+
+383
+00:32:16,740 --> 00:32:21,540
+السؤال أخدناه ذاكرين المبنى؟ أبو خمستاشر طابق و لا
+
+384
+00:32:21,540 --> 00:32:25,580
+خلتوه تلات طوابق اللي بينهم ذاكرينه؟ تمام هذا نفس
+
+385
+00:32:25,580 --> 00:32:31,400
+المبنى 45 متر المرة هيك هذه الحجر خبطناها مظبوط؟
+
+386
+00:32:31,400 --> 00:32:34,280
+خبطناها هيك المرة هذه بده اخبطه بزاوية صار ال
+
+387
+00:32:34,280 --> 00:32:39,000
+project in motion اذا بيقولي a stone نفس الحجر is
+
+388
+00:32:39,000 --> 00:32:42,260
+a throne from the top of a building هذه ال
+
+389
+00:32:42,260 --> 00:32:47,610
+building و أنا قبفتهأبوارد at an angle of 30
+
+390
+00:32:47,610 --> 00:32:51,510
+degree to the horizontal اذا ان انا قذفته مش لفوق
+
+391
+00:32:51,510 --> 00:32:56,330
+او لزاوية نقضارها 30 درجة تمام؟ with an initial
+
+392
+00:32:56,330 --> 00:33:00,890
+speed والسبيد 20 متر per second قبل ما اكمل مش
+
+393
+00:33:00,890 --> 00:33:04,930
+احنا بهيمن العلمات؟ بدنا نجيب علامات اول حاجة اشوف
+
+394
+00:33:04,930 --> 00:33:08,900
+العشرين هادي هل العشرين هادي ثنية ولا صادية؟إذا
+
+395
+00:33:08,900 --> 00:33:12,320
+أول خطوة بدي أعملها إيش؟ أحللها، ودى التحليل لحاله
+
+396
+00:33:12,320 --> 00:33:16,400
+بياخد اتنين من عشرة، إذا أول خطوة في هذه الأسئلة
+
+397
+00:33:16,400 --> 00:33:20,600
+بدي أحلل الصراع الكدائية، إذا مش محللة، تمام، إذا
+
+398
+00:33:20,600 --> 00:33:24,900
+أنا هجيت عشان أحل يا بنات، هه، طبعا كتبت هنا، بس
+
+399
+00:33:24,900 --> 00:33:26,520
+عشان أرتب المسألة
+
+400
+00:33:33,430 --> 00:33:39,670
+Vinitial X Vinitial Cos فيتا وبتساوي عشرين Cos
+
+401
+00:33:39,670 --> 00:33:43,610
+تلاتين وبتساوي سبعت عشر point تلاتة متر per second
+
+402
+00:33:44,960 --> 00:33:50,400
+هي أول واحدة التانية V-initial Y سوى V-initial سين
+
+403
+00:33:50,400 --> 00:33:54,060
+الثيتا سين التلاتين نص وهذه عشرين عشرة متر per
+
+404
+00:33:54,060 --> 00:33:57,620
+second هاي أول خطوة لازم أعملها في كل أسئلة رابو
+
+405
+00:33:57,620 --> 00:34:00,940
+جاك تلموشي أول حاجة بتطلع عليه الصراع الابتدائية
+
+406
+00:34:00,940 --> 00:34:05,180
+إذا أعطانيها بدي أحللها لسني صاضية طب مرات بيقولي
+
+407
+00:34:05,180 --> 00:34:10,760
+أنا قدفتها بالشكل الأفقيالصادية سفر والثانوية
+
+408
+00:34:10,760 --> 00:34:15,160
+للدنية الرقم تمام؟ إذا في الآخر أنا قلتله هذه كذا
+
+409
+00:34:15,160 --> 00:34:20,120
+وهذه سفر إذا أنا حللت وبرضه أخدت العالمتين اتفجنا
+
+410
+00:34:20,120 --> 00:34:25,200
+يا بنات؟ حلو أكمل السؤال the height from which the
+
+411
+00:34:25,200 --> 00:34:29,940
+stone is thrown is 45 meters above the ground وقال
+
+412
+00:34:29,940 --> 00:34:35,220
+لهذه تقريبا تعمل 15 طابق مشكلة اتفجنا؟ مش مشكلةقال
+
+413
+00:34:35,220 --> 00:34:40,120
+لي هيا انضرب و نزل نزل نزل لمواصل الأرض صح؟ و انا
+
+414
+00:34:40,120 --> 00:34:42,380
+حطت ال origin قال لي مانت شايف انا حطتك ال origin
+
+415
+00:34:42,380 --> 00:34:48,500
+هنا هالجت على مواصل الأرض كدهش موضعه؟ سالب خمسة و
+
+416
+00:34:48,500 --> 00:34:52,900
+أربعين لأنه تحت ال origin فانا واقتفرج نشوف إيش
+
+417
+00:34:52,900 --> 00:34:59,640
+بدهHow long does it take the stone to reach the
+
+418
+00:34:59,640 --> 00:35:06,140
+ground؟ زمن وصوله للأرض زمن طيب الزمن سيني ولا
+
+419
+00:35:06,140 --> 00:35:11,140
+صاضي لا هيك لا هيك أول أعمل test هذه المعادلة
+
+420
+00:35:11,140 --> 00:35:14,360
+الوحيدة الغلبانة أشوفها بتخدمني ولا لا قلتله اطلع
+
+421
+00:35:14,360 --> 00:35:20,240
+فيها زمن لكن هذه بعرفهابعرفهاش إذا بتخدمنيش شوف
+
+422
+00:35:20,240 --> 00:35:24,240
+غيرها زمان ممكن أحشعته من هنا و لا لأ حلو اللي
+
+423
+00:35:24,240 --> 00:35:28,180
+تطلع عليها الحلوه هادي واي فاينال ماقصه خمسة
+
+424
+00:35:28,180 --> 00:35:33,400
+واربعين وواي إينيشيال سفر وواي إينيشيال هديهياك
+
+425
+00:35:33,400 --> 00:35:39,460
+عشرة واتيه بديها والجيه بعرفها ضبطت طلعت المظلوم
+
+426
+00:35:39,460 --> 00:35:46,360
+إذا بقوله ايه هاي ايهبقوله Y5 ناقص Y initial
+
+427
+00:35:46,360 --> 00:35:51,960
+بتساوي V Y initial في T ناقص half GT تربيع كتبت
+
+428
+00:35:51,960 --> 00:35:56,920
+القانون قلتله هذه عبارة عن ناقص خمسة واربعين ناقص
+
+429
+00:35:56,920 --> 00:36:03,920
+سفر بتساوي عشرة T ناقص نص الهادي أربعة و تسعة نص
+
+430
+00:36:03,920 --> 00:36:07,820
+التسعة و تمانية T تربيع قال هذه معادلة من الدرجة
+
+431
+00:36:07,820 --> 00:36:11,760
+التانية واحد يجي يقولي والله أنا بنساه بقوله أنا
+
+432
+00:36:11,760 --> 00:36:16,440
+بغش شكيا في الامتحانانسى براحتك لو انت في الدار
+
+433
+00:36:16,440 --> 00:36:19,100
+تقدر تجيبه القانون تبقى على درجة تانية ولا لأ
+
+434
+00:36:19,100 --> 00:36:23,620
+القانون العام تمام اعتبر حالك في الدار شاحته من
+
+435
+00:36:23,620 --> 00:36:26,780
+أخوك اللي بياخده في الصف اللي مش عارف اي صف او
+
+436
+00:36:26,780 --> 00:36:32,620
+أختك تمام؟ و دلعنا الزمن قلت له T طلعت 4.22
+
+437
+00:36:32,620 --> 00:36:35,080
+seconds حلناه
+
+438
+00:36:36,790 --> 00:36:40,650
+حتى القانون العام لو انسيتوه بنسمحكم بنعليق بديكم
+
+439
+00:36:40,650 --> 00:36:43,490
+إياه قانون العام تبع الحالة طبعا في معادلات
+
+440
+00:36:43,490 --> 00:36:48,030
+مابتدهاش قانون عام بتنحلل بنمجص أخدتوا أيامها طبعا
+
+441
+00:36:48,030 --> 00:36:52,250
+احنا بنحاول نجيبلكوش شغلة تاخد وجد قانون عام
+
+442
+00:36:52,250 --> 00:36:56,730
+وغلبها هذه الشغلات طلعت الزمن وصدقناك وطلعناه احكي
+
+443
+00:37:00,460 --> 00:37:04,300
+القانون العام بين K ذاكر القانون العام اللي T
+
+444
+00:37:04,300 --> 00:37:07,800
+بيساوي سلب بي زاد أو ناقص يجب تربيع الى بي تربيع
+
+445
+00:37:07,800 --> 00:37:14,070
+ناقص 4A C ع 2A ده كان أنا سمحتك تنسيهأنا سامع حاجة
+
+446
+00:37:14,070 --> 00:37:18,770
+تنسيها، بس بتعرفش A وB وC؟ A معامل X تربية أو B
+
+447
+00:37:18,770 --> 00:37:24,070
+معامل X وC تخر؟ مظلومة لأ؟ إذا إيش ما يكون يكون،
+
+448
+00:37:24,070 --> 00:37:27,130
+إن شاء الله يكون جرود، القول العام بيجيبه، تمانية
+
+449
+00:37:27,130 --> 00:37:31,750
+بنتين؟ حلو، طلعتي لك T، أي أول مقلوب، إيش بده
+
+450
+00:37:31,750 --> 00:37:38,150
+الكيماء؟ What is the speed of the stone؟just
+
+451
+00:37:38,150 --> 00:37:41,430
+before it strike the ground قبل ما يضرب الأرض
+
+452
+00:37:41,430 --> 00:37:47,950
+مباشرة سرعة النهائية طيب اتطلع و ايش كاتب what is
+
+453
+00:37:47,950 --> 00:37:53,010
+the speed لو جلك what is the velocity تفرج ايه
+
+454
+00:37:53,010 --> 00:37:58,870
+معناه speed ايوة اذا انك بتفرج لو رحنا اقوم و اقول
+
+455
+00:37:58,870 --> 00:38:01,110
+ايش معناه speed اقوم و اقول سرعة ايش معناه
+
+456
+00:38:01,110 --> 00:38:04,410
+velocity سرعة لكن احنا من أسبابنا اتعلمنا ان ال
+
+457
+00:38:04,410 --> 00:38:08,920
+speed و السرعة و ال velocity ماذا يبعدطيب .. منفع
+
+458
+00:38:08,920 --> 00:38:13,040
+أجيب ال speed بدون معرف ال velocity؟ لأ لأن ال
+
+459
+00:38:13,040 --> 00:38:17,320
+speed مقدار ال velocity زي ما تقولي بدي مقدار
+
+460
+00:38:17,320 --> 00:38:21,140
+vector بقولك بديمي ال vector صح ولا لأ؟ اذا انا
+
+461
+00:38:21,140 --> 00:38:25,480
+بدي اول حاجة اجيب ال velocity هي ال velocity اكم
+
+462
+00:38:25,480 --> 00:38:28,800
+مركبة بتتوقع تنتهي .. تنتهي .. تنتهي .. تنتهي ..
+
+463
+00:38:28,800 --> 00:38:29,320
+تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي
+
+464
+00:38:29,320 --> 00:38:30,060
+.. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي ..
+
+465
+00:38:30,060 --> 00:38:33,420
+تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي
+
+466
+00:38:33,420 --> 00:38:33,700
+.. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي ..
+
+467
+00:38:33,700 --> 00:38:41,530
+تنتهي .. تنتبقول له V X Final ايش علاقتها بال X
+
+468
+00:38:41,530 --> 00:38:51,030
+initial نفسها طموحيها يوردين أسعابها وانا لو
+
+469
+00:38:51,030 --> 00:38:55,050
+كتبتها دي كمان مره ايه علامات بقول له اه اليك
+
+470
+00:38:55,050 --> 00:38:59,950
+علامة احكي الجزء لما تكون V X Final نزلت من نفس
+
+471
+00:38:59,950 --> 00:39:08,810
+الزاوية لأنك بيه sign كتابة طيب نزلت من ..وين هذه
+
+472
+00:39:08,810 --> 00:39:12,950
+انا عارفه ايش عوضت اه
+
+473
+00:39:12,950 --> 00:39:23,410
+اه حسب وين مش بالضرورة مش بالضرورة انا ايش عوضت
+
+474
+00:39:23,410 --> 00:39:29,590
+قلت هجيت هذه 17.3 فانت تاكل ال cosine مش رقم طيب
+
+475
+00:39:29,590 --> 00:39:35,210
+هذا رقم هذه 720 دقيقة سنية مسموح تتغير؟ عادة
+
+476
+00:39:35,210 --> 00:39:42,150
+للأولى اه اه لأ اهرقم ال V لحالة تمام هي عيب الدرع
+
+477
+00:39:42,150 --> 00:39:46,130
+زي مهينة فتكمل ال feta بتختلف حسب ال feta الجديدة
+
+478
+00:39:46,130 --> 00:39:52,530
+هجيت هادي اعملتش عشان اجيبها و لا انا بس نجلت جولت
+
+479
+00:39:52,530 --> 00:39:56,050
+بس مجرد ليش انا بديك علامات عليها عشانك بتأكدلي
+
+480
+00:39:56,050 --> 00:40:00,400
+معلومة فيزيائية ان الصراع الصيني لا تتغيرصح؟ انه
+
+481
+00:40:00,400 --> 00:40:03,000
+نهائية ولا تدائية ضي بعض ولا لأ؟ هذه معلومة
+
+482
+00:40:03,000 --> 00:40:07,640
+فيزيائية تبليها واخد عليها علامات ايه ضال؟ بتدي
+
+483
+00:40:07,640 --> 00:40:12,280
+الصادية النهائية الصادية النهائية هيها مش انت
+
+484
+00:40:12,280 --> 00:40:18,500
+جيبتي توي وقلت 4.22 اذا بقدر اقول VY final بتسوي
+
+485
+00:40:18,500 --> 00:40:24,060
+VY initial نقش G في T اللي بتسوي هذه عشرة نقس تسعة
+
+486
+00:40:24,060 --> 00:40:29,170
+point تمانية في أربع point two twoجدش طلعت بالسالب
+
+487
+00:40:29,170 --> 00:40:33,910
+جدش نجلوني واحد تلاتين point تلاتة meter per
+
+488
+00:40:33,910 --> 00:40:41,050
+second طلعت سالب لها معنى ولا مالهاش معنى انها لا
+
+489
+00:40:41,050 --> 00:40:45,630
+أسفل اه لإن واحد يقول لأ احنا علمونا السالب نرفضه
+
+490
+00:40:45,630 --> 00:40:49,370
+هذا الزمن صح او لا هذه لأ بالعكس لو طلعت موجة
+
+491
+00:40:49,370 --> 00:40:55,270
+برفضهالأنه نازله لأنه نازله هدى جبته و هدى جبته
+
+492
+00:40:55,270 --> 00:41:03,030
+بقل رجول V final طالعه متساوي 17.3 I ناقص 31.3 J
+
+493
+00:41:03,030 --> 00:41:08,370
+مثل البرسكند ولا لأ؟ لو جالي اودي دي ال velocity
+
+494
+00:41:08,370 --> 00:41:14,330
+بقوله خلص السؤال صح لو جالي velocity خلص لكن بده
+
+495
+00:41:14,330 --> 00:41:17,830
+أثبيت هذا بده بال magnitude لكن لو جالي اودي دي ال
+
+496
+00:41:17,830 --> 00:41:21,400
+velocity بقوله يعطيني العافية خلص السؤالصحيحيك ولا
+
+497
+00:41:21,400 --> 00:41:26,580
+لأ؟ بدي ال magnitude .. إيه؟ سهل جزر .. هذا ربي
+
+498
+00:41:26,580 --> 00:41:30,800
+تربية و هذا تربية و بشتغله حتى لو كان في عشاء
+
+499
+00:41:30,800 --> 00:41:34,980
+بالرب ع ولا لأ؟ و هذي نفس العملية بقدر أجيب ال
+
+500
+00:41:34,980 --> 00:41:37,820
+velocity من التقانون التالت بس يجب أن أحط سلب مني
+
+501
+00:41:37,820 --> 00:41:43,180
+أنا هان؟ هذي قصدية؟ اه يجب أن أحط السلب أنا؟ براو
+
+502
+00:41:43,180 --> 00:41:51,390
+عليك تمامحلو إذا معناته طلعت أنا الزمن و روحت جيبت
+
+503
+00:41:51,390 --> 00:41:55,710
+الصاضية و قولتله السلب يعني down و قولتله ال X هدا
+
+504
+00:41:55,710 --> 00:42:02,970
+هي هي هي جيبلي speed سؤال سهل خلصنا
+
+505
+00:42:02,970 --> 00:42:07,750
+أي صفر صار نرجع
+
+506
+00:42:12,970 --> 00:42:16,090
+طبعا انا ماعرفش انتوا عندكم محلول مرة واحدة اظنني
+
+507
+00:42:16,090 --> 00:42:20,170
+هذا المثال انا هنا محلول مرتين واتفجت مع الشباب
+
+508
+00:42:20,170 --> 00:42:23,190
+انه هذا الحل التاني عشان مش مكتوب عينكم هحطه على
+
+509
+00:42:23,190 --> 00:42:27,790
+مجموعة الواتس عشان مايقعدوش تصوروا يعني و تتعبوا
+
+510
+00:42:27,790 --> 00:42:31,150
+حياتكم و تكتبوا ورايا الحل الأولان هو حل الكتاب
+
+511
+00:42:31,150 --> 00:42:34,230
+اللي بين يديكم الكتاب هيك حالة انا عم بدي أحل
+
+512
+00:42:34,230 --> 00:42:39,750
+بطريقة أسهل ايش أسوي يا بنات طبعا كان بدي أحله أول
+
+513
+00:42:39,750 --> 00:42:54,760
+اشوف السؤال ايش بيقولنشفح السؤال وبعدين نحله نفض
+
+514
+00:42:54,760 --> 00:43:02,420
+اللوح عشان الصح صح نحنا وياكم اتطلع
+
+515
+00:43:02,420 --> 00:43:07,100
+يا بنادر واحدة اخر الحياطة معها برودة بدها تطخها
+
+516
+00:43:07,100 --> 00:43:12,800
+الجلمبدها تصيده اول ما تطلع الارصاصة من البروضة
+
+517
+00:43:12,800 --> 00:43:17,720
+انا بتفلّت الجلام هجيت هي بدها تنشّن في البداية
+
+518
+00:43:17,720 --> 00:43:21,580
+عشان تصيب الجلام للواحدة الأولى بتقولك انا مديش هو
+
+519
+00:43:21,580 --> 00:43:24,800
+نشّن على الجلام بدي اعمل حساب انه بدي ينزل اه
+
+520
+00:43:24,800 --> 00:43:30,360
+بقولها لا هو مين اللي بديه ينزل الجلام مش انا ايه
+
+521
+00:43:30,360 --> 00:43:34,220
+عشان يخليه ينزل للأعلى انا بتفلته تصارع الجاذبية
+
+522
+00:43:34,220 --> 00:43:40,690
+طب هي البروضةالارصاصة لما طلعت الجاذبية بدهاش تأثر
+
+523
+00:43:40,690 --> 00:43:45,450
+عليها، إذا هتنزلها. إذا المعنى تقول إيه بتسوي اللي
+
+524
+00:43:45,450 --> 00:43:52,690
+بعيدة؟ بدها تنش على الجلم و هو واقف. و انا ساعتها
+
+525
+00:43:52,690 --> 00:43:57,390
+بدي أنزل. المسافة العمودية اللي نزلوا الجلم،
+
+526
+00:43:57,390 --> 00:44:02,390
+البرودة هتنزله، الارصاصة هتنزله، إذا هيصيبوا بعض،
+
+527
+00:44:02,390 --> 00:44:08,030
+بدون ما تعملوا حسابات نزول الجلم.مش مصدق زي ما انت
+
+528
+00:44:08,030 --> 00:44:13,090
+مش مصدقه لأ بدي أثبت هذا الكلام من حياتك بدي أثبت
+
+529
+00:44:13,090 --> 00:44:18,770
+نقرأ السؤال أول بيقول لأ projectile projectile
+
+530
+00:44:18,770 --> 00:44:21,690
+مقضوة في رصاصة طوي قلت عنها انا مش انا بدي أقضفها
+
+531
+00:44:21,690 --> 00:44:25,690
+a projectile is fired at a target هدف اللي هو
+
+532
+00:44:25,690 --> 00:44:31,860
+القلبتمى in such a way that the projectile leaves
+
+533
+00:44:31,860 --> 00:44:35,180
+the gun at the same time the target is dropped
+
+534
+00:44:35,180 --> 00:44:38,640
+from rest اذا اول ما الارصاصة طلعت من البرودة انت
+
+535
+00:44:38,640 --> 00:44:41,900
+فالتي تيدك اذا نبدأ الحركة بالنفس اللحظة ولا لأ
+
+536
+00:44:41,900 --> 00:44:47,380
+واحد حركته projectile اللي هي الارصاصة والجلم لما
+
+537
+00:44:47,380 --> 00:44:53,390
+انزله حركة سقوط حر ولا لأ سقوط حرحلو show that
+
+538
+00:44:53,390 --> 00:44:58,950
+اثبت that if the gun is initially aimed اذا
+
+539
+00:44:58,950 --> 00:45:05,170
+الارصاصة وجهتها خطتها في اتجاه aimed at the
+
+540
+00:45:05,170 --> 00:45:09,910
+stationary target عند القلم لم يكن واقف انت وجهتها
+
+541
+00:45:09,910 --> 00:45:15,670
+على القلم وهو واقف stationary يعني ثابت target the
+
+542
+00:45:15,670 --> 00:45:18,770
+projectile hits the falling target as shown in the
+
+543
+00:45:18,770 --> 00:45:23,970
+figureطيب ليش انا جربت على السيارة و الشرطي
+
+544
+00:45:23,970 --> 00:45:28,070
+ذاكرينهم لما الشرطي لاحق السيارة واحد كان في قانون
+
+545
+00:45:28,070 --> 00:45:30,210
+السوري التاني كان في انصرات ولا كانوا في نفس
+
+546
+00:45:30,210 --> 00:45:35,650
+الموقع اذا عشان الارصاصة تخبط الهدف لازم يكونوا في
+
+547
+00:45:35,650 --> 00:45:41,630
+نفس الموقع ولا لا حلو جالي هاي راسمتيأنا بدي أثبت
+
+548
+00:45:41,630 --> 00:45:47,010
+إني أنا وجهتها هيك، ها، هيها، ماعملتش حساب نزولها،
+
+549
+00:45:47,010 --> 00:45:50,710
+تمام؟ هجيت وين اتجابلوا؟ قولتله اتجابلوا ها، هجيت
+
+550
+00:45:50,710 --> 00:45:54,590
+هذا الارتفاع تبع الحمرة اللي هو ال target و لا تبع
+
+551
+00:45:54,590 --> 00:45:58,750
+الزرقة، بيختلفوا عن بعض، إذن هي ترك السؤال إن why
+
+552
+00:45:58,750 --> 00:46:06,440
+لا الحمرة و why لا الزرقة واحد، تمام؟ أنا هذاخط
+
+553
+00:46:06,440 --> 00:46:11,500
+لما جيت وهذه الخط بتعتبر الزاوية ثيتا وهذه زاوية
+
+554
+00:46:11,500 --> 00:46:14,060
+الخط Alpha ده بتثبتلي أن Alpha و Theta زي بعض
+
+555
+00:46:14,060 --> 00:46:19,040
+Alpha و Theta زي بعض هاي اللي بدي أثبته كيف كده
+
+556
+00:46:19,040 --> 00:46:22,560
+Alpha و Theta هجيت Theta الشي هي زاوية انطلاق
+
+557
+00:46:22,560 --> 00:46:27,460
+الرصاصة Alpha هي الزاوية اللي بيعملها الخط ما بين
+
+558
+00:46:27,460 --> 00:46:33,090
+الرصاصة و ال target هو واقفمش انا هيك عملتها هجيت
+
+559
+00:46:33,090 --> 00:46:38,410
+انا هيك .. هيك نشنتها هجيت هذه الزاوية، إيش هي؟
+
+560
+00:46:38,410 --> 00:46:42,410
+زاوية انطلاق الرصاصة والزاوية اللي بيعملها الخط
+
+561
+00:46:42,410 --> 00:46:48,990
+هذا مع ال .. مع ال X-axis، هي هي طيب، بنثبت، لكن
+
+562
+00:46:48,990 --> 00:46:52,090
+بتقدروا تقولوا إيه؟ فلتوكوا من project in motion
+
+563
+00:46:52,090 --> 00:46:57,410
+هذا الخط أنا مددته هيكبتقدر تقولي تاني الزاوية
+
+564
+00:46:57,410 --> 00:47:02,130
+بيساوي مقابل ع مجاور؟ هذا المقابل بتاعتبره H؟
+
+565
+00:47:02,130 --> 00:47:07,890
+بالفعل؟ إذا بتقدر تقولي إنه تام الـ Alpha بيساوي H
+
+566
+00:47:07,890 --> 00:47:13,550
+على XX هذه المسافة كلها؟ صح ولا لأ؟ تمام، نيجي،
+
+567
+00:47:13,550 --> 00:47:19,390
+هالجيت، فانتقم الهدف بعدين ونعود عليها هذا اللي هو
+
+568
+00:47:19,390 --> 00:47:26,170
+الـ Target الهدف كيف بيمشي سقوط حر؟صح؟ وهذا الـ
+
+569
+00:47:26,170 --> 00:47:31,270
+projectile ليه صح صح الـ projectile
+
+570
+00:47:31,270 --> 00:47:35,530
+هيك عملنا لما قلنا سيارة و قلنا trooper ذاكرين
+
+571
+00:47:35,530 --> 00:47:40,110
+وهذه عملنا نفس العملية هذا سقوط حر قلت له في
+
+572
+00:47:40,110 --> 00:47:44,050
+السقوط الحر كان فيه قانون بيقول Y final نقص Y
+
+573
+00:47:44,050 --> 00:47:49,270
+initial بتسوي V initial Y أو بدون هذه حتى مهمش T
+
+574
+00:47:49,270 --> 00:47:54,840
+تربيع T نقص half GT تربيعتطلعولي على الجلام اللى
+
+575
+00:47:54,840 --> 00:48:01,180
+كان بيدى كده سرعته الابتدائية؟ سفر مش انا بدفلته
+
+576
+00:48:01,180 --> 00:48:07,520
+اذا سرعته الابتدائية سفر ولا لأ تمام هداك من وين
+
+577
+00:48:07,520 --> 00:48:11,800
+بدأ الجلام بدأ من هذه النقطة ولا لأ اذا Y initial
+
+578
+00:48:11,800 --> 00:48:14,860
+بتسوي H ولا لأ اذا هذا H
+
+579
+00:48:19,310 --> 00:48:27,930
+اللي هو Y هذي H وهذه Y بتساوي هذي كم قلنا سفر ناقص
+
+580
+00:48:27,930 --> 00:48:43,110
+نص GT تربيع تمام هيك؟ حلو أي شي صح سعيد معايا؟
+
+581
+00:48:45,500 --> 00:48:49,580
+الوعي انيش اه انا اتعكس طب اه اه اه اه نقص اتش
+
+582
+00:48:49,580 --> 00:48:56,460
+صحيح اه تمام تمام
+
+583
+00:48:56,460 --> 00:49:00,040
+يا سامي بقى ال menu بنعيده المرة الجاية بديش اعوك
+
+584
+00:49:00,040 --> 00:49:00,520
+دكتورنا
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/4GxkJ1fxBBI_raw.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/4GxkJ1fxBBI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..377a2adbcb3c3c3fa5b2055476f08b19993da756
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/4GxkJ1fxBBI_raw.srt
@@ -0,0 +1,2384 @@
+1
+00:00:05,090 --> 00:00:10,410
+تمام يا بنات نستأنف اللي بدناه chapter رقم أربعة و
+
+2
+00:00:10,410 --> 00:00:14,150
+اللي قلنا تقريبا معلومات chapter اتنين بدنا نعيدها
+
+3
+00:00:14,150 --> 00:00:20,950
+بس على two copies واحدة صينية و واحدة صادية حكينا
+
+4
+00:00:20,950 --> 00:00:27,430
+ان الحركة باتجاهين او الحركة المستوية نتعامل معاها
+
+5
+00:00:27,430 --> 00:00:34,090
+على انها حركة صينية X motion و
+
+6
+00:00:34,090 --> 00:00:34,730
+Y motion
+
+7
+00:00:38,680 --> 00:00:43,200
+وحكينا لو كانت التصاروح ثابت معناته التصاروح
+
+8
+00:00:43,200 --> 00:00:48,040
+بمركبتين تبعته الصينية ووساطية ثوابت وبالتالي
+
+9
+00:00:48,040 --> 00:00:54,860
+بيصير في عندي قوانين VX final بتساوي VX initial
+
+10
+00:00:54,860 --> 00:01:01,230
+زاد EX في الـT مظبوط ولا لأ؟وفي عندي x final مخص x
+
+11
+00:01:01,230 --> 00:01:07,630
+initial بتسوي vx initial في t زي نص ax في t تربية
+
+12
+00:01:07,630 --> 00:01:14,190
+وكما في قانون عندي vx final تربية بتسوي vx initial
+
+13
+00:01:14,190 --> 00:01:20,830
+تربية زي اتنين ax x final مخص x initial نفس
+
+14
+00:01:20,830 --> 00:01:25,370
+القوانين اللي بكتبهم للحركة الصادريةاذا بتكون في
+
+15
+00:01:25,370 --> 00:01:30,230
+عندى حركتين ثينية وصاضية وكل سؤال عبارة عن سؤالين
+
+16
+00:01:30,230 --> 00:01:36,980
+ثيني وصاضي مين المشترك بينالتنتين الزمن مش هيك
+
+17
+00:01:36,980 --> 00:01:42,160
+اتفقنا؟ بدي نيجي الأن إيش في أمثلة طبيعية لحركة
+
+18
+00:01:42,160 --> 00:01:46,280
+مستوية قاللي حركة المقظوفات إذا ن project ال
+
+19
+00:01:46,280 --> 00:01:52,000
+motion هجيت إيش تعريف حركة المقظوفات؟ بنقول أي جسم
+
+20
+00:01:52,000 --> 00:01:59,590
+بتقظفه و بتفلطه لما تفلطه مين بده يتحكم فيهغير
+
+21
+00:01:59,590 --> 00:02:03,350
+الجاذبية الأرضية، مش فيه غير الجاذبية الأرضية، إذن
+
+22
+00:02:03,350 --> 00:02:07,670
+هذه بنسميها حركة المغضوفات. لو نيجي نتذكر ما هو
+
+23
+00:02:07,670 --> 00:02:13,810
+تعريف السقوط الحر، هو جسم مين بيأثر فيه فقط، برضه
+
+24
+00:02:13,810 --> 00:02:18,050
+تسارع الجاذبية الأرضية، إذن تعريف السقوط الحر و
+
+25
+00:02:18,050 --> 00:02:22,560
+تعريف ال projectile motion نفس الشيء.طب إيش مفروجة
+
+26
+00:02:22,560 --> 00:02:27,100
+عن بعض؟ جال في السقوط الحر كنت أنا أشتريت أن تكون
+
+27
+00:02:27,100 --> 00:02:31,940
+الصراع الابتدائية لا لا أعلى لا لا أسفل بس ممنوع
+
+28
+00:02:31,940 --> 00:02:38,380
+تكون بزاوية معينة بمعنى آخر الصراع الابتدائية إذا
+
+29
+00:02:38,380 --> 00:02:42,750
+إلها مركبة سينية بقول هذا project in motionإذا
+
+30
+00:02:42,750 --> 00:02:48,010
+مركبتها الصينية سفر بقول سقوط حُر بمعنى آخر السقوط
+
+31
+00:02:48,010 --> 00:02:52,090
+الحُر هو projectile motion بس حالة خاصة إذا ال
+
+32
+00:02:52,090 --> 00:02:57,470
+projectile motion هو بحتوي تلقائيا من السقوط الحُر
+
+33
+00:02:57,470 --> 00:03:02,760
+نجي نشوف إيش بعرفه بقول if a particleGiven an
+
+34
+00:03:02,760 --> 00:03:07,460
+initial velocity اعترطة سرعة ابتدائية and then
+
+35
+00:03:07,460 --> 00:03:13,360
+follows above اتبعت مصار هذا المصار مين بتحتتم فيه
+
+36
+00:03:13,360 --> 00:03:17,740
+determined only by gravity يحدده فقط الجاذبية
+
+37
+00:03:17,740 --> 00:03:22,780
+الأرضية we have projected motion تمام نذكر chapter
+
+38
+00:03:22,780 --> 00:03:30,690
+2 تسارع الجاذبية الأرضيةكيف اتجاهه؟ لأسفل سيني ولا
+
+39
+00:03:30,690 --> 00:03:37,730
+صاضي؟ صاضي إذا معناته في حركة المقذوفات التصارع
+
+40
+00:03:37,730 --> 00:03:45,770
+تبعي فقط صاضي ولا لأ؟ مش هيك؟ ليه حتى السالب؟لأنه
+
+41
+00:03:45,770 --> 00:03:52,430
+لازفر وحطيت J لأنه عمودي لو إجتفالتكم الآن من هذه
+
+42
+00:03:52,430 --> 00:03:58,350
+المعلومات جديش EX لحركة المغضوب فعلا يا عيني عليكم
+
+43
+00:04:00,640 --> 00:04:06,900
+إذاً حركة المغذوفات هي عبارة عن حركتين صينية
+
+44
+00:04:06,900 --> 00:04:11,560
+بتسارع سفر وصادية بتسارع الجاذبية الأرضية ولا لأ
+
+45
+00:04:11,560 --> 00:04:17,400
+كما يعني معناته هذه القوانين سارية المفعول إيش بده
+
+46
+00:04:17,400 --> 00:04:24,280
+يحط محل EX؟ سفر إذاً هذه روحت صح؟ وهذه EX روحت
+
+47
+00:04:24,280 --> 00:04:32,660
+وهذه EX روحتليه يتطلع؟ هذه و هذه إخوة، هذه VX
+
+48
+00:04:32,660 --> 00:04:36,220
+Final بيستوي VX Initial، ربه حقيا كادى، إذا هذا
+
+49
+00:04:36,220 --> 00:04:38,780
+القانون هو نفسه هذا القانون، هذا مابش لازم يعمل
+
+50
+00:04:38,780 --> 00:04:43,700
+مرة، ليه نقول إيش ده بيقول؟ بيقول لما تقوللي
+
+51
+00:04:43,700 --> 00:04:46,840
+الصراعة الإبتدائية الصينية هي نفسها النهائية، يعني
+
+52
+00:04:46,840 --> 00:04:51,560
+الصراعة الصينية بتتغير؟ثابتة سرعة الصينية ليش؟ قال
+
+53
+00:04:51,560 --> 00:04:56,920
+لي أصل مافيش تسارع صيني والتسارع تعني تغير سرعة
+
+54
+00:04:56,920 --> 00:05:01,940
+إذا السرعة ماتغيرتش فهي تسارع وإذا مافيش تسارع
+
+55
+00:05:01,940 --> 00:05:07,780
+مسموح للسرعة تتغير؟ لأ إذا السرعة الصينية ثابتة
+
+56
+00:05:07,780 --> 00:05:11,040
+هذا القانون أخدناه في الصف الرابع ابتدائي المسافة
+
+57
+00:05:11,040 --> 00:05:13,940
+بالسواء سرعة بزمن وهذا القانون صار المفقود طول
+
+58
+00:05:13,940 --> 00:05:19,270
+مافيش تسارعوهيسر المفعول مسافة بساوي سرعة عظمة بس
+
+59
+00:05:19,270 --> 00:05:24,510
+سينى سينى جال الصابر جالي وين في a y حط محلها سالب
+
+60
+00:05:24,510 --> 00:05:29,290
+g مظبوطا لا نجرى القوانين المناظرة يا بنات بقوله
+
+61
+00:05:29,290 --> 00:05:37,230
+هنا v y final بساوي v y initial كان زائد a y بيصيه
+
+62
+00:05:37,230 --> 00:05:44,780
+سالب gوهنا بدّي الـ X تلحق وطوار Y final نقص Y
+
+63
+00:05:44,780 --> 00:05:50,880
+initial بيساوي VY initial في T ناقص نص GT تربيع و
+
+64
+00:05:50,880 --> 00:05:58,220
+VY final تربيع ساوي VY initial تربيع ناقص 2G وY
+
+65
+00:05:58,220 --> 00:06:03,320
+final نقص Y initial هذه حركة المغضوفات إذا حركة
+
+66
+00:06:03,320 --> 00:06:08,060
+المغضوفات هي مجموعة حركتين حركة سينية بسرعة ثابتة
+
+67
+00:06:08,700 --> 00:06:14,340
+وحركة صادية سقوط حُر بتسارع الجاذبية الأرضية يعني
+
+68
+00:06:14,340 --> 00:06:19,500
+سقوط حُر تمام؟ تمام إذا إيش بيقوللي؟ بيقوللي as
+
+69
+00:06:19,500 --> 00:06:23,420
+the acceleration of gravity is always straight
+
+70
+00:06:23,420 --> 00:06:27,340
+downward وهذه معلومة كنا بنعرفها تمام؟ with a
+
+71
+00:06:27,340 --> 00:06:31,700
+magnitude of G the acceleration of a projectile
+
+72
+00:06:31,700 --> 00:06:39,430
+كتبت هذا بيعني أنههذا يعني أن محرك البردكتيل يمكن
+
+73
+00:06:39,430 --> 00:06:47,790
+أن يكون مجموح عركتين من محركة رقميةحركة عمودية
+
+74
+00:06:47,790 --> 00:06:51,990
+تصاروحها بالساوي سالب جي وعارفين ليش حطينا السالب
+
+75
+00:06:51,990 --> 00:06:55,470
+عشان انا كل حاجة الأعلى positive وكل حاجة الأسفل
+
+76
+00:06:55,470 --> 00:07:01,150
+سالبة and a horizontal motion with no acceleration
+
+77
+00:07:01,150 --> 00:07:05,610
+no acceleration بتعني constant velocity ولا لأ تمى
+
+78
+00:07:05,610 --> 00:07:08,370
+جالي لو اعتبرت هدول القوانين اللي انا كتبتهم
+
+79
+00:07:08,370 --> 00:07:11,790
+هيكتبهم على اعتبار ان هو اعتبر هنا x initial و y
+
+80
+00:07:11,790 --> 00:07:17,450
+initial صفر تمىهدول القوانين عرفناهم هو بما نفسه
+
+81
+00:07:17,450 --> 00:07:22,470
+هذا وهذا ما أصلا مش قانون هذه معلومة انه مافيش
+
+82
+00:07:22,470 --> 00:07:26,510
+تصارع صيني بتعني انه الصراع الصينية ابتدائية ولا
+
+83
+00:07:26,510 --> 00:07:29,910
+نهائية بتفرق لأ و هذا القانون الوحيد اللي موجود
+
+84
+00:07:29,910 --> 00:07:36,690
+مسافة بتصارع صراع في زمن ده ما بقوللي
+
+85
+00:07:36,690 --> 00:07:42,990
+لو إيدي اتطلعت هذي شايفين القانون بدي أخد الزمن
+
+86
+00:07:42,990 --> 00:07:49,810
+منهبقدر أقول T بتسوي X Final نقص X Initial على VX
+
+87
+00:07:49,810 --> 00:07:56,790
+Initial صح ولا لأ؟ قال يحملي هذا وعوضه هنا هتجيبلك
+
+88
+00:07:56,790 --> 00:08:03,230
+معادلة بين Y و X صح؟ لإنه بدّل T إيش بده أجيب؟X
+
+89
+00:08:03,230 --> 00:08:08,670
+قاللي لو اتيت عوضت ال T من هذه المعادلة و حطيتها
+
+90
+00:08:08,670 --> 00:08:15,030
+في هذه المعادلة هتطلع هكذا معادلة قاللي هذه الطلاب
+
+91
+00:08:15,030 --> 00:08:18,210
+قالوا أخدناها و الطالبات قالوا ما أخدناش لسه أنا
+
+92
+00:08:18,210 --> 00:08:21,690
+شوف الطالبات التانين إيش بقولوا معادلة زي هذه Y
+
+93
+00:08:21,690 --> 00:08:30,970
+بتساوي AX-BX تربيع معادلة إيش هذه؟ اللي هي قطة
+
+94
+00:08:30,970 --> 00:08:38,020
+مكافئةبسموه بارابولا سمعتوا كلمة بارابولا بارابولا
+
+95
+00:08:38,020 --> 00:08:44,420
+ماخدتوش في القلب كل لحظة جديد طيب اذكركم فيها هذه
+
+96
+00:08:44,420 --> 00:08:51,760
+او هذهطبعا ممكن هادي و هادي نسميها برابولة قطعة
+
+97
+00:08:51,760 --> 00:08:56,580
+مكافئة بيسموها تمام جالي معناته ايش بقول بقول هادي
+
+98
+00:08:56,580 --> 00:08:58,660
+انت ايش بتجيب قولتله انا هادي بجيبلك حركة
+
+99
+00:08:58,660 --> 00:09:03,880
+المقذوفات جالي معناته المقذوفات تتبع مسار شكله هيك
+
+100
+00:09:03,880 --> 00:09:10,380
+يعني كل جسميقدف لازم يتبع بربولا مش عشوائي هكذا
+
+101
+00:09:10,380 --> 00:09:14,480
+المعاجلة جابت رياضيات احنا مابدناش .. مابدناش صفات
+
+102
+00:09:14,480 --> 00:09:18,960
+لا بربولا ولا حاجة بس بدنا نحط في مخنا كلمة بربولا
+
+103
+00:09:18,960 --> 00:09:22,620
+معناط قطعة مكافئة هتاخدوها في ال Calculus هتاخدوها
+
+104
+00:09:22,620 --> 00:09:28,680
+هؤلاء الشباب هاخدوها قبلكم؟ معاكم؟ أخدتوها؟ المهم
+
+105
+00:09:28,680 --> 00:09:34,860
+هي شكلهايعني أي جسم بأقضفه يا بنات، أي جسم بأقضفه،
+
+106
+00:09:34,860 --> 00:09:38,300
+مش اللي بده يحدد مصاره الجاذبية الأرضية، معناته
+
+107
+00:09:38,300 --> 00:09:43,640
+مصاره هيه، نمنجكت، شايفينه؟ هذا هو المصار، خلّيني
+
+108
+00:09:43,640 --> 00:09:47,820
+أقول جزء من دائرة، هيك بده يكون مصاره، من هنا
+
+109
+00:09:47,820 --> 00:09:54,220
+أطلقته، هذه النقطة أقصى ارتفاع ولا لأ؟وصل هنا
+
+110
+00:09:54,220 --> 00:09:59,600
+اتطلعوا قذفته بزاوية معينة هجيت انا هاي قذفته
+
+111
+00:09:59,600 --> 00:10:03,280
+بزاوية معطوه المعطية بتقدروا هذه الصورة الابتدائية
+
+112
+00:10:03,280 --> 00:10:07,900
+تجيبلولي مراكبتينها الصينية والصادية هاي مراكبة
+
+113
+00:10:07,900 --> 00:10:10,900
+الصينية وهي الصادية هجيت هذه المراكبة الصينية
+
+114
+00:10:10,900 --> 00:10:17,710
+مسموح انها تتغير؟ لأطب حلو مصاصحين انت قلتوا ممنوع
+
+115
+00:10:17,710 --> 00:10:22,790
+تتغير عند أقصى ارتفاع في حركة المغلوفات كده السرعة
+
+116
+00:10:22,790 --> 00:10:27,430
+ال Y صفر بس ال X ثابت بيه هنا اللي قال صفر غلط
+
+117
+00:10:27,430 --> 00:10:32,850
+ثابت ليه؟ لأن في مراكبة سنية موجودة اذا ال Y الصفر
+
+118
+00:10:33,440 --> 00:10:39,200
+والصينية موجودة بمعنى آخر لو أديكم في ال quiz عند
+
+119
+00:10:39,200 --> 00:10:43,000
+أقصى ارتفاع في حركة المقضوفات أول خيار بيقول Zero
+
+120
+00:10:43,000 --> 00:10:46,060
+عشان تتعلموا عليه و تقولوا غلط ال Y هو Zero إذن هو
+
+121
+00:10:46,060 --> 00:10:50,480
+مش Zero طب بيجي سؤال تاني بيقولك السرعة الإبتدائية
+
+122
+00:10:50,480 --> 00:10:54,700
+في حركة المقضوفات وكتبلك هذه العلاقة V initial
+
+123
+00:10:54,700 --> 00:11:00,040
+وحطت هيك بتساوي خمسة I زائد تلاتة J متر per second
+
+124
+00:11:01,110 --> 00:11:04,050
+هذه حركة .. هذه حركة المغلوفات وهذه السرعة
+
+125
+00:11:04,050 --> 00:11:08,450
+الأبتدائية بدي أسأل عند أقصى ارتفاع كده السرعة؟
+
+126
+00:11:08,450 --> 00:11:11,750
+أبسط ليش؟
+
+127
+00:11:11,750 --> 00:11:18,670
+صح؟ لأنه بس الصينية طب كده الصينية؟ خمسة بتتغير؟
+
+128
+00:11:18,670 --> 00:11:23,870
+لأ إذا في بداية أو عند أقصى ارتفاع أو نهاية كده؟
+
+129
+00:11:23,870 --> 00:11:28,870
+خمسة أبسط تحكي فجد صح؟ كأن في مجتمع الجبل لو كان
+
+130
+00:11:28,870 --> 00:11:32,220
+..لو كان سفر فالاسم يكون المركبات اللي بيبقى
+
+131
+00:11:32,220 --> 00:11:36,220
+واضحة؟ هذا لو كان سفر ومي جالك سفر؟ وانا بقولك عند
+
+132
+00:11:36,220 --> 00:11:41,280
+أقصى ارتفاع جديش السرعة إذا جلت سفر بقوللي غلط مش
+
+133
+00:11:41,280 --> 00:11:46,740
+سفر إذا اللي عند أقصى ارتفاع جديش السرعة مش سفر مش
+
+134
+00:11:46,740 --> 00:11:50,340
+سفر إيه جالهوا ليه؟ خمسة جالوا خمسة ماجلوايه
+
+135
+00:11:50,340 --> 00:11:58,820
+السفر؟ ممنوع تقولي سفرولا مرة ..ولا مرة ..ولا مرة
+
+136
+00:11:58,820 --> 00:12:05,520
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+137
+00:12:05,520 --> 00:12:05,560
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+138
+00:12:05,560 --> 00:12:05,960
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+139
+00:12:05,960 --> 00:12:05,960
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+140
+00:12:05,960 --> 00:12:06,160
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+141
+00:12:06,160 --> 00:12:07,180
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+142
+00:12:07,180 --> 00:12:10,880
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+143
+00:12:10,880 --> 00:12:16,040
+..ولا مرة ..ولا مرة
+
+144
+00:12:16,040 --> 00:12:22,740
+..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة ..ولا مرة
+
+145
+00:12:23,540 --> 00:12:26,480
+لأ مش هلأ هو فى بس اللى هو المحور السيني اللى هو
+
+146
+00:12:26,480 --> 00:12:34,500
+الـG الـG سفر طلع لكن كلها سفر لأ الزنية عشان كده
+
+147
+00:12:34,500 --> 00:12:38,740
+لما حكيتلك هنا طلعيهتجيب على هذه السرعة التدعية
+
+148
+00:12:38,740 --> 00:12:43,120
+هنضع أقصى التفاح هذه بصير سفر لكن هذه تتغيرش إذا
+
+149
+00:12:43,120 --> 00:12:45,980
+جدتش سرعة عندها أقصى التفاح بقوله خمسة ضلت الصينية
+
+150
+00:12:45,980 --> 00:12:51,340
+الصادية روحت عشان كده تطلع هي السهم شايفينه هجيت
+
+151
+00:12:51,340 --> 00:12:55,780
+هذا هيجو من أطول هذا ولا هذا مش هذا أطول معناته
+
+152
+00:12:55,780 --> 00:13:00,570
+الصادقال الصيني زي ما هوطلع انت من النقطة الصاضي
+
+153
+00:13:00,570 --> 00:13:05,650
+ضال روح الصاضي الصيني زي ما هو الصيني زي ما هو
+
+154
+00:13:05,650 --> 00:13:10,250
+الصيني زي ما هو الصاضي قاعد بيغير لأنه في تصارع
+
+155
+00:13:10,250 --> 00:13:14,930
+صاضي و التصارع الصاضي بيعني تغير الصراع الصاضية و
+
+156
+00:13:14,930 --> 00:13:19,750
+معدم وجود التصارع الصيني بيعني ان المركبة الصينية
+
+157
+00:13:19,750 --> 00:13:29,400
+ممنوعة تتغير تمام يا بنات؟ أي استفسار؟ تمام؟الان
+
+158
+00:13:29,400 --> 00:13:33,680
+العنوان ايش بيقول horizontal range and maximum
+
+159
+00:13:33,680 --> 00:13:37,660
+height of a projectile بدنا نشتغل قانونين ممنوع
+
+160
+00:13:37,660 --> 00:13:42,360
+نحفظهم مش مطلوب مننا نحفظهم وانا بقول مش مطلوب مش
+
+161
+00:13:42,360 --> 00:13:47,420
+مطلوب ممنوع نحفظهم اقوى من انه مش مطلوب بمعنى اخر
+
+162
+00:13:47,420 --> 00:13:51,260
+لو واحد جال ال range وروحت انا بصين حافظ القانون
+
+163
+00:13:51,260 --> 00:13:57,070
+وحطته وعوضت بجبلهوش لكي يشتقوا من اولهو محطوطين
+
+164
+00:13:57,070 --> 00:14:06,550
+قوانين لكن ممنوع تحفظهم تمى نرجع للرسمة هل جيت انا
+
+165
+00:14:06,550 --> 00:14:10,430
+و اتفقت اي حاجة في حركة المغضب فات بدي اجسمها
+
+166
+00:14:10,430 --> 00:14:17,010
+لنصين صح سيني و صعديكل المعطيات بدك تعرف ليها
+
+167
+00:14:17,010 --> 00:14:21,850
+سينية ولا صادية والمطاليب بتطلع انت ايش طالب سيني
+
+168
+00:14:21,850 --> 00:14:26,230
+ولا صادي اذا انت طالب حاجة سينية باجيها صح ولا لأ
+
+169
+00:14:26,230 --> 00:14:29,930
+واذا انت طالب حاجة صادية باجيها هجيت لما يقوللي
+
+170
+00:14:29,930 --> 00:14:34,190
+maximum height ارتفاع اقولكم سيني ولا صادي why اذا
+
+171
+00:14:34,190 --> 00:14:38,230
+why اذا انت هنا بدوا ال range ال range ايش معناته
+
+172
+00:14:38,230 --> 00:14:42,850
+ال مدى اذا بدوا مسافة سينية ولا لأ اذا انت هنا
+
+173
+00:14:43,510 --> 00:14:48,750
+اتفجنا هيك؟ حلو جالي طيب انت هذه الصراع الابتدائية
+
+174
+00:14:48,750 --> 00:14:54,230
+بدي أعطيك إياها هذي سنية أم صادية؟إذاً بدي أحللها
+
+175
+00:14:54,230 --> 00:14:59,930
+الشغل اللي مش جسمها chapter 3 تعلمتك إياه عشان
+
+176
+00:14:59,930 --> 00:15:04,410
+تعرف كيف تحلل أي vector ولا لأ إذاً أول خطوة بدك
+
+177
+00:15:04,410 --> 00:15:09,810
+تعملها الآن عشان تجيب ال range الصورة الإبتدائية
+
+178
+00:15:09,810 --> 00:15:17,010
+جسم ليها نصين يعني حللها بقوله بسيطة V initial
+
+179
+00:15:17,010 --> 00:15:23,550
+الصينية هي V initial cos θو Vinitial الصعبية
+
+180
+00:15:23,550 --> 00:15:30,330
+Vinitial Sine فيتا مظلوط ولا لأ تم ايش بدك قال لي
+
+181
+00:15:30,330 --> 00:15:33,930
+بدي ال maximum height اول حاجة بدي ال maximum
+
+182
+00:15:33,930 --> 00:15:37,270
+height في الرسم مابينا ال maximum height تو ايه
+
+183
+00:15:37,270 --> 00:15:40,310
+عايش اختلافنا ان عند ال maximum height ايش هو
+
+184
+00:15:40,310 --> 00:15:46,670
+السفر؟الـ VY Final الـ VY مش الـ V ما هو مش السرعة
+
+185
+00:15:46,670 --> 00:15:50,990
+الكلية الـ VY صح ولا .. قللي شوفلي هالقانون الحلو
+
+186
+00:15:50,990 --> 00:15:55,690
+هذا إيش بدك تعوض هنا عند maximum height؟ سفر هذا
+
+187
+00:15:55,690 --> 00:16:00,870
+.. هاي .. بظبط؟ VY Final مقص VY Initial انت بدأت
+
+188
+00:16:00,870 --> 00:16:04,350
+من هنا VY Initial هو سفر و VY Final هو H ال
+
+189
+00:16:04,350 --> 00:16:08,390
+maximum height صح ولا لا؟ إذا يلا نعود أنا وياكم
+
+190
+00:16:08,390 --> 00:16:20,490
+هذه سفرفاح ولا لأ ها دي هيها V initial sin θ كل
+
+191
+00:16:20,490 --> 00:16:26,210
+تربية معقز اتنين G و Y final هي H و Y initial صفر
+
+192
+00:16:26,210 --> 00:16:33,890
+لكل مسح صحيح تمام ايش بده قلتله بدي H بدك احسن من
+
+193
+00:16:33,890 --> 00:16:41,710
+هيك معاجلة تجيبلك H هاي HH بيتساوي V initial تربيع
+
+194
+00:16:41,710 --> 00:16:48,130
+Sine تربيع F تعة 2G صحيك ولا لأ؟ هذا و هي طلعته
+
+195
+00:16:48,130 --> 00:16:54,810
+القانون اللي ممنوع نحفظه و ممنوع نحفظه اتفجنا؟ بنا
+
+196
+00:16:54,810 --> 00:16:59,430
+نتطلع عليه بس، مسموح نتطلع عليه؟ في sign ولا فيش
+
+197
+00:16:59,430 --> 00:17:04,630
+sign؟ جديش أكبر قيمة للـSign؟ واحد، لو جالك أكبر
+
+198
+00:17:04,630 --> 00:17:11,670
+قيمة للـH جديش؟يعني V initial تربيه على 2G صح؟
+
+199
+00:17:11,670 --> 00:17:18,090
+يعني لما هذه تكون واحد هذه sign ايش تزاوية اللي
+
+200
+00:17:18,090 --> 00:17:22,190
+signها واحد تسعين يعني بيقوللي اقصى ارتفاع بيكون
+
+201
+00:17:22,190 --> 00:17:26,170
+لما اتطلعه هيك ولا لأ لما يكون عمودي منطق ولا مش
+
+202
+00:17:26,170 --> 00:17:32,950
+منطق هذا منطق خلصت طبعا تطلعوا انتوا انا واحد
+
+203
+00:17:32,950 --> 00:17:35,970
+بيقوللي طب ليش انت ماروحتش شينماهي why بقوله عشان
+
+204
+00:17:35,970 --> 00:17:39,790
+فيها زمن وزمن ما بعرفوشفبالتالي هذه المعاجلة
+
+205
+00:17:39,790 --> 00:17:45,510
+تخدمني و احد للمعاجلة هذه طب نيجي لل range ال
+
+206
+00:17:45,510 --> 00:17:50,570
+range يعني بده X صح ولا قاللي هيها X هيها مافيش
+
+207
+00:17:50,570 --> 00:17:56,810
+أحلى منها فيها زمن ولا فيش طب أنا بعرفش الزمن طب
+
+208
+00:17:56,810 --> 00:18:01,270
+في معاجلة غيرها هو عشان أروح عليها هنا طلع شوية
+
+209
+00:18:01,270 --> 00:18:05,250
+هنا ماكانش في زمن واحد شوفت معاجلة تانية هنا في
+
+210
+00:18:05,250 --> 00:18:09,770
+الصين اللي كان معاجله فيهفي غيرها؟ إذا غصب من عنك
+
+211
+00:18:09,770 --> 00:18:13,690
+بتكشل لها هذه المعادلة بتخليها تخدمك احكيها الجهة
+
+212
+00:18:13,690 --> 00:18:18,250
+تجيك T من أول معادلة Y؟ الـG عادة ها هجيت الـT غصب
+
+213
+00:18:18,250 --> 00:18:21,850
+من عنك بتدول عليها فأنا عجالة في عندي معلومة بيقول
+
+214
+00:18:21,850 --> 00:18:26,730
+الزمن بيصحلك تشحتها من ال Y منظر ل .. لأن الزمن
+
+215
+00:18:26,730 --> 00:18:33,130
+سيني ولا صاضي؟أذا بإمكاني أخده من الصديق ولا لا؟
+
+216
+00:18:33,130 --> 00:18:37,450
+قاللي تقدر تاخدها من هناك كيف أخدها من هناك؟ بدي و
+
+217
+00:18:37,450 --> 00:18:40,590
+اي final و بدي و اي initial؟ قاللي هنا عند النقطة
+
+218
+00:18:40,590 --> 00:18:43,030
+هذه مين يقولي أشهر اهدافيات النقطة هذه؟ Zero Zero
+
+219
+00:18:43,030 --> 00:18:44,210
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+220
+00:18:44,210 --> 00:18:48,970
+Zero Zero Zero Zero Zero
+
+221
+00:18:48,970 --> 00:18:54,750
+Zero Zero Zero Zero
+
+222
+00:18:54,750 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+223
+00:18:55,110 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+224
+00:18:55,110 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+225
+00:18:55,110 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+226
+00:18:55,110 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+227
+00:18:55,110 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+228
+00:18:55,110 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+229
+00:18:55,110 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+230
+00:18:55,110 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+231
+00:18:55,110 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+232
+00:18:55,110 --> 00:18:55,110
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+233
+00:18:55,110 --> 00:18:55,230
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+234
+00:18:55,230 --> 00:18:59,210
+ZeroR و 0 R و 0 نفترض الـ R عشرة بقول عشرة و صفر
+
+235
+00:18:59,210 --> 00:19:03,030
+ولا لأ اذا هذه إحداثية عشرة و صفر نركز على
+
+236
+00:19:03,030 --> 00:19:06,930
+الإحداثية الصاضية الإحداث الصاضي لهذه كده و هذه
+
+237
+00:19:06,930 --> 00:19:12,190
+صفر و صفر زي الصاضي إذا لما بدي أعود هنا صفر ناخد
+
+238
+00:19:12,190 --> 00:19:19,450
+صفر صح؟ و لا تحكي الصيني تمام انت قلت بدا نشحت
+
+239
+00:19:19,450 --> 00:19:26,080
+الزمن منها صح؟ وبالتالي من العودماذا يسمى الـ y
+
+240
+00:19:26,080 --> 00:19:34,060
+final؟ صفر y initial صفر بتساوي v و هنا أنا و هذه
+
+241
+00:19:34,060 --> 00:19:43,700
+y اذا v initial sin θ في t ناقص نص g صحيك؟ في حد
+
+242
+00:19:43,700 --> 00:19:48,240
+ماعرفش يجيب ال t هلجيت؟ جسم المعادلة على t عشان
+
+243
+00:19:48,240 --> 00:19:55,170
+اطير هذه و اطير هذهطلّع الـ T إذا الـ T اللي بتدور
+
+244
+00:19:55,170 --> 00:20:00,810
+عليها صفر مقال صفر صفر اه يحصل بعدين اتنين V
+
+245
+00:20:00,810 --> 00:20:07,130
+Initial Sine of Theta على Y الزمن اللي انغلبك جبته
+
+246
+00:20:07,130 --> 00:20:13,290
+ولا ماتبتهوش الان بتجيه الجهاد X Final هي R ال
+
+247
+00:20:13,290 --> 00:20:20,790
+range X Initial صفر صح بتسوي V Initial Cosine of
+
+248
+00:20:20,790 --> 00:20:30,490
+Thetaبدي الـ T هيا مظبوط؟ حط اتنين V initial sin
+
+249
+00:20:30,490 --> 00:20:36,930
+فيتا V initial في V initial اذا بيساوي V initial
+
+250
+00:20:36,930 --> 00:20:41,350
+تربية اتنين sin فيتا cos فيتا ايش القدرة في مخهم؟
+
+251
+00:20:41,350 --> 00:20:48,050
+sin اتنين فيتا اذا هذه sin اتنين فيتا على G هاي ال
+
+252
+00:20:48,050 --> 00:20:54,850
+range اللي بتدور عليه وبرضه ممنوعنا نحفظهاتفجنا بس
+
+253
+00:20:54,850 --> 00:20:59,970
+برضه مسموح نتطلع عليه ما هي أكبر قيمة لل range لما
+
+254
+00:20:59,970 --> 00:21:06,150
+sin 2θ تسوى 1 اللي هي V initial تربيع على G طب هي
+
+255
+00:21:06,150 --> 00:21:11,570
+sin 2θ و احنا بنعرف ان ال theta sin 90 هو الواحد
+
+256
+00:21:11,570 --> 00:21:15,690
+اذا لازم θ تكون 45 ولا لأ عشان كده بيقوللي ايش
+
+257
+00:21:15,690 --> 00:21:20,520
+بيقوللي يا ترى لو بدك أكبر rangeكيف تحط الزاوية
+
+258
+00:21:20,520 --> 00:21:25,920
+بقوله 45 وانت مغمض صح ولا لأ اذا انت نشن على زاوية
+
+259
+00:21:25,920 --> 00:21:32,900
+45 بتحصل على اكبر range ممكن صحيح ولا لأ تمام طبعا
+
+260
+00:21:32,900 --> 00:21:35,640
+انتوا زمان اخدتوا في الرياضيات في التفاضل و
+
+261
+00:21:35,640 --> 00:21:39,120
+التكامل في توجيهي لما تجيبوا الشغل عشان تكون ال
+
+262
+00:21:39,120 --> 00:21:43,600
+function اكبر او اصغر ذاكرين هو تطبيقات التفاضل
+
+263
+00:21:43,600 --> 00:21:47,880
+مااخدتوهاش في توجيهي لما
+
+264
+00:21:47,880 --> 00:21:56,410
+يكون عنكمخلّيني اكتب Y بديش اكتب صد Y بيتساوي 2X
+
+265
+00:21:56,410 --> 00:22:01,790
+تربيع زي 3X و لو سألكم ماهي قيمة X اللي بتخلي Y
+
+266
+00:22:01,790 --> 00:22:06,630
+اكبر ما يمكن او اصغر مايمكن ايش كنتوا تسووا كنتوا
+
+267
+00:22:06,630 --> 00:22:11,010
+تشتقوا و تسووا بصفر قال يعني لو هد اشتقتوا بالنسبة
+
+268
+00:22:11,010 --> 00:22:16,550
+للثيتا و سويتوا بصفر هيطلع عندك ثيت 45 قصب عنك صح؟
+
+269
+00:22:17,310 --> 00:22:25,070
+لكن هذا كلكلس خلصناه تبع توجيهي تمام حلو إذا ال
+
+270
+00:22:25,070 --> 00:22:30,730
+maximum height أول حاجة عملتها حللت السرعة
+
+271
+00:22:30,730 --> 00:22:34,930
+الإبتدائية إلى سنية وصادية ولا لأ بقت كده بقوله at
+
+272
+00:22:34,930 --> 00:22:41,170
+the maximum height الشي هو السفر السرعة الصادية هي
+
+273
+00:22:41,170 --> 00:22:48,790
+السفر بقول using the equation حطيت طلعت الهذه ال
+
+274
+00:22:48,790 --> 00:22:52,810
+range قال لي to find the range we need the time
+
+275
+00:22:52,810 --> 00:22:55,970
+لأنه قال لي هذه المعادلة بتجيب ال range فيها زمان
+
+276
+00:22:55,970 --> 00:23:00,330
+بتجيز زمان we need the time of a flight زمان
+
+277
+00:23:00,330 --> 00:23:04,410
+الطيران يعني زمان الكل تمام nothing that for the
+
+278
+00:23:04,410 --> 00:23:07,590
+total time of a flight while finally بتساوي سفر
+
+279
+00:23:07,590 --> 00:23:12,290
+ذكيني الرسم اللي راحت سفر و سفر كان هنا وصار هنا
+
+280
+00:23:12,290 --> 00:23:17,010
+برغم انه اتحرك لكن اتحرك مسافة أفقية مسافة عمودية
+
+281
+00:23:17,010 --> 00:23:17,550
+لا احكي
+
+282
+00:23:20,200 --> 00:23:23,620
+في ال .. مش هيك VY اصلا ايوة VY في وين ال سفر ال Y
+
+283
+00:23:23,620 --> 00:23:28,460
+سفر كمان ال Y سفر ال Y سفر؟ لأ انت حسبتها لأ وين
+
+284
+00:23:28,460 --> 00:23:32,020
+مش عندها اقصر تفهة و مين جالك هدى عندها اقصر تفهة
+
+285
+00:23:32,020 --> 00:23:36,540
+هدى
+
+286
+00:23:36,540 --> 00:23:42,900
+وين هدى لمّا كان عوضت هدى هدى عوضت على سفر هدى هدى
+
+287
+00:23:42,900 --> 00:23:48,770
+عوضت على سفرهنا عوضت مع ال wi-fi من الديل اتف اي
+
+288
+00:23:48,770 --> 00:23:50,690
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+289
+00:23:50,690 --> 00:23:51,030
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+290
+00:23:51,030 --> 00:23:51,450
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+291
+00:23:51,450 --> 00:23:51,610
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+292
+00:23:51,610 --> 00:23:56,150
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+293
+00:23:56,150 --> 00:23:56,250
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+294
+00:23:56,250 --> 00:24:02,190
+وين وين وين وين وين وين وين وين وين
+
+295
+00:24:02,190 --> 00:24:02,190
+وين وين وين وين وين وين وين وين وين وين وين وين
+
+296
+00:24:02,190 --> 00:24:12,910
+وين وين وين وين وين وين وين وين
+
+297
+00:24:12,910 --> 00:24:17,150
+وينطبقايا نكون جنبها ايه لو انا بدي احطهم جنب بعض
+
+298
+00:24:17,150 --> 00:24:22,550
+تمام؟ حلو احكي ليش لما جينا الزمن ماعوضش في
+
+299
+00:24:22,550 --> 00:24:28,230
+القانون الأول ها؟ هو انت ايش بدك؟ تمام انت جيبت
+
+300
+00:24:28,230 --> 00:24:34,690
+الزمن من ها ايش مطلوب؟ X ولا V؟ Y؟ ايش مطلوب منك؟
+
+301
+00:24:34,690 --> 00:24:41,130
+ال range ايش هو؟ ال X ليش ماعرفها؟ ماجيبوا من ها
+
+302
+00:24:41,130 --> 00:24:47,800
+مدذك حلوبتعرفى هادى؟ كدهش؟ من جده كان اقصى ارتفاع؟
+
+303
+00:24:47,800 --> 00:24:52,820
+انا بدي زمان لكله مش انا بدي زمان لكله؟ هل السرعة
+
+304
+00:24:52,820 --> 00:24:56,440
+النهائية لما وصل الارض عرفها انت؟ عشان كده ماعرفتش
+
+305
+00:24:56,440 --> 00:25:02,240
+اخده لإنه the why final يا بنكي هادى ماعرفهاش واحد
+
+306
+00:25:02,240 --> 00:25:04,760
+يقول طب جيه بيه اقصى ارتفاع وضروف اتنين مش دايما
+
+307
+00:25:06,130 --> 00:25:11,210
+صح؟ انا مدي ال rage من نقطة البداية للنهاية صح؟
+
+308
+00:25:11,210 --> 00:25:14,990
+معاتو بدي الزمن من نقطة البداية للنهاية بعرف
+
+309
+00:25:14,990 --> 00:25:19,250
+السرعة الصادية عند النهاية؟ بعرفش، اذا نهاية
+
+310
+00:25:19,250 --> 00:25:23,590
+تخدمني المعادلة، تخدمنيش، بقدرش اجيب منها، لأنه في
+
+311
+00:25:23,590 --> 00:25:32,450
+شغلات مجاهية غير الزمن، عرفتي ليش؟ غيرها، لأ،
+
+312
+00:25:32,450 --> 00:25:37,720
+ذاكرة لما قلتلكم ان هي القانون هادا ع من مخكم؟لأ
+
+313
+00:25:37,720 --> 00:25:43,560
+ممكن تدرسوكوا هذه حالة خاصة .. هذه حالة خاصة زمان
+
+314
+00:25:43,560 --> 00:25:48,420
+السقوط لا يساوي زمان الهبوط وقلنا على أيام الشباب
+
+315
+00:25:48,420 --> 00:25:54,600
+قلتهم امحوا هذا القانون من مخكم وانا قلتلكم هذا مش
+
+316
+00:25:54,600 --> 00:26:01,790
+قانون تمامإذا جبت ال T من هذا القلول لأن كله بعرفه
+
+317
+00:26:01,790 --> 00:26:05,370
+إلا ال T لكن عايز قلون تاني في شغلات تانية مش
+
+318
+00:26:05,370 --> 00:26:11,150
+معروفة طلعت ال T و منها طلعت ال range و قال كلنا
+
+319
+00:26:11,150 --> 00:26:19,330
+بنعرف أن sin θ بتسوى 1 لما θ تسوى 90 درجة عند 2 θ
+
+320
+00:26:19,330 --> 00:26:25,090
+يعني θ تكون 45 درجة تمامThis is because the
+
+321
+00:26:25,090 --> 00:26:30,250
+maximum value of sin 2θ is 1 And this occurs لما
+
+322
+00:26:30,250 --> 00:26:37,770
+2θ تسوى 90 أو تسوى 45 أه، لحد الآن ماشي الأمور؟
+
+323
+00:26:37,770 --> 00:26:44,330
+ماشي الأمور، شوفها لك وزاد قال لي شوفلي خمس حجار
+
+324
+00:26:44,330 --> 00:26:51,450
+بدي أضربهم بنفس ال speed لكن ب directions مختلفة
+
+325
+00:26:51,450 --> 00:26:57,980
+شايفين الزوايا؟كل واحد له زاوية خاصة بيه تمام؟ إيش
+
+326
+00:26:57,980 --> 00:27:02,160
+بده؟ بيقولي أ projectile launched أطلقات from the
+
+327
+00:27:02,160 --> 00:27:05,140
+origin كلهم هايهم الخمسة طالعين من النقطة نفسها
+
+328
+00:27:05,140 --> 00:27:09,540
+صحيح؟ واحد، اتنين، تلاتة، أربعة، خمسة from the
+
+329
+00:27:09,540 --> 00:27:14,560
+origin with the same initial speed بصحيح اللي يقول
+
+330
+00:27:14,560 --> 00:27:20,410
+ليه؟ with the same initial velocity؟ ليش؟لأنه
+
+331
+00:27:20,410 --> 00:27:25,610
+اتجاهات مختلفة إذا جالي speed بصحله لأنه نفترض
+
+332
+00:27:25,610 --> 00:27:29,030
+خمسة كلهم خمسة بس واحد بيعمل زي و تلاتي و واحد
+
+333
+00:27:29,030 --> 00:27:32,430
+بيعمل زي و خمستاشر و واحد خمسة و أربعين فبسمحله
+
+334
+00:27:32,430 --> 00:27:35,310
+يقولي initial speed لكن ممنوع يقولي initial
+
+335
+00:27:35,310 --> 00:27:38,090
+velocity لأنه لو جالي initial velocity بقوله الراص
+
+336
+00:27:38,090 --> 00:27:42,610
+مابتقولش هيك الراص مابتقولش هيك صح ولا لأ طيب
+
+337
+00:27:42,610 --> 00:27:47,190
+initial speed but at various angles زوايا مختلفة
+
+338
+00:27:47,190 --> 00:27:51,540
+زي ما تشايفينFor which of the launch angles the
+
+339
+00:27:51,540 --> 00:27:55,060
+time of flight is the largest؟ قال لمين من هدول
+
+340
+00:27:55,060 --> 00:27:58,740
+هياخد أكبر الزمن عشان يصل للأرض؟ شفين الزمن شفته؟
+
+341
+00:27:58,740 --> 00:28:00,360
+ايوه و احنا قاعدين نتطلع
+
+342
+00:28:03,110 --> 00:28:06,870
+معناته بيعتمد ع فيتا ولا لا كل ما فيتا كبرت كل ما
+
+343
+00:28:06,870 --> 00:28:10,750
+صينها كبر و أكتر حد لما يصير تسعين إذا بتتوقعوا
+
+344
+00:28:10,750 --> 00:28:15,230
+مين أكبر واحد؟ الخمسة وسبعين حسب هذا القانون اللي
+
+345
+00:28:15,230 --> 00:28:20,230
+by chance جيبنا احنا وياكم إذا بيقولي هتكون الخمسة
+
+346
+00:28:20,230 --> 00:28:23,310
+أش ولا الخمسة واربعين الخمسة واربعين الأكبر إيه
+
+347
+00:28:23,310 --> 00:28:29,030
+تدري ببالكم مش أكبر زمان ولا خمسة وسبعين ولا كلهم
+
+348
+00:28:29,030 --> 00:28:34,670
+مزعج ولا واحدة منهم خمسة وسبعينخمس صح شجلشي و براو
+
+349
+00:28:34,670 --> 00:28:37,290
+عليكي يعني هيجيكم سؤال عالمودي مرة أكبر إشي و مرة
+
+350
+00:28:37,290 --> 00:28:42,450
+أقل إشي لأنه احنا بنكرر السؤال بتغيير صيغة بسيطة
+
+351
+00:28:42,450 --> 00:28:47,770
+صحين يا بنات تمام بيجينا نشوف هالكوزين ورا بعض
+
+352
+00:28:47,770 --> 00:28:52,490
+نشوفهم صحين ولا لأ بيقولي in a projectile motion
+
+353
+00:28:52,490 --> 00:28:57,170
+projectile motion حركة مغنوفات صح ولا لأ كيف
+
+354
+00:28:57,170 --> 00:29:02,730
+تصاروحات تجاههعمودي لأسفل في حد مش عارف المعلومة
+
+355
+00:29:02,730 --> 00:29:07,330
+دي ده ما تشوفش السؤال بيقول in a projectile motion
+
+356
+00:29:07,330 --> 00:29:11,870
+at what point عند أي نقطة أثناء الحركة along the
+
+357
+00:29:11,870 --> 00:29:15,870
+path أثناء مسار تبع الحركة اللي هو بربه لتفقنا
+
+358
+00:29:15,870 --> 00:29:20,990
+ذاكرين are the velocity and the acceleration
+
+359
+00:29:20,990 --> 00:29:25,390
+vectors are perpendicular to each other ايش عن ال
+
+360
+00:29:25,390 --> 00:29:30,950
+perpendicular؟ حلوأول نروح تسارع في حدا مختلف
+
+361
+00:29:30,950 --> 00:29:36,230
+عليه؟ كيف اتجاهه؟ لأسفة لأسفة بدي عند أي نقطة
+
+362
+00:29:36,230 --> 00:29:42,590
+السرعة بتكون أفقية عند أقصى الارتفاع لأن هذا صادق
+
+363
+00:29:42,590 --> 00:29:45,150
+بيقول لي بدي السرعة تكون عمودية على الصادق إيش
+
+364
+00:29:45,150 --> 00:29:49,110
+يعني؟ سينية يعني السرعة تكون بس سينية بس سينية
+
+365
+00:29:49,110 --> 00:29:51,630
+بيقولي عند أقصى الارتفاع لأنه في مراكبة صادقة
+
+366
+00:29:51,630 --> 00:29:55,390
+للسرعة عند أقصى الارتفاع أذن مين بدي يكون؟ هذا هو
+
+367
+00:30:01,720 --> 00:30:04,600
+مش معاكم ال z و بعدين project of motion بيصيب ال z
+
+368
+00:30:04,600 --> 00:30:08,340
+في fireworks فاتغلبيش حالك ميدناش نخش في التفاصيل
+
+369
+00:30:10,060 --> 00:30:14,340
+هل the launch point يعني نقطة البداية الانطلاق ولا
+
+370
+00:30:14,340 --> 00:30:18,320
+هي نقطة ال landing point landing يعني هبوط نقطة
+
+371
+00:30:18,320 --> 00:30:21,500
+الهبوط ولا the highest point ولا ولا فيه نقطة ال
+
+372
+00:30:21,500 --> 00:30:26,000
+highest point تمام شوف السؤال بدي أكرره أغير كلمة
+
+373
+00:30:26,000 --> 00:30:30,200
+في السؤال بدي كلمة perpendicular بدي أحط parallel
+
+374
+00:30:30,200 --> 00:30:36,980
+أطلع السؤال إيش بيصير؟ وكتيش السرعة بتكون فقط
+
+375
+00:30:36,980 --> 00:30:39,600
+صادية وين؟
+
+376
+00:30:41,010 --> 00:30:45,210
+فكر منيحا ولا
+
+377
+00:30:45,210 --> 00:30:51,430
+مرة ولا في نقطة عند نقطة البداية بتكون عند أقصى
+
+378
+00:30:51,430 --> 00:30:54,490
+ارتفاع بيكونوا مش اتفاقنا بـ Urban Declar و عند
+
+379
+00:30:54,490 --> 00:30:59,330
+اللي هو Note برضه بيكون الناس في زاوية مظلوط هيك
+
+380
+00:30:59,330 --> 00:31:03,310
+ولا لأ؟ هاي الرسمة ها نتذكر مع بعض بعيننا الله
+
+381
+00:31:03,310 --> 00:31:07,990
+هادى الرسمة هى نعيدها وين هاجد بايدها؟
+
+382
+00:31:11,330 --> 00:31:19,090
+هل السرعة صدية؟ لأ، السرعة صدية؟ السرعة صدية؟ اذا
+
+383
+00:31:19,090 --> 00:31:21,410
+هذه النقطة و لا هذه النقطة و لا هذه النقطة؟ ولا
+
+384
+00:31:21,410 --> 00:31:27,070
+واحدة، اذا nowhere، اذا الجواب الصح عرفتوا كيف
+
+385
+00:31:27,070 --> 00:31:30,770
+السؤال طالع ايش غيرنا؟ كل ما غيرنا في السؤال صار
+
+386
+00:31:30,770 --> 00:31:38,130
+جواب nowhere كله
+
+387
+00:31:38,130 --> 00:31:40,090
+سامع عربي و لا في حد سامع صيني؟
+
+388
+00:31:43,200 --> 00:31:49,530
+عربي؟ تمه .. انشوف اي سئلةجالي هذا example 4.3
+
+389
+00:31:49,530 --> 00:31:55,050
+الكتاب مغلبنا جايب السؤال صائب في البداية انا اروح
+
+390
+00:31:55,050 --> 00:31:59,310
+على 4.4 اول بعدين ارجع ل 4.3 تمام خلينا نبدأ
+
+391
+00:31:59,310 --> 00:32:04,390
+بالسهل هذا بعدين نجيه هذا سؤال زي الشرط والسيارة
+
+392
+00:32:04,390 --> 00:32:08,870
+ذاكرينهم هذا مشبوه بعدين نجيه قصة حياته من أولي
+
+393
+00:32:08,870 --> 00:32:12,270
+جديد وانا هايله بطريقتين بعدين نشوفه كل كل هذا عدي
+
+394
+00:32:12,270 --> 00:32:16,740
+رجعتله نيجي هذا السؤال هذا حلوبراو عليكي بشبيه
+
+395
+00:32:16,740 --> 00:32:21,540
+السؤال أخدناه ذاكرين المبنى؟ أبو خمستاشر طابق و لا
+
+396
+00:32:21,540 --> 00:32:25,580
+خلتوه تلات طوابق اللي بينهم ذاكرينه؟ تمام هذا نفس
+
+397
+00:32:25,580 --> 00:32:31,400
+المبنى 45 متر المرة هيك هذه الحجر خبطناها مظبوط؟
+
+398
+00:32:31,400 --> 00:32:34,280
+خبطناها هيك المرة هذه بده اخبطه بزاوية صار ال
+
+399
+00:32:34,280 --> 00:32:39,000
+project in motion اذا بيقولي a stone نفس الحجر is
+
+400
+00:32:39,000 --> 00:32:42,260
+a throne from the top of a building هذه ال
+
+401
+00:32:42,260 --> 00:32:47,610
+building و أنا قبفتهأبوارد at an angle of 30
+
+402
+00:32:47,610 --> 00:32:51,510
+degree to the horizontal اذا ان انا قذفته مش لفوق
+
+403
+00:32:51,510 --> 00:32:56,330
+او لزاوية نقضارها 30 درجة تمام؟ with an initial
+
+404
+00:32:56,330 --> 00:33:00,890
+speed والسبيد 20 متر per second قبل ما اكمل مش
+
+405
+00:33:00,890 --> 00:33:04,930
+احنا بهيمن العلمات؟ بدنا نجيب علامات اول حاجة اشوف
+
+406
+00:33:04,930 --> 00:33:08,900
+العشرين هادي هل العشرين هادي ثنية ولا صادية؟إذا
+
+407
+00:33:08,900 --> 00:33:12,320
+أول خطوة بدي أعملها إيش؟ أحللها، ودى التحليل لحاله
+
+408
+00:33:12,320 --> 00:33:16,400
+بياخد اتنين من عشرة، إذا أول خطوة في هذه الأسئلة
+
+409
+00:33:16,400 --> 00:33:20,600
+بدي أحلل الصراع الكدائية، إذا مش محللة، تمام، إذا
+
+410
+00:33:20,600 --> 00:33:24,900
+أنا هجيت عشان أحل يا بنات، هه، طبعا كتبت هنا، بس
+
+411
+00:33:24,900 --> 00:33:26,520
+عشان أرتب المسألة
+
+412
+00:33:33,430 --> 00:33:39,670
+Vinitial X Vinitial Cos فيتا وبتساوي عشرين Cos
+
+413
+00:33:39,670 --> 00:33:43,610
+تلاتين وبتساوي سبعت عشر point تلاتة متر per second
+
+414
+00:33:44,960 --> 00:33:50,400
+هي أول واحدة التانية V-initial Y سوى V-initial سين
+
+415
+00:33:50,400 --> 00:33:54,060
+الثيتا سين التلاتين نص وهذه عشرين عشرة متر per
+
+416
+00:33:54,060 --> 00:33:57,620
+second هاي أول خطوة لازم أعملها في كل أسئلة رابو
+
+417
+00:33:57,620 --> 00:34:00,940
+جاك تلموشي أول حاجة بتطلع عليه الصراع الابتدائية
+
+418
+00:34:00,940 --> 00:34:05,180
+إذا أعطانيها بدي أحللها لسني صاضية طب مرات بيقولي
+
+419
+00:34:05,180 --> 00:34:10,760
+أنا قدفتها بالشكل الأفقيالصادية سفر والثانوية
+
+420
+00:34:10,760 --> 00:34:15,160
+للدنية الرقم تمام؟ إذا في الآخر أنا قلتله هذه كذا
+
+421
+00:34:15,160 --> 00:34:20,120
+وهذه سفر إذا أنا حللت وبرضه أخدت العالمتين اتفجنا
+
+422
+00:34:20,120 --> 00:34:25,200
+يا بنات؟ حلو أكمل السؤال the height from which the
+
+423
+00:34:25,200 --> 00:34:29,940
+stone is thrown is 45 meters above the ground وقال
+
+424
+00:34:29,940 --> 00:34:35,220
+لهذه تقريبا تعمل 15 طابق مشكلة اتفجنا؟ مش مشكلةقال
+
+425
+00:34:35,220 --> 00:34:40,120
+لي هيا انضرب و نزل نزل نزل لمواصل الأرض صح؟ و انا
+
+426
+00:34:40,120 --> 00:34:42,380
+حطت ال origin قال لي مانت شايف انا حطتك ال origin
+
+427
+00:34:42,380 --> 00:34:48,500
+هنا هالجت على مواصل الأرض كدهش موضعه؟ سالب خمسة و
+
+428
+00:34:48,500 --> 00:34:52,900
+أربعين لأنه تحت ال origin فانا واقتفرج نشوف إيش
+
+429
+00:34:52,900 --> 00:34:59,640
+بدهHow long does it take the stone to reach the
+
+430
+00:34:59,640 --> 00:35:06,140
+ground؟ زمن وصوله للأرض زمن طيب الزمن سيني ولا
+
+431
+00:35:06,140 --> 00:35:11,140
+صاضي لا هيك لا هيك أول أعمل test هذه المعادلة
+
+432
+00:35:11,140 --> 00:35:14,360
+الوحيدة الغلبانة أشوفها بتخدمني ولا لا قلتله اطلع
+
+433
+00:35:14,360 --> 00:35:20,240
+فيها زمن لكن هذه بعرفهابعرفهاش إذا بتخدمنيش شوف
+
+434
+00:35:20,240 --> 00:35:24,240
+غيرها زمان ممكن أحشعته من هنا و لا لأ حلو اللي
+
+435
+00:35:24,240 --> 00:35:28,180
+تطلع عليها الحلوه هادي واي فاينال ماقصه خمسة
+
+436
+00:35:28,180 --> 00:35:33,400
+واربعين وواي إينيشيال سفر وواي إينيشيال هديهياك
+
+437
+00:35:33,400 --> 00:35:39,460
+عشرة واتيه بديها والجيه بعرفها ضبطت طلعت المظلوم
+
+438
+00:35:39,460 --> 00:35:46,360
+إذا بقوله ايه هاي ايهبقوله Y5 ناقص Y initial
+
+439
+00:35:46,360 --> 00:35:51,960
+بتساوي V Y initial في T ناقص half GT تربيع كتبت
+
+440
+00:35:51,960 --> 00:35:56,920
+القانون قلتله هذه عبارة عن ناقص خمسة واربعين ناقص
+
+441
+00:35:56,920 --> 00:36:03,920
+سفر بتساوي عشرة T ناقص نص الهادي أربعة و تسعة نص
+
+442
+00:36:03,920 --> 00:36:07,820
+التسعة و تمانية T تربيع قال هذه معادلة من الدرجة
+
+443
+00:36:07,820 --> 00:36:11,760
+التانية واحد يجي يقولي والله أنا بنساه بقوله أنا
+
+444
+00:36:11,760 --> 00:36:16,440
+بغش شكيا في الامتحانانسى براحتك لو انت في الدار
+
+445
+00:36:16,440 --> 00:36:19,100
+تقدر تجيبه القانون تبقى على درجة تانية ولا لأ
+
+446
+00:36:19,100 --> 00:36:23,620
+القانون العام تمام اعتبر حالك في الدار شاحته من
+
+447
+00:36:23,620 --> 00:36:26,780
+أخوك اللي بياخده في الصف اللي مش عارف اي صف او
+
+448
+00:36:26,780 --> 00:36:32,620
+أختك تمام؟ و دلعنا الزمن قلت له T طلعت 4.22
+
+449
+00:36:32,620 --> 00:36:35,080
+seconds حلناه
+
+450
+00:36:36,790 --> 00:36:40,650
+حتى القانون العام لو انسيتوه بنسمحكم بنعليق بديكم
+
+451
+00:36:40,650 --> 00:36:43,490
+إياه قانون العام تبع الحالة طبعا في معادلات
+
+452
+00:36:43,490 --> 00:36:48,030
+مابتدهاش قانون عام بتنحلل بنمجص أخدتوا أيامها طبعا
+
+453
+00:36:48,030 --> 00:36:52,250
+احنا بنحاول نجيبلكوش شغلة تاخد وجد قانون عام
+
+454
+00:36:52,250 --> 00:36:56,730
+وغلبها هذه الشغلات طلعت الزمن وصدقناك وطلعناه احكي
+
+455
+00:37:00,460 --> 00:37:04,300
+القانون العام بين K ذاكر القانون العام اللي T
+
+456
+00:37:04,300 --> 00:37:07,800
+بيساوي سلب بي زاد أو ناقص يجب تربيع الى بي تربيع
+
+457
+00:37:07,800 --> 00:37:14,070
+ناقص 4A C ع 2A ده كان أنا سمحتك تنسيهأنا سامع حاجة
+
+458
+00:37:14,070 --> 00:37:18,770
+تنسيها، بس بتعرفش A وB وC؟ A معامل X تربية أو B
+
+459
+00:37:18,770 --> 00:37:24,070
+معامل X وC تخر؟ مظلومة لأ؟ إذا إيش ما يكون يكون،
+
+460
+00:37:24,070 --> 00:37:27,130
+إن شاء الله يكون جرود، القول العام بيجيبه، تمانية
+
+461
+00:37:27,130 --> 00:37:31,750
+بنتين؟ حلو، طلعتي لك T، أي أول مقلوب، إيش بده
+
+462
+00:37:31,750 --> 00:37:38,150
+الكيماء؟ What is the speed of the stone؟just
+
+463
+00:37:38,150 --> 00:37:41,430
+before it strike the ground قبل ما يضرب الأرض
+
+464
+00:37:41,430 --> 00:37:47,950
+مباشرة سرعة النهائية طيب اتطلع و ايش كاتب what is
+
+465
+00:37:47,950 --> 00:37:53,010
+the speed لو جلك what is the velocity تفرج ايه
+
+466
+00:37:53,010 --> 00:37:58,870
+معناه speed ايوة اذا انك بتفرج لو رحنا اقوم و اقول
+
+467
+00:37:58,870 --> 00:38:01,110
+ايش معناه speed اقوم و اقول سرعة ايش معناه
+
+468
+00:38:01,110 --> 00:38:04,410
+velocity سرعة لكن احنا من أسبابنا اتعلمنا ان ال
+
+469
+00:38:04,410 --> 00:38:08,920
+speed و السرعة و ال velocity ماذا يبعدطيب .. منفع
+
+470
+00:38:08,920 --> 00:38:13,040
+أجيب ال speed بدون معرف ال velocity؟ لأ لأن ال
+
+471
+00:38:13,040 --> 00:38:17,320
+speed مقدار ال velocity زي ما تقولي بدي مقدار
+
+472
+00:38:17,320 --> 00:38:21,140
+vector بقولك بديمي ال vector صح ولا لأ؟ اذا انا
+
+473
+00:38:21,140 --> 00:38:25,480
+بدي اول حاجة اجيب ال velocity هي ال velocity اكم
+
+474
+00:38:25,480 --> 00:38:28,800
+مركبة بتتوقع تنتهي .. تنتهي .. تنتهي .. تنتهي ..
+
+475
+00:38:28,800 --> 00:38:29,320
+تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي
+
+476
+00:38:29,320 --> 00:38:30,060
+.. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي ..
+
+477
+00:38:30,060 --> 00:38:33,420
+تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي
+
+478
+00:38:33,420 --> 00:38:33,700
+.. تنتهي .. تنتهي .. تنتهي .. تنتهي .. تنتهي ..
+
+479
+00:38:33,700 --> 00:38:41,530
+تنتهي .. تنتبقول له V X Final ايش علاقتها بال X
+
+480
+00:38:41,530 --> 00:38:51,030
+initial نفسها طموحيها يوردين أسعابها وانا لو
+
+481
+00:38:51,030 --> 00:38:55,050
+كتبتها دي كمان مره ايه علامات بقول له اه اليك
+
+482
+00:38:55,050 --> 00:38:59,950
+علامة احكي الجزء لما تكون V X Final نزلت من نفس
+
+483
+00:38:59,950 --> 00:39:08,810
+الزاوية لأنك بيه sign كتابة طيب نزلت من ..وين هذه
+
+484
+00:39:08,810 --> 00:39:12,950
+انا عارفه ايش عوضت اه
+
+485
+00:39:12,950 --> 00:39:23,410
+اه حسب وين مش بالضرورة مش بالضرورة انا ايش عوضت
+
+486
+00:39:23,410 --> 00:39:29,590
+قلت هجيت هذه 17.3 فانت تاكل ال cosine مش رقم طيب
+
+487
+00:39:29,590 --> 00:39:35,210
+هذا رقم هذه 720 دقيقة سنية مسموح تتغير؟ عادة
+
+488
+00:39:35,210 --> 00:39:42,150
+للأولى اه اه لأ اهرقم ال V لحالة تمام هي عيب الدرع
+
+489
+00:39:42,150 --> 00:39:46,130
+زي مهينة فتكمل ال feta بتختلف حسب ال feta الجديدة
+
+490
+00:39:46,130 --> 00:39:52,530
+هجيت هادي اعملتش عشان اجيبها و لا انا بس نجلت جولت
+
+491
+00:39:52,530 --> 00:39:56,050
+بس مجرد ليش انا بديك علامات عليها عشانك بتأكدلي
+
+492
+00:39:56,050 --> 00:40:00,400
+معلومة فيزيائية ان الصراع الصيني لا تتغيرصح؟ انه
+
+493
+00:40:00,400 --> 00:40:03,000
+نهائية ولا تدائية ضي بعض ولا لأ؟ هذه معلومة
+
+494
+00:40:03,000 --> 00:40:07,640
+فيزيائية تبليها واخد عليها علامات ايه ضال؟ بتدي
+
+495
+00:40:07,640 --> 00:40:12,280
+الصادية النهائية الصادية النهائية هيها مش انت
+
+496
+00:40:12,280 --> 00:40:18,500
+جيبتي توي وقلت 4.22 اذا بقدر اقول VY final بتسوي
+
+497
+00:40:18,500 --> 00:40:24,060
+VY initial نقش G في T اللي بتسوي هذه عشرة نقس تسعة
+
+498
+00:40:24,060 --> 00:40:29,170
+point تمانية في أربع point two twoجدش طلعت بالسالب
+
+499
+00:40:29,170 --> 00:40:33,910
+جدش نجلوني واحد تلاتين point تلاتة meter per
+
+500
+00:40:33,910 --> 00:40:41,050
+second طلعت سالب لها معنى ولا مالهاش معنى انها لا
+
+501
+00:40:41,050 --> 00:40:45,630
+أسفل اه لإن واحد يقول لأ احنا علمونا السالب نرفضه
+
+502
+00:40:45,630 --> 00:40:49,370
+هذا الزمن صح او لا هذه لأ بالعكس لو طلعت موجة
+
+503
+00:40:49,370 --> 00:40:55,270
+برفضهالأنه نازله لأنه نازله هدى جبته و هدى جبته
+
+504
+00:40:55,270 --> 00:41:03,030
+بقل رجول V final طالعه متساوي 17.3 I ناقص 31.3 J
+
+505
+00:41:03,030 --> 00:41:08,370
+مثل البرسكند ولا لأ؟ لو جالي اودي دي ال velocity
+
+506
+00:41:08,370 --> 00:41:14,330
+بقوله خلص السؤال صح لو جالي velocity خلص لكن بده
+
+507
+00:41:14,330 --> 00:41:17,830
+أثبيت هذا بده بال magnitude لكن لو جالي اودي دي ال
+
+508
+00:41:17,830 --> 00:41:21,400
+velocity بقوله يعطيني العافية خلص السؤالصحيحيك ولا
+
+509
+00:41:21,400 --> 00:41:26,580
+لأ؟ بدي ال magnitude .. إيه؟ سهل جزر .. هذا ربي
+
+510
+00:41:26,580 --> 00:41:30,800
+تربية و هذا تربية و بشتغله حتى لو كان في عشاء
+
+511
+00:41:30,800 --> 00:41:34,980
+بالرب ع ولا لأ؟ و هذي نفس العملية بقدر أجيب ال
+
+512
+00:41:34,980 --> 00:41:37,820
+velocity من التقانون التالت بس يجب أن أحط سلب مني
+
+513
+00:41:37,820 --> 00:41:43,180
+أنا هان؟ هذي قصدية؟ اه يجب أن أحط السلب أنا؟ براو
+
+514
+00:41:43,180 --> 00:41:51,390
+عليك تمامحلو إذا معناته طلعت أنا الزمن و روحت جيبت
+
+515
+00:41:51,390 --> 00:41:55,710
+الصاضية و قولتله السلب يعني down و قولتله ال X هدا
+
+516
+00:41:55,710 --> 00:42:02,970
+هي هي هي جيبلي speed سؤال سهل خلصنا
+
+517
+00:42:02,970 --> 00:42:07,750
+أي صفر صار نرجع
+
+518
+00:42:12,970 --> 00:42:16,090
+طبعا انا ماعرفش انتوا عندكم محلول مرة واحدة اظنني
+
+519
+00:42:16,090 --> 00:42:20,170
+هذا المثال انا هنا محلول مرتين واتفجت مع الشباب
+
+520
+00:42:20,170 --> 00:42:23,190
+انه هذا الحل التاني عشان مش مكتوب عينكم هحطه على
+
+521
+00:42:23,190 --> 00:42:27,790
+مجموعة الواتس عشان مايقعدوش تصوروا يعني و تتعبوا
+
+522
+00:42:27,790 --> 00:42:31,150
+حياتكم و تكتبوا ورايا الحل الأولان هو حل الكتاب
+
+523
+00:42:31,150 --> 00:42:34,230
+اللي بين يديكم الكتاب هيك حالة انا عم بدي أحل
+
+524
+00:42:34,230 --> 00:42:39,750
+بطريقة أسهل ايش أسوي يا بنات طبعا كان بدي أحله أول
+
+525
+00:42:39,750 --> 00:42:54,760
+اشوف السؤال ايش بيقولنشفح السؤال وبعدين نحله نفض
+
+526
+00:42:54,760 --> 00:43:02,420
+اللوح عشان الصح صح نحنا وياكم اتطلع
+
+527
+00:43:02,420 --> 00:43:07,100
+يا بنادر واحدة اخر الحياطة معها برودة بدها تطخها
+
+528
+00:43:07,100 --> 00:43:12,800
+الجلمبدها تصيده اول ما تطلع الارصاصة من البروضة
+
+529
+00:43:12,800 --> 00:43:17,720
+انا بتفلّت الجلام هجيت هي بدها تنشّن في البداية
+
+530
+00:43:17,720 --> 00:43:21,580
+عشان تصيب الجلام للواحدة الأولى بتقولك انا مديش هو
+
+531
+00:43:21,580 --> 00:43:24,800
+نشّن على الجلام بدي اعمل حساب انه بدي ينزل اه
+
+532
+00:43:24,800 --> 00:43:30,360
+بقولها لا هو مين اللي بديه ينزل الجلام مش انا ايه
+
+533
+00:43:30,360 --> 00:43:34,220
+عشان يخليه ينزل للأعلى انا بتفلته تصارع الجاذبية
+
+534
+00:43:34,220 --> 00:43:40,690
+طب هي البروضةالارصاصة لما طلعت الجاذبية بدهاش تأثر
+
+535
+00:43:40,690 --> 00:43:45,450
+عليها، إذا هتنزلها. إذا المعنى تقول إيه بتسوي اللي
+
+536
+00:43:45,450 --> 00:43:52,690
+بعيدة؟ بدها تنش على الجلم و هو واقف. و انا ساعتها
+
+537
+00:43:52,690 --> 00:43:57,390
+بدي أنزل. المسافة العمودية اللي نزلوا الجلم،
+
+538
+00:43:57,390 --> 00:44:02,390
+البرودة هتنزله، الارصاصة هتنزله، إذا هيصيبوا بعض،
+
+539
+00:44:02,390 --> 00:44:08,030
+بدون ما تعملوا حسابات نزول الجلم.مش مصدق زي ما انت
+
+540
+00:44:08,030 --> 00:44:13,090
+مش مصدقه لأ بدي أثبت هذا الكلام من حياتك بدي أثبت
+
+541
+00:44:13,090 --> 00:44:18,770
+نقرأ السؤال أول بيقول لأ projectile projectile
+
+542
+00:44:18,770 --> 00:44:21,690
+مقضوة في رصاصة طوي قلت عنها انا مش انا بدي أقضفها
+
+543
+00:44:21,690 --> 00:44:25,690
+a projectile is fired at a target هدف اللي هو
+
+544
+00:44:25,690 --> 00:44:31,860
+القلبتمى in such a way that the projectile leaves
+
+545
+00:44:31,860 --> 00:44:35,180
+the gun at the same time the target is dropped
+
+546
+00:44:35,180 --> 00:44:38,640
+from rest اذا اول ما الارصاصة طلعت من البرودة انت
+
+547
+00:44:38,640 --> 00:44:41,900
+فالتي تيدك اذا نبدأ الحركة بالنفس اللحظة ولا لأ
+
+548
+00:44:41,900 --> 00:44:47,380
+واحد حركته projectile اللي هي الارصاصة والجلم لما
+
+549
+00:44:47,380 --> 00:44:53,390
+انزله حركة سقوط حر ولا لأ سقوط حرحلو show that
+
+550
+00:44:53,390 --> 00:44:58,950
+اثبت that if the gun is initially aimed اذا
+
+551
+00:44:58,950 --> 00:45:05,170
+الارصاصة وجهتها خطتها في اتجاه aimed at the
+
+552
+00:45:05,170 --> 00:45:09,910
+stationary target عند القلم لم يكن واقف انت وجهتها
+
+553
+00:45:09,910 --> 00:45:15,670
+على القلم وهو واقف stationary يعني ثابت target the
+
+554
+00:45:15,670 --> 00:45:18,770
+projectile hits the falling target as shown in the
+
+555
+00:45:18,770 --> 00:45:23,970
+figureطيب ليش انا جربت على السيارة و الشرطي
+
+556
+00:45:23,970 --> 00:45:28,070
+ذاكرينهم لما الشرطي لاحق السيارة واحد كان في قانون
+
+557
+00:45:28,070 --> 00:45:30,210
+السوري التاني كان في انصرات ولا كانوا في نفس
+
+558
+00:45:30,210 --> 00:45:35,650
+الموقع اذا عشان الارصاصة تخبط الهدف لازم يكونوا في
+
+559
+00:45:35,650 --> 00:45:41,630
+نفس الموقع ولا لا حلو جالي هاي راسمتيأنا بدي أثبت
+
+560
+00:45:41,630 --> 00:45:47,010
+إني أنا وجهتها هيك، ها، هيها، ماعملتش حساب نزولها،
+
+561
+00:45:47,010 --> 00:45:50,710
+تمام؟ هجيت وين اتجابلوا؟ قولتله اتجابلوا ها، هجيت
+
+562
+00:45:50,710 --> 00:45:54,590
+هذا الارتفاع تبع الحمرة اللي هو ال target و لا تبع
+
+563
+00:45:54,590 --> 00:45:58,750
+الزرقة، بيختلفوا عن بعض، إذن هي ترك السؤال إن why
+
+564
+00:45:58,750 --> 00:46:06,440
+لا الحمرة و why لا الزرقة واحد، تمام؟ أنا هذاخط
+
+565
+00:46:06,440 --> 00:46:11,500
+لما جيت وهذه الخط بتعتبر الزاوية ثيتا وهذه زاوية
+
+566
+00:46:11,500 --> 00:46:14,060
+الخط Alpha ده بتثبتلي أن Alpha و Theta زي بعض
+
+567
+00:46:14,060 --> 00:46:19,040
+Alpha و Theta زي بعض هاي اللي بدي أثبته كيف كده
+
+568
+00:46:19,040 --> 00:46:22,560
+Alpha و Theta هجيت Theta الشي هي زاوية انطلاق
+
+569
+00:46:22,560 --> 00:46:27,460
+الرصاصة Alpha هي الزاوية اللي بيعملها الخط ما بين
+
+570
+00:46:27,460 --> 00:46:33,090
+الرصاصة و ال target هو واقفمش انا هيك عملتها هجيت
+
+571
+00:46:33,090 --> 00:46:38,410
+انا هيك .. هيك نشنتها هجيت هذه الزاوية، إيش هي؟
+
+572
+00:46:38,410 --> 00:46:42,410
+زاوية انطلاق الرصاصة والزاوية اللي بيعملها الخط
+
+573
+00:46:42,410 --> 00:46:48,990
+هذا مع ال .. مع ال X-axis، هي هي طيب، بنثبت، لكن
+
+574
+00:46:48,990 --> 00:46:52,090
+بتقدروا تقولوا إيه؟ فلتوكوا من project in motion
+
+575
+00:46:52,090 --> 00:46:57,410
+هذا الخط أنا مددته هيكبتقدر تقولي تاني الزاوية
+
+576
+00:46:57,410 --> 00:47:02,130
+بيساوي مقابل ع مجاور؟ هذا المقابل بتاعتبره H؟
+
+577
+00:47:02,130 --> 00:47:07,890
+بالفعل؟ إذا بتقدر تقولي إنه تام الـ Alpha بيساوي H
+
+578
+00:47:07,890 --> 00:47:13,550
+على XX هذه المسافة كلها؟ صح ولا لأ؟ تمام، نيجي،
+
+579
+00:47:13,550 --> 00:47:19,390
+هالجيت، فانتقم الهدف بعدين ونعود عليها هذا اللي هو
+
+580
+00:47:19,390 --> 00:47:26,170
+الـ Target الهدف كيف بيمشي سقوط حر؟صح؟ وهذا الـ
+
+581
+00:47:26,170 --> 00:47:31,270
+projectile ليه صح صح الـ projectile
+
+582
+00:47:31,270 --> 00:47:35,530
+هيك عملنا لما قلنا سيارة و قلنا trooper ذاكرين
+
+583
+00:47:35,530 --> 00:47:40,110
+وهذه عملنا نفس العملية هذا سقوط حر قلت له في
+
+584
+00:47:40,110 --> 00:47:44,050
+السقوط الحر كان فيه قانون بيقول Y final نقص Y
+
+585
+00:47:44,050 --> 00:47:49,270
+initial بتسوي V initial Y أو بدون هذه حتى مهمش T
+
+586
+00:47:49,270 --> 00:47:54,840
+تربيع T نقص half GT تربيعتطلعولي على الجلام اللى
+
+587
+00:47:54,840 --> 00:48:01,180
+كان بيدى كده سرعته الابتدائية؟ سفر مش انا بدفلته
+
+588
+00:48:01,180 --> 00:48:07,520
+اذا سرعته الابتدائية سفر ولا لأ تمام هداك من وين
+
+589
+00:48:07,520 --> 00:48:11,800
+بدأ الجلام بدأ من هذه النقطة ولا لأ اذا Y initial
+
+590
+00:48:11,800 --> 00:48:14,860
+بتسوي H ولا لأ اذا هذا H
+
+591
+00:48:19,310 --> 00:48:27,930
+اللي هو Y هذي H وهذه Y بتساوي هذي كم قلنا سفر ناقص
+
+592
+00:48:27,930 --> 00:48:43,110
+نص GT تربيع تمام هيك؟ حلو أي شي صح سعيد معايا؟
+
+593
+00:48:45,500 --> 00:48:49,580
+الوعي انيش اه انا اتعكس طب اه اه اه اه نقص اتش
+
+594
+00:48:49,580 --> 00:48:56,460
+صحيح اه تمام تمام
+
+595
+00:48:56,460 --> 00:49:00,040
+يا سامي بقى ال menu بنعيده المرة الجاية بديش اعوك
+
+596
+00:49:00,040 --> 00:49:00,520
+دكتورنا
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/E6HOsl9lEzQ_postprocess.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/E6HOsl9lEzQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e97e65ed573b177ef3a89c4b3bdd54a482076014
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/E6HOsl9lEzQ_postprocess.srt
@@ -0,0 +1,2736 @@
+1
+00:00:05,010 --> 00:00:10,110
+تمام يا بنات هنبدأ اليوم ان شاء الله بـ Chapter 2
+
+2
+00:00:10,110 --> 00:00:14,550
+بعد بسم الله الرحمن الرحيم حكينا انه في هذا ال
+
+3
+00:00:14,550 --> 00:00:20,110
+chapter العنوان تبعه هو motion in one dimension او
+
+4
+00:00:20,110 --> 00:00:26,600
+ال linear motion الحركة في خط واحد باتجاه واحدحركة
+
+5
+00:00:26,600 --> 00:00:32,280
+بيعني فيه سرعة وأحيانا بيكون فيه تصارع بالتالي
+
+6
+00:00:32,280 --> 00:00:37,200
+هنتحدث عن المفاهيم الفيزيائية التالية بدنا نحكي
+
+7
+00:00:37,200 --> 00:00:42,320
+ايش هو ال position موضع جسماذا اتغير الموضع مانا
+
+8
+00:00:42,320 --> 00:00:46,720
+تحصل عندي velocity بينا نميز ما بين ال velocity و
+
+9
+00:00:46,720 --> 00:00:51,880
+ال speed ثم احيانا اذا اتغيرت السرعة صار في عندي
+
+10
+00:00:51,880 --> 00:00:56,180
+تسارق acceleration لما تكون ال acceleration
+
+11
+00:00:56,180 --> 00:01:00,000
+constant في حالة خاصة هنتعرف عليها و نشتق
+
+12
+00:01:00,000 --> 00:01:05,180
+المعادلات اللي بتحكمها حالة من حالات الحركة باتجاه
+
+13
+00:01:05,180 --> 00:01:11,270
+واحد وبتسارق ثابت هيالـ Free Falling Objects هذه
+
+14
+00:01:11,270 --> 00:01:15,370
+هي المواضيع اللي هنشرحها في هذا الـ Chapter تقريبا
+
+15
+00:01:15,370 --> 00:01:19,150
+المواضيع مرت عليكم في الصف الحدي عشر إلى حد كبير
+
+16
+00:01:19,150 --> 00:01:23,390
+وبالتالي اختارنا ال problems اللي تعمل refreshing
+
+17
+00:01:23,390 --> 00:01:29,310
+لمعلوماتكم بدناش نجور عليكم لأن أغلب المواضيع و
+
+18
+00:01:29,310 --> 00:01:32,750
+الأسئلة مرت عليكم بصورة أو باخرة في المدرسة
+
+19
+00:01:32,750 --> 00:01:38,100
+بالتالي بدنا نعمل refreshing إعادةإحياء للمعلومات
+
+20
+00:01:38,100 --> 00:01:42,940
+اللي مرت علينا في الصف الحادي عشر وبدنا انحل هذه
+
+21
+00:01:42,940 --> 00:01:48,000
+الأسئلة فقط القليلة تعتبر نسبيا المطلوب مننا
+
+22
+00:01:48,000 --> 00:01:55,400
+انحلها احكي مالجيتهاش
+
+23
+00:02:01,650 --> 00:02:06,010
+هي الأسئلة لبعد ال chapter بعد ال summary مش أنا
+
+24
+00:02:06,010 --> 00:02:10,210
+حكيت المرة دى كل chapter مش آخر الكتاب آخر ال
+
+25
+00:02:10,210 --> 00:02:14,190
+chapter تمام آخر الكتاب مش هيجي الصفة معايا عشان
+
+26
+00:02:14,190 --> 00:02:19,030
+بالمرة آخر الكتاب فيه إجابات للأسئلة الفردية
+
+27
+00:02:19,030 --> 00:02:22,570
+إجابات مش انتوا بتحلوا بيشوفوا حالكم حلته صح ولا
+
+28
+00:02:22,570 --> 00:02:27,070
+لأ إذا السؤال فردي إجابته بتلاقوها في آخر الكتاب
+
+29
+00:02:27,700 --> 00:02:33,440
+هتلاقي العنوان answer to all problems مظبوط؟ إذا
+
+30
+00:02:33,440 --> 00:02:37,680
+اللي في آخر الكتاب إجابات لكن السؤال بنصه بلحمه
+
+31
+00:02:37,680 --> 00:02:42,180
+بدمه موجود في نهاية الشكتر في summary أو في
+
+32
+00:02:42,180 --> 00:02:45,280
+objective questions أو في conceptual questions
+
+33
+00:02:45,280 --> 00:02:48,580
+وبعدين في problems ابتدى ل problems الأسئلة هذه
+
+34
+00:02:48,580 --> 00:02:56,560
+تمام هيك؟ تمام غيرها حلو نبدأposition موضع
+
+35
+00:02:56,560 --> 00:03:02,640
+velocity سرعة speed سرعة فرق بينهم فيه فرق من ان
+
+36
+00:03:02,640 --> 00:03:08,100
+انا اتعرف عليه تمام بنقول كل كمية فيزيائية له رمز
+
+37
+00:03:08,100 --> 00:03:14,400
+متعرف عليه ولا لأ ال T للزمن من كلمة time ال M لل
+
+38
+00:03:14,400 --> 00:03:19,060
+mass من كلمة mass اللي هي الكتلةالـ Position
+
+39
+00:03:19,060 --> 00:03:25,260
+اتفقوا ياخدوا X إله إذا الـ Position of a particle
+
+40
+00:03:25,260 --> 00:03:29,440
+هناخد إله الـ X طبعا إيه الـ X من الصيني المحور
+
+41
+00:03:29,440 --> 00:03:33,340
+الصيني تمام يا بنات؟ إذا الـ Position of a
+
+42
+00:03:33,340 --> 00:03:38,240
+particle اللي هنرمزله بالرمز X إيش تعرفه؟ Its
+
+43
+00:03:38,240 --> 00:03:44,540
+location موضعموضع location من موضع is the location
+
+44
+00:03:44,540 --> 00:03:48,440
+with respect to a reference point اذا انت مفهوش
+
+45
+00:03:48,440 --> 00:03:52,300
+تقولي والله انا موضعي خمسة متر بدون ما تقولي عن
+
+46
+00:03:52,300 --> 00:03:57,880
+ايش هذه الاش بيسميها reference point نقطة مرجعية
+
+47
+00:03:57,880 --> 00:04:03,940
+تمام هجيك لما نيجي نقول هاي حيطة مرجع ولا مش مرجع
+
+48
+00:04:03,940 --> 00:04:09,670
+مرجع تمام وهي سيارةهيجيت واضح ان السيارة بتبعد عن
+
+49
+00:04:09,670 --> 00:04:14,410
+الحيطة مسافة ما نقدر نقول بالبلدي موضع السيارة عن
+
+50
+00:04:14,410 --> 00:04:18,110
+الحيطة ولا لأ اذا هذا موضع السيارة عن الحيطة هذا
+
+51
+00:04:18,110 --> 00:04:22,430
+reference point اذا as a particle moves لما يتحرك
+
+52
+00:04:22,430 --> 00:04:27,460
+الجسم ما زال يتحرك اتغير موضعه ولا لأإذن صلوا
+
+53
+00:04:27,460 --> 00:04:32,640
+موضعين موضع ابتدائي وموضع نهائي لأنه كانوا صار إذن
+
+54
+00:04:32,640 --> 00:04:37,620
+و as a particle moves و الجسم بتحرك from an
+
+55
+00:04:37,620 --> 00:04:41,740
+initial position initial position صار الأن عنده
+
+56
+00:04:41,740 --> 00:04:46,420
+موضعين ميز بينهم X و X مينفعش قال الموضع الابتدائي
+
+57
+00:04:46,420 --> 00:04:51,620
+بده حط عليه XI من كلمة initial والموضع النهائي حط
+
+58
+00:04:51,620 --> 00:04:57,210
+X وحط F من كلمة finalإذن as a particle moves from
+
+59
+00:04:57,210 --> 00:05:03,690
+an initial position XI to a final position X final
+
+60
+00:05:03,690 --> 00:05:09,230
+بصله .. بنقول عنه نزاح، مظبوط ولا؟ صلّه إزاحة، its
+
+61
+00:05:09,230 --> 00:05:13,370
+displacement يعني إزاحة، بصارت إزاحته، إيش بيك
+
+62
+00:05:13,370 --> 00:05:18,550
+تعرفها؟ بيقولوا هي السيارة، هيمش هذا موضوع اقتدائي
+
+63
+00:05:18,550 --> 00:05:23,610
+انت بتسوي T initialي انا بداية الحركة تمام؟ قولي
+
+64
+00:05:23,610 --> 00:05:29,750
+اتحركت السيارة انزحت ولا ما انزحتش لموضع جديد
+
+65
+00:05:29,750 --> 00:05:34,490
+الموضع الجديد هادي ولا مش هادى المسافة تمام؟ ليش
+
+66
+00:05:34,490 --> 00:05:38,170
+هادى مش هالجه مش مشكلة المفروض تكون تمام؟ في عندي
+
+67
+00:05:38,170 --> 00:05:42,770
+مشكلة في ال .. في ال word اللى عندنا تمام؟ حلو
+
+68
+00:05:43,640 --> 00:05:48,680
+خيلوها انتوا السيارة هنا تمام؟ حلو هاجيكا و
+
+69
+00:05:48,680 --> 00:05:54,060
+بيدقولكوا جدش مقدار إزاحتها يعني نفترض من عند
+
+70
+00:05:54,060 --> 00:05:59,520
+الحيطة هذه تمام؟ كانت هنا صارت هنا كانت تبعد اتنين
+
+71
+00:05:59,520 --> 00:06:02,620
+متر صارت تبعد خمسة متر جدش انزحت؟ برافو عليك، كيف
+
+72
+00:06:02,620 --> 00:06:08,060
+عملتوا؟ خمسة ناقص اتنين صح ولا لا؟ يعني قلتوا موضع
+
+73
+00:06:08,060 --> 00:06:11,440
+النهائي ناقص الموضع الابتدائي ولا لا؟ هذه بيسميها
+
+74
+00:06:11,440 --> 00:06:18,090
+الإزاحةتغيرت الموضوع والتغير ان المظله بالرمزة
+
+75
+00:06:18,090 --> 00:06:23,870
+delta ولا مش delta دلتا اكس طيب ما هدى delta
+
+76
+00:06:23,870 --> 00:06:31,610
+بنعرفها تانا نشوف هدى شفتوها جمال كده هدى delta
+
+77
+00:06:31,610 --> 00:06:36,620
+برضه بس هدى capital delta و هدى small deltaأه و
+
+78
+00:06:36,620 --> 00:06:41,120
+الله صالها صمت مش هذه حروف و كل حرف اوميجا اخدناها
+
+79
+00:06:41,120 --> 00:06:45,220
+احنا احنا اخدناها اوميجا انا اديتكم اياها بس هذه
+
+80
+00:06:45,220 --> 00:06:49,600
+انا ب .. اعتقد انها مرت عليكم في ال calculus ولا
+
+81
+00:06:49,600 --> 00:06:53,480
+مرة جوية جولتس دلتا تقول السفر ولا مرة ولا مرة
+
+82
+00:06:54,500 --> 00:06:57,720
+بلاش، هيكم عرفتوها، احنا هيك بنحكي عشان تعرف انه
+
+83
+00:06:57,720 --> 00:07:02,500
+فيه capital و small، تمام؟ تلقى ثقافة، هذه المهمة
+
+84
+00:07:02,500 --> 00:07:07,040
+delta، هذا رمز، كل الناس بتعرف ال capital delta
+
+85
+00:07:07,040 --> 00:07:11,260
+فرق ولا مش فرقفقه ده هو الرمز اللي قدناها هدى
+
+86
+00:07:11,260 --> 00:07:13,960
+delta إيه لها شغلها تبني جيها إذا تقدروا إن شاء
+
+87
+00:07:13,960 --> 00:07:15,660
+الله كمان أسبوع أسبوعين بتاخدوها في ال calculus
+
+88
+00:07:15,660 --> 00:07:19,500
+بتقولولي واه والله مرت علينا برضه بيسموها delta
+
+89
+00:07:19,500 --> 00:07:22,520
+بيقولوش اسمها delta خلص delta و هديك delta تمام؟
+
+90
+00:07:22,520 --> 00:07:26,080
+إذا معناته اللي لما قلتها وقلتولي خمسة ناقص ثلاثة
+
+91
+00:07:26,080 --> 00:07:29,940
+يعني x final ناقص x initial ولا لأ إذا هدى تعريف
+
+92
+00:07:29,940 --> 00:07:34,920
+ال displacement الموضع النهائي ناقص الموضع لبتدائي
+
+93
+00:07:34,920 --> 00:07:39,810
+displacement مظبوط ولا لأ؟سهل الأمور لسه ماعملناش
+
+94
+00:07:39,810 --> 00:07:47,410
+حاجة remark ملاحظة يعني remark ايش يعني ملاحظة
+
+95
+00:07:47,410 --> 00:07:53,310
+هتمر علينا remarkات كتيرة حلو جالي إزاحة و جالي في
+
+96
+00:07:53,310 --> 00:07:59,430
+كلمة اسمها مسافة صح اذا distance مسافة و
+
+97
+00:07:59,430 --> 00:08:03,630
+displacement إزاحة جالي there is a difference هناك
+
+98
+00:08:03,630 --> 00:08:07,720
+فرق differenceمظبوط between distance and
+
+99
+00:08:07,720 --> 00:08:14,200
+displacement ايش هو الفورق قاللي هاي جسم كان هنا
+
+100
+00:08:14,200 --> 00:08:21,420
+جذر و شم الهوى و وصل هنا هيجيت وين نقطة بدايته
+
+101
+00:08:21,420 --> 00:08:25,580
+هيها وين نقطة نهايته هيها اذا بتحكيلي عن
+
+102
+00:08:25,580 --> 00:08:32,070
+displacement مالكاش دعواء كيف وصل النهايةهيتجذر
+
+103
+00:08:32,070 --> 00:08:38,010
+اختصر ماختصرش انا الي دعوة وين كان وين صار اذا قلت
+
+104
+00:08:38,010 --> 00:08:41,850
+بداية و نهاية معناته displacement اذا بدك كيف وصل
+
+105
+00:08:41,850 --> 00:08:45,970
+معناته بتحكي عن مسافة ندي المثل البلدي اللي انتوا
+
+106
+00:08:45,970 --> 00:08:48,530
+طالعين من الجامعة و رايحين على خانونس تكرته
+
+107
+00:08:48,530 --> 00:08:53,290
+مواصلات مظبوط ولا لأ احيانا تصدف السيارة راحت على
+
+108
+00:08:53,290 --> 00:08:55,670
+خانونس عادي اللي في شارع صلاح الدي لما وصلت خانونس
+
+109
+00:08:55,670 --> 00:08:59,990
+ومرات من جلة الركاب أخدله راكب على المغازيوخد وراك
+
+110
+00:08:59,990 --> 00:09:04,750
+عادى للبلح مش بيضلوا جذر اذا انت بدك displacement
+
+111
+00:09:04,750 --> 00:09:08,030
+بتحط رجل عريجل في غزة ما هو انطلق من غزة و بتقوله
+
+112
+00:09:08,030 --> 00:09:12,090
+لما اتصل خانونس قولي بروح بجيب خط من غزة لخانونس
+
+113
+00:09:12,090 --> 00:09:16,270
+بقولها دى ايه زاعته صح ولا لأ اذا بدك مسافة بنفع
+
+114
+00:09:16,270 --> 00:09:20,030
+تحط رجل عريجل ولا بده ايجي لوراهبدي أجري وراه، راح
+
+115
+00:09:20,030 --> 00:09:23,410
+على المغازي، بدي ألحجه، راح على الدير، بدي ألحجه،
+
+116
+00:09:23,410 --> 00:09:28,230
+ميل على هنا ولا هنا، بدي ألحجه، صح ولا لأ؟ لما بدي
+
+117
+00:09:28,230 --> 00:09:32,230
+ألحجه، معناته أنت بتحكي عن مسافة، لكن لما بدي تحكي
+
+118
+00:09:32,230 --> 00:09:36,750
+عن إزاحة، بيهمك نقطتي البداية والنهاية فقط، هي
+
+119
+00:09:36,750 --> 00:09:41,690
+هذا، وهي نقطة النهاية، من كان يصل هيك ولا لأ؟ وهنا
+
+120
+00:09:41,690 --> 00:09:46,050
+قعدت بجزر، برضه وصل، هل جيت هذه الإزاحة وهذه
+
+121
+00:09:46,050 --> 00:09:52,560
+المسافة؟ من أكبر؟المسافة صح أو لأ؟ في مجال ممكن
+
+122
+00:09:52,560 --> 00:09:58,180
+المسافة واليزاح يتساويأه إذا مش يوم خطأ أحد ما
+
+123
+00:09:58,180 --> 00:10:01,780
+تعبش حاله لف لف له هنا و هنا صح ولا لأ؟ إذا
+
+124
+00:10:01,780 --> 00:10:04,480
+بيقوللي إيش ال difference؟ الكلام البلدي اللي
+
+125
+00:10:04,480 --> 00:10:10,140
+حكيته بيقوللي distance هي كمية قياسية is a scalar
+
+126
+00:10:10,140 --> 00:10:13,920
+quantity طبعا كمية قياسية وكمية مش قياسية هذا
+
+127
+00:10:13,920 --> 00:10:17,540
+موضوع chapter 3 هنزيه تفصيلا بس الآن بيقوله كيف
+
+128
+00:10:17,540 --> 00:10:22,640
+حالك؟is a scalar quantity كمية قياسية طب إيش
+
+129
+00:10:22,640 --> 00:10:24,920
+تعريفها؟ ماكانش دعوة هجت في الـ scalar و مش الـ
+
+130
+00:10:24,920 --> 00:10:30,060
+scalar بيقولي is the actual length الطول الحقيقي
+
+131
+00:10:30,060 --> 00:10:34,710
+actual حقيقي مرك عليكمالطول الحقيقي الـ Actual
+
+132
+00:10:34,710 --> 00:10:40,610
+Length of the path للطريق Followed by a particle
+
+133
+00:10:40,610 --> 00:10:44,770
+تبحّى أي جسم سيارة ولا طيارة ولا واحد قاعد بيجذّر
+
+134
+00:10:44,770 --> 00:10:48,310
+هذا هو تعريف الـ Distance إذا الـ Distance اللي
+
+135
+00:10:48,310 --> 00:10:51,590
+بيجتبح حاجة السيارة و المراحة لإنها بيدك الطول
+
+136
+00:10:51,590 --> 00:10:56,320
+الحقيقي للرحلة Where راح و وين إجامع أن الـ
+
+137
+00:10:56,320 --> 00:11:04,680
+Displacement هو كمية فائعة متجهة مش قياسية تمام؟
+
+138
+00:11:04,680 --> 00:11:11,900
+ايش تقريفه؟ هي المقارنة الأقصر بين الاسم والمقارنة
+
+139
+00:11:11,900 --> 00:11:15,940
+الأخيرة من البرتقال إذن بهمك فقط نقطتي البداية
+
+140
+00:11:15,940 --> 00:11:20,860
+والنهاية وإن كان وإن صار إيش في الطريق سوى؟ مالكاش
+
+141
+00:11:20,860 --> 00:11:26,450
+جعوة مالكاش جعوة، هذي الـ Displacement تمامبيقولّي
+
+142
+00:11:26,450 --> 00:11:31,670
+حكاية Scalar و Vector أجّي قضيتهم لـ Chapter 3 We
+
+143
+00:11:31,670 --> 00:11:39,190
+Shall المستقبل القريب كمان أسبوع اتريد نعمل Vector
+
+144
+00:11:39,190 --> 00:11:43,090
+Quantities in detail بكل التفاصيل تبعتهم في
+
+145
+00:11:43,090 --> 00:11:46,230
+Chapter 3 الشبطر اللي جاي احنا الآن في أي شبطر؟
+
+146
+00:11:46,230 --> 00:11:50,090
+نين لسه بدنا .. Vectors قالوا طيب مانت بتقولي
+
+147
+00:11:50,090 --> 00:11:54,800
+Displacement كي بتتعامل معاها DisplacementVictor
+
+148
+00:11:54,800 --> 00:11:59,240
+يعني بدك تقولي شرق ولا غرب، بدك تقولي فوق ولا تحت،
+
+149
+00:11:59,240 --> 00:12:02,620
+واحنا لسه ماخدناش chapter تلاتة، بقوله بسيطة، ده
+
+150
+00:12:02,620 --> 00:12:06,660
+ده ده ده، انت بتعرف موجة بوسالب؟ ماعشان بنعرف موجة
+
+151
+00:12:06,660 --> 00:12:12,260
+بوسالب؟ خدلي الموجب لما تكون الحركة رايحة يمينطب
+
+152
+00:12:12,260 --> 00:12:16,960
+لما تكون يسار صارت سالب هذه لما الحركة تكون أفقية
+
+153
+00:12:16,960 --> 00:12:22,540
+طيب السقوط الحر أفقي و لا عمودي عمودي قال لي ويه
+
+154
+00:12:22,540 --> 00:12:25,640
+بدك تاخده ماللي التالي اللي لفوق إيش بدك تاخده
+
+155
+00:12:25,640 --> 00:12:28,880
+مودب و اللي لتحت سالب طب أحد بيقول من وين جيبناها
+
+156
+00:12:28,880 --> 00:12:32,760
+قالوا هو أنت بتعرف لما كنا نور الصمت هذا المحاور
+
+157
+00:12:32,760 --> 00:12:37,380
+ذاكرينهالمشكلة اللي نرسمها هي المحور الصادق يكون
+
+158
+00:12:37,380 --> 00:12:42,280
+اتجاه الموجب لأعلى والصيني ليمين يعني هيك بدي
+
+159
+00:12:42,280 --> 00:12:45,920
+ااخده يعني انت اول ما تشوف سالب هى بتقول هذه رايحة
+
+160
+00:12:45,920 --> 00:12:50,100
+يسار اول ما تشوف سالب وهى عموديا بتقول هذا نازل
+
+161
+00:12:50,100 --> 00:12:55,490
+لأسفل صح ولا لأin this chapter اللي هو chapter 2
+
+162
+00:12:55,490 --> 00:12:59,290
+ماوصلنا لـ chapter 3 we use إيش بقت تستخدم؟ جالي
+
+163
+00:12:59,290 --> 00:13:03,630
+ال positive و ال negative نعرفه مظبوطة إيه؟ تمام
+
+164
+00:13:03,630 --> 00:13:08,530
+to the indicate عشان نشير vector not direction لل
+
+165
+00:13:08,530 --> 00:13:12,210
+vector اتجاه ال vector vector direction direction
+
+166
+00:13:12,210 --> 00:13:16,990
+تجاه و ال vector القمية المتجهة تمام إيش يعني؟
+
+167
+00:13:16,990 --> 00:13:20,370
+بيقولي for horizontal motion horizontal أفقية
+
+168
+00:13:20,370 --> 00:13:26,930
+بناهاللحركة الأفقية بدنا نحدد و نصف إلى الجانب
+
+169
+00:13:26,930 --> 00:13:30,830
+اللي عايش على اليمين كمصطلح الـ Positive Direction
+
+170
+00:13:30,830 --> 00:13:35,410
+إذا الـ Positive معناتها يمين اتفجنا؟ هذا اتفاق
+
+171
+00:13:35,410 --> 00:13:39,830
+والله غيرناه مع بعض، ممكن، لكن هذا الاتفاق الـ
+
+172
+00:13:39,830 --> 00:13:46,890
+Default، تسألي؟تمام؟ while .. بينما for vertical
+
+173
+00:13:46,890 --> 00:13:50,210
+motion ها .. هذي horizontal أفوخي .. vertical
+
+174
+00:13:50,210 --> 00:13:57,670
+عمودي للحركة العمودية we specify حددنا the upward
+
+175
+00:13:57,670 --> 00:14:02,250
+.. upward .. إيش يعني up؟ لأعلى .. إذا الاتجاه
+
+176
+00:14:02,250 --> 00:14:07,090
+اللي لأعلى هو ال positive اتفجنا؟ هيك اتفجنا .. تم
+
+177
+00:14:09,350 --> 00:14:14,650
+العين قال لي تغير الموضوع صار في حركة حركة معناته
+
+178
+00:14:14,650 --> 00:14:19,210
+في سرعة في سرعة بنسمي أول حاجة ال average velocity
+
+179
+00:14:19,210 --> 00:14:24,150
+السرعة المتوسطة تمام هل جيتوا احنا مروحين على
+
+180
+00:14:24,150 --> 00:14:28,410
+خانونس نركب سيارة ولا لأ سرعة السيارة من غزة
+
+181
+00:14:28,410 --> 00:14:32,720
+لخانونس ثابتةبضرها يعني هو حد مقدر يقولي طيب بدي
+
+182
+00:14:32,720 --> 00:14:37,760
+سرعة ساعتها أنت بتقولي سرعة بدي سرعة متوسطة ولا لأ
+
+183
+00:14:37,760 --> 00:14:41,100
+عشان أقدر أديك لأن مرة كانت واقفة و مرة كانت سريعة
+
+184
+00:14:41,100 --> 00:14:44,740
+و مرة كانت بطيئة صحيح ولا لأ؟ إذا أن أنت لما تحكي
+
+185
+00:14:44,740 --> 00:14:50,300
+عن سرعات مش ثابتة بتحكي عن متوسط السرعة average
+
+186
+00:14:50,300 --> 00:14:54,710
+velocity يعني سرعة متوسطةتمام يا بنات؟ كل واحد
+
+187
+00:14:54,710 --> 00:14:59,690
+فيكم لو قلتله النسافة من هنا لخانونس نفترض تلاتين
+
+188
+00:14:59,690 --> 00:15:03,590
+كيلومتر وانت أخدتها بساعة بتقدر تجيبلي سرعة
+
+189
+00:15:03,590 --> 00:15:07,910
+السيارة كمتوسطة ولا لأ؟ اه التلاتين كيلومتر ع
+
+190
+00:15:07,910 --> 00:15:13,240
+الساعة بجيبلكي إياها صح ولا لأ؟ تم اذا بقولليالـ
+
+191
+00:15:13,240 --> 00:15:16,220
+Average Velocity إذا ما هي معانات الـ Average؟
+
+192
+00:15:16,220 --> 00:15:20,000
+متوسطة الـ Average Velocity of a particle is
+
+193
+00:15:20,000 --> 00:15:24,480
+defined as .. إيش رمز السرعة يا بنات؟ V ما زال بدك
+
+194
+00:15:24,480 --> 00:15:28,580
+average بحطه بار فوق الحرف هذه معاناتها متوسطة
+
+195
+00:15:28,580 --> 00:15:35,860
+نهاي رمزها V وفي الشرطة هذهدلتا X على دلتا T دلتا
+
+196
+00:15:35,860 --> 00:15:40,260
+X الإزاحة اللي اتوقعتها أنا وياك اللي هي X final
+
+197
+00:15:40,260 --> 00:15:44,280
+نقص X initial ولا لأ؟ ودلتا T هي الدلتا اللي إلها
+
+198
+00:15:44,280 --> 00:15:49,280
+small تمام؟ اللي هي برضه T final نقص T initial
+
+199
+00:15:49,280 --> 00:15:54,530
+دائما الدلتا بتعني تغيرالتفاجنة تمت جلي بسيطة
+
+200
+00:15:54,530 --> 00:15:59,970
+فضلاها السرعة المتوسطة هي الإزاحة على الزمن
+
+201
+00:15:59,970 --> 00:16:03,970
+التفاجنة طوجنا على خانون السلتين كيلومتر على
+
+202
+00:16:03,970 --> 00:16:08,490
+الساعة الفترة الزمنية اللي استغرقت رحلتها من غزا
+
+203
+00:16:08,490 --> 00:16:14,790
+لخانونس حلوبقول ليه؟ القانون إيش بيقول؟ بيقول حسب
+
+204
+00:16:14,790 --> 00:16:19,250
+الكلام هجت وين كانت في غزة صح؟ و وين وصلت؟ خلوا
+
+205
+00:16:19,250 --> 00:16:22,830
+ناس هجت في القانون مبين انه روح المغازي ولا مارحش؟
+
+206
+00:16:22,830 --> 00:16:28,090
+لأ مالكاش دعوة إيش علاش بتعتمد فقط؟ بس البداية و
+
+207
+00:16:28,090 --> 00:16:32,170
+النهاية إذا the average velocity depends only
+
+208
+00:16:32,170 --> 00:16:36,010
+تعتمد فقط on the initial and the final positions
+
+209
+00:16:36,010 --> 00:16:42,980
+of the particle أمي طيب سيارة كانت في غزةتمام و
+
+210
+00:16:42,980 --> 00:16:47,280
+قصدرت و قهضت راحتها و أخر الليل وصلت غزة اجيت بدي
+
+211
+00:16:47,280 --> 00:16:50,840
+اجيب ال body displacement تبعتها سفر طب و ال
+
+212
+00:16:50,840 --> 00:16:54,940
+average velocity سفر ان شاء الله خمس ساعات قعدت
+
+213
+00:16:54,940 --> 00:16:59,820
+سفر على خمس ساعات ولا عشرين ساعة ما السفرتمام؟ إذا
+
+214
+00:16:59,820 --> 00:17:03,780
+أي جسم ببدأ من نقطة وبرجعلها لديه سرعته المتوسطة؟
+
+215
+00:17:03,780 --> 00:17:08,240
+سفر بيقول ليه؟ إيش معناته؟ بيقول ليه this means
+
+216
+00:17:08,240 --> 00:17:13,780
+that ما زال السرعة المتوسطة تعتمد فقط على نقطتي
+
+217
+00:17:13,780 --> 00:17:18,460
+البداية والنهاية إذا تساوت نقطتي البداية والنهاية
+
+218
+00:17:18,460 --> 00:17:24,250
+فاش سرعة this means that if a particleit starts
+
+219
+00:17:24,250 --> 00:17:27,970
+from a point بدأ من نقطة and returns back to the
+
+220
+00:17:27,970 --> 00:17:32,210
+same point ورجع إلها نفسها this is displacement
+
+221
+00:17:32,210 --> 00:17:37,650
+بتكون إذعتها وبالتالي سرعتها المتوسطة zero صح ولا
+
+222
+00:17:37,650 --> 00:17:42,390
+لأ؟ هذه معلومة معروفة مافيش فيها إشي إحنا متفقين
+
+223
+00:17:42,390 --> 00:17:46,150
+اللي عندها سؤاله تنط على طول احكي شايفك خايفة أنا
+
+224
+00:17:49,720 --> 00:17:53,960
+هذه الـ Average Velocity هي بتعريفها يا بنتي
+
+225
+00:17:53,960 --> 00:17:57,760
+هتبديك المسافة استنيني شوية الـ Average Velocity
+
+226
+00:17:57,760 --> 00:18:01,160
+تعريفها العلمي اللي كل الناس بعرفه هي displacement
+
+227
+00:18:01,160 --> 00:18:07,300
+ع زمان و ليست مسافة ع زمان فيم تعنيها؟ ليش اسمك؟
+
+228
+00:18:07,300 --> 00:18:12,250
+ايش اسمك انت؟ أسيل؟ ليش يسموك أسيل؟عشان ايه عبارة
+
+229
+00:18:12,250 --> 00:18:16,090
+عن أبوك و أمك؟ مصطلح ان كل حاجة بدنا نتعرفها المهم
+
+230
+00:18:16,090 --> 00:18:20,590
+ايه يا بنت ايه؟ انه احنا كنا نتفق كعالم انه هاجي
+
+231
+00:18:20,590 --> 00:18:24,750
+هيك تعريفها هاجيت فيه velocity مش توجب تليك في
+
+232
+00:18:24,750 --> 00:18:29,130
+حاجة اسمها speed؟ اذا احنا مظلمنهاش المسافة هنديها
+
+233
+00:18:29,130 --> 00:18:33,830
+speed استني شوية علينا تمام؟ اذا بدنا نتفق ايش فيه
+
+234
+00:18:33,830 --> 00:18:35,870
+ال velocity و ايش ال speed؟ اتفقوا الناس ال
+
+235
+00:18:35,870 --> 00:18:38,450
+velocity اللي هدعوا بيجي سبلاش من كل المسافة؟دي
+
+236
+00:18:38,450 --> 00:18:42,390
+اسم لاسمى، اتفقنا؟ في شانات كتيرة مفهوش تقولي ليش،
+
+237
+00:18:42,390 --> 00:18:49,050
+هات هي اتفاق، ليش الشرق عملوا شرق؟ ليش معكسوهوش؟
+
+238
+00:18:49,050 --> 00:18:54,270
+ليش الساعة بتلف هيك؟ معكسوهاش، اتفاقات، تمام هيك؟
+
+239
+00:18:54,270 --> 00:18:57,930
+ففي أمور كتير خلاص، اتفاق و بقى، لنفترض لو أنت كنت
+
+240
+00:18:57,930 --> 00:19:02,090
+معاه وغيرتي ممكن يردوا عليكي وغيروا، خلوها مختلفة،
+
+241
+00:19:02,090 --> 00:19:07,850
+ففهمتوا عليكي؟ ففي أمور default بتصيرانتبه ..
+
+242
+00:19:07,850 --> 00:19:11,970
+Average Speed .. Average Speed .. هي .. طب هو
+
+243
+00:19:11,970 --> 00:19:14,970
+Average فلسفة تخلصنا منها ومعناتها بالعربي سرعة
+
+244
+00:19:14,970 --> 00:19:18,990
+متوسطة .. Average Speed سرعة متوسطة .. بس الآن
+
+245
+00:19:18,990 --> 00:19:21,490
+بيقول .. هي و اللي رأى مغازك كيف بدي أسوي فيه هذا
+
+246
+00:19:21,490 --> 00:19:26,030
+.. قال لي هنا بجيبهالـ Average Speed بدك تجيبلي
+
+247
+00:19:26,030 --> 00:19:29,170
+المسافة على الزمن وليست الإزاحة على الزمن وبالتالي
+
+248
+00:19:29,170 --> 00:19:32,090
+لو وقع المجازي بتحسبها ولا لأ؟ هاي نحسبناها يا
+
+249
+00:19:32,090 --> 00:19:37,070
+عزيزي إذا ما هو تعريف الـ Average Speed؟ Differs،
+
+250
+00:19:37,070 --> 00:19:41,370
+تختلف عن الـ Average Velocity اتفقنا هيك كيف
+
+251
+00:19:41,370 --> 00:19:45,210
+بتختلف؟ بقولي in that it covers في الـ Average
+
+252
+00:19:45,210 --> 00:19:48,910
+Speed بيبقى تغطيلي it covers the total distance
+
+253
+00:19:48,910 --> 00:19:52,510
+بطل ال displacementthe total distance rather than
+
+254
+00:19:52,510 --> 00:19:56,350
+وليست ال total displacement rather than the total
+
+255
+00:19:56,350 --> 00:19:59,450
+displacement يعني كيف القلوب ده تصير? other
+
+256
+00:19:59,450 --> 00:20:02,970
+distance بتساوي ال displacement ولا ال distance؟
+
+257
+00:20:02,970 --> 00:20:07,430
+distance على زمان والزمان زمان ماتغيرش ولا لأ؟
+
+258
+00:20:07,430 --> 00:20:12,490
+زمان زمان ارضيتي هال gate هالمسافة مازالة ماناهاش؟
+
+259
+00:20:12,490 --> 00:20:20,700
+الها تعريف الها speed اتفجنا؟ تمامقاللي الصرعة
+
+260
+00:20:20,700 --> 00:20:25,280
+كمية ماهياش من الكميات الأساسية تبع علم الميكانيكا
+
+261
+00:20:25,280 --> 00:20:30,140
+انت المحاضرة الماضية قلتلي في تلت كميات أساسية في
+
+262
+00:20:30,140 --> 00:20:34,760
+علم الميكانيكا mass و length و time طيب ال
+
+263
+00:20:34,760 --> 00:20:39,420
+velocity ما قلتلي ده مظبوط ماقالتلي كل كمية هتمر
+
+264
+00:20:39,420 --> 00:20:43,450
+عليك بعد كده بيكترجح ل هدول التلاتةتما الـ
+
+265
+00:20:43,450 --> 00:20:46,990
+Velocity الـ dimension تبعها L على T وبالتالي
+
+266
+00:20:46,990 --> 00:20:50,410
+وحدات في متر per second او centimeter per second
+
+267
+00:20:50,410 --> 00:20:54,470
+او foot per second صح؟ اذا بيقولي بقص I unit of
+
+268
+00:20:54,470 --> 00:20:57,510
+velocity ايش هتكون؟ متر per second ده أنا رجعتها
+
+269
+00:20:57,510 --> 00:21:01,730
+وصلات كمية معروفة وعارف عنها كل حاجة اتفجنا يا
+
+270
+00:21:01,730 --> 00:21:05,850
+بنات؟ أيه الصفة صح؟
+
+271
+00:21:05,850 --> 00:21:10,740
+remarkجالي بدك اتميزي واحدة واحدة بين speed و
+
+272
+00:21:10,740 --> 00:21:15,300
+velocity صح ولا .. جالي اتطلعوا يا بنات لما اقولكم
+
+273
+00:21:15,300 --> 00:21:21,240
+velocity بدي اقولكم the velocity of a car صورة ايش
+
+274
+00:21:21,240 --> 00:21:30,140
+سيارة velocity is fifty kilometer per hour هيك
+
+275
+00:21:30,140 --> 00:21:35,200
+بيتكونش كملت لازم تقولي كده في الاتجاه to the east
+
+276
+00:21:35,200 --> 00:21:40,940
+خلصتأو to the west هيك منيح او تقولي up او تقولي
+
+277
+00:21:40,940 --> 00:21:44,620
+down هذه بتحكي عن ال velocity لكن طب يابو تقولي
+
+278
+00:21:44,620 --> 00:21:49,260
+the speed of the car is fifty kilometer per hour
+
+279
+00:21:49,260 --> 00:21:54,500
+نقطة خلصت speed speed فلتوا من ال distance speed
+
+280
+00:21:54,500 --> 00:21:59,660
+اذا ال speed تعريفها هي مقدار ال velocity مقدار ال
+
+281
+00:21:59,660 --> 00:22:03,320
+velocity بدون direction ال speed مقدار ال velocity
+
+282
+00:22:04,620 --> 00:22:07,880
+دخلت المعلومة جوا؟ ايش بتفرج ال speed عن ال
+
+283
+00:22:07,880 --> 00:22:11,400
+velocity؟ ال speed مقدار السرعة اقول بالعربي سرعة
+
+284
+00:22:11,400 --> 00:22:15,120
+سيارة خمسين كيلومتر بالساعة شرقا جدتش ال speed
+
+285
+00:22:15,120 --> 00:22:19,540
+بتاعتها؟ خمسين كيلومتر بالساعة نقطة بقولش شرقا ولا
+
+286
+00:22:19,540 --> 00:22:23,940
+غربا تمام؟ تاخد بس المقدار هذا ال speed و ال
+
+287
+00:22:23,940 --> 00:22:28,640
+velocity فهمتها جالي طب هل ال average speed هي
+
+288
+00:22:28,640 --> 00:22:32,060
+مقدار ال average velocity؟ بيقولي لأ لما تدخل ال
+
+289
+00:22:32,060 --> 00:22:37,030
+average بتبطلإذا بيقوللي الـ remark even though
+
+290
+00:22:37,030 --> 00:22:40,830
+بالرغم من أنه المعلومة اللي أديتكم ياها الأولى ال
+
+291
+00:22:40,830 --> 00:22:43,630
+speed is the magnitude of the velocity ال speed هو
+
+292
+00:22:43,630 --> 00:22:48,430
+مقدار ال velocity إلا إنه the average speed is not
+
+293
+00:22:48,430 --> 00:22:51,470
+the magnitude of the average velocity اتفجنا يا
+
+294
+00:22:51,470 --> 00:22:58,250
+بنات؟ تمام هيك؟ هديك مثال عليه هديت ال speed مقدار
+
+295
+00:22:58,250 --> 00:23:02,750
+ال velocityتمام؟ الـ Average Speed ماهياش مقدار
+
+296
+00:23:02,750 --> 00:23:06,090
+الـ Average Velocity اتفقنا؟ قعدتش تقولي ليه ليش،
+
+297
+00:23:06,090 --> 00:23:09,090
+اتنى شوية شوية بنضل نقول ليه ليش لما كل في كل حاجة
+
+298
+00:23:09,090 --> 00:23:14,390
+أيها ليش بنقول عنها اتفقنا؟ حلو، quiz نحن اتفقنا
+
+299
+00:23:14,390 --> 00:23:17,910
+كل من أكم شريحة بإن نشوف حالنا بنحكي عربي ولا صيني
+
+300
+00:23:18,730 --> 00:23:22,050
+تمام احنا مش خدنا لسه عشان نقول فهمنا ولا مافهمنا
+
+301
+00:23:22,050 --> 00:23:24,670
+اش ماخدناش حاجة اخدنا الفرق بين ال distance و
+
+302
+00:23:24,670 --> 00:23:29,110
+displacement صح؟ واخدنا الفرق بين average speed و
+
+303
+00:23:29,110 --> 00:23:35,860
+average velocity صح؟ حلو اش بقولي؟ under whichof
+
+304
+00:23:35,860 --> 00:23:39,560
+the following conditions هنا conditions معناته شرط
+
+305
+00:23:39,560 --> 00:23:44,680
+تحت أي من هذه الشروط is the magnitude of the
+
+306
+00:23:44,680 --> 00:23:48,800
+average velocity of a particle moving in one
+
+307
+00:23:48,800 --> 00:23:52,460
+direction smaller than the average speed over some
+
+308
+00:23:52,460 --> 00:23:56,200
+time interval أنا أول سألتكم وجاوبتوني صح قلتلكم
+
+309
+00:23:56,200 --> 00:24:01,590
+المسافة والإزاحةدايمًا جات بعض؟ طب هل ممكن الإزاحة
+
+310
+00:24:01,590 --> 00:24:06,090
+تكون أكبر من المسافة؟ ولا ممكن؟ هنا بيقوللي واكتيش
+
+311
+00:24:06,090 --> 00:24:10,570
+بتكون الإزاحة أقل من المسافة، بيددك تلت حركات، و
+
+312
+00:24:10,570 --> 00:24:15,310
+بتقوللي في هذه الحركات الإزاحة أقل، مش ممكن يقولك
+
+313
+00:24:15,310 --> 00:24:22,170
+أكبر، أقل ولا بتساوي، وهي كأنها، اشوفA particle
+
+314
+00:24:22,170 --> 00:24:27,190
+moves in the X direction without reversing واحد
+
+315
+00:24:27,190 --> 00:24:33,090
+ماشي ايديل ومارجعيش بتسويها هل الإزاحة أقل من
+
+316
+00:24:33,090 --> 00:24:36,850
+المسافة؟ لأ إذا هذا ال condition غلط صح ولا لأ؟
+
+317
+00:24:36,850 --> 00:24:41,850
+أنا بدي أي حركة فيها الإزاحة أقل من المسافة هنا زي
+
+318
+00:24:41,850 --> 00:24:48,580
+بعض ولا لأ؟ زي بعض حلوA particle moves in the
+
+319
+00:24:48,580 --> 00:24:54,360
+negative X direction without reversing نفس العملية
+
+320
+00:24:54,360 --> 00:24:58,500
+يعني زي ما حكينا احنا جامعتنا بتطلع الشارع
+
+321
+00:24:58,500 --> 00:25:01,940
+التلاتيني بيسموها صح؟ هجيت لما نروح الشرق وين
+
+322
+00:25:01,940 --> 00:25:07,120
+بيخلص الشارع التلاتيني؟ وين بيخلص؟ أيش المنطقة
+
+323
+00:25:07,120 --> 00:25:10,440
+اللي بيخلص عندها؟ لأ جاب للساحة أيش المنطقة
+
+324
+00:25:10,440 --> 00:25:13,780
+بيسموها؟ وين سكان الزتون؟ عصقولة مافيش حد سكن
+
+325
+00:25:13,780 --> 00:25:18,500
+عصقولة هنا؟تعرفوا منطقة عصقولة؟هذه بتخلص شارع
+
+326
+00:25:18,500 --> 00:25:22,360
+التلاتين ساعتها لأ بتروح لفوق على الساحة لأ بتروح
+
+327
+00:25:22,360 --> 00:25:26,640
+على مسجد الشافعي اللي هو أشهر مسجد في الحرق تمام؟
+
+328
+00:25:26,640 --> 00:25:30,160
+إذا بيخلص الشارع وين عند عزجولة؟ واحد مشي لما خلص
+
+329
+00:25:30,160 --> 00:25:34,080
+عند عزجولة إزحته مسافته زي بعض ولا لأ؟ تمام طب
+
+330
+00:25:34,080 --> 00:25:37,660
+واحد قال أنا بديش أروح على عزجولة بدي أروح تجاه
+
+331
+00:25:37,660 --> 00:25:41,260
+البحر وين بيخلص هذا الشارع؟ شارع الرشيد شارع البحر
+
+332
+00:25:41,260 --> 00:25:46,860
+هي هي الإزاحة والمسافة بختلفوا عن بعض؟ لأإذا في
+
+333
+00:25:46,860 --> 00:25:51,640
+الحالتين زي بعض طب يشوف a particle moves in the
+
+334
+00:25:51,640 --> 00:25:55,200
+positive x direction يعني رايح على أسجولة و رجع و
+
+335
+00:25:55,200 --> 00:26:01,340
+في المفترج الطيران بتعرفوه تسمعوا فيه جابلي
+
+336
+00:26:01,340 --> 00:26:08,140
+الجامعة برا عليكم هجيت هو وصل على أسجولة و رجع in
+
+337
+00:26:08,140 --> 00:26:12,350
+the x direction and then reverses و رجعتمام مين
+
+338
+00:26:12,350 --> 00:26:15,650
+أكبر؟ المسافة ولا الإزاحة؟ المسافة إذاً هنا
+
+339
+00:26:15,650 --> 00:26:19,630
+الإزاحة أقل من المسافة إذاً معناته ال average
+
+340
+00:26:19,630 --> 00:26:23,470
+velocity أقل من ال average speed ولا لأ؟ إذاً
+
+341
+00:26:23,470 --> 00:26:27,630
+معناته هو بيقوللي مين من التلاتة هدول ال average
+
+342
+00:26:27,630 --> 00:26:30,350
+velocity أقل من ال average speed؟ مين من التلاتة
+
+343
+00:26:30,350 --> 00:26:34,950
+دول؟ ال C وفي الآخر بيقوللي واحد غلب يقولك و I'm
+
+344
+00:26:34,950 --> 00:26:38,570
+under no conditions لأ إذاً هادي قطعا ولا لأ؟
+
+345
+00:26:38,570 --> 00:26:44,240
+اسأليه احكي يا Cاحكي .. احكي ..
+
+346
+00:26:51,950 --> 00:26:54,950
+برافو عليك ايش؟ بدي نقطتي البداية والنهاية فهمتوا
+
+347
+00:26:54,950 --> 00:26:58,850
+عليّ؟ احكي بدي نقطتي البداية والنهاية البداية من
+
+348
+00:26:58,850 --> 00:27:02,730
+الجامعة ولا لأ؟ والنهاية الطيران الطيران هيو لو
+
+349
+00:27:02,730 --> 00:27:06,750
+غوّشت أنا بقى باس معنى تبع الطيران هيو لكن عزجولة
+
+350
+00:27:06,750 --> 00:27:11,750
+بعيدة أو بالتالي تطلعوا أنتوا المسافة بدي أجيس من
+
+351
+00:27:11,750 --> 00:27:16,090
+هان لعزجولة و بعدين أرجع للطيران مسافة كبيرة غير
+
+352
+00:27:16,090 --> 00:27:22,320
+عن اليزاحة من هان لعزجولة كلها أقل من كيلوبتجيش نص
+
+353
+00:27:22,320 --> 00:27:37,820
+كيلو من محور الطيران او دور الطيران احكي بالظبط
+
+354
+00:27:37,820 --> 00:27:38,620
+بالظبط احكي
+
+355
+00:27:44,700 --> 00:27:47,600
+الـ Average Speed و الـ Average Velocity جت بعض
+
+356
+00:27:47,600 --> 00:27:51,380
+لأن الشوء الـ Average Velocity جالي جسم لسمة عزمان
+
+357
+00:27:51,380 --> 00:27:56,830
+صح؟ و الـ Average Speed مسافة عزمان صح؟ بيفرقوامش
+
+358
+00:27:56,830 --> 00:27:59,830
+المسافة نفس الإزاحة؟ و الزمان زمان و احنا الزمان
+
+359
+00:27:59,830 --> 00:28:04,250
+مابنلاعبش فيه؟ عشان كده كانت ضحكت في التالتة مين
+
+360
+00:28:04,250 --> 00:28:09,030
+أكبر؟ المسافة ولا الإزاحة؟ اللي راح و رجع حلو إذا
+
+361
+00:28:09,030 --> 00:28:13,050
+معاتوا ال average velocity أقل من ال average speed
+
+362
+00:28:13,050 --> 00:28:19,030
+ولا لأ؟ اه وهي بيقوللي مين من التلاتة هدول تمام؟
+
+363
+00:28:19,030 --> 00:28:22,230
+the average velocity is smaller than the average
+
+364
+00:28:22,230 --> 00:28:27,150
+speed بقوله هذه التالتة صح ولا لأ؟ما تخجلوش انت
+
+365
+00:28:27,150 --> 00:28:29,790
+بتسأل و احكي يا أسيل فجيت المسافة أكبر من الإتاح
+
+366
+00:28:29,790 --> 00:28:34,950
+تمامًا بس الزمان ليش ممكن .. اه حلو هجيت أنت طلعت
+
+367
+00:28:34,950 --> 00:28:39,770
+و استغرقت مراتي اللي .. اللي واجت معاكي بياخد ساعة
+
+368
+00:28:39,770 --> 00:28:42,850
+و مراتي بياخد معاكي نص ساعة زمان زمان انا في
+
+369
+00:28:42,850 --> 00:28:48,510
+النهاية انت لما تصل الطيران سيارة راح .. بديها تصل
+
+370
+00:28:48,510 --> 00:28:53,390
+الطيران اجي عبالها تتجذر تمام؟ اذا الزمان بديك
+
+371
+00:28:53,390 --> 00:28:58,720
+تاخديه كله كل الزمانفهمت عليّ كيف؟ حتى و لو بدك
+
+372
+00:28:58,720 --> 00:29:02,700
+إذاحة طب هو أنتي وصلت الطيران مش أخدت و أجيت أكتار
+
+373
+00:29:02,700 --> 00:29:07,080
+لما وصلت الطيران لما أنتي وصلت عزجولة و رجعت صح؟
+
+374
+00:29:07,080 --> 00:29:11,540
+انت هجيت انتي من وين انطلقتي؟ من الجامعة و وين
+
+375
+00:29:11,540 --> 00:29:17,100
+خلصتي؟ عند الطيران تمام؟ بنفع ألغي عزجولة و أنتي
+
+376
+00:29:17,100 --> 00:29:22,380
+روحت عزجولة؟بدي .. بدي أحملها في حزبتي؟! بالتالي
+
+377
+00:29:22,380 --> 00:29:26,840
+الزمن تبعك بدي تحسبه، ماينفعش تطير زمن، لأن الزمن
+
+378
+00:29:26,840 --> 00:29:31,260
+شغلها حقيقية، انت كنت وانت سرتي، هد أخد معاك الوجد
+
+379
+00:29:31,260 --> 00:29:34,340
+ولا لا؟! بدي كل الوجد اللي أخده معاك، بغض النظر في
+
+380
+00:29:34,340 --> 00:29:37,340
+الطريق، إيه سويت؟! يعني انت لما روحت خلونس، لما
+
+381
+00:29:37,340 --> 00:29:41,240
+تروحي عدل، نفس الزمن بتاخديه وانت بتميل ع المغازة
+
+382
+00:29:41,240 --> 00:29:44,960
+وع الدير؟! إذا ان انت لما تقولي رحليتي استقلقت،
+
+383
+00:29:44,960 --> 00:29:48,200
+بدي تاخدي في عين الاعتبار كل شيء ولا لا؟!إذا بديك
+
+384
+00:29:48,200 --> 00:29:53,660
+الزمن الحقيقي يا بنتي هذا زمن حقيقي كله تمانية
+
+385
+00:29:53,660 --> 00:30:00,800
+بنات غيره مثال جالي
+
+386
+00:30:00,800 --> 00:30:05,400
+سيارة قاعدة بتتحرك ما زالتحركت موضوع حبدالله زي ما
+
+387
+00:30:05,400 --> 00:30:10,580
+هو لأ بتغير جالي the figure shown ال figure اللي
+
+388
+00:30:10,580 --> 00:30:14,030
+انت شايفه figure يعني ايش ما اسمهااللي انت شايفه
+
+389
+00:30:14,030 --> 00:30:19,670
+شون يعني اللي شايفه represent يمثل represent the
+
+390
+00:30:19,670 --> 00:30:25,630
+variation تغير of position with time for a car
+
+391
+00:30:25,630 --> 00:30:31,510
+بيفرجيك كيف اتغير موضع سيارة بالنسبة للزمن كيف ده
+
+392
+00:30:31,510 --> 00:30:35,150
+اللي كانت السيارة عند النقطة A صارت عند النقطة B
+
+393
+00:30:35,150 --> 00:30:39,610
+صارت عند النقطة C صارت عند النقطة D ثم E ثم وقفت
+
+394
+00:30:39,610 --> 00:30:45,960
+عند F امي محطات ادي خلنا نقولتمى قاللي عند النقطة
+
+395
+00:30:45,960 --> 00:30:51,920
+E كانت تبعد عن ال origin 30 متر هيك ده .. هذي
+
+396
+00:30:51,920 --> 00:30:57,720
+معطيات عند النقطة B صارت 52 متر شوفوا عند النقطة C
+
+397
+00:30:57,720 --> 00:31:02,180
+رجعت ولا مارجعتش جربت في الأول كانت تبعد و بعدين
+
+398
+00:31:02,180 --> 00:31:07,810
+جربت عشان نفهمها بس لأنه كانت 52 جديد صارت38 جربت
+
+399
+00:31:07,810 --> 00:31:12,330
+هنا وجعت لنقطة الأصل جربت أكتر هنا بالسالب جلب
+
+400
+00:31:12,330 --> 00:31:15,830
+اتجاه المعاكس وكأنه انطلقت من هذه النقطة يا بنات
+
+401
+00:31:15,830 --> 00:31:21,510
+مشيت و بعدين رجعت بعدين رجعت هنا ما زادت هنا صارت
+
+402
+00:31:21,510 --> 00:31:25,730
+بالسالب ولا مش بالسالب؟ مش سالب وظلت ماشية هيك لما
+
+403
+00:31:25,730 --> 00:31:30,730
+وصلت النقطة F كانت ناقص 53 متر موجة بوسالي بيفهمنا
+
+404
+00:31:30,730 --> 00:31:37,800
+إيش معناتها معناته يسار يمين حلوبقول لي ايش بدك
+
+405
+00:31:37,800 --> 00:31:42,420
+امنك هاد دراسة مافهمتها هاد مواضع ومحطات وكل واح
+
+406
+00:31:42,420 --> 00:31:47,600
+محطة جديش غابت وجديش الزمن اللي استغرقه جالي لما
+
+407
+00:31:47,600 --> 00:31:52,380
+وصل النقطة ايه اخد عشر ثواني النقطة B صار عشرين
+
+408
+00:31:52,380 --> 00:32:00,380
+ثانية النقطة C دي تلاتين ايه خمسين اربعين او خمسين
+
+409
+00:32:00,380 --> 00:32:04,840
+جديش اخدته الرحلة خمسين هاد حقيقة ساعة بتقدر توقف
+
+410
+00:32:04,840 --> 00:32:08,850
+الساعةماحد مقدر يوقف الزمن هذه الزمن بدي أعده بغض
+
+411
+00:32:08,850 --> 00:32:13,330
+النظر أنت روحت عدل ولا جزرت فهمت عليها؟ حلو إيش
+
+412
+00:32:13,330 --> 00:32:19,250
+بدك؟ قاللي بدي find يعني أوجد the displacement
+
+413
+00:32:22,020 --> 00:32:25,360
+فاصلة The average velocity قال لما ضعفتي الأول
+
+414
+00:32:25,360 --> 00:32:30,460
+عرفتي التانية ولا لأ ما هي التانية ال displacement
+
+415
+00:32:30,460 --> 00:32:34,160
+ع زمان جديش الزمان الكل تابع الرحلة خمسين ثانية
+
+416
+00:32:34,160 --> 00:32:37,780
+براو تمام و إيش بدك كمان قال لي I'm the average
+
+417
+00:32:37,780 --> 00:32:42,460
+speed لما بيجي ال speed بدي إزاحة ولا بيجي مسافة
+
+418
+00:32:42,460 --> 00:32:47,000
+براو علينا نيجي واحدة واحدة إيش بدك قال لي
+
+419
+00:32:47,000 --> 00:32:55,520
+displacement إذا إيهبدي Delta X ولا لأ Delta X ايش
+
+420
+00:32:55,520 --> 00:33:02,400
+تعني Delta X Bravo عليكم X final ناقص X initial
+
+421
+00:33:02,400 --> 00:33:06,700
+اليك دعوة كيف وصلراح ع المغازي راح ع الانصارات
+
+422
+00:33:06,700 --> 00:33:13,120
+ماكنش دعوة قلني حلو بتساوي هه نكتب القانون X final
+
+423
+00:33:13,120 --> 00:33:17,900
+ناقص X initial ولا لا نيجي لل final هاي هاي ال
+
+424
+00:33:17,900 --> 00:33:21,720
+final كداش ناقص تلاتة و خمسين نقولها مانامدكي
+
+425
+00:33:21,720 --> 00:33:22,520
+إياها مانامدكي إياها مانامدكي إياها مانامدكي إياها
+
+426
+00:33:22,520 --> 00:33:23,300
+مانامدكي إياها مانامدكي إياها مانامدكي إياها
+
+427
+00:33:23,300 --> 00:33:24,340
+مانامدكي إياها مانامدكي إياها مانامدكي إياها
+
+428
+00:33:24,340 --> 00:33:26,320
+مانامدكي إياها مانامدكي إياها مانامدكي إياها
+
+429
+00:33:26,320 --> 00:33:32,580
+مانامدكي إياها مانامدكي إياها مانامدكي إالصحيحة
+
+430
+00:33:32,580 --> 00:33:40,280
+بقول ناقص 83 متر اختبأ انا ايش ايه؟ هاي اول مطلوب
+
+431
+00:33:40,280 --> 00:33:43,280
+شوف المطلوب التاني مثله قال لي بدي ال average
+
+432
+00:33:43,280 --> 00:33:48,760
+velocity جسم على 50 ولا لأ؟ اذا بقوله V average
+
+433
+00:33:48,760 --> 00:33:53,200
+اللي بتسوي delta X على delta T delta X هيها ولا
+
+434
+00:33:53,200 --> 00:33:59,360
+لأ؟ ها دي بتسوي .. بحطها ناقص 83 على 50 one point
+
+435
+00:34:00,690 --> 00:34:05,370
+سبعة متر بيرث كان بالسالب لو عملتها بالكالكوليتر
+
+436
+00:34:05,370 --> 00:34:10,250
+هتطلع one point six ستة صح؟ ليش خليتها سبعة؟ شفتوا
+
+437
+00:34:10,250 --> 00:34:13,790
+كيف؟ لو كانت one point six أربعة بخليها سبعة؟ براو
+
+438
+00:34:13,790 --> 00:34:16,290
+عليكم، بس عشان نتذكر اللي عملناه لإن واحد
+
+439
+00:34:16,290 --> 00:34:18,450
+بالكالكوليتر جولب يلاحقوا عليه، أنا هذي طلعت عندي
+
+440
+00:34:18,450 --> 00:34:21,790
+الكالكوليتر تبعتي ستة ستة، سبعة دي ترمي
+
+441
+00:34:21,790 --> 00:34:24,450
+الكالكوليتر تقولي بتاعي أعمل غلط، لأ الكالكوليتر
+
+442
+00:34:24,450 --> 00:34:28,150
+بتاعي أعمل صح، ستة ستة بس مكتوبها سبعة، اتفاجنا؟
+
+443
+00:34:28,150 --> 00:34:35,780
+تم؟جال ليه الآن؟ بدي الـAvalanche Speed، بقوله يا
+
+444
+00:34:35,780 --> 00:34:39,380
+ورا دي، بدي المسافة كلها، بدي نلحقه، راح على
+
+445
+00:34:39,380 --> 00:34:41,760
+المغازي، راح على انصرات، راح على الدقر، راح على
+
+446
+00:34:41,760 --> 00:34:46,360
+الجرارة، كله بدينا نفلي وراه، صح؟ المحطة تنبينها
+
+447
+00:34:46,360 --> 00:34:50,310
+عيني ولا لأ؟بدي المسافة بين كل المحطات وبعدين
+
+448
+00:34:50,310 --> 00:34:53,430
+أجمعهم وإنت قاعد بتجيبني المسافات ماكانش دعوة
+
+449
+00:34:53,430 --> 00:34:56,730
+بالسالب والموجب لأن السالب والموجب معناته اتجاه
+
+450
+00:34:56,730 --> 00:35:02,530
+صح؟ حلو يلّا يا بنات شوفوني إيش بدي أسوي اطلعوني
+
+451
+00:35:02,530 --> 00:35:08,090
+وين كان هو؟ عند إيه؟ وين صار أول محطة؟ مديش
+
+452
+00:35:08,090 --> 00:35:12,550
+المسافة اللي مشيها؟لأ لأ لأ مداشي the horse من A ل
+
+453
+00:35:12,550 --> 00:35:17,150
+B كان بواب عليكي كان تلاتين سالتين و خمسين و اتنين
+
+454
+00:35:17,150 --> 00:35:20,990
+و عشرين متر مش ماشي اتنين و عشرين متر اذا هذه
+
+455
+00:35:20,990 --> 00:35:25,330
+اتنين و عشرين متر طيب من B ل C رجع و رجوع دل بالكو
+
+456
+00:35:25,330 --> 00:35:32,150
+من B ل C رجع و رجوع اربعتاش على المتر اربعتاش على
+
+457
+00:35:32,150 --> 00:35:34,890
+المتر حتى لو بالسالب من اللي جعوا فيها هي تطلع
+
+458
+00:35:34,890 --> 00:35:38,650
+سالب اربعتاش اذا طلعت اربعتاش على المتر مديش سالب
+
+459
+00:35:40,410 --> 00:35:44,750
+بدي من ابرار عليكم مسافات طيب الآن من C ل D من
+
+460
+00:35:44,750 --> 00:35:54,330
+يقول جديش براو عليكم 38 متر طيب من D ل E 37 متر
+
+461
+00:35:54,330 --> 00:36:00,010
+طيب من E ل F 16
+
+462
+00:36:00,010 --> 00:36:09,030
+16 بطل حقناهابطرح بطعم الكالكوليتر صدقوني 16
+
+463
+00:36:09,030 --> 00:36:14,710
+عملتها مع اللي جابلكم 16 هي كانت ال total distance
+
+464
+00:36:14,710 --> 00:36:19,570
+هدول كلهم زي لما نرجع للسيارة راحت على المغازي
+
+465
+00:36:19,570 --> 00:36:23,610
+جمعتها ولا لأ؟ راحت عن سراط بدي اجمعها ولا لأ؟ اذا
+
+466
+00:36:23,610 --> 00:36:28,130
+كل المحطات بدي اجمعها فانا جيبت كل المحطات اجمع
+
+467
+00:36:28,130 --> 00:36:36,020
+طلعت 127 مترالان ما هي ال average distance 127 على
+
+468
+00:36:36,020 --> 00:36:41,320
+50تمام؟ قاللي اذا الأولى زى ما انتوا شايفين حلناها
+
+469
+00:36:41,320 --> 00:36:46,640
+احنا وياكم طلعت ال displacement ناقص 83 متر جبت ال
+
+470
+00:36:46,640 --> 00:36:50,480
+average velocity بسهولة اللى طلعت ناقص 1.7 اللى
+
+471
+00:36:50,480 --> 00:36:55,460
+هيقولنا 1.66 تمام؟ لما قاللي ال average speed
+
+472
+00:36:55,460 --> 00:37:00,480
+قاللي we want to find the total distance بدك الآن
+
+473
+00:37:00,480 --> 00:37:05,120
+مش نقطة البداية و النهاية بدك كل المحطات واحدة
+
+474
+00:37:05,120 --> 00:37:09,760
+واحدةتمه .. هو هنا طبعا سهل على حاله قاللي انت من
+
+475
+00:37:09,760 --> 00:37:14,700
+الرسمة واضح انه هانمشي من A لB و بعدين من B لF
+
+476
+00:37:14,700 --> 00:37:19,340
+رجوع طبعا فقاللي خد واحدة هيك و تقعد مجين زي هيك
+
+477
+00:37:19,340 --> 00:37:23,800
+او بتعمل زي ما عملت انا كل ما حطت قاللي قداش طلعت
+
+478
+00:37:23,800 --> 00:37:28,460
+قاللي والله طلعت 127 انتبهولي في ريمارك حطيتها انا
+
+479
+00:37:28,460 --> 00:37:32,300
+ملاحظة قولتلك ال average speed لا تساوي ال
+
+480
+00:37:32,300 --> 00:37:36,150
+magnitude لل average velocityوإلا و ساعتها دي تجيب
+
+481
+00:37:36,150 --> 00:37:41,690
+ديش 1.7 طلعت وها دي 2.5 الرقمين زي بعض لأ هذا
+
+482
+00:37:41,690 --> 00:37:46,550
+بيأكد ان ال average speed لا تقرب لل average
+
+483
+00:37:46,550 --> 00:37:50,330
+velocity مابيش قرابة ممكن يتساوى ممكن واحدة تكون
+
+484
+00:37:50,330 --> 00:37:55,970
+أكبر غيرت زمانالزمن دلّه خمسين لأن هذه رحلة هذه
+
+485
+00:37:55,970 --> 00:38:00,390
+زمن رحلة بس انت لما تقولني بدك speed بقولك بدي
+
+486
+00:38:00,390 --> 00:38:06,470
+مسافة تمام؟ لأنه اصلا ليش اختلفوا لأنه هداك لو
+
+487
+00:38:06,470 --> 00:38:11,150
+واحد ادي اللي كان اخد زمن اقصر لكن عشان جذر صار في
+
+488
+00:38:11,150 --> 00:38:16,920
+عنده الزمن الأعلى اه يا بناتصرت .. احكي .. السالب
+
+489
+00:38:16,920 --> 00:38:20,800
+دايما بحمله .. لما جيه مسافات .. اه مسافات .. برا
+
+490
+00:38:20,800 --> 00:38:23,500
+.. قياسية .. اه لما بيجيه يجيه مسافات ماكانش
+
+491
+00:38:23,500 --> 00:38:25,820
+بالسالب .. مش شيل الدعوة .. هو في الآخر راح على
+
+492
+00:38:25,820 --> 00:38:29,440
+المغازي و رجع .. مرة موجعب و مرة سالب .. نفترض راح
+
+493
+00:38:29,440 --> 00:38:32,220
+على المغازي اتنين كيلو و رجع اتنين كيلو .. بتكون
+
+494
+00:38:32,220 --> 00:38:35,160
+اربعة ولا لأ .. لكن هو بياخد في السالب علم اعتباره
+
+495
+00:38:35,160 --> 00:38:37,940
+بتطلع صفر .. لأنه اتنين كيلو و موجعبه اتنين كيلو
+
+496
+00:38:37,940 --> 00:38:39,900
+.. سالب .. احكي يا بنتي ..
+
+497
+00:38:42,990 --> 00:38:52,870
+أه كيف؟ جب هادي نقص هادي والله هي هيك مباشرة تمام؟
+
+498
+00:38:52,870 --> 00:39:04,970
+غيرها لأ حتى الأن بحكي عربي أكيد بدي أصدقكم ها طيب
+
+499
+00:39:04,970 --> 00:39:09,990
+اتفقنا السيارة هي ماشية من غزة لخانونسسرعتها
+
+500
+00:39:09,990 --> 00:39:14,370
+مختلفة ولا لأ؟ مرة بطيئة و مرة سريعة ابتقدروا لو
+
+501
+00:39:14,370 --> 00:39:19,570
+سألتكم لمّا كانت علىمفترض جنسيرات جديش كانت
+
+502
+00:39:19,570 --> 00:39:23,570
+صلوعتها ممكن تقوله ولا لأ؟ في آيك اللحظة هناك
+
+503
+00:39:23,570 --> 00:39:27,070
+بقولك عند لحظة معينة بقدر أقولك بس ساعتها بتحكيش
+
+504
+00:39:27,070 --> 00:39:33,830
+عن متوسط تحكي عن صلعة لحظية لحظية صح ولا لأ تمام
+
+505
+00:39:33,830 --> 00:39:37,390
+هل جيتوا احنا أخدنا لغة انجليزية من الرودا لما
+
+506
+00:39:37,390 --> 00:39:41,100
+جينا الجامعه احنا بناخد لغة انجليزية صح؟وامي فرحت
+
+507
+00:39:41,100 --> 00:39:45,680
+علينا في الراوضة باب إيش معناته وشباك ويندو إيش
+
+508
+00:39:45,680 --> 00:39:48,980
+معناته صح ولا .. هجيتش معنى لحظة بالإنجليزي
+
+509
+00:39:48,980 --> 00:39:55,840
+Instant سمعتوا فيها Instant والله خدتوها بس خلاص
+
+510
+00:39:55,840 --> 00:40:04,520
+يا خسارة الراوضة ممرتش عليكم مرت Instant لحظة
+
+511
+00:40:04,520 --> 00:40:10,770
+Instantaneous لحظةمحبوب ان دي بأصله Instantaneous
+
+512
+00:40:10,770 --> 00:40:13,950
+ممكن تكون وما مرتش عليكم بس instant لا تكون مرت
+
+513
+00:40:13,950 --> 00:40:19,370
+بلاش لحظة باللغة العربية مرت عليكم ايش معنى لحظة؟
+
+514
+00:40:19,370 --> 00:40:24,230
+احنا هتقولكم ايش تعريف لحظة؟ فترة زمانية طويلة ولا
+
+515
+00:40:24,230 --> 00:40:27,910
+قصيرة جدا؟ قصيرة جدا صح ايه معناته؟ مش هيك مخزنة
+
+516
+00:40:27,910 --> 00:40:33,410
+عندي كل كلمة انها معنى دي و مخي اما قولي لحظة
+
+517
+00:40:33,410 --> 00:40:41,950
+بقوله مائة سنة لأ معروفة طيبهذه ماذا؟ فترة زمانية
+
+518
+00:40:41,950 --> 00:40:47,250
+ممكن تكون مائة سنة و ممكن تكون لحظة ولا لا بديها
+
+519
+00:40:47,250 --> 00:40:52,430
+تكون أكيد لحظة لو أعملتلك كيك ايش هذا؟ تقول إلى
+
+520
+00:40:52,430 --> 00:40:56,610
+السفر لذا غصب عنها لحظة ولا مش لحظة؟ حلو انت ايش
+
+521
+00:40:56,610 --> 00:41:01,500
+عرفتلي ال average velocity تتطلع؟ لو هذهصارت تقول
+
+522
+00:41:01,500 --> 00:41:05,640
+إلى السفر صارت لحظة لما صارت لحظة و صارت .. بطلت
+
+523
+00:41:05,640 --> 00:41:09,340
+سرعة متوسطة صارت سرعة لحظية طب كيف بدي أسويها؟
+
+524
+00:41:09,340 --> 00:41:14,260
+بسيطة بس أسعلها limit
+
+525
+00:41:14,260 --> 00:41:21,580
+نُهَة تعرفون نُهَة؟ من نهاية نُهَة لما delta T
+
+526
+00:41:21,580 --> 00:41:26,960
+تقول إلى السفر هذه السرعة المتوسطة لما نحطت هذه
+
+527
+00:41:26,960 --> 00:41:34,230
+جمت هذه بطلت متوسطةصارت صراعي ايش؟ لحظية لحظية
+
+528
+00:41:34,230 --> 00:41:40,010
+ليش؟ لأن الفترة الزمنية صارت لحظة خلاص؟ بطل مطلقا؟
+
+529
+00:41:40,010 --> 00:41:45,090
+اه .. لحظة يعني بدل ما كانت الفترة الزمنية من غزة
+
+530
+00:41:45,090 --> 00:41:49,550
+لخانونس ساعة بتكون عند ما كانت في انصرات بقوله بعد
+
+531
+00:41:49,550 --> 00:41:54,050
+عشرين دقيقة عشرين دقيقة زي عشرين جزء من الدقيقة
+
+532
+00:41:54,050 --> 00:41:57,930
+خلاص عشرين بس انت وصلت يعني عشان بقيس عند لحظة
+
+533
+00:42:00,090 --> 00:42:07,790
+بالظبط صارت لحظية برا انت اللي عايش عامل limit نهى
+
+534
+00:42:07,790 --> 00:42:12,710
+هزيت مخي هي جالويت عن الكالكولاس هذا و عرفوا تعريف
+
+535
+00:42:12,710 --> 00:42:23,410
+هذا مش تقع أذكركوا دال ساط على دال سي بتساوي نهى
+
+536
+00:42:23,410 --> 00:42:28,810
+لما دال سي تقول إلى السفر دالتا ساط على دال سي
+
+537
+00:42:29,880 --> 00:42:37,560
+قلولي ماخدنهوش انا استخدمته ناس استخدمته اشتققتي
+
+538
+00:42:37,560 --> 00:42:39,440
+مش اشتققتي
+
+539
+00:42:42,540 --> 00:42:46,360
+طيب و هو عشان هو احنا هنا بنستخدمه نعرف إيش معناه
+
+540
+00:42:46,360 --> 00:42:50,040
+التعريف قاعد برجعلك انه عرفته و أخدته قللي إيش
+
+541
+00:42:50,040 --> 00:42:55,220
+معناته قللي هذا إله مع .. تعريف آخر هذا become
+
+542
+00:42:55,220 --> 00:42:58,820
+instant .. إيش معناه limit عشان تفهموا إيش استخدام
+
+543
+00:42:58,820 --> 00:43:02,680
+ال limit ال limit يعني صار يقول إلى السفر و فيه
+
+544
+00:43:02,680 --> 00:43:06,150
+هناك فرق ما بين يساوي سفر و يقول إلى السفرصح ولا
+
+545
+00:43:06,150 --> 00:43:09,950
+لا؟ جاللي هذه لحظة جاللي هذه علم ال calculus قالوا
+
+546
+00:43:09,950 --> 00:43:14,130
+هذه مشتقة X بالنسبالي الزمن مشتقة X بالنسبالي
+
+547
+00:43:14,130 --> 00:43:22,670
+الزمن فما أخدناه مازم نطبقه صح؟ طيب إيش بجرب
+
+548
+00:43:22,670 --> 00:43:28,510
+الاشتقاق لميل؟ الميل هو هيك بتعرفيه كويك ما شاء
+
+549
+00:43:28,510 --> 00:43:33,850
+الله عليكيلأن المهل ضل الزاوية ولا لا؟ وضل الزاوية
+
+550
+00:43:33,850 --> 00:43:37,150
+مقابل ع مجاور ولا لا؟ قال لي و الله هاي مقابل و
+
+551
+00:43:37,150 --> 00:43:40,670
+هاي مجاور، هاي مقابل و هاي مجاور، طو الرسمة مش كان
+
+552
+00:43:40,670 --> 00:43:46,710
+في عندي X و T، المقابل X، و المجاور T، إذن هذا مهل
+
+553
+00:43:46,710 --> 00:43:51,430
+المماز، وهين اشتقاق، إذن إيش بقوللي؟ بقوللي في
+
+554
+00:43:51,430 --> 00:43:54,710
+الرسمة الحلوة اللي طو رسمتها أنا وياك، وحلينا
+
+555
+00:43:54,710 --> 00:44:00,080
+عليها سؤال، ذاكرينها؟ من A لFجالي لو بدك تجيب ال
+
+556
+00:44:00,080 --> 00:44:03,640
+average velocity من دون ما تحل حاجة على الرصد قال
+
+557
+00:44:03,640 --> 00:44:07,600
+لي سهل لأ شوف ال average velocity ها مش انت قلتلي
+
+558
+00:44:07,600 --> 00:44:10,580
+ال average velocity بهمن نقطتي البداية والنهاية
+
+559
+00:44:10,580 --> 00:44:14,620
+جالي ارسله خط من البداية للنهاية هذا الخط جيب ميلو
+
+560
+00:44:14,620 --> 00:44:19,680
+هي ال average velocity ميلو مسموه طول لأ مش delta
+
+561
+00:44:19,680 --> 00:44:25,140
+x حد delta t و delta x هيالمقابل والـ delta T هي
+
+562
+00:44:25,140 --> 00:44:29,620
+المجاور إذا بيقولي in the position-time graph هذا
+
+563
+00:44:29,620 --> 00:44:34,040
+ال graph رسمة يعني بيسموها position-time graph
+
+564
+00:44:34,040 --> 00:44:38,500
+يعني رسمة ما بين ال position والزمن تمام؟ بيقولي
+
+565
+00:44:38,500 --> 00:44:41,100
+the average velocity is the slope، ال slope يعني
+
+566
+00:44:41,100 --> 00:44:47,110
+الميلالميل The slope of the line لو خط between the
+
+567
+00:44:47,110 --> 00:44:50,750
+initial and the final poles طيب هذه ال average طب
+
+568
+00:44:50,750 --> 00:44:54,250
+و ليه instantaneous هو في الطريق في لحظة واحدة ولا
+
+569
+00:44:54,250 --> 00:45:00,090
+عدة لحظات إذا عن كل لحظة جيبلي مماس بدي عند اللحظة
+
+570
+00:45:00,090 --> 00:45:04,110
+خمسة بقولك خمسة هي النقطة خمسة صح عند النقطة هذه
+
+571
+00:45:04,110 --> 00:45:08,740
+جيبولي مماس تعرفش جيبولي مماستمام؟ المماس خط ولا
+
+572
+00:45:08,740 --> 00:45:11,920
+مش خط؟ خط دي بني ميلو، هي السرعة اللحظية عند هذه
+
+573
+00:45:11,920 --> 00:45:15,480
+النقطة طب شوفولي النقطة B يا بنات، دي بني مماسها
+
+574
+00:45:15,480 --> 00:45:21,720
+مماسها مش سفر، ميلو السفر مماسها وفقي، عشان كده
+
+575
+00:45:21,720 --> 00:45:25,060
+ميلو سفر، معناته بقدر اقول السرعة اللحظية عند
+
+576
+00:45:25,060 --> 00:45:28,400
+النقطة B بتساوي سفر؟ يعني عند النقطة B كانت واقفة
+
+577
+00:45:28,400 --> 00:45:32,180
+يا سيل ولا لأ؟ كانت واقفة، اه لإن عند النقطة B بدي
+
+578
+00:45:32,180 --> 00:45:38,530
+يرجعوالواحد لما يرجع بيجف لحظيا هي صحيحة تمام؟ اذا
+
+579
+00:45:38,530 --> 00:45:44,690
+بيقول لي while the instantaneous velocity at some
+
+580
+00:45:44,690 --> 00:45:48,610
+instant طبعا at some instant لعند لحظات معينة is
+
+581
+00:45:48,610 --> 00:45:55,100
+the slope ميلof the tangent المماس ميل المماس at
+
+582
+00:45:55,100 --> 00:45:58,040
+that instant هذه النقطة هذه يا بنات شايفين هذه
+
+583
+00:45:58,040 --> 00:46:00,980
+النقطة هذه أول ال average خلصنا منها الخط الأخضر
+
+584
+00:46:00,980 --> 00:46:05,120
+هو ال average ميله طيب خلصت .. هجيت عند نقطة هذه
+
+585
+00:46:05,120 --> 00:46:10,260
+شايفينها عند لحظة ما نفترض خمسة بدي أجيب السرعة
+
+586
+00:46:10,260 --> 00:46:16,230
+اللحظية جيبولي مماس في حد برسم غير المماس هذا؟بدي
+
+587
+00:46:16,230 --> 00:46:20,470
+ميلو يوردي مثلا ميلو ممكن نعمل هيك ونقول المقابل
+
+588
+00:46:20,470 --> 00:46:24,270
+عن مجاور هذه الصورة اللحظية طب عند النقطة مين
+
+589
+00:46:24,270 --> 00:46:29,870
+اشتفكتوا سفر عند النقطة أي ان كانت دي طبعا كيف
+
+590
+00:46:29,870 --> 00:46:35,980
+يتضغط كيف ميلو تتوقع مجابه ولا سالبسالم لأنه نازل
+
+591
+00:46:35,980 --> 00:46:40,620
+لأنه احنا دايما نعرف ان هذا خط و هذا خط بقول هذا
+
+592
+00:46:40,620 --> 00:46:45,360
+ميله موجب هذا ميله هذا متزايد هذا متناقص صح ولا لأ
+
+593
+00:46:45,360 --> 00:46:50,160
+هايكم شاطرين في الكلب كلاص ما شاء الله عليكم غدا
+
+594
+00:46:50,160 --> 00:46:52,700
+نظرا احنا بنقول متزايد و متناقص صح ولا لأ كلامك
+
+595
+00:46:52,700 --> 00:46:59,280
+صحيح كلامك صحيح تمى عنده نقطة أف تطلعوه ما هو
+
+596
+00:46:59,280 --> 00:47:03,570
+كويجيف عنده نقطة أفمش هو بيجيب؟ خلاص يعطيه العافية
+
+597
+00:47:03,570 --> 00:47:09,410
+اذا بيقوللي هدول ال slope
+
+598
+00:47:09,410 --> 00:47:12,830
+للخطوط اللي بتكون مماس لنقطة م ما ايه بدي ان
+
+599
+00:47:12,830 --> 00:47:15,370
+استنتين was velocity at that point لحد اللي انا
+
+600
+00:47:15,370 --> 00:47:20,850
+محكي عربي؟ بكتير مش شهر حلو براو هلجيت السرعة
+
+601
+00:47:20,850 --> 00:47:24,470
+انتشرت سرعة متوسطة و سرعة لحظية صح ولا لا؟ ايه اسم
+
+602
+00:47:24,470 --> 00:47:28,100
+الجنتين؟ رغمرغد طلع يا رغد احنا قلنا السرعة
+
+603
+00:47:28,100 --> 00:47:31,760
+المتوسطة ال average velocity بتعتمد على نقطتي ايش؟
+
+604
+00:47:31,760 --> 00:47:36,020
+البداية و النهاية تجاهليها ال gate السرعة هي عبارة
+
+605
+00:47:36,020 --> 00:47:42,040
+عن مسافة ع زمن صح؟ المسافة عبارة عن خط و الزمن خط
+
+606
+00:47:42,040 --> 00:47:46,920
+بدي اجربه و اديب علاقة بينه و بيني المماس اذا انت
+
+607
+00:47:46,920 --> 00:47:50,360
+بتحكي عن average velocity اللي بهمك فقط نقطتي
+
+608
+00:47:50,360 --> 00:47:53,200
+البداية و النهاية اعمللي خط بين البداية و النهاية
+
+609
+00:47:53,200 --> 00:47:56,720
+هذا الخط اللي ميل؟جيبه هو الـ Average Velocity
+
+610
+00:47:56,720 --> 00:48:01,140
+خلصها من الـ Average Velocity الـ Instantaneous
+
+611
+00:48:01,140 --> 00:48:04,720
+Velocity عند لحظة تمام .. اذا ماعرف كام لحظة في
+
+612
+00:48:04,720 --> 00:48:08,780
+عندك كتير و انت لما يقولك أوجد الصراع اللحظية بفعل
+
+613
+00:48:08,780 --> 00:48:11,640
+يقولك أوجد الصراع اللحظية و يسكت؟ بده يقوله عند أي
+
+614
+00:48:11,640 --> 00:48:15,660
+لحظة، عند لحظة تمام، يعني عند نقطة ما ولا لأ؟
+
+615
+00:48:15,660 --> 00:48:20,010
+قاللي جيبلي نقطة هادية و جيبلي إيها مماسةمماس جيب
+
+616
+00:48:20,010 --> 00:48:25,030
+مانو هاي الصورة اللحظية بس هاي اللي بنحكي بالبلد
+
+617
+00:48:25,030 --> 00:48:31,450
+غيرها احكيه القانون V تساوي DX على D نفسه هو لطبع
+
+618
+00:48:31,450 --> 00:48:36,450
+ال M ولا غيره هو نفسه ماهذا تعرف لا هذامش هاد
+
+619
+00:48:36,450 --> 00:48:40,150
+تعريفه؟ بدل ما تجيب ال limit و تغلب بحالك مستعرون
+
+620
+00:48:40,150 --> 00:48:43,930
+ال calculus هيحونا؟ جالوا اشتقوا خلاص؟ هو نفسه يا
+
+621
+00:48:43,930 --> 00:48:47,210
+بنتي هاد تعريفنا خدناه في ال calculus خدناه في ..
+
+622
+00:48:47,210 --> 00:48:50,830
+في توجيه؟ في توجيه هو نفسه بدل ما تجيب ال limit و
+
+623
+00:48:50,830 --> 00:48:54,370
+تغلب حالي اتعلمتوا كيف تجيبوا ال limit ولا لأ؟
+
+624
+00:48:54,370 --> 00:48:58,650
+اتعلمتوا كيف تجيبوا ال limit؟ ال limit .. النهار
+
+625
+00:48:58,650 --> 00:49:00,830
+انتوا بدأتوا في ال calculus في ال limit و لا
+
+626
+00:49:00,830 --> 00:49:03,030
+موصلتوش لسه هتاخدوه هتخافوش
+
+627
+00:49:05,700 --> 00:49:09,820
+بقول ان الـ instantaneous speed is the magnitude
+
+628
+00:49:09,820 --> 00:49:12,400
+of the instantaneous velocity ماذا على الجدول
+
+629
+00:49:12,400 --> 00:49:18,180
+ترميها؟ اه في ال instantaneous هو نفسها تمام خلينا
+
+630
+00:49:18,180 --> 00:49:21,740
+هال example بس طولنا معاكم بقى مش تتحملوني
+
+631
+00:49:21,740 --> 00:49:25,200
+تتحملوني عشان الشعب بتنفي غيركم فتقولكم انتوا
+
+632
+00:49:25,200 --> 00:49:28,840
+بتسألوا كتير برضه شغل ميزة يعني فاخدتوا معايا و
+
+633
+00:49:28,840 --> 00:49:34,840
+جيت أكترطبعا بيقولي a particle moves along the x
+
+634
+00:49:34,840 --> 00:49:38,740
+-axis الجسم بتحرك على المحور الصيني يعني أفقي ولا
+
+635
+00:49:38,740 --> 00:49:44,620
+مش أفقي أفقي قاللي its position موضعه varies يتغير
+
+636
+00:49:44,620 --> 00:49:50,780
+varies من veryتمام؟ with time according to أنا
+
+637
+00:49:50,780 --> 00:49:56,600
+مديك X تبعته بتتعلق بالزمن وإلها معادلة تغيير
+
+638
+00:49:56,600 --> 00:50:03,580
+معادلة X بالنسبة للزمن اديتك إياها كتالي X بتساوي
+
+639
+00:50:03,580 --> 00:50:09,220
+ناقص أربعة T زائد اتنين T تربيع هذه المعادلة اللي
+
+640
+00:50:09,220 --> 00:50:13,760
+اديتك إياهاتما جالي X بتجيسها بالمتر و T بتجيسها
+
+641
+00:50:13,760 --> 00:50:17,140
+بالsecond يعني احنا بنستخدم الاص I system صح ولا
+
+642
+00:50:17,140 --> 00:50:23,560
+لأ؟ ايش بده؟ جالي بدي التالي find the displacement
+
+643
+00:50:23,560 --> 00:50:28,060
+ايش قانون ال displacement؟ X final نخس X initial
+
+644
+00:50:28,060 --> 00:50:34,340
+ده X صح؟ لفترين من صفر لواحد و من واحد لتلاتة
+
+645
+00:50:34,340 --> 00:50:42,390
+واحدة واحدة ايه؟ بقوله ها الأولىدالتا X من صفر
+
+646
+00:50:42,390 --> 00:50:48,370
+لواحد بيقولوا بتسوي X لما T بتساوي واحد second
+
+647
+00:50:48,370 --> 00:50:54,190
+ناقص X لما T بتساوي صفر هل يا X final ناقص X
+
+648
+00:50:54,190 --> 00:50:58,520
+initial صح ولا لأ؟جالي طب كيف اجيب هذه؟ قلتله ها
+
+649
+00:50:58,520 --> 00:51:04,280
+بداك تعوض محلتي كده؟ بواحد بتساوي ناقص أربعة في
+
+650
+00:51:04,280 --> 00:51:08,420
+واحد ناقص أربعة زاد اتنين في واحد تربية اذا ناقص
+
+651
+00:51:08,420 --> 00:51:13,580
+اتنين ناقص ها ناقص أربعة في سفر و اتنين في سفر
+
+652
+00:51:13,580 --> 00:51:18,920
+تربية صحيك؟
+
+653
+00:51:18,920 --> 00:51:23,500
+هاي أول فترة جبتلها كده انزاح الجسيم طيب اتنين؟
+
+654
+00:51:24,070 --> 00:51:28,490
+ماذا تريد؟ تريد دالتا X من واحد second لتلاتة
+
+655
+00:51:28,490 --> 00:51:34,810
+second بتساوي X لما ت بتساوي تلاتة second مقص X
+
+656
+00:51:34,810 --> 00:51:41,310
+لما ت بتساوي واحد second فحق ولا لأ لما ت بتساوي
+
+657
+00:51:41,310 --> 00:51:46,710
+تلاتة مقص عربعة في تلاتة مقص اتنعاش زاد اتنين في
+
+658
+00:51:46,710 --> 00:51:51,890
+تلاتة تربيه تسعة تمانتعاش ستة ستة
+
+659
+00:51:53,350 --> 00:51:59,170
+ناقص لما تيبت سوا واحد ما هنا طلعتها ناقص اتنين
+
+660
+00:51:59,170 --> 00:52:07,910
+ستة ناقص ناقص صارت كده؟ تمانية متر صحيك تمام أول
+
+661
+00:52:07,910 --> 00:52:11,870
+مطلوب خلصتلك هي جالي المطلوب التاني تحصيل حاصل إيش
+
+662
+00:52:11,870 --> 00:52:15,930
+بدك؟ جالي في المطلوب التاني طلع إيش بدهنقول
+
+663
+00:52:15,930 --> 00:52:21,210
+Calculate the average Velocity Velocity During
+
+664
+00:52:21,210 --> 00:52:25,130
+these two intervals ما هي Delta X على Delta T صح؟
+
+665
+00:52:25,130 --> 00:52:29,210
+في الأولى Delta T one secondفي الفترة التانية ده
+
+666
+00:52:29,210 --> 00:52:35,830
+تتيه 2 second إذا معناته نرجع بي واحد V average
+
+667
+00:52:35,830 --> 00:52:41,250
+بتساوي ناقص 2 ع واحد ناقص 2 meter per second وفي
+
+668
+00:52:41,250 --> 00:52:48,750
+التانية V average بتساوي تمامية ع 2 ساوية 4 meter
+
+669
+00:52:48,750 --> 00:52:51,170
+per second وإن شاء الله بتكونوا متابعين معايا لحد
+
+670
+00:52:51,170 --> 00:52:52,750
+الآن تمام
+
+671
+00:52:55,640 --> 00:53:01,490
+اشتقتي في توجيهي صح؟ شوف اي طالب في الآخرCalculate
+
+672
+00:53:01,490 --> 00:53:06,970
+The Instantaneous .. إيش يعني؟ اللحظة .. Velocity
+
+673
+00:53:06,970 --> 00:53:09,750
+.. منفع يقول Instantaneous و Velocity يسكت؟ بده
+
+674
+00:53:09,750 --> 00:53:13,730
+يحدد اللحظة .. حدد ولا ماحددش؟ حدد .. هلجيت ال
+
+675
+00:53:13,730 --> 00:53:16,910
+Instantaneous Velocity إيش تعريفها؟ هي المستقلة،
+
+676
+00:53:16,910 --> 00:53:22,670
+لا بتدي Limit ولا بتجلب حالي بقوله V بدون شرطة
+
+677
+00:53:22,670 --> 00:53:29,500
+بتساوي DX على DT .. هي الـ X اللي بده أشتقهامش هاد
+
+678
+00:53:29,500 --> 00:53:36,100
+اللي اعطاني ايه؟ مين اشتق معاه؟ اشتق ايه؟ بها و
+
+679
+00:53:36,100 --> 00:53:42,100
+علينا ناقص أربعة زائد أربعة T هذه أربعة هلجيت ..
+
+680
+00:53:42,100 --> 00:53:46,600
+ماخلصتيش؟ بدوا عين T بتساوي اتنين و نص بقولوا
+
+681
+00:53:46,600 --> 00:53:49,920
+بتساوني ناقص أربعة زائد أربعة في اتنين و نص عشرة
+
+682
+00:53:52,640 --> 00:53:58,520
+صح ولا لأ؟ إذا السرعة عند 2.5 كانت 6 متر per
+
+683
+00:53:58,520 --> 00:54:03,980
+second طبعا اتطلعوا هنا المتوسط مختلف كليا تمام يا
+
+684
+00:54:03,980 --> 00:54:05,140
+بنات يعطينا العافية
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/E6HOsl9lEzQ_raw.json b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/E6HOsl9lEzQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0200d0bc68b0ff627be43b6614357a70b6a1dc51
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/E6HOsl9lEzQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2487, "start": 5.01, "end": 24.87, "text": "تمام يا بنات هنبدأ اليوم ان شاء الله بـ Chapter 2 بعد بسم الله الرحمن الرحيم حكينا انه في هذا ال chapter العنوان تبعه هو motion in one dimension او ال linear motion الحركة في خط واحد باتجاه واحد", "tokens": [39237, 10943, 35186, 4724, 8315, 2655, 8032, 1863, 44510, 10721, 45595, 20498, 16472, 13412, 16606, 21984, 4724, 39184, 18874, 568, 39182, 4724, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 11331, 4117, 1829, 8315, 16472, 3224, 8978, 23758, 2423, 7187, 18863, 1863, 2407, 7649, 6055, 3555, 3615, 3224, 31439, 5394, 294, 472, 10139, 1975, 2407, 2423, 8213, 5394, 21542, 31747, 3660, 8978, 16490, 9566, 36764, 24401, 4724, 9307, 7435, 40294, 36764, 24401], "avg_logprob": -0.19145975374195673, "compression_ratio": 1.5538461538461539, "no_speech_prob": 1.519918441772461e-05, "words": [{"start": 5.01, "end": 5.45, "word": "تمام", "probability": 0.558197021484375}, {"start": 5.45, "end": 5.55, "word": " 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209.44, "end": 210.06, "word": " الصيني", "probability": 0.9793294270833334}, {"start": 210.06, "end": 210.56, "word": " تمام", "probability": 0.86572265625}, {"start": 210.56, "end": 210.66, "word": " يا", "probability": 0.97216796875}, {"start": 210.66, "end": 211.46, "word": " بنات؟", "probability": 0.8385009765625}, {"start": 211.46, "end": 211.72, "word": " إذا", "probability": 0.853759765625}, {"start": 211.72, "end": 212.34, "word": " الـ", "probability": 0.6728515625}, {"start": 212.34, "end": 212.68, "word": " Position", "probability": 0.89306640625}, {"start": 212.68, "end": 213.04, "word": " of", "probability": 0.978515625}, {"start": 213.04, "end": 213.34, "word": " a", "probability": 0.9736328125}, {"start": 213.34, "end": 213.96, "word": " particle", "probability": 0.865234375}, {"start": 213.96, "end": 214.6, "word": " اللي", "probability": 0.919677734375}, {"start": 214.6, "end": 215.4, "word": " هنرمزله", "probability": 0.9546712239583334}, {"start": 215.4, "end": 216.04, "word": " بالرمز", "probability": 0.9827880859375}, {"start": 216.04, "end": 216.56, "word": " X", "probability": 0.99072265625}, {"start": 216.56, "end": 217.38, "word": " إيش", "probability": 0.8984375}, {"start": 217.38, "end": 218.04, "word": " تعرفه؟", "probability": 0.8956298828125}, {"start": 218.04, "end": 218.24, "word": " Its", "probability": 0.56640625}, {"start": 218.24, "end": 218.98, "word": " location", "probability": 0.853515625}, {"start": 218.98, "end": 220.26, "word": " موضع", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 10, "seek": 24690, "start": 220.94, "end": 246.9, "text": "موضع location من موضع is the location with respect to a reference point اذا انت مفهوش تقولي والله انا موضعي خمسة متر بدون ما تقولي عن ايش هذه الاش بيسميها reference point نقطة مرجعية تمام هجيك لما نيجي نقول هاي حيطة مرجع ولا مش مرجع مرجع تمام وهي سيارة", "tokens": [2304, 2407, 11242, 3615, 4914, 9154, 3714, 2407, 11242, 3615, 307, 264, 4914, 365, 3104, 281, 257, 6408, 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"probability": 0.601416015625}, {"start": 228.44, "end": 228.8, "word": " تقولي", "probability": 0.8846028645833334}, {"start": 228.8, "end": 229.16, "word": " والله", "probability": 0.7421875}, {"start": 229.16, "end": 229.44, "word": " انا", "probability": 0.8447265625}, {"start": 229.44, "end": 230.04, "word": " موضعي", "probability": 0.96015625}, {"start": 230.04, "end": 230.9, "word": " خمسة", "probability": 0.8123779296875}, {"start": 230.9, "end": 231.32, "word": " متر", "probability": 0.966796875}, {"start": 231.32, "end": 231.72, "word": " بدون", "probability": 0.975341796875}, {"start": 231.72, "end": 231.84, "word": " ما", "probability": 0.497314453125}, {"start": 231.84, "end": 232.12, "word": " تقولي", "probability": 0.9716796875}, {"start": 232.12, "end": 232.3, "word": " عن", "probability": 0.990234375}, {"start": 232.3, "end": 232.74, "word": " ايش", "probability": 0.765380859375}, {"start": 232.74, "end": 233.68, "word": " هذه", "probability": 0.5537109375}, {"start": 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242.46, "word": " حيطة", "probability": 0.9598388671875}, {"start": 242.46, "end": 243.22, "word": " مرجع", "probability": 0.8419596354166666}, {"start": 243.22, "end": 243.34, "word": " ولا", "probability": 0.7822265625}, {"start": 243.34, "end": 243.52, "word": " مش", "probability": 0.98583984375}, {"start": 243.52, "end": 243.94, "word": " مرجع", "probability": 0.98193359375}, {"start": 243.94, "end": 244.86, "word": " مرجع", "probability": 0.78076171875}, {"start": 244.86, "end": 245.76, "word": " تمام", "probability": 0.97216796875}, {"start": 245.76, "end": 246.28, "word": " وهي", "probability": 0.76171875}, {"start": 246.28, "end": 246.9, "word": " سيارة", "probability": 0.9764404296875}], "temperature": 1.0}, {"id": 11, "seek": 26613, "start": 247.91, "end": 266.13, "text": "هيجيت واضح ان السيارة بتبعد عن الحيطة مسافة ما نقدر نقول بالبلدي موضع السيارة عن الحيطة ولا لأ اذا هذا موضع السيارة عن الحيطة هذا reference point اذا as a particle moves لما يتحرك الجسم ما زال يتحرك اتغير موضعه ولا لأ", "tokens": [3224, 1829, 7435, 36081, 4032, 46958, 5016, 16472, 21136, 1829, 9640, 3660, 39894, 3555, 22488, 18871, 21542, 1829, 9566, 3660, 47524, 31845, 3660, 19446, 8717, 28543, 2288, 8717, 39648, 20666, 36150, 16254, 3714, 2407, 11242, 3615, 21136, 1829, 9640, 3660, 18871, 21542, 1829, 9566, 3660, 49429, 5296, 10721, 1975, 15730, 23758, 3714, 2407, 11242, 3615, 21136, 1829, 9640, 3660, 18871, 21542, 1829, 9566, 3660, 23758, 6408, 935, 1975, 15730, 382, 257, 12359, 6067, 5296, 15042, 7251, 2655, 5016, 31747, 25724, 38251, 19446, 30767, 6027, 7251, 2655, 5016, 31747, 1975, 2655, 17082, 13546, 3714, 2407, 11242, 3615, 3224, 49429, 5296, 10721], "avg_logprob": -0.17574256894612075, "compression_ratio": 1.9308510638297873, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 247.91, "end": 248.33, "word": "هيجيت", "probability": 0.50128173828125}, {"start": 248.33, "end": 248.69, "word": " واضح", "probability": 0.9576822916666666}, {"start": 248.69, "end": 248.83, 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عن", "probability": 0.9599609375}, {"start": 254.41, "end": 254.85, "word": " الحيطة", "probability": 0.9886474609375}, {"start": 254.85, "end": 255.01, "word": " ولا", "probability": 0.8447265625}, {"start": 255.01, "end": 255.35, "word": " لأ", "probability": 0.7176513671875}, {"start": 255.35, "end": 255.99, "word": " اذا", "probability": 0.58819580078125}, {"start": 255.99, "end": 256.25, "word": " هذا", "probability": 0.7998046875}, {"start": 256.25, "end": 256.67, "word": " موضع", "probability": 0.9876708984375}, {"start": 256.67, "end": 257.23, "word": " السيارة", "probability": 0.99365234375}, {"start": 257.23, "end": 257.43, "word": " عن", "probability": 0.978515625}, {"start": 257.43, "end": 257.91, "word": " الحيطة", "probability": 0.9913330078125}, {"start": 257.91, "end": 258.11, "word": " هذا", "probability": 0.62353515625}, {"start": 258.11, "end": 258.35, "word": " reference", "probability": 0.159423828125}, {"start": 258.35, "end": 259.05, "word": " point", "probability": 0.9892578125}, {"start": 259.05, "end": 260.13, "word": " اذا", "probability": 0.77587890625}, {"start": 260.13, "end": 260.55, "word": " as", "probability": 0.71533203125}, {"start": 260.55, "end": 260.77, "word": " a", "probability": 0.841796875}, {"start": 260.77, "end": 261.21, "word": " particle", "probability": 0.9267578125}, {"start": 261.21, "end": 261.77, "word": " moves", "probability": 0.8251953125}, {"start": 261.77, "end": 261.99, "word": " لما", "probability": 0.884033203125}, {"start": 261.99, "end": 262.43, "word": " يتحرك", "probability": 0.9697265625}, {"start": 262.43, "end": 262.99, "word": " الجسم", "probability": 0.98486328125}, {"start": 262.99, "end": 263.99, "word": " ما", "probability": 0.346923828125}, {"start": 263.99, "end": 264.15, "word": " زال", "probability": 0.8896484375}, {"start": 264.15, "end": 264.77, "word": " يتحرك", "probability": 0.8809814453125}, {"start": 264.77, "end": 265.19, "word": " اتغير", "probability": 0.9453125}, 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المثل البلدي اللي انتوا طالعين من الجامعة و رايحين على خانونس تكرته مواصلات مظبوط ولا لأ احيانا تصدف السيارة راحت على خانونس عادي اللي في شارع صلاح الدي لما وصلت خانونس ومرات من جلة الركاب أخدله راكب على المغازي", "tokens": [3224, 36081, 7435, 8848, 2288, 1975, 46456, 9381, 2288, 3714, 47283, 2655, 9381, 2288, 8592, 1975, 8315, 45595, 11778, 3615, 2407, 3660, 4032, 9957, 25961, 4032, 9957, 20328, 9640, 1975, 15730, 12174, 1211, 2655, 4724, 28259, 10632, 4032, 8717, 11296, 10632, 20449, 8315, 47395, 21899, 1975, 15730, 47525, 4117, 9122, 33911, 4032, 36520, 20449, 8315, 47395, 39894, 5016, 4117, 1829, 18871, 47524, 31845, 3660, 8717, 16254, 9673, 12984, 1211, 29739, 1211, 16254, 13672, 1829, 16472, 2655, 14407, 23032, 6027, 3615, 9957, 9154, 25724, 10943, 27884, 4032, 12602, 47302, 5016, 9957, 15844, 16490, 7649, 11536, 3794, 6055, 37983, 47395, 3714, 2407, 33546, 1211, 9307, 3714, 19913, 3555, 2407, 9566, 49429, 5296, 10721, 1975, 5016, 1829, 7649, 995, 6055, 9381, 3215, 5172, 21136, 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"text": "وخد وراك عادى للبلح مش بيضلوا جذر اذا انت بدك displacement بتحط رجل عريجل في غزة ما هو انطلق من غزة و بتقوله لما اتصل خانونس قولي بروح بجيب خط من غزة لخانونس بقولها دى ايه زاعته صح ولا لأ اذا بدك مسافة بنفع تحط رجل عريجل ولا بده ايجي لوراه", "tokens": [2407, 9778, 3215, 4032, 23557, 4117, 6225, 18513, 7578, 24976, 36150, 5016, 37893, 4724, 1829, 11242, 1211, 14407, 10874, 8848, 2288, 1975, 15730, 16472, 2655, 47525, 4117, 21899, 39894, 5016, 9566, 12602, 7435, 1211, 6225, 16572, 7435, 1211, 8978, 32771, 11622, 3660, 19446, 31439, 16472, 9566, 1211, 4587, 9154, 32771, 11622, 3660, 4032, 39894, 39648, 3224, 5296, 15042, 1975, 2655, 36520, 16490, 7649, 11536, 3794, 12174, 12610, 1829, 4724, 32887, 5016, 4724, 7435, 1829, 3555, 16490, 9566, 9154, 32771, 11622, 3660, 5296, 9778, 7649, 11536, 3794, 4724, 39648, 11296, 11778, 7578, 1975, 1829, 3224, 30767, 995, 34268, 3224, 20328, 5016, 49429, 5296, 10721, 1975, 15730, 47525, 4117, 47524, 31845, 3660, 44945, 5172, 3615, 6055, 5016, 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Vector Quantities in detail بكل التفاصيل تبعتهم في Chapter 3 الشبطر اللي جاي احنا الآن في أي شبطر؟ نين لسه بدنا .. 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displacement ع زمان و ليست مسافة ع زمان فيم تعنيها؟ ليش اسمك؟ ايش اسمك انت؟ أسيل؟ ليش يسموك أسيل؟", "tokens": [3224, 24192, 2423, 39184, 316, 3623, 17814, 905, 507, 39896, 39894, 3615, 16572, 5172, 11296, 35186, 4724, 29399, 1829, 8032, 2655, 3555, 16254, 4117, 9673, 3794, 31845, 3660, 44713, 22653, 22653, 13412, 2407, 10632, 2423, 39184, 316, 3623, 17814, 905, 507, 37279, 16572, 5172, 11296, 18863, 19528, 1829, 13672, 1829, 28242, 2423, 8315, 3794, 45030, 28480, 3224, 39896, 21899, 6225, 30767, 2304, 7649, 4032, 32239, 14851, 47524, 31845, 3660, 6225, 30767, 2304, 7649, 8978, 2304, 37279, 22653, 11296, 22807, 32239, 8592, 24525, 2304, 4117, 22807, 1975, 1829, 8592, 24525, 2304, 4117, 16472, 2655, 22807, 5551, 3794, 26895, 22807, 32239, 8592, 7251, 38251, 2407, 4117, 5551, 3794, 26895, 22807], "avg_logprob": -0.2469896816332406, "compression_ratio": 1.799043062200957, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1069.72, "end": 1070.34, "word": "هذه", "probability": 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" الـ", "probability": 0.7783203125}, {"start": 1076.74, "end": 1077.22, "word": " Average", "probability": 0.870361328125}, {"start": 1077.22, "end": 1077.76, "word": " Velocity", "probability": 0.9781901041666666}, {"start": 1077.76, "end": 1078.42, "word": " تعريفها", "probability": 0.8897705078125}, {"start": 1078.42, "end": 1078.94, "word": " العلمي", "probability": 0.9609375}, {"start": 1078.94, "end": 1079.06, "word": " اللي", "probability": 0.9267578125}, {"start": 1079.06, "end": 1079.32, "word": " كل", "probability": 0.8896484375}, {"start": 1079.32, "end": 1079.64, "word": " الناس", "probability": 0.9822591145833334}, {"start": 1079.64, "end": 1080.28, "word": " بعرفه", "probability": 0.7478841145833334}, {"start": 1080.28, "end": 1080.7, "word": " هي", "probability": 0.787109375}, {"start": 1080.7, "end": 1081.16, "word": " displacement", "probability": 0.71630859375}, {"start": 1081.16, "end": 1081.56, "word": " ع", "probability": 0.5107421875}, {"start": 1081.56, "end": 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remark even though بالرغم من أنه المعلومة اللي أديتكم ياها الأولى ال speed is the magnitude of the velocity ال speed هو مقدار ال velocity إلا إنه the average speed is not the magnitude of the average velocity اتفجنا يا بنات؟ تمام هيك؟ هديك مثال عليه هديت ال speed مقدار ال velocity", "tokens": [28814, 15730, 4724, 1829, 39648, 20292, 2423, 39184, 7942, 754, 1673, 20666, 2288, 17082, 2304, 9154, 14739, 3224, 9673, 30241, 20498, 3660, 13672, 1829, 5551, 16254, 2655, 24793, 35186, 11296, 16247, 12610, 7578, 2423, 3073, 307, 264, 15668, 295, 264, 9269, 2423, 3073, 31439, 3714, 28543, 9640, 2423, 9269, 11933, 15040, 36145, 3224, 264, 4274, 3073, 307, 406, 264, 15668, 295, 264, 4274, 9269, 1975, 2655, 5172, 7435, 8315, 35186, 4724, 8315, 2655, 22807, 46811, 10943, 39896, 4117, 22807, 8032, 16254, 4117, 50113, 6027, 47356, 8032, 16254, 2655, 2423, 3073, 3714, 28543, 9640, 2423, 9269], "avg_logprob": -0.2674153648937742, "compression_ratio": 1.7768240343347639, "no_speech_prob": 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{"start": 3216.46, "end": 3216.92, "word": " ناقص", "probability": 0.8194580078125}, {"start": 3216.92, "end": 3217.42, "word": " أربعة", "probability": 0.7350260416666666}, {"start": 3217.42, "end": 3217.86, "word": " زائد", "probability": 0.7142740885416666}, {"start": 3217.86, "end": 3218.52, "word": " أربعة", "probability": 0.9296875}, {"start": 3218.52, "end": 3218.74, "word": " T", "probability": 0.64013671875}, {"start": 3218.74, "end": 3219.58, "word": " هذه", "probability": 0.350341796875}, {"start": 3219.58, "end": 3220.1, "word": " أربعة", "probability": 0.9630533854166666}, {"start": 3220.1, "end": 3221.78, "word": " هلجيت", "probability": 0.7532958984375}, {"start": 3221.78, "end": 3222.1, "word": " ..", "probability": 0.400634765625}, {"start": 3222.1, "end": 3223.58, "word": " ماخلصتيش؟", "probability": 0.7228480747767857}, {"start": 3223.58, "end": 3223.88, "word": " بدوا", "probability": 0.5283203125}, {"start": 3223.88, "end": 3224.12, "word": " عين", "probability": 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0.5302734375}, {"start": 3229.08, "end": 3229.26, "word": " اتنين", "probability": 0.9591064453125}, {"start": 3229.26, "end": 3229.34, "word": " و", "probability": 0.99365234375}, {"start": 3229.34, "end": 3229.5, "word": " نص", "probability": 0.9697265625}, {"start": 3229.5, "end": 3229.92, "word": " عشرة", "probability": 0.8681640625}], "temperature": 1.0}, {"id": 138, "seek": 324514, "start": 3232.64, "end": 3245.14, "text": "صح ولا لأ؟ إذا السرعة عند 2.5 كانت 6 متر per second طبعا اتطلعوا هنا المتوسط مختلف كليا تمام يا بنات يعطينا العافية", "tokens": [9381, 5016, 49429, 5296, 10721, 22807, 11933, 15730, 21136, 2288, 27884, 43242, 568, 13, 20, 25961, 2655, 1386, 44650, 2288, 680, 1150, 23032, 3555, 3615, 995, 1975, 2655, 9566, 1211, 3615, 14407, 34105, 9673, 2655, 41779, 9566, 3714, 46456, 46538, 9122, 20292, 995, 46811, 10943, 35186, 4724, 8315, 2655, 37495, 9566, 1829, 8315, 18863, 31845, 10632], "avg_logprob": -0.20175439223908542, "compression_ratio": 1.3448275862068966, 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"probability": 0.58349609375}, {"start": 3238.52, "end": 3239.0, "word": " second", "probability": 0.943359375}, {"start": 3239.0, "end": 3239.94, "word": " طبعا", "probability": 0.9222412109375}, {"start": 3239.94, "end": 3240.74, "word": " اتطلعوا", "probability": 0.9075520833333334}, {"start": 3240.74, "end": 3241.22, "word": " هنا", "probability": 0.95703125}, {"start": 3241.22, "end": 3242.6, "word": " المتوسط", "probability": 0.9801025390625}, {"start": 3242.6, "end": 3243.04, "word": " مختلف", "probability": 0.96630859375}, {"start": 3243.04, "end": 3243.58, "word": " كليا", "probability": 0.7832845052083334}, {"start": 3243.58, "end": 3243.92, "word": " تمام", "probability": 0.929443359375}, {"start": 3243.92, "end": 3243.98, "word": " يا", "probability": 0.96923828125}, {"start": 3243.98, "end": 3244.36, "word": " بنات", "probability": 0.9052734375}, {"start": 3244.36, "end": 3244.78, "word": " يعطينا", "probability": 0.81646728515625}, {"start": 3244.78, "end": 3245.14, "word": " العافية", "probability": 0.9498697916666666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3245.1745, "duration_after_vad": 3159.4399999999823}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/E6HOsl9lEzQ_raw.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/E6HOsl9lEzQ_raw.srt
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+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/E6HOsl9lEzQ_raw.srt
@@ -0,0 +1,2736 @@
+1
+00:00:05,010 --> 00:00:10,110
+تمام يا بنات هنبدأ اليوم ان شاء الله بـ Chapter 2
+
+2
+00:00:10,110 --> 00:00:14,550
+بعد بسم الله الرحمن الرحيم حكينا انه في هذا ال
+
+3
+00:00:14,550 --> 00:00:20,110
+chapter العنوان تبعه هو motion in one dimension او
+
+4
+00:00:20,110 --> 00:00:26,600
+ال linear motion الحركة في خط واحد باتجاه واحدحركة
+
+5
+00:00:26,600 --> 00:00:32,280
+بيعني فيه سرعة وأحيانا بيكون فيه تصارع بالتالي
+
+6
+00:00:32,280 --> 00:00:37,200
+هنتحدث عن المفاهيم الفيزيائية التالية بدنا نحكي
+
+7
+00:00:37,200 --> 00:00:42,320
+ايش هو ال position موضع جسماذا اتغير الموضع مانا
+
+8
+00:00:42,320 --> 00:00:46,720
+تحصل عندي velocity بينا نميز ما بين ال velocity و
+
+9
+00:00:46,720 --> 00:00:51,880
+ال speed ثم احيانا اذا اتغيرت السرعة صار في عندي
+
+10
+00:00:51,880 --> 00:00:56,180
+تسارق acceleration لما تكون ال acceleration
+
+11
+00:00:56,180 --> 00:01:00,000
+constant في حالة خاصة هنتعرف عليها و نشتق
+
+12
+00:01:00,000 --> 00:01:05,180
+المعادلات اللي بتحكمها حالة من حالات الحركة باتجاه
+
+13
+00:01:05,180 --> 00:01:11,270
+واحد وبتسارق ثابت هيالـ Free Falling Objects هذه
+
+14
+00:01:11,270 --> 00:01:15,370
+هي المواضيع اللي هنشرحها في هذا الـ Chapter تقريبا
+
+15
+00:01:15,370 --> 00:01:19,150
+المواضيع مرت عليكم في الصف الحدي عشر إلى حد كبير
+
+16
+00:01:19,150 --> 00:01:23,390
+وبالتالي اختارنا ال problems اللي تعمل refreshing
+
+17
+00:01:23,390 --> 00:01:29,310
+لمعلوماتكم بدناش نجور عليكم لأن أغلب المواضيع و
+
+18
+00:01:29,310 --> 00:01:32,750
+الأسئلة مرت عليكم بصورة أو باخرة في المدرسة
+
+19
+00:01:32,750 --> 00:01:38,100
+بالتالي بدنا نعمل refreshing إعادةإحياء للمعلومات
+
+20
+00:01:38,100 --> 00:01:42,940
+اللي مرت علينا في الصف الحادي عشر وبدنا انحل هذه
+
+21
+00:01:42,940 --> 00:01:48,000
+الأسئلة فقط القليلة تعتبر نسبيا المطلوب مننا
+
+22
+00:01:48,000 --> 00:01:55,400
+انحلها احكي مالجيتهاش
+
+23
+00:02:01,650 --> 00:02:06,010
+هي الأسئلة لبعد ال chapter بعد ال summary مش أنا
+
+24
+00:02:06,010 --> 00:02:10,210
+حكيت المرة دى كل chapter مش آخر الكتاب آخر ال
+
+25
+00:02:10,210 --> 00:02:14,190
+chapter تمام آخر الكتاب مش هيجي الصفة معايا عشان
+
+26
+00:02:14,190 --> 00:02:19,030
+بالمرة آخر الكتاب فيه إجابات للأسئلة الفردية
+
+27
+00:02:19,030 --> 00:02:22,570
+إجابات مش انتوا بتحلوا بيشوفوا حالكم حلته صح ولا
+
+28
+00:02:22,570 --> 00:02:27,070
+لأ إذا السؤال فردي إجابته بتلاقوها في آخر الكتاب
+
+29
+00:02:27,700 --> 00:02:33,440
+هتلاقي العنوان answer to all problems مظبوط؟ إذا
+
+30
+00:02:33,440 --> 00:02:37,680
+اللي في آخر الكتاب إجابات لكن السؤال بنصه بلحمه
+
+31
+00:02:37,680 --> 00:02:42,180
+بدمه موجود في نهاية الشكتر في summary أو في
+
+32
+00:02:42,180 --> 00:02:45,280
+objective questions أو في conceptual questions
+
+33
+00:02:45,280 --> 00:02:48,580
+وبعدين في problems ابتدى ل problems الأسئلة هذه
+
+34
+00:02:48,580 --> 00:02:56,560
+تمام هيك؟ تمام غيرها حلو نبدأposition موضع
+
+35
+00:02:56,560 --> 00:03:02,640
+velocity سرعة speed سرعة فرق بينهم فيه فرق من ان
+
+36
+00:03:02,640 --> 00:03:08,100
+انا اتعرف عليه تمام بنقول كل كمية فيزيائية له رمز
+
+37
+00:03:08,100 --> 00:03:14,400
+متعرف عليه ولا لأ ال T للزمن من كلمة time ال M لل
+
+38
+00:03:14,400 --> 00:03:19,060
+mass من كلمة mass اللي هي الكتلةالـ Position
+
+39
+00:03:19,060 --> 00:03:25,260
+اتفقوا ياخدوا X إله إذا الـ Position of a particle
+
+40
+00:03:25,260 --> 00:03:29,440
+هناخد إله الـ X طبعا إيه الـ X من الصيني المحور
+
+41
+00:03:29,440 --> 00:03:33,340
+الصيني تمام يا بنات؟ إذا الـ Position of a
+
+42
+00:03:33,340 --> 00:03:38,240
+particle اللي هنرمزله بالرمز X إيش تعرفه؟ Its
+
+43
+00:03:38,240 --> 00:03:44,540
+location موضعموضع location من موضع is the location
+
+44
+00:03:44,540 --> 00:03:48,440
+with respect to a reference point اذا انت مفهوش
+
+45
+00:03:48,440 --> 00:03:52,300
+تقولي والله انا موضعي خمسة متر بدون ما تقولي عن
+
+46
+00:03:52,300 --> 00:03:57,880
+ايش هذه الاش بيسميها reference point نقطة مرجعية
+
+47
+00:03:57,880 --> 00:04:03,940
+تمام هجيك لما نيجي نقول هاي حيطة مرجع ولا مش مرجع
+
+48
+00:04:03,940 --> 00:04:09,670
+مرجع تمام وهي سيارةهيجيت واضح ان السيارة بتبعد عن
+
+49
+00:04:09,670 --> 00:04:14,410
+الحيطة مسافة ما نقدر نقول بالبلدي موضع السيارة عن
+
+50
+00:04:14,410 --> 00:04:18,110
+الحيطة ولا لأ اذا هذا موضع السيارة عن الحيطة هذا
+
+51
+00:04:18,110 --> 00:04:22,430
+reference point اذا as a particle moves لما يتحرك
+
+52
+00:04:22,430 --> 00:04:27,460
+الجسم ما زال يتحرك اتغير موضعه ولا لأإذن صلوا
+
+53
+00:04:27,460 --> 00:04:32,640
+موضعين موضع ابتدائي وموضع نهائي لأنه كانوا صار إذن
+
+54
+00:04:32,640 --> 00:04:37,620
+و as a particle moves و الجسم بتحرك from an
+
+55
+00:04:37,620 --> 00:04:41,740
+initial position initial position صار الأن عنده
+
+56
+00:04:41,740 --> 00:04:46,420
+موضعين ميز بينهم X و X مينفعش قال الموضع الابتدائي
+
+57
+00:04:46,420 --> 00:04:51,620
+بده حط عليه XI من كلمة initial والموضع النهائي حط
+
+58
+00:04:51,620 --> 00:04:57,210
+X وحط F من كلمة finalإذن as a particle moves from
+
+59
+00:04:57,210 --> 00:05:03,690
+an initial position XI to a final position X final
+
+60
+00:05:03,690 --> 00:05:09,230
+بصله .. بنقول عنه نزاح، مظبوط ولا؟ صلّه إزاحة، its
+
+61
+00:05:09,230 --> 00:05:13,370
+displacement يعني إزاحة، بصارت إزاحته، إيش بيك
+
+62
+00:05:13,370 --> 00:05:18,550
+تعرفها؟ بيقولوا هي السيارة، هيمش هذا موضوع اقتدائي
+
+63
+00:05:18,550 --> 00:05:23,610
+انت بتسوي T initialي انا بداية الحركة تمام؟ قولي
+
+64
+00:05:23,610 --> 00:05:29,750
+اتحركت السيارة انزحت ولا ما انزحتش لموضع جديد
+
+65
+00:05:29,750 --> 00:05:34,490
+الموضع الجديد هادي ولا مش هادى المسافة تمام؟ ليش
+
+66
+00:05:34,490 --> 00:05:38,170
+هادى مش هالجه مش مشكلة المفروض تكون تمام؟ في عندي
+
+67
+00:05:38,170 --> 00:05:42,770
+مشكلة في ال .. في ال word اللى عندنا تمام؟ حلو
+
+68
+00:05:43,640 --> 00:05:48,680
+خيلوها انتوا السيارة هنا تمام؟ حلو هاجيكا و
+
+69
+00:05:48,680 --> 00:05:54,060
+بيدقولكوا جدش مقدار إزاحتها يعني نفترض من عند
+
+70
+00:05:54,060 --> 00:05:59,520
+الحيطة هذه تمام؟ كانت هنا صارت هنا كانت تبعد اتنين
+
+71
+00:05:59,520 --> 00:06:02,620
+متر صارت تبعد خمسة متر جدش انزحت؟ برافو عليك، كيف
+
+72
+00:06:02,620 --> 00:06:08,060
+عملتوا؟ خمسة ناقص اتنين صح ولا لا؟ يعني قلتوا موضع
+
+73
+00:06:08,060 --> 00:06:11,440
+النهائي ناقص الموضع الابتدائي ولا لا؟ هذه بيسميها
+
+74
+00:06:11,440 --> 00:06:18,090
+الإزاحةتغيرت الموضوع والتغير ان المظله بالرمزة
+
+75
+00:06:18,090 --> 00:06:23,870
+delta ولا مش delta دلتا اكس طيب ما هدى delta
+
+76
+00:06:23,870 --> 00:06:31,610
+بنعرفها تانا نشوف هدى شفتوها جمال كده هدى delta
+
+77
+00:06:31,610 --> 00:06:36,620
+برضه بس هدى capital delta و هدى small deltaأه و
+
+78
+00:06:36,620 --> 00:06:41,120
+الله صالها صمت مش هذه حروف و كل حرف اوميجا اخدناها
+
+79
+00:06:41,120 --> 00:06:45,220
+احنا احنا اخدناها اوميجا انا اديتكم اياها بس هذه
+
+80
+00:06:45,220 --> 00:06:49,600
+انا ب .. اعتقد انها مرت عليكم في ال calculus ولا
+
+81
+00:06:49,600 --> 00:06:53,480
+مرة جوية جولتس دلتا تقول السفر ولا مرة ولا مرة
+
+82
+00:06:54,500 --> 00:06:57,720
+بلاش، هيكم عرفتوها، احنا هيك بنحكي عشان تعرف انه
+
+83
+00:06:57,720 --> 00:07:02,500
+فيه capital و small، تمام؟ تلقى ثقافة، هذه المهمة
+
+84
+00:07:02,500 --> 00:07:07,040
+delta، هذا رمز، كل الناس بتعرف ال capital delta
+
+85
+00:07:07,040 --> 00:07:11,260
+فرق ولا مش فرقفقه ده هو الرمز اللي قدناها هدى
+
+86
+00:07:11,260 --> 00:07:13,960
+delta إيه لها شغلها تبني جيها إذا تقدروا إن شاء
+
+87
+00:07:13,960 --> 00:07:15,660
+الله كمان أسبوع أسبوعين بتاخدوها في ال calculus
+
+88
+00:07:15,660 --> 00:07:19,500
+بتقولولي واه والله مرت علينا برضه بيسموها delta
+
+89
+00:07:19,500 --> 00:07:22,520
+بيقولوش اسمها delta خلص delta و هديك delta تمام؟
+
+90
+00:07:22,520 --> 00:07:26,080
+إذا معناته اللي لما قلتها وقلتولي خمسة ناقص ثلاثة
+
+91
+00:07:26,080 --> 00:07:29,940
+يعني x final ناقص x initial ولا لأ إذا هدى تعريف
+
+92
+00:07:29,940 --> 00:07:34,920
+ال displacement الموضع النهائي ناقص الموضع لبتدائي
+
+93
+00:07:34,920 --> 00:07:39,810
+displacement مظبوط ولا لأ؟سهل الأمور لسه ماعملناش
+
+94
+00:07:39,810 --> 00:07:47,410
+حاجة remark ملاحظة يعني remark ايش يعني ملاحظة
+
+95
+00:07:47,410 --> 00:07:53,310
+هتمر علينا remarkات كتيرة حلو جالي إزاحة و جالي في
+
+96
+00:07:53,310 --> 00:07:59,430
+كلمة اسمها مسافة صح اذا distance مسافة و
+
+97
+00:07:59,430 --> 00:08:03,630
+displacement إزاحة جالي there is a difference هناك
+
+98
+00:08:03,630 --> 00:08:07,720
+فرق differenceمظبوط between distance and
+
+99
+00:08:07,720 --> 00:08:14,200
+displacement ايش هو الفورق قاللي هاي جسم كان هنا
+
+100
+00:08:14,200 --> 00:08:21,420
+جذر و شم الهوى و وصل هنا هيجيت وين نقطة بدايته
+
+101
+00:08:21,420 --> 00:08:25,580
+هيها وين نقطة نهايته هيها اذا بتحكيلي عن
+
+102
+00:08:25,580 --> 00:08:32,070
+displacement مالكاش دعواء كيف وصل النهايةهيتجذر
+
+103
+00:08:32,070 --> 00:08:38,010
+اختصر ماختصرش انا الي دعوة وين كان وين صار اذا قلت
+
+104
+00:08:38,010 --> 00:08:41,850
+بداية و نهاية معناته displacement اذا بدك كيف وصل
+
+105
+00:08:41,850 --> 00:08:45,970
+معناته بتحكي عن مسافة ندي المثل البلدي اللي انتوا
+
+106
+00:08:45,970 --> 00:08:48,530
+طالعين من الجامعة و رايحين على خانونس تكرته
+
+107
+00:08:48,530 --> 00:08:53,290
+مواصلات مظبوط ولا لأ احيانا تصدف السيارة راحت على
+
+108
+00:08:53,290 --> 00:08:55,670
+خانونس عادي اللي في شارع صلاح الدي لما وصلت خانونس
+
+109
+00:08:55,670 --> 00:08:59,990
+ومرات من جلة الركاب أخدله راكب على المغازيوخد وراك
+
+110
+00:08:59,990 --> 00:09:04,750
+عادى للبلح مش بيضلوا جذر اذا انت بدك displacement
+
+111
+00:09:04,750 --> 00:09:08,030
+بتحط رجل عريجل في غزة ما هو انطلق من غزة و بتقوله
+
+112
+00:09:08,030 --> 00:09:12,090
+لما اتصل خانونس قولي بروح بجيب خط من غزة لخانونس
+
+113
+00:09:12,090 --> 00:09:16,270
+بقولها دى ايه زاعته صح ولا لأ اذا بدك مسافة بنفع
+
+114
+00:09:16,270 --> 00:09:20,030
+تحط رجل عريجل ولا بده ايجي لوراهبدي أجري وراه، راح
+
+115
+00:09:20,030 --> 00:09:23,410
+على المغازي، بدي ألحجه، راح على الدير، بدي ألحجه،
+
+116
+00:09:23,410 --> 00:09:28,230
+ميل على هنا ولا هنا، بدي ألحجه، صح ولا لأ؟ لما بدي
+
+117
+00:09:28,230 --> 00:09:32,230
+ألحجه، معناته أنت بتحكي عن مسافة، لكن لما بدي تحكي
+
+118
+00:09:32,230 --> 00:09:36,750
+عن إزاحة، بيهمك نقطتي البداية والنهاية فقط، هي
+
+119
+00:09:36,750 --> 00:09:41,690
+هذا، وهي نقطة النهاية، من كان يصل هيك ولا لأ؟ وهنا
+
+120
+00:09:41,690 --> 00:09:46,050
+قعدت بجزر، برضه وصل، هل جيت هذه الإزاحة وهذه
+
+121
+00:09:46,050 --> 00:09:52,560
+المسافة؟ من أكبر؟المسافة صح أو لأ؟ في مجال ممكن
+
+122
+00:09:52,560 --> 00:09:58,180
+المسافة واليزاح يتساويأه إذا مش يوم خطأ أحد ما
+
+123
+00:09:58,180 --> 00:10:01,780
+تعبش حاله لف لف له هنا و هنا صح ولا لأ؟ إذا
+
+124
+00:10:01,780 --> 00:10:04,480
+بيقوللي إيش ال difference؟ الكلام البلدي اللي
+
+125
+00:10:04,480 --> 00:10:10,140
+حكيته بيقوللي distance هي كمية قياسية is a scalar
+
+126
+00:10:10,140 --> 00:10:13,920
+quantity طبعا كمية قياسية وكمية مش قياسية هذا
+
+127
+00:10:13,920 --> 00:10:17,540
+موضوع chapter 3 هنزيه تفصيلا بس الآن بيقوله كيف
+
+128
+00:10:17,540 --> 00:10:22,640
+حالك؟is a scalar quantity كمية قياسية طب إيش
+
+129
+00:10:22,640 --> 00:10:24,920
+تعريفها؟ ماكانش دعوة هجت في الـ scalar و مش الـ
+
+130
+00:10:24,920 --> 00:10:30,060
+scalar بيقولي is the actual length الطول الحقيقي
+
+131
+00:10:30,060 --> 00:10:34,710
+actual حقيقي مرك عليكمالطول الحقيقي الـ Actual
+
+132
+00:10:34,710 --> 00:10:40,610
+Length of the path للطريق Followed by a particle
+
+133
+00:10:40,610 --> 00:10:44,770
+تبحّى أي جسم سيارة ولا طيارة ولا واحد قاعد بيجذّر
+
+134
+00:10:44,770 --> 00:10:48,310
+هذا هو تعريف الـ Distance إذا الـ Distance اللي
+
+135
+00:10:48,310 --> 00:10:51,590
+بيجتبح حاجة السيارة و المراحة لإنها بيدك الطول
+
+136
+00:10:51,590 --> 00:10:56,320
+الحقيقي للرحلة Where راح و وين إجامع أن الـ
+
+137
+00:10:56,320 --> 00:11:04,680
+Displacement هو كمية فائعة متجهة مش قياسية تمام؟
+
+138
+00:11:04,680 --> 00:11:11,900
+ايش تقريفه؟ هي المقارنة الأقصر بين الاسم والمقارنة
+
+139
+00:11:11,900 --> 00:11:15,940
+الأخيرة من البرتقال إذن بهمك فقط نقطتي البداية
+
+140
+00:11:15,940 --> 00:11:20,860
+والنهاية وإن كان وإن صار إيش في الطريق سوى؟ مالكاش
+
+141
+00:11:20,860 --> 00:11:26,450
+جعوة مالكاش جعوة، هذي الـ Displacement تمامبيقولّي
+
+142
+00:11:26,450 --> 00:11:31,670
+حكاية Scalar و Vector أجّي قضيتهم لـ Chapter 3 We
+
+143
+00:11:31,670 --> 00:11:39,190
+Shall المستقبل القريب كمان أسبوع اتريد نعمل Vector
+
+144
+00:11:39,190 --> 00:11:43,090
+Quantities in detail بكل التفاصيل تبعتهم في
+
+145
+00:11:43,090 --> 00:11:46,230
+Chapter 3 الشبطر اللي جاي احنا الآن في أي شبطر؟
+
+146
+00:11:46,230 --> 00:11:50,090
+نين لسه بدنا .. Vectors قالوا طيب مانت بتقولي
+
+147
+00:11:50,090 --> 00:11:54,800
+Displacement كي بتتعامل معاها DisplacementVictor
+
+148
+00:11:54,800 --> 00:11:59,240
+يعني بدك تقولي شرق ولا غرب، بدك تقولي فوق ولا تحت،
+
+149
+00:11:59,240 --> 00:12:02,620
+واحنا لسه ماخدناش chapter تلاتة، بقوله بسيطة، ده
+
+150
+00:12:02,620 --> 00:12:06,660
+ده ده ده، انت بتعرف موجة بوسالب؟ ماعشان بنعرف موجة
+
+151
+00:12:06,660 --> 00:12:12,260
+بوسالب؟ خدلي الموجب لما تكون الحركة رايحة يمينطب
+
+152
+00:12:12,260 --> 00:12:16,960
+لما تكون يسار صارت سالب هذه لما الحركة تكون أفقية
+
+153
+00:12:16,960 --> 00:12:22,540
+طيب السقوط الحر أفقي و لا عمودي عمودي قال لي ويه
+
+154
+00:12:22,540 --> 00:12:25,640
+بدك تاخده ماللي التالي اللي لفوق إيش بدك تاخده
+
+155
+00:12:25,640 --> 00:12:28,880
+مودب و اللي لتحت سالب طب أحد بيقول من وين جيبناها
+
+156
+00:12:28,880 --> 00:12:32,760
+قالوا هو أنت بتعرف لما كنا نور الصمت هذا المحاور
+
+157
+00:12:32,760 --> 00:12:37,380
+ذاكرينهالمشكلة اللي نرسمها هي المحور الصادق يكون
+
+158
+00:12:37,380 --> 00:12:42,280
+اتجاه الموجب لأعلى والصيني ليمين يعني هيك بدي
+
+159
+00:12:42,280 --> 00:12:45,920
+ااخده يعني انت اول ما تشوف سالب هى بتقول هذه رايحة
+
+160
+00:12:45,920 --> 00:12:50,100
+يسار اول ما تشوف سالب وهى عموديا بتقول هذا نازل
+
+161
+00:12:50,100 --> 00:12:55,490
+لأسفل صح ولا لأin this chapter اللي هو chapter 2
+
+162
+00:12:55,490 --> 00:12:59,290
+ماوصلنا لـ chapter 3 we use إيش بقت تستخدم؟ جالي
+
+163
+00:12:59,290 --> 00:13:03,630
+ال positive و ال negative نعرفه مظبوطة إيه؟ تمام
+
+164
+00:13:03,630 --> 00:13:08,530
+to the indicate عشان نشير vector not direction لل
+
+165
+00:13:08,530 --> 00:13:12,210
+vector اتجاه ال vector vector direction direction
+
+166
+00:13:12,210 --> 00:13:16,990
+تجاه و ال vector القمية المتجهة تمام إيش يعني؟
+
+167
+00:13:16,990 --> 00:13:20,370
+بيقولي for horizontal motion horizontal أفقية
+
+168
+00:13:20,370 --> 00:13:26,930
+بناهاللحركة الأفقية بدنا نحدد و نصف إلى الجانب
+
+169
+00:13:26,930 --> 00:13:30,830
+اللي عايش على اليمين كمصطلح الـ Positive Direction
+
+170
+00:13:30,830 --> 00:13:35,410
+إذا الـ Positive معناتها يمين اتفجنا؟ هذا اتفاق
+
+171
+00:13:35,410 --> 00:13:39,830
+والله غيرناه مع بعض، ممكن، لكن هذا الاتفاق الـ
+
+172
+00:13:39,830 --> 00:13:46,890
+Default، تسألي؟تمام؟ while .. بينما for vertical
+
+173
+00:13:46,890 --> 00:13:50,210
+motion ها .. هذي horizontal أفوخي .. vertical
+
+174
+00:13:50,210 --> 00:13:57,670
+عمودي للحركة العمودية we specify حددنا the upward
+
+175
+00:13:57,670 --> 00:14:02,250
+.. upward .. إيش يعني up؟ لأعلى .. إذا الاتجاه
+
+176
+00:14:02,250 --> 00:14:07,090
+اللي لأعلى هو ال positive اتفجنا؟ هيك اتفجنا .. تم
+
+177
+00:14:09,350 --> 00:14:14,650
+العين قال لي تغير الموضوع صار في حركة حركة معناته
+
+178
+00:14:14,650 --> 00:14:19,210
+في سرعة في سرعة بنسمي أول حاجة ال average velocity
+
+179
+00:14:19,210 --> 00:14:24,150
+السرعة المتوسطة تمام هل جيتوا احنا مروحين على
+
+180
+00:14:24,150 --> 00:14:28,410
+خانونس نركب سيارة ولا لأ سرعة السيارة من غزة
+
+181
+00:14:28,410 --> 00:14:32,720
+لخانونس ثابتةبضرها يعني هو حد مقدر يقولي طيب بدي
+
+182
+00:14:32,720 --> 00:14:37,760
+سرعة ساعتها أنت بتقولي سرعة بدي سرعة متوسطة ولا لأ
+
+183
+00:14:37,760 --> 00:14:41,100
+عشان أقدر أديك لأن مرة كانت واقفة و مرة كانت سريعة
+
+184
+00:14:41,100 --> 00:14:44,740
+و مرة كانت بطيئة صحيح ولا لأ؟ إذا أن أنت لما تحكي
+
+185
+00:14:44,740 --> 00:14:50,300
+عن سرعات مش ثابتة بتحكي عن متوسط السرعة average
+
+186
+00:14:50,300 --> 00:14:54,710
+velocity يعني سرعة متوسطةتمام يا بنات؟ كل واحد
+
+187
+00:14:54,710 --> 00:14:59,690
+فيكم لو قلتله النسافة من هنا لخانونس نفترض تلاتين
+
+188
+00:14:59,690 --> 00:15:03,590
+كيلومتر وانت أخدتها بساعة بتقدر تجيبلي سرعة
+
+189
+00:15:03,590 --> 00:15:07,910
+السيارة كمتوسطة ولا لأ؟ اه التلاتين كيلومتر ع
+
+190
+00:15:07,910 --> 00:15:13,240
+الساعة بجيبلكي إياها صح ولا لأ؟ تم اذا بقولليالـ
+
+191
+00:15:13,240 --> 00:15:16,220
+Average Velocity إذا ما هي معانات الـ Average؟
+
+192
+00:15:16,220 --> 00:15:20,000
+متوسطة الـ Average Velocity of a particle is
+
+193
+00:15:20,000 --> 00:15:24,480
+defined as .. إيش رمز السرعة يا بنات؟ V ما زال بدك
+
+194
+00:15:24,480 --> 00:15:28,580
+average بحطه بار فوق الحرف هذه معاناتها متوسطة
+
+195
+00:15:28,580 --> 00:15:35,860
+نهاي رمزها V وفي الشرطة هذهدلتا X على دلتا T دلتا
+
+196
+00:15:35,860 --> 00:15:40,260
+X الإزاحة اللي اتوقعتها أنا وياك اللي هي X final
+
+197
+00:15:40,260 --> 00:15:44,280
+نقص X initial ولا لأ؟ ودلتا T هي الدلتا اللي إلها
+
+198
+00:15:44,280 --> 00:15:49,280
+small تمام؟ اللي هي برضه T final نقص T initial
+
+199
+00:15:49,280 --> 00:15:54,530
+دائما الدلتا بتعني تغيرالتفاجنة تمت جلي بسيطة
+
+200
+00:15:54,530 --> 00:15:59,970
+فضلاها السرعة المتوسطة هي الإزاحة على الزمن
+
+201
+00:15:59,970 --> 00:16:03,970
+التفاجنة طوجنا على خانون السلتين كيلومتر على
+
+202
+00:16:03,970 --> 00:16:08,490
+الساعة الفترة الزمنية اللي استغرقت رحلتها من غزا
+
+203
+00:16:08,490 --> 00:16:14,790
+لخانونس حلوبقول ليه؟ القانون إيش بيقول؟ بيقول حسب
+
+204
+00:16:14,790 --> 00:16:19,250
+الكلام هجت وين كانت في غزة صح؟ و وين وصلت؟ خلوا
+
+205
+00:16:19,250 --> 00:16:22,830
+ناس هجت في القانون مبين انه روح المغازي ولا مارحش؟
+
+206
+00:16:22,830 --> 00:16:28,090
+لأ مالكاش دعوة إيش علاش بتعتمد فقط؟ بس البداية و
+
+207
+00:16:28,090 --> 00:16:32,170
+النهاية إذا the average velocity depends only
+
+208
+00:16:32,170 --> 00:16:36,010
+تعتمد فقط on the initial and the final positions
+
+209
+00:16:36,010 --> 00:16:42,980
+of the particle أمي طيب سيارة كانت في غزةتمام و
+
+210
+00:16:42,980 --> 00:16:47,280
+قصدرت و قهضت راحتها و أخر الليل وصلت غزة اجيت بدي
+
+211
+00:16:47,280 --> 00:16:50,840
+اجيب ال body displacement تبعتها سفر طب و ال
+
+212
+00:16:50,840 --> 00:16:54,940
+average velocity سفر ان شاء الله خمس ساعات قعدت
+
+213
+00:16:54,940 --> 00:16:59,820
+سفر على خمس ساعات ولا عشرين ساعة ما السفرتمام؟ إذا
+
+214
+00:16:59,820 --> 00:17:03,780
+أي جسم ببدأ من نقطة وبرجعلها لديه سرعته المتوسطة؟
+
+215
+00:17:03,780 --> 00:17:08,240
+سفر بيقول ليه؟ إيش معناته؟ بيقول ليه this means
+
+216
+00:17:08,240 --> 00:17:13,780
+that ما زال السرعة المتوسطة تعتمد فقط على نقطتي
+
+217
+00:17:13,780 --> 00:17:18,460
+البداية والنهاية إذا تساوت نقطتي البداية والنهاية
+
+218
+00:17:18,460 --> 00:17:24,250
+فاش سرعة this means that if a particleit starts
+
+219
+00:17:24,250 --> 00:17:27,970
+from a point بدأ من نقطة and returns back to the
+
+220
+00:17:27,970 --> 00:17:32,210
+same point ورجع إلها نفسها this is displacement
+
+221
+00:17:32,210 --> 00:17:37,650
+بتكون إذعتها وبالتالي سرعتها المتوسطة zero صح ولا
+
+222
+00:17:37,650 --> 00:17:42,390
+لأ؟ هذه معلومة معروفة مافيش فيها إشي إحنا متفقين
+
+223
+00:17:42,390 --> 00:17:46,150
+اللي عندها سؤاله تنط على طول احكي شايفك خايفة أنا
+
+224
+00:17:49,720 --> 00:17:53,960
+هذه الـ Average Velocity هي بتعريفها يا بنتي
+
+225
+00:17:53,960 --> 00:17:57,760
+هتبديك المسافة استنيني شوية الـ Average Velocity
+
+226
+00:17:57,760 --> 00:18:01,160
+تعريفها العلمي اللي كل الناس بعرفه هي displacement
+
+227
+00:18:01,160 --> 00:18:07,300
+ع زمان و ليست مسافة ع زمان فيم تعنيها؟ ليش اسمك؟
+
+228
+00:18:07,300 --> 00:18:12,250
+ايش اسمك انت؟ أسيل؟ ليش يسموك أسيل؟عشان ايه عبارة
+
+229
+00:18:12,250 --> 00:18:16,090
+عن أبوك و أمك؟ مصطلح ان كل حاجة بدنا نتعرفها المهم
+
+230
+00:18:16,090 --> 00:18:20,590
+ايه يا بنت ايه؟ انه احنا كنا نتفق كعالم انه هاجي
+
+231
+00:18:20,590 --> 00:18:24,750
+هيك تعريفها هاجيت فيه velocity مش توجب تليك في
+
+232
+00:18:24,750 --> 00:18:29,130
+حاجة اسمها speed؟ اذا احنا مظلمنهاش المسافة هنديها
+
+233
+00:18:29,130 --> 00:18:33,830
+speed استني شوية علينا تمام؟ اذا بدنا نتفق ايش فيه
+
+234
+00:18:33,830 --> 00:18:35,870
+ال velocity و ايش ال speed؟ اتفقوا الناس ال
+
+235
+00:18:35,870 --> 00:18:38,450
+velocity اللي هدعوا بيجي سبلاش من كل المسافة؟دي
+
+236
+00:18:38,450 --> 00:18:42,390
+اسم لاسمى، اتفقنا؟ في شانات كتيرة مفهوش تقولي ليش،
+
+237
+00:18:42,390 --> 00:18:49,050
+هات هي اتفاق، ليش الشرق عملوا شرق؟ ليش معكسوهوش؟
+
+238
+00:18:49,050 --> 00:18:54,270
+ليش الساعة بتلف هيك؟ معكسوهاش، اتفاقات، تمام هيك؟
+
+239
+00:18:54,270 --> 00:18:57,930
+ففي أمور كتير خلاص، اتفاق و بقى، لنفترض لو أنت كنت
+
+240
+00:18:57,930 --> 00:19:02,090
+معاه وغيرتي ممكن يردوا عليكي وغيروا، خلوها مختلفة،
+
+241
+00:19:02,090 --> 00:19:07,850
+ففهمتوا عليكي؟ ففي أمور default بتصيرانتبه ..
+
+242
+00:19:07,850 --> 00:19:11,970
+Average Speed .. Average Speed .. هي .. طب هو
+
+243
+00:19:11,970 --> 00:19:14,970
+Average فلسفة تخلصنا منها ومعناتها بالعربي سرعة
+
+244
+00:19:14,970 --> 00:19:18,990
+متوسطة .. Average Speed سرعة متوسطة .. بس الآن
+
+245
+00:19:18,990 --> 00:19:21,490
+بيقول .. هي و اللي رأى مغازك كيف بدي أسوي فيه هذا
+
+246
+00:19:21,490 --> 00:19:26,030
+.. قال لي هنا بجيبهالـ Average Speed بدك تجيبلي
+
+247
+00:19:26,030 --> 00:19:29,170
+المسافة على الزمن وليست الإزاحة على الزمن وبالتالي
+
+248
+00:19:29,170 --> 00:19:32,090
+لو وقع المجازي بتحسبها ولا لأ؟ هاي نحسبناها يا
+
+249
+00:19:32,090 --> 00:19:37,070
+عزيزي إذا ما هو تعريف الـ Average Speed؟ Differs،
+
+250
+00:19:37,070 --> 00:19:41,370
+تختلف عن الـ Average Velocity اتفقنا هيك كيف
+
+251
+00:19:41,370 --> 00:19:45,210
+بتختلف؟ بقولي in that it covers في الـ Average
+
+252
+00:19:45,210 --> 00:19:48,910
+Speed بيبقى تغطيلي it covers the total distance
+
+253
+00:19:48,910 --> 00:19:52,510
+بطل ال displacementthe total distance rather than
+
+254
+00:19:52,510 --> 00:19:56,350
+وليست ال total displacement rather than the total
+
+255
+00:19:56,350 --> 00:19:59,450
+displacement يعني كيف القلوب ده تصير? other
+
+256
+00:19:59,450 --> 00:20:02,970
+distance بتساوي ال displacement ولا ال distance؟
+
+257
+00:20:02,970 --> 00:20:07,430
+distance على زمان والزمان زمان ماتغيرش ولا لأ؟
+
+258
+00:20:07,430 --> 00:20:12,490
+زمان زمان ارضيتي هال gate هالمسافة مازالة ماناهاش؟
+
+259
+00:20:12,490 --> 00:20:20,700
+الها تعريف الها speed اتفجنا؟ تمامقاللي الصرعة
+
+260
+00:20:20,700 --> 00:20:25,280
+كمية ماهياش من الكميات الأساسية تبع علم الميكانيكا
+
+261
+00:20:25,280 --> 00:20:30,140
+انت المحاضرة الماضية قلتلي في تلت كميات أساسية في
+
+262
+00:20:30,140 --> 00:20:34,760
+علم الميكانيكا mass و length و time طيب ال
+
+263
+00:20:34,760 --> 00:20:39,420
+velocity ما قلتلي ده مظبوط ماقالتلي كل كمية هتمر
+
+264
+00:20:39,420 --> 00:20:43,450
+عليك بعد كده بيكترجح ل هدول التلاتةتما الـ
+
+265
+00:20:43,450 --> 00:20:46,990
+Velocity الـ dimension تبعها L على T وبالتالي
+
+266
+00:20:46,990 --> 00:20:50,410
+وحدات في متر per second او centimeter per second
+
+267
+00:20:50,410 --> 00:20:54,470
+او foot per second صح؟ اذا بيقولي بقص I unit of
+
+268
+00:20:54,470 --> 00:20:57,510
+velocity ايش هتكون؟ متر per second ده أنا رجعتها
+
+269
+00:20:57,510 --> 00:21:01,730
+وصلات كمية معروفة وعارف عنها كل حاجة اتفجنا يا
+
+270
+00:21:01,730 --> 00:21:05,850
+بنات؟ أيه الصفة صح؟
+
+271
+00:21:05,850 --> 00:21:10,740
+remarkجالي بدك اتميزي واحدة واحدة بين speed و
+
+272
+00:21:10,740 --> 00:21:15,300
+velocity صح ولا .. جالي اتطلعوا يا بنات لما اقولكم
+
+273
+00:21:15,300 --> 00:21:21,240
+velocity بدي اقولكم the velocity of a car صورة ايش
+
+274
+00:21:21,240 --> 00:21:30,140
+سيارة velocity is fifty kilometer per hour هيك
+
+275
+00:21:30,140 --> 00:21:35,200
+بيتكونش كملت لازم تقولي كده في الاتجاه to the east
+
+276
+00:21:35,200 --> 00:21:40,940
+خلصتأو to the west هيك منيح او تقولي up او تقولي
+
+277
+00:21:40,940 --> 00:21:44,620
+down هذه بتحكي عن ال velocity لكن طب يابو تقولي
+
+278
+00:21:44,620 --> 00:21:49,260
+the speed of the car is fifty kilometer per hour
+
+279
+00:21:49,260 --> 00:21:54,500
+نقطة خلصت speed speed فلتوا من ال distance speed
+
+280
+00:21:54,500 --> 00:21:59,660
+اذا ال speed تعريفها هي مقدار ال velocity مقدار ال
+
+281
+00:21:59,660 --> 00:22:03,320
+velocity بدون direction ال speed مقدار ال velocity
+
+282
+00:22:04,620 --> 00:22:07,880
+دخلت المعلومة جوا؟ ايش بتفرج ال speed عن ال
+
+283
+00:22:07,880 --> 00:22:11,400
+velocity؟ ال speed مقدار السرعة اقول بالعربي سرعة
+
+284
+00:22:11,400 --> 00:22:15,120
+سيارة خمسين كيلومتر بالساعة شرقا جدتش ال speed
+
+285
+00:22:15,120 --> 00:22:19,540
+بتاعتها؟ خمسين كيلومتر بالساعة نقطة بقولش شرقا ولا
+
+286
+00:22:19,540 --> 00:22:23,940
+غربا تمام؟ تاخد بس المقدار هذا ال speed و ال
+
+287
+00:22:23,940 --> 00:22:28,640
+velocity فهمتها جالي طب هل ال average speed هي
+
+288
+00:22:28,640 --> 00:22:32,060
+مقدار ال average velocity؟ بيقولي لأ لما تدخل ال
+
+289
+00:22:32,060 --> 00:22:37,030
+average بتبطلإذا بيقوللي الـ remark even though
+
+290
+00:22:37,030 --> 00:22:40,830
+بالرغم من أنه المعلومة اللي أديتكم ياها الأولى ال
+
+291
+00:22:40,830 --> 00:22:43,630
+speed is the magnitude of the velocity ال speed هو
+
+292
+00:22:43,630 --> 00:22:48,430
+مقدار ال velocity إلا إنه the average speed is not
+
+293
+00:22:48,430 --> 00:22:51,470
+the magnitude of the average velocity اتفجنا يا
+
+294
+00:22:51,470 --> 00:22:58,250
+بنات؟ تمام هيك؟ هديك مثال عليه هديت ال speed مقدار
+
+295
+00:22:58,250 --> 00:23:02,750
+ال velocityتمام؟ الـ Average Speed ماهياش مقدار
+
+296
+00:23:02,750 --> 00:23:06,090
+الـ Average Velocity اتفقنا؟ قعدتش تقولي ليه ليش،
+
+297
+00:23:06,090 --> 00:23:09,090
+اتنى شوية شوية بنضل نقول ليه ليش لما كل في كل حاجة
+
+298
+00:23:09,090 --> 00:23:14,390
+أيها ليش بنقول عنها اتفقنا؟ حلو، quiz نحن اتفقنا
+
+299
+00:23:14,390 --> 00:23:17,910
+كل من أكم شريحة بإن نشوف حالنا بنحكي عربي ولا صيني
+
+300
+00:23:18,730 --> 00:23:22,050
+تمام احنا مش خدنا لسه عشان نقول فهمنا ولا مافهمنا
+
+301
+00:23:22,050 --> 00:23:24,670
+اش ماخدناش حاجة اخدنا الفرق بين ال distance و
+
+302
+00:23:24,670 --> 00:23:29,110
+displacement صح؟ واخدنا الفرق بين average speed و
+
+303
+00:23:29,110 --> 00:23:35,860
+average velocity صح؟ حلو اش بقولي؟ under whichof
+
+304
+00:23:35,860 --> 00:23:39,560
+the following conditions هنا conditions معناته شرط
+
+305
+00:23:39,560 --> 00:23:44,680
+تحت أي من هذه الشروط is the magnitude of the
+
+306
+00:23:44,680 --> 00:23:48,800
+average velocity of a particle moving in one
+
+307
+00:23:48,800 --> 00:23:52,460
+direction smaller than the average speed over some
+
+308
+00:23:52,460 --> 00:23:56,200
+time interval أنا أول سألتكم وجاوبتوني صح قلتلكم
+
+309
+00:23:56,200 --> 00:24:01,590
+المسافة والإزاحةدايمًا جات بعض؟ طب هل ممكن الإزاحة
+
+310
+00:24:01,590 --> 00:24:06,090
+تكون أكبر من المسافة؟ ولا ممكن؟ هنا بيقوللي واكتيش
+
+311
+00:24:06,090 --> 00:24:10,570
+بتكون الإزاحة أقل من المسافة، بيددك تلت حركات، و
+
+312
+00:24:10,570 --> 00:24:15,310
+بتقوللي في هذه الحركات الإزاحة أقل، مش ممكن يقولك
+
+313
+00:24:15,310 --> 00:24:22,170
+أكبر، أقل ولا بتساوي، وهي كأنها، اشوفA particle
+
+314
+00:24:22,170 --> 00:24:27,190
+moves in the X direction without reversing واحد
+
+315
+00:24:27,190 --> 00:24:33,090
+ماشي ايديل ومارجعيش بتسويها هل الإزاحة أقل من
+
+316
+00:24:33,090 --> 00:24:36,850
+المسافة؟ لأ إذا هذا ال condition غلط صح ولا لأ؟
+
+317
+00:24:36,850 --> 00:24:41,850
+أنا بدي أي حركة فيها الإزاحة أقل من المسافة هنا زي
+
+318
+00:24:41,850 --> 00:24:48,580
+بعض ولا لأ؟ زي بعض حلوA particle moves in the
+
+319
+00:24:48,580 --> 00:24:54,360
+negative X direction without reversing نفس العملية
+
+320
+00:24:54,360 --> 00:24:58,500
+يعني زي ما حكينا احنا جامعتنا بتطلع الشارع
+
+321
+00:24:58,500 --> 00:25:01,940
+التلاتيني بيسموها صح؟ هجيت لما نروح الشرق وين
+
+322
+00:25:01,940 --> 00:25:07,120
+بيخلص الشارع التلاتيني؟ وين بيخلص؟ أيش المنطقة
+
+323
+00:25:07,120 --> 00:25:10,440
+اللي بيخلص عندها؟ لأ جاب للساحة أيش المنطقة
+
+324
+00:25:10,440 --> 00:25:13,780
+بيسموها؟ وين سكان الزتون؟ عصقولة مافيش حد سكن
+
+325
+00:25:13,780 --> 00:25:18,500
+عصقولة هنا؟تعرفوا منطقة عصقولة؟هذه بتخلص شارع
+
+326
+00:25:18,500 --> 00:25:22,360
+التلاتين ساعتها لأ بتروح لفوق على الساحة لأ بتروح
+
+327
+00:25:22,360 --> 00:25:26,640
+على مسجد الشافعي اللي هو أشهر مسجد في الحرق تمام؟
+
+328
+00:25:26,640 --> 00:25:30,160
+إذا بيخلص الشارع وين عند عزجولة؟ واحد مشي لما خلص
+
+329
+00:25:30,160 --> 00:25:34,080
+عند عزجولة إزحته مسافته زي بعض ولا لأ؟ تمام طب
+
+330
+00:25:34,080 --> 00:25:37,660
+واحد قال أنا بديش أروح على عزجولة بدي أروح تجاه
+
+331
+00:25:37,660 --> 00:25:41,260
+البحر وين بيخلص هذا الشارع؟ شارع الرشيد شارع البحر
+
+332
+00:25:41,260 --> 00:25:46,860
+هي هي الإزاحة والمسافة بختلفوا عن بعض؟ لأإذا في
+
+333
+00:25:46,860 --> 00:25:51,640
+الحالتين زي بعض طب يشوف a particle moves in the
+
+334
+00:25:51,640 --> 00:25:55,200
+positive x direction يعني رايح على أسجولة و رجع و
+
+335
+00:25:55,200 --> 00:26:01,340
+في المفترج الطيران بتعرفوه تسمعوا فيه جابلي
+
+336
+00:26:01,340 --> 00:26:08,140
+الجامعة برا عليكم هجيت هو وصل على أسجولة و رجع in
+
+337
+00:26:08,140 --> 00:26:12,350
+the x direction and then reverses و رجعتمام مين
+
+338
+00:26:12,350 --> 00:26:15,650
+أكبر؟ المسافة ولا الإزاحة؟ المسافة إذاً هنا
+
+339
+00:26:15,650 --> 00:26:19,630
+الإزاحة أقل من المسافة إذاً معناته ال average
+
+340
+00:26:19,630 --> 00:26:23,470
+velocity أقل من ال average speed ولا لأ؟ إذاً
+
+341
+00:26:23,470 --> 00:26:27,630
+معناته هو بيقوللي مين من التلاتة هدول ال average
+
+342
+00:26:27,630 --> 00:26:30,350
+velocity أقل من ال average speed؟ مين من التلاتة
+
+343
+00:26:30,350 --> 00:26:34,950
+دول؟ ال C وفي الآخر بيقوللي واحد غلب يقولك و I'm
+
+344
+00:26:34,950 --> 00:26:38,570
+under no conditions لأ إذاً هادي قطعا ولا لأ؟
+
+345
+00:26:38,570 --> 00:26:44,240
+اسأليه احكي يا Cاحكي .. احكي ..
+
+346
+00:26:51,950 --> 00:26:54,950
+برافو عليك ايش؟ بدي نقطتي البداية والنهاية فهمتوا
+
+347
+00:26:54,950 --> 00:26:58,850
+عليّ؟ احكي بدي نقطتي البداية والنهاية البداية من
+
+348
+00:26:58,850 --> 00:27:02,730
+الجامعة ولا لأ؟ والنهاية الطيران الطيران هيو لو
+
+349
+00:27:02,730 --> 00:27:06,750
+غوّشت أنا بقى باس معنى تبع الطيران هيو لكن عزجولة
+
+350
+00:27:06,750 --> 00:27:11,750
+بعيدة أو بالتالي تطلعوا أنتوا المسافة بدي أجيس من
+
+351
+00:27:11,750 --> 00:27:16,090
+هان لعزجولة و بعدين أرجع للطيران مسافة كبيرة غير
+
+352
+00:27:16,090 --> 00:27:22,320
+عن اليزاحة من هان لعزجولة كلها أقل من كيلوبتجيش نص
+
+353
+00:27:22,320 --> 00:27:37,820
+كيلو من محور الطيران او دور الطيران احكي بالظبط
+
+354
+00:27:37,820 --> 00:27:38,620
+بالظبط احكي
+
+355
+00:27:44,700 --> 00:27:47,600
+الـ Average Speed و الـ Average Velocity جت بعض
+
+356
+00:27:47,600 --> 00:27:51,380
+لأن الشوء الـ Average Velocity جالي جسم لسمة عزمان
+
+357
+00:27:51,380 --> 00:27:56,830
+صح؟ و الـ Average Speed مسافة عزمان صح؟ بيفرقوامش
+
+358
+00:27:56,830 --> 00:27:59,830
+المسافة نفس الإزاحة؟ و الزمان زمان و احنا الزمان
+
+359
+00:27:59,830 --> 00:28:04,250
+مابنلاعبش فيه؟ عشان كده كانت ضحكت في التالتة مين
+
+360
+00:28:04,250 --> 00:28:09,030
+أكبر؟ المسافة ولا الإزاحة؟ اللي راح و رجع حلو إذا
+
+361
+00:28:09,030 --> 00:28:13,050
+معاتوا ال average velocity أقل من ال average speed
+
+362
+00:28:13,050 --> 00:28:19,030
+ولا لأ؟ اه وهي بيقوللي مين من التلاتة هدول تمام؟
+
+363
+00:28:19,030 --> 00:28:22,230
+the average velocity is smaller than the average
+
+364
+00:28:22,230 --> 00:28:27,150
+speed بقوله هذه التالتة صح ولا لأ؟ما تخجلوش انت
+
+365
+00:28:27,150 --> 00:28:29,790
+بتسأل و احكي يا أسيل فجيت المسافة أكبر من الإتاح
+
+366
+00:28:29,790 --> 00:28:34,950
+تمامًا بس الزمان ليش ممكن .. اه حلو هجيت أنت طلعت
+
+367
+00:28:34,950 --> 00:28:39,770
+و استغرقت مراتي اللي .. اللي واجت معاكي بياخد ساعة
+
+368
+00:28:39,770 --> 00:28:42,850
+و مراتي بياخد معاكي نص ساعة زمان زمان انا في
+
+369
+00:28:42,850 --> 00:28:48,510
+النهاية انت لما تصل الطيران سيارة راح .. بديها تصل
+
+370
+00:28:48,510 --> 00:28:53,390
+الطيران اجي عبالها تتجذر تمام؟ اذا الزمان بديك
+
+371
+00:28:53,390 --> 00:28:58,720
+تاخديه كله كل الزمانفهمت عليّ كيف؟ حتى و لو بدك
+
+372
+00:28:58,720 --> 00:29:02,700
+إذاحة طب هو أنتي وصلت الطيران مش أخدت و أجيت أكتار
+
+373
+00:29:02,700 --> 00:29:07,080
+لما وصلت الطيران لما أنتي وصلت عزجولة و رجعت صح؟
+
+374
+00:29:07,080 --> 00:29:11,540
+انت هجيت انتي من وين انطلقتي؟ من الجامعة و وين
+
+375
+00:29:11,540 --> 00:29:17,100
+خلصتي؟ عند الطيران تمام؟ بنفع ألغي عزجولة و أنتي
+
+376
+00:29:17,100 --> 00:29:22,380
+روحت عزجولة؟بدي .. بدي أحملها في حزبتي؟! بالتالي
+
+377
+00:29:22,380 --> 00:29:26,840
+الزمن تبعك بدي تحسبه، ماينفعش تطير زمن، لأن الزمن
+
+378
+00:29:26,840 --> 00:29:31,260
+شغلها حقيقية، انت كنت وانت سرتي، هد أخد معاك الوجد
+
+379
+00:29:31,260 --> 00:29:34,340
+ولا لا؟! بدي كل الوجد اللي أخده معاك، بغض النظر في
+
+380
+00:29:34,340 --> 00:29:37,340
+الطريق، إيه سويت؟! يعني انت لما روحت خلونس، لما
+
+381
+00:29:37,340 --> 00:29:41,240
+تروحي عدل، نفس الزمن بتاخديه وانت بتميل ع المغازة
+
+382
+00:29:41,240 --> 00:29:44,960
+وع الدير؟! إذا ان انت لما تقولي رحليتي استقلقت،
+
+383
+00:29:44,960 --> 00:29:48,200
+بدي تاخدي في عين الاعتبار كل شيء ولا لا؟!إذا بديك
+
+384
+00:29:48,200 --> 00:29:53,660
+الزمن الحقيقي يا بنتي هذا زمن حقيقي كله تمانية
+
+385
+00:29:53,660 --> 00:30:00,800
+بنات غيره مثال جالي
+
+386
+00:30:00,800 --> 00:30:05,400
+سيارة قاعدة بتتحرك ما زالتحركت موضوع حبدالله زي ما
+
+387
+00:30:05,400 --> 00:30:10,580
+هو لأ بتغير جالي the figure shown ال figure اللي
+
+388
+00:30:10,580 --> 00:30:14,030
+انت شايفه figure يعني ايش ما اسمهااللي انت شايفه
+
+389
+00:30:14,030 --> 00:30:19,670
+شون يعني اللي شايفه represent يمثل represent the
+
+390
+00:30:19,670 --> 00:30:25,630
+variation تغير of position with time for a car
+
+391
+00:30:25,630 --> 00:30:31,510
+بيفرجيك كيف اتغير موضع سيارة بالنسبة للزمن كيف ده
+
+392
+00:30:31,510 --> 00:30:35,150
+اللي كانت السيارة عند النقطة A صارت عند النقطة B
+
+393
+00:30:35,150 --> 00:30:39,610
+صارت عند النقطة C صارت عند النقطة D ثم E ثم وقفت
+
+394
+00:30:39,610 --> 00:30:45,960
+عند F امي محطات ادي خلنا نقولتمى قاللي عند النقطة
+
+395
+00:30:45,960 --> 00:30:51,920
+E كانت تبعد عن ال origin 30 متر هيك ده .. هذي
+
+396
+00:30:51,920 --> 00:30:57,720
+معطيات عند النقطة B صارت 52 متر شوفوا عند النقطة C
+
+397
+00:30:57,720 --> 00:31:02,180
+رجعت ولا مارجعتش جربت في الأول كانت تبعد و بعدين
+
+398
+00:31:02,180 --> 00:31:07,810
+جربت عشان نفهمها بس لأنه كانت 52 جديد صارت38 جربت
+
+399
+00:31:07,810 --> 00:31:12,330
+هنا وجعت لنقطة الأصل جربت أكتر هنا بالسالب جلب
+
+400
+00:31:12,330 --> 00:31:15,830
+اتجاه المعاكس وكأنه انطلقت من هذه النقطة يا بنات
+
+401
+00:31:15,830 --> 00:31:21,510
+مشيت و بعدين رجعت بعدين رجعت هنا ما زادت هنا صارت
+
+402
+00:31:21,510 --> 00:31:25,730
+بالسالب ولا مش بالسالب؟ مش سالب وظلت ماشية هيك لما
+
+403
+00:31:25,730 --> 00:31:30,730
+وصلت النقطة F كانت ناقص 53 متر موجة بوسالي بيفهمنا
+
+404
+00:31:30,730 --> 00:31:37,800
+إيش معناتها معناته يسار يمين حلوبقول لي ايش بدك
+
+405
+00:31:37,800 --> 00:31:42,420
+امنك هاد دراسة مافهمتها هاد مواضع ومحطات وكل واح
+
+406
+00:31:42,420 --> 00:31:47,600
+محطة جديش غابت وجديش الزمن اللي استغرقه جالي لما
+
+407
+00:31:47,600 --> 00:31:52,380
+وصل النقطة ايه اخد عشر ثواني النقطة B صار عشرين
+
+408
+00:31:52,380 --> 00:32:00,380
+ثانية النقطة C دي تلاتين ايه خمسين اربعين او خمسين
+
+409
+00:32:00,380 --> 00:32:04,840
+جديش اخدته الرحلة خمسين هاد حقيقة ساعة بتقدر توقف
+
+410
+00:32:04,840 --> 00:32:08,850
+الساعةماحد مقدر يوقف الزمن هذه الزمن بدي أعده بغض
+
+411
+00:32:08,850 --> 00:32:13,330
+النظر أنت روحت عدل ولا جزرت فهمت عليها؟ حلو إيش
+
+412
+00:32:13,330 --> 00:32:19,250
+بدك؟ قاللي بدي find يعني أوجد the displacement
+
+413
+00:32:22,020 --> 00:32:25,360
+فاصلة The average velocity قال لما ضعفتي الأول
+
+414
+00:32:25,360 --> 00:32:30,460
+عرفتي التانية ولا لأ ما هي التانية ال displacement
+
+415
+00:32:30,460 --> 00:32:34,160
+ع زمان جديش الزمان الكل تابع الرحلة خمسين ثانية
+
+416
+00:32:34,160 --> 00:32:37,780
+براو تمام و إيش بدك كمان قال لي I'm the average
+
+417
+00:32:37,780 --> 00:32:42,460
+speed لما بيجي ال speed بدي إزاحة ولا بيجي مسافة
+
+418
+00:32:42,460 --> 00:32:47,000
+براو علينا نيجي واحدة واحدة إيش بدك قال لي
+
+419
+00:32:47,000 --> 00:32:55,520
+displacement إذا إيهبدي Delta X ولا لأ Delta X ايش
+
+420
+00:32:55,520 --> 00:33:02,400
+تعني Delta X Bravo عليكم X final ناقص X initial
+
+421
+00:33:02,400 --> 00:33:06,700
+اليك دعوة كيف وصلراح ع المغازي راح ع الانصارات
+
+422
+00:33:06,700 --> 00:33:13,120
+ماكنش دعوة قلني حلو بتساوي هه نكتب القانون X final
+
+423
+00:33:13,120 --> 00:33:17,900
+ناقص X initial ولا لا نيجي لل final هاي هاي ال
+
+424
+00:33:17,900 --> 00:33:21,720
+final كداش ناقص تلاتة و خمسين نقولها مانامدكي
+
+425
+00:33:21,720 --> 00:33:22,520
+إياها مانامدكي إياها مانامدكي إياها مانامدكي إياها
+
+426
+00:33:22,520 --> 00:33:23,300
+مانامدكي إياها مانامدكي إياها مانامدكي إياها
+
+427
+00:33:23,300 --> 00:33:24,340
+مانامدكي إياها مانامدكي إياها مانامدكي إياها
+
+428
+00:33:24,340 --> 00:33:26,320
+مانامدكي إياها مانامدكي إياها مانامدكي إياها
+
+429
+00:33:26,320 --> 00:33:32,580
+مانامدكي إياها مانامدكي إياها مانامدكي إالصحيحة
+
+430
+00:33:32,580 --> 00:33:40,280
+بقول ناقص 83 متر اختبأ انا ايش ايه؟ هاي اول مطلوب
+
+431
+00:33:40,280 --> 00:33:43,280
+شوف المطلوب التاني مثله قال لي بدي ال average
+
+432
+00:33:43,280 --> 00:33:48,760
+velocity جسم على 50 ولا لأ؟ اذا بقوله V average
+
+433
+00:33:48,760 --> 00:33:53,200
+اللي بتسوي delta X على delta T delta X هيها ولا
+
+434
+00:33:53,200 --> 00:33:59,360
+لأ؟ ها دي بتسوي .. بحطها ناقص 83 على 50 one point
+
+435
+00:34:00,690 --> 00:34:05,370
+سبعة متر بيرث كان بالسالب لو عملتها بالكالكوليتر
+
+436
+00:34:05,370 --> 00:34:10,250
+هتطلع one point six ستة صح؟ ليش خليتها سبعة؟ شفتوا
+
+437
+00:34:10,250 --> 00:34:13,790
+كيف؟ لو كانت one point six أربعة بخليها سبعة؟ براو
+
+438
+00:34:13,790 --> 00:34:16,290
+عليكم، بس عشان نتذكر اللي عملناه لإن واحد
+
+439
+00:34:16,290 --> 00:34:18,450
+بالكالكوليتر جولب يلاحقوا عليه، أنا هذي طلعت عندي
+
+440
+00:34:18,450 --> 00:34:21,790
+الكالكوليتر تبعتي ستة ستة، سبعة دي ترمي
+
+441
+00:34:21,790 --> 00:34:24,450
+الكالكوليتر تقولي بتاعي أعمل غلط، لأ الكالكوليتر
+
+442
+00:34:24,450 --> 00:34:28,150
+بتاعي أعمل صح، ستة ستة بس مكتوبها سبعة، اتفاجنا؟
+
+443
+00:34:28,150 --> 00:34:35,780
+تم؟جال ليه الآن؟ بدي الـAvalanche Speed، بقوله يا
+
+444
+00:34:35,780 --> 00:34:39,380
+ورا دي، بدي المسافة كلها، بدي نلحقه، راح على
+
+445
+00:34:39,380 --> 00:34:41,760
+المغازي، راح على انصرات، راح على الدقر، راح على
+
+446
+00:34:41,760 --> 00:34:46,360
+الجرارة، كله بدينا نفلي وراه، صح؟ المحطة تنبينها
+
+447
+00:34:46,360 --> 00:34:50,310
+عيني ولا لأ؟بدي المسافة بين كل المحطات وبعدين
+
+448
+00:34:50,310 --> 00:34:53,430
+أجمعهم وإنت قاعد بتجيبني المسافات ماكانش دعوة
+
+449
+00:34:53,430 --> 00:34:56,730
+بالسالب والموجب لأن السالب والموجب معناته اتجاه
+
+450
+00:34:56,730 --> 00:35:02,530
+صح؟ حلو يلّا يا بنات شوفوني إيش بدي أسوي اطلعوني
+
+451
+00:35:02,530 --> 00:35:08,090
+وين كان هو؟ عند إيه؟ وين صار أول محطة؟ مديش
+
+452
+00:35:08,090 --> 00:35:12,550
+المسافة اللي مشيها؟لأ لأ لأ مداشي the horse من A ل
+
+453
+00:35:12,550 --> 00:35:17,150
+B كان بواب عليكي كان تلاتين سالتين و خمسين و اتنين
+
+454
+00:35:17,150 --> 00:35:20,990
+و عشرين متر مش ماشي اتنين و عشرين متر اذا هذه
+
+455
+00:35:20,990 --> 00:35:25,330
+اتنين و عشرين متر طيب من B ل C رجع و رجوع دل بالكو
+
+456
+00:35:25,330 --> 00:35:32,150
+من B ل C رجع و رجوع اربعتاش على المتر اربعتاش على
+
+457
+00:35:32,150 --> 00:35:34,890
+المتر حتى لو بالسالب من اللي جعوا فيها هي تطلع
+
+458
+00:35:34,890 --> 00:35:38,650
+سالب اربعتاش اذا طلعت اربعتاش على المتر مديش سالب
+
+459
+00:35:40,410 --> 00:35:44,750
+بدي من ابرار عليكم مسافات طيب الآن من C ل D من
+
+460
+00:35:44,750 --> 00:35:54,330
+يقول جديش براو عليكم 38 متر طيب من D ل E 37 متر
+
+461
+00:35:54,330 --> 00:36:00,010
+طيب من E ل F 16
+
+462
+00:36:00,010 --> 00:36:09,030
+16 بطل حقناهابطرح بطعم الكالكوليتر صدقوني 16
+
+463
+00:36:09,030 --> 00:36:14,710
+عملتها مع اللي جابلكم 16 هي كانت ال total distance
+
+464
+00:36:14,710 --> 00:36:19,570
+هدول كلهم زي لما نرجع للسيارة راحت على المغازي
+
+465
+00:36:19,570 --> 00:36:23,610
+جمعتها ولا لأ؟ راحت عن سراط بدي اجمعها ولا لأ؟ اذا
+
+466
+00:36:23,610 --> 00:36:28,130
+كل المحطات بدي اجمعها فانا جيبت كل المحطات اجمع
+
+467
+00:36:28,130 --> 00:36:36,020
+طلعت 127 مترالان ما هي ال average distance 127 على
+
+468
+00:36:36,020 --> 00:36:41,320
+50تمام؟ قاللي اذا الأولى زى ما انتوا شايفين حلناها
+
+469
+00:36:41,320 --> 00:36:46,640
+احنا وياكم طلعت ال displacement ناقص 83 متر جبت ال
+
+470
+00:36:46,640 --> 00:36:50,480
+average velocity بسهولة اللى طلعت ناقص 1.7 اللى
+
+471
+00:36:50,480 --> 00:36:55,460
+هيقولنا 1.66 تمام؟ لما قاللي ال average speed
+
+472
+00:36:55,460 --> 00:37:00,480
+قاللي we want to find the total distance بدك الآن
+
+473
+00:37:00,480 --> 00:37:05,120
+مش نقطة البداية و النهاية بدك كل المحطات واحدة
+
+474
+00:37:05,120 --> 00:37:09,760
+واحدةتمه .. هو هنا طبعا سهل على حاله قاللي انت من
+
+475
+00:37:09,760 --> 00:37:14,700
+الرسمة واضح انه هانمشي من A لB و بعدين من B لF
+
+476
+00:37:14,700 --> 00:37:19,340
+رجوع طبعا فقاللي خد واحدة هيك و تقعد مجين زي هيك
+
+477
+00:37:19,340 --> 00:37:23,800
+او بتعمل زي ما عملت انا كل ما حطت قاللي قداش طلعت
+
+478
+00:37:23,800 --> 00:37:28,460
+قاللي والله طلعت 127 انتبهولي في ريمارك حطيتها انا
+
+479
+00:37:28,460 --> 00:37:32,300
+ملاحظة قولتلك ال average speed لا تساوي ال
+
+480
+00:37:32,300 --> 00:37:36,150
+magnitude لل average velocityوإلا و ساعتها دي تجيب
+
+481
+00:37:36,150 --> 00:37:41,690
+ديش 1.7 طلعت وها دي 2.5 الرقمين زي بعض لأ هذا
+
+482
+00:37:41,690 --> 00:37:46,550
+بيأكد ان ال average speed لا تقرب لل average
+
+483
+00:37:46,550 --> 00:37:50,330
+velocity مابيش قرابة ممكن يتساوى ممكن واحدة تكون
+
+484
+00:37:50,330 --> 00:37:55,970
+أكبر غيرت زمانالزمن دلّه خمسين لأن هذه رحلة هذه
+
+485
+00:37:55,970 --> 00:38:00,390
+زمن رحلة بس انت لما تقولني بدك speed بقولك بدي
+
+486
+00:38:00,390 --> 00:38:06,470
+مسافة تمام؟ لأنه اصلا ليش اختلفوا لأنه هداك لو
+
+487
+00:38:06,470 --> 00:38:11,150
+واحد ادي اللي كان اخد زمن اقصر لكن عشان جذر صار في
+
+488
+00:38:11,150 --> 00:38:16,920
+عنده الزمن الأعلى اه يا بناتصرت .. احكي .. السالب
+
+489
+00:38:16,920 --> 00:38:20,800
+دايما بحمله .. لما جيه مسافات .. اه مسافات .. برا
+
+490
+00:38:20,800 --> 00:38:23,500
+.. قياسية .. اه لما بيجيه يجيه مسافات ماكانش
+
+491
+00:38:23,500 --> 00:38:25,820
+بالسالب .. مش شيل الدعوة .. هو في الآخر راح على
+
+492
+00:38:25,820 --> 00:38:29,440
+المغازي و رجع .. مرة موجعب و مرة سالب .. نفترض راح
+
+493
+00:38:29,440 --> 00:38:32,220
+على المغازي اتنين كيلو و رجع اتنين كيلو .. بتكون
+
+494
+00:38:32,220 --> 00:38:35,160
+اربعة ولا لأ .. لكن هو بياخد في السالب علم اعتباره
+
+495
+00:38:35,160 --> 00:38:37,940
+بتطلع صفر .. لأنه اتنين كيلو و موجعبه اتنين كيلو
+
+496
+00:38:37,940 --> 00:38:39,900
+.. سالب .. احكي يا بنتي ..
+
+497
+00:38:42,990 --> 00:38:52,870
+أه كيف؟ جب هادي نقص هادي والله هي هيك مباشرة تمام؟
+
+498
+00:38:52,870 --> 00:39:04,970
+غيرها لأ حتى الأن بحكي عربي أكيد بدي أصدقكم ها طيب
+
+499
+00:39:04,970 --> 00:39:09,990
+اتفقنا السيارة هي ماشية من غزة لخانونسسرعتها
+
+500
+00:39:09,990 --> 00:39:14,370
+مختلفة ولا لأ؟ مرة بطيئة و مرة سريعة ابتقدروا لو
+
+501
+00:39:14,370 --> 00:39:19,570
+سألتكم لمّا كانت علىمفترض جنسيرات جديش كانت
+
+502
+00:39:19,570 --> 00:39:23,570
+صلوعتها ممكن تقوله ولا لأ؟ في آيك اللحظة هناك
+
+503
+00:39:23,570 --> 00:39:27,070
+بقولك عند لحظة معينة بقدر أقولك بس ساعتها بتحكيش
+
+504
+00:39:27,070 --> 00:39:33,830
+عن متوسط تحكي عن صلعة لحظية لحظية صح ولا لأ تمام
+
+505
+00:39:33,830 --> 00:39:37,390
+هل جيتوا احنا أخدنا لغة انجليزية من الرودا لما
+
+506
+00:39:37,390 --> 00:39:41,100
+جينا الجامعه احنا بناخد لغة انجليزية صح؟وامي فرحت
+
+507
+00:39:41,100 --> 00:39:45,680
+علينا في الراوضة باب إيش معناته وشباك ويندو إيش
+
+508
+00:39:45,680 --> 00:39:48,980
+معناته صح ولا .. هجيتش معنى لحظة بالإنجليزي
+
+509
+00:39:48,980 --> 00:39:55,840
+Instant سمعتوا فيها Instant والله خدتوها بس خلاص
+
+510
+00:39:55,840 --> 00:40:04,520
+يا خسارة الراوضة ممرتش عليكم مرت Instant لحظة
+
+511
+00:40:04,520 --> 00:40:10,770
+Instantaneous لحظةمحبوب ان دي بأصله Instantaneous
+
+512
+00:40:10,770 --> 00:40:13,950
+ممكن تكون وما مرتش عليكم بس instant لا تكون مرت
+
+513
+00:40:13,950 --> 00:40:19,370
+بلاش لحظة باللغة العربية مرت عليكم ايش معنى لحظة؟
+
+514
+00:40:19,370 --> 00:40:24,230
+احنا هتقولكم ايش تعريف لحظة؟ فترة زمانية طويلة ولا
+
+515
+00:40:24,230 --> 00:40:27,910
+قصيرة جدا؟ قصيرة جدا صح ايه معناته؟ مش هيك مخزنة
+
+516
+00:40:27,910 --> 00:40:33,410
+عندي كل كلمة انها معنى دي و مخي اما قولي لحظة
+
+517
+00:40:33,410 --> 00:40:41,950
+بقوله مائة سنة لأ معروفة طيبهذه ماذا؟ فترة زمانية
+
+518
+00:40:41,950 --> 00:40:47,250
+ممكن تكون مائة سنة و ممكن تكون لحظة ولا لا بديها
+
+519
+00:40:47,250 --> 00:40:52,430
+تكون أكيد لحظة لو أعملتلك كيك ايش هذا؟ تقول إلى
+
+520
+00:40:52,430 --> 00:40:56,610
+السفر لذا غصب عنها لحظة ولا مش لحظة؟ حلو انت ايش
+
+521
+00:40:56,610 --> 00:41:01,500
+عرفتلي ال average velocity تتطلع؟ لو هذهصارت تقول
+
+522
+00:41:01,500 --> 00:41:05,640
+إلى السفر صارت لحظة لما صارت لحظة و صارت .. بطلت
+
+523
+00:41:05,640 --> 00:41:09,340
+سرعة متوسطة صارت سرعة لحظية طب كيف بدي أسويها؟
+
+524
+00:41:09,340 --> 00:41:14,260
+بسيطة بس أسعلها limit
+
+525
+00:41:14,260 --> 00:41:21,580
+نُهَة تعرفون نُهَة؟ من نهاية نُهَة لما delta T
+
+526
+00:41:21,580 --> 00:41:26,960
+تقول إلى السفر هذه السرعة المتوسطة لما نحطت هذه
+
+527
+00:41:26,960 --> 00:41:34,230
+جمت هذه بطلت متوسطةصارت صراعي ايش؟ لحظية لحظية
+
+528
+00:41:34,230 --> 00:41:40,010
+ليش؟ لأن الفترة الزمنية صارت لحظة خلاص؟ بطل مطلقا؟
+
+529
+00:41:40,010 --> 00:41:45,090
+اه .. لحظة يعني بدل ما كانت الفترة الزمنية من غزة
+
+530
+00:41:45,090 --> 00:41:49,550
+لخانونس ساعة بتكون عند ما كانت في انصرات بقوله بعد
+
+531
+00:41:49,550 --> 00:41:54,050
+عشرين دقيقة عشرين دقيقة زي عشرين جزء من الدقيقة
+
+532
+00:41:54,050 --> 00:41:57,930
+خلاص عشرين بس انت وصلت يعني عشان بقيس عند لحظة
+
+533
+00:42:00,090 --> 00:42:07,790
+بالظبط صارت لحظية برا انت اللي عايش عامل limit نهى
+
+534
+00:42:07,790 --> 00:42:12,710
+هزيت مخي هي جالويت عن الكالكولاس هذا و عرفوا تعريف
+
+535
+00:42:12,710 --> 00:42:23,410
+هذا مش تقع أذكركوا دال ساط على دال سي بتساوي نهى
+
+536
+00:42:23,410 --> 00:42:28,810
+لما دال سي تقول إلى السفر دالتا ساط على دال سي
+
+537
+00:42:29,880 --> 00:42:37,560
+قلولي ماخدنهوش انا استخدمته ناس استخدمته اشتققتي
+
+538
+00:42:37,560 --> 00:42:39,440
+مش اشتققتي
+
+539
+00:42:42,540 --> 00:42:46,360
+طيب و هو عشان هو احنا هنا بنستخدمه نعرف إيش معناه
+
+540
+00:42:46,360 --> 00:42:50,040
+التعريف قاعد برجعلك انه عرفته و أخدته قللي إيش
+
+541
+00:42:50,040 --> 00:42:55,220
+معناته قللي هذا إله مع .. تعريف آخر هذا become
+
+542
+00:42:55,220 --> 00:42:58,820
+instant .. إيش معناه limit عشان تفهموا إيش استخدام
+
+543
+00:42:58,820 --> 00:43:02,680
+ال limit ال limit يعني صار يقول إلى السفر و فيه
+
+544
+00:43:02,680 --> 00:43:06,150
+هناك فرق ما بين يساوي سفر و يقول إلى السفرصح ولا
+
+545
+00:43:06,150 --> 00:43:09,950
+لا؟ جاللي هذه لحظة جاللي هذه علم ال calculus قالوا
+
+546
+00:43:09,950 --> 00:43:14,130
+هذه مشتقة X بالنسبالي الزمن مشتقة X بالنسبالي
+
+547
+00:43:14,130 --> 00:43:22,670
+الزمن فما أخدناه مازم نطبقه صح؟ طيب إيش بجرب
+
+548
+00:43:22,670 --> 00:43:28,510
+الاشتقاق لميل؟ الميل هو هيك بتعرفيه كويك ما شاء
+
+549
+00:43:28,510 --> 00:43:33,850
+الله عليكيلأن المهل ضل الزاوية ولا لا؟ وضل الزاوية
+
+550
+00:43:33,850 --> 00:43:37,150
+مقابل ع مجاور ولا لا؟ قال لي و الله هاي مقابل و
+
+551
+00:43:37,150 --> 00:43:40,670
+هاي مجاور، هاي مقابل و هاي مجاور، طو الرسمة مش كان
+
+552
+00:43:40,670 --> 00:43:46,710
+في عندي X و T، المقابل X، و المجاور T، إذن هذا مهل
+
+553
+00:43:46,710 --> 00:43:51,430
+المماز، وهين اشتقاق، إذن إيش بقوللي؟ بقوللي في
+
+554
+00:43:51,430 --> 00:43:54,710
+الرسمة الحلوة اللي طو رسمتها أنا وياك، وحلينا
+
+555
+00:43:54,710 --> 00:44:00,080
+عليها سؤال، ذاكرينها؟ من A لFجالي لو بدك تجيب ال
+
+556
+00:44:00,080 --> 00:44:03,640
+average velocity من دون ما تحل حاجة على الرصد قال
+
+557
+00:44:03,640 --> 00:44:07,600
+لي سهل لأ شوف ال average velocity ها مش انت قلتلي
+
+558
+00:44:07,600 --> 00:44:10,580
+ال average velocity بهمن نقطتي البداية والنهاية
+
+559
+00:44:10,580 --> 00:44:14,620
+جالي ارسله خط من البداية للنهاية هذا الخط جيب ميلو
+
+560
+00:44:14,620 --> 00:44:19,680
+هي ال average velocity ميلو مسموه طول لأ مش delta
+
+561
+00:44:19,680 --> 00:44:25,140
+x حد delta t و delta x هيالمقابل والـ delta T هي
+
+562
+00:44:25,140 --> 00:44:29,620
+المجاور إذا بيقولي in the position-time graph هذا
+
+563
+00:44:29,620 --> 00:44:34,040
+ال graph رسمة يعني بيسموها position-time graph
+
+564
+00:44:34,040 --> 00:44:38,500
+يعني رسمة ما بين ال position والزمن تمام؟ بيقولي
+
+565
+00:44:38,500 --> 00:44:41,100
+the average velocity is the slope، ال slope يعني
+
+566
+00:44:41,100 --> 00:44:47,110
+الميلالميل The slope of the line لو خط between the
+
+567
+00:44:47,110 --> 00:44:50,750
+initial and the final poles طيب هذه ال average طب
+
+568
+00:44:50,750 --> 00:44:54,250
+و ليه instantaneous هو في الطريق في لحظة واحدة ولا
+
+569
+00:44:54,250 --> 00:45:00,090
+عدة لحظات إذا عن كل لحظة جيبلي مماس بدي عند اللحظة
+
+570
+00:45:00,090 --> 00:45:04,110
+خمسة بقولك خمسة هي النقطة خمسة صح عند النقطة هذه
+
+571
+00:45:04,110 --> 00:45:08,740
+جيبولي مماس تعرفش جيبولي مماستمام؟ المماس خط ولا
+
+572
+00:45:08,740 --> 00:45:11,920
+مش خط؟ خط دي بني ميلو، هي السرعة اللحظية عند هذه
+
+573
+00:45:11,920 --> 00:45:15,480
+النقطة طب شوفولي النقطة B يا بنات، دي بني مماسها
+
+574
+00:45:15,480 --> 00:45:21,720
+مماسها مش سفر، ميلو السفر مماسها وفقي، عشان كده
+
+575
+00:45:21,720 --> 00:45:25,060
+ميلو سفر، معناته بقدر اقول السرعة اللحظية عند
+
+576
+00:45:25,060 --> 00:45:28,400
+النقطة B بتساوي سفر؟ يعني عند النقطة B كانت واقفة
+
+577
+00:45:28,400 --> 00:45:32,180
+يا سيل ولا لأ؟ كانت واقفة، اه لإن عند النقطة B بدي
+
+578
+00:45:32,180 --> 00:45:38,530
+يرجعوالواحد لما يرجع بيجف لحظيا هي صحيحة تمام؟ اذا
+
+579
+00:45:38,530 --> 00:45:44,690
+بيقول لي while the instantaneous velocity at some
+
+580
+00:45:44,690 --> 00:45:48,610
+instant طبعا at some instant لعند لحظات معينة is
+
+581
+00:45:48,610 --> 00:45:55,100
+the slope ميلof the tangent المماس ميل المماس at
+
+582
+00:45:55,100 --> 00:45:58,040
+that instant هذه النقطة هذه يا بنات شايفين هذه
+
+583
+00:45:58,040 --> 00:46:00,980
+النقطة هذه أول ال average خلصنا منها الخط الأخضر
+
+584
+00:46:00,980 --> 00:46:05,120
+هو ال average ميله طيب خلصت .. هجيت عند نقطة هذه
+
+585
+00:46:05,120 --> 00:46:10,260
+شايفينها عند لحظة ما نفترض خمسة بدي أجيب السرعة
+
+586
+00:46:10,260 --> 00:46:16,230
+اللحظية جيبولي مماس في حد برسم غير المماس هذا؟بدي
+
+587
+00:46:16,230 --> 00:46:20,470
+ميلو يوردي مثلا ميلو ممكن نعمل هيك ونقول المقابل
+
+588
+00:46:20,470 --> 00:46:24,270
+عن مجاور هذه الصورة اللحظية طب عند النقطة مين
+
+589
+00:46:24,270 --> 00:46:29,870
+اشتفكتوا سفر عند النقطة أي ان كانت دي طبعا كيف
+
+590
+00:46:29,870 --> 00:46:35,980
+يتضغط كيف ميلو تتوقع مجابه ولا سالبسالم لأنه نازل
+
+591
+00:46:35,980 --> 00:46:40,620
+لأنه احنا دايما نعرف ان هذا خط و هذا خط بقول هذا
+
+592
+00:46:40,620 --> 00:46:45,360
+ميله موجب هذا ميله هذا متزايد هذا متناقص صح ولا لأ
+
+593
+00:46:45,360 --> 00:46:50,160
+هايكم شاطرين في الكلب كلاص ما شاء الله عليكم غدا
+
+594
+00:46:50,160 --> 00:46:52,700
+نظرا احنا بنقول متزايد و متناقص صح ولا لأ كلامك
+
+595
+00:46:52,700 --> 00:46:59,280
+صحيح كلامك صحيح تمى عنده نقطة أف تطلعوه ما هو
+
+596
+00:46:59,280 --> 00:47:03,570
+كويجيف عنده نقطة أفمش هو بيجيب؟ خلاص يعطيه العافية
+
+597
+00:47:03,570 --> 00:47:09,410
+اذا بيقوللي هدول ال slope
+
+598
+00:47:09,410 --> 00:47:12,830
+للخطوط اللي بتكون مماس لنقطة م ما ايه بدي ان
+
+599
+00:47:12,830 --> 00:47:15,370
+استنتين was velocity at that point لحد اللي انا
+
+600
+00:47:15,370 --> 00:47:20,850
+محكي عربي؟ بكتير مش شهر حلو براو هلجيت السرعة
+
+601
+00:47:20,850 --> 00:47:24,470
+انتشرت سرعة متوسطة و سرعة لحظية صح ولا لا؟ ايه اسم
+
+602
+00:47:24,470 --> 00:47:28,100
+الجنتين؟ رغمرغد طلع يا رغد احنا قلنا السرعة
+
+603
+00:47:28,100 --> 00:47:31,760
+المتوسطة ال average velocity بتعتمد على نقطتي ايش؟
+
+604
+00:47:31,760 --> 00:47:36,020
+البداية و النهاية تجاهليها ال gate السرعة هي عبارة
+
+605
+00:47:36,020 --> 00:47:42,040
+عن مسافة ع زمن صح؟ المسافة عبارة عن خط و الزمن خط
+
+606
+00:47:42,040 --> 00:47:46,920
+بدي اجربه و اديب علاقة بينه و بيني المماس اذا انت
+
+607
+00:47:46,920 --> 00:47:50,360
+بتحكي عن average velocity اللي بهمك فقط نقطتي
+
+608
+00:47:50,360 --> 00:47:53,200
+البداية و النهاية اعمللي خط بين البداية و النهاية
+
+609
+00:47:53,200 --> 00:47:56,720
+هذا الخط اللي ميل؟جيبه هو الـ Average Velocity
+
+610
+00:47:56,720 --> 00:48:01,140
+خلصها من الـ Average Velocity الـ Instantaneous
+
+611
+00:48:01,140 --> 00:48:04,720
+Velocity عند لحظة تمام .. اذا ماعرف كام لحظة في
+
+612
+00:48:04,720 --> 00:48:08,780
+عندك كتير و انت لما يقولك أوجد الصراع اللحظية بفعل
+
+613
+00:48:08,780 --> 00:48:11,640
+يقولك أوجد الصراع اللحظية و يسكت؟ بده يقوله عند أي
+
+614
+00:48:11,640 --> 00:48:15,660
+لحظة، عند لحظة تمام، يعني عند نقطة ما ولا لأ؟
+
+615
+00:48:15,660 --> 00:48:20,010
+قاللي جيبلي نقطة هادية و جيبلي إيها مماسةمماس جيب
+
+616
+00:48:20,010 --> 00:48:25,030
+مانو هاي الصورة اللحظية بس هاي اللي بنحكي بالبلد
+
+617
+00:48:25,030 --> 00:48:31,450
+غيرها احكيه القانون V تساوي DX على D نفسه هو لطبع
+
+618
+00:48:31,450 --> 00:48:36,450
+ال M ولا غيره هو نفسه ماهذا تعرف لا هذامش هاد
+
+619
+00:48:36,450 --> 00:48:40,150
+تعريفه؟ بدل ما تجيب ال limit و تغلب بحالك مستعرون
+
+620
+00:48:40,150 --> 00:48:43,930
+ال calculus هيحونا؟ جالوا اشتقوا خلاص؟ هو نفسه يا
+
+621
+00:48:43,930 --> 00:48:47,210
+بنتي هاد تعريفنا خدناه في ال calculus خدناه في ..
+
+622
+00:48:47,210 --> 00:48:50,830
+في توجيه؟ في توجيه هو نفسه بدل ما تجيب ال limit و
+
+623
+00:48:50,830 --> 00:48:54,370
+تغلب حالي اتعلمتوا كيف تجيبوا ال limit ولا لأ؟
+
+624
+00:48:54,370 --> 00:48:58,650
+اتعلمتوا كيف تجيبوا ال limit؟ ال limit .. النهار
+
+625
+00:48:58,650 --> 00:49:00,830
+انتوا بدأتوا في ال calculus في ال limit و لا
+
+626
+00:49:00,830 --> 00:49:03,030
+موصلتوش لسه هتاخدوه هتخافوش
+
+627
+00:49:05,700 --> 00:49:09,820
+بقول ان الـ instantaneous speed is the magnitude
+
+628
+00:49:09,820 --> 00:49:12,400
+of the instantaneous velocity ماذا على الجدول
+
+629
+00:49:12,400 --> 00:49:18,180
+ترميها؟ اه في ال instantaneous هو نفسها تمام خلينا
+
+630
+00:49:18,180 --> 00:49:21,740
+هال example بس طولنا معاكم بقى مش تتحملوني
+
+631
+00:49:21,740 --> 00:49:25,200
+تتحملوني عشان الشعب بتنفي غيركم فتقولكم انتوا
+
+632
+00:49:25,200 --> 00:49:28,840
+بتسألوا كتير برضه شغل ميزة يعني فاخدتوا معايا و
+
+633
+00:49:28,840 --> 00:49:34,840
+جيت أكترطبعا بيقولي a particle moves along the x
+
+634
+00:49:34,840 --> 00:49:38,740
+-axis الجسم بتحرك على المحور الصيني يعني أفقي ولا
+
+635
+00:49:38,740 --> 00:49:44,620
+مش أفقي أفقي قاللي its position موضعه varies يتغير
+
+636
+00:49:44,620 --> 00:49:50,780
+varies من veryتمام؟ with time according to أنا
+
+637
+00:49:50,780 --> 00:49:56,600
+مديك X تبعته بتتعلق بالزمن وإلها معادلة تغيير
+
+638
+00:49:56,600 --> 00:50:03,580
+معادلة X بالنسبة للزمن اديتك إياها كتالي X بتساوي
+
+639
+00:50:03,580 --> 00:50:09,220
+ناقص أربعة T زائد اتنين T تربيع هذه المعادلة اللي
+
+640
+00:50:09,220 --> 00:50:13,760
+اديتك إياهاتما جالي X بتجيسها بالمتر و T بتجيسها
+
+641
+00:50:13,760 --> 00:50:17,140
+بالsecond يعني احنا بنستخدم الاص I system صح ولا
+
+642
+00:50:17,140 --> 00:50:23,560
+لأ؟ ايش بده؟ جالي بدي التالي find the displacement
+
+643
+00:50:23,560 --> 00:50:28,060
+ايش قانون ال displacement؟ X final نخس X initial
+
+644
+00:50:28,060 --> 00:50:34,340
+ده X صح؟ لفترين من صفر لواحد و من واحد لتلاتة
+
+645
+00:50:34,340 --> 00:50:42,390
+واحدة واحدة ايه؟ بقوله ها الأولىدالتا X من صفر
+
+646
+00:50:42,390 --> 00:50:48,370
+لواحد بيقولوا بتسوي X لما T بتساوي واحد second
+
+647
+00:50:48,370 --> 00:50:54,190
+ناقص X لما T بتساوي صفر هل يا X final ناقص X
+
+648
+00:50:54,190 --> 00:50:58,520
+initial صح ولا لأ؟جالي طب كيف اجيب هذه؟ قلتله ها
+
+649
+00:50:58,520 --> 00:51:04,280
+بداك تعوض محلتي كده؟ بواحد بتساوي ناقص أربعة في
+
+650
+00:51:04,280 --> 00:51:08,420
+واحد ناقص أربعة زاد اتنين في واحد تربية اذا ناقص
+
+651
+00:51:08,420 --> 00:51:13,580
+اتنين ناقص ها ناقص أربعة في سفر و اتنين في سفر
+
+652
+00:51:13,580 --> 00:51:18,920
+تربية صحيك؟
+
+653
+00:51:18,920 --> 00:51:23,500
+هاي أول فترة جبتلها كده انزاح الجسيم طيب اتنين؟
+
+654
+00:51:24,070 --> 00:51:28,490
+ماذا تريد؟ تريد دالتا X من واحد second لتلاتة
+
+655
+00:51:28,490 --> 00:51:34,810
+second بتساوي X لما ت بتساوي تلاتة second مقص X
+
+656
+00:51:34,810 --> 00:51:41,310
+لما ت بتساوي واحد second فحق ولا لأ لما ت بتساوي
+
+657
+00:51:41,310 --> 00:51:46,710
+تلاتة مقص عربعة في تلاتة مقص اتنعاش زاد اتنين في
+
+658
+00:51:46,710 --> 00:51:51,890
+تلاتة تربيه تسعة تمانتعاش ستة ستة
+
+659
+00:51:53,350 --> 00:51:59,170
+ناقص لما تيبت سوا واحد ما هنا طلعتها ناقص اتنين
+
+660
+00:51:59,170 --> 00:52:07,910
+ستة ناقص ناقص صارت كده؟ تمانية متر صحيك تمام أول
+
+661
+00:52:07,910 --> 00:52:11,870
+مطلوب خلصتلك هي جالي المطلوب التاني تحصيل حاصل إيش
+
+662
+00:52:11,870 --> 00:52:15,930
+بدك؟ جالي في المطلوب التاني طلع إيش بدهنقول
+
+663
+00:52:15,930 --> 00:52:21,210
+Calculate the average Velocity Velocity During
+
+664
+00:52:21,210 --> 00:52:25,130
+these two intervals ما هي Delta X على Delta T صح؟
+
+665
+00:52:25,130 --> 00:52:29,210
+في الأولى Delta T one secondفي الفترة التانية ده
+
+666
+00:52:29,210 --> 00:52:35,830
+تتيه 2 second إذا معناته نرجع بي واحد V average
+
+667
+00:52:35,830 --> 00:52:41,250
+بتساوي ناقص 2 ع واحد ناقص 2 meter per second وفي
+
+668
+00:52:41,250 --> 00:52:48,750
+التانية V average بتساوي تمامية ع 2 ساوية 4 meter
+
+669
+00:52:48,750 --> 00:52:51,170
+per second وإن شاء الله بتكونوا متابعين معايا لحد
+
+670
+00:52:51,170 --> 00:52:52,750
+الآن تمام
+
+671
+00:52:55,640 --> 00:53:01,490
+اشتقتي في توجيهي صح؟ شوف اي طالب في الآخرCalculate
+
+672
+00:53:01,490 --> 00:53:06,970
+The Instantaneous .. إيش يعني؟ اللحظة .. Velocity
+
+673
+00:53:06,970 --> 00:53:09,750
+.. منفع يقول Instantaneous و Velocity يسكت؟ بده
+
+674
+00:53:09,750 --> 00:53:13,730
+يحدد اللحظة .. حدد ولا ماحددش؟ حدد .. هلجيت ال
+
+675
+00:53:13,730 --> 00:53:16,910
+Instantaneous Velocity إيش تعريفها؟ هي المستقلة،
+
+676
+00:53:16,910 --> 00:53:22,670
+لا بتدي Limit ولا بتجلب حالي بقوله V بدون شرطة
+
+677
+00:53:22,670 --> 00:53:29,500
+بتساوي DX على DT .. هي الـ X اللي بده أشتقهامش هاد
+
+678
+00:53:29,500 --> 00:53:36,100
+اللي اعطاني ايه؟ مين اشتق معاه؟ اشتق ايه؟ بها و
+
+679
+00:53:36,100 --> 00:53:42,100
+علينا ناقص أربعة زائد أربعة T هذه أربعة هلجيت ..
+
+680
+00:53:42,100 --> 00:53:46,600
+ماخلصتيش؟ بدوا عين T بتساوي اتنين و نص بقولوا
+
+681
+00:53:46,600 --> 00:53:49,920
+بتساوني ناقص أربعة زائد أربعة في اتنين و نص عشرة
+
+682
+00:53:52,640 --> 00:53:58,520
+صح ولا لأ؟ إذا السرعة عند 2.5 كانت 6 متر per
+
+683
+00:53:58,520 --> 00:54:03,980
+second طبعا اتطلعوا هنا المتوسط مختلف كليا تمام يا
+
+684
+00:54:03,980 --> 00:54:05,140
+بنات يعطينا العافية
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Gsr87nrM9VY.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Gsr87nrM9VY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0272ad0dd230274d0f7197f6cf174ff4142e60be
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Gsr87nrM9VY.srt
@@ -0,0 +1,1902 @@
+1
+00:00:05,280 --> 00:00:08,640
+تمام، بعد ما نسمي باسم الله الرحمن الرحيم، أنتم
+
+2
+00:00:08,640 --> 00:00:13,360
+عارفين أني أنا هكون معاكم في مساق المادة، بنسميها
+
+3
+00:00:13,360 --> 00:00:17,000
+مساق في الجامعة، الـ Calculus مساق، والفيزياء مساق، و
+
+4
+00:00:17,000 --> 00:00:22,710
+ما يقدم في الهندسة، مساق الفيزياء العامة ألف، هنكون
+
+5
+00:00:22,710 --> 00:00:27,170
+مع بعض أسبوعيًا ثلاث مرات، زي ما هو محطوط في الجدول.
+
+6
+00:00:27,170 --> 00:00:31,530
+وهذا معناه ثلاث ساعات معتمدة، دير بالكم، ساعة معتمدة
+
+7
+00:00:31,530 --> 00:00:35,230
+يعني أسبوعيًا كم ساعة؟ يعني المادة اللي ثلاث ساعات
+
+8
+00:00:35,230 --> 00:00:39,910
+معتمدة، هتشوفوها في الجدول، ثلاث مرات.  القرآن الكريم،
+
+9
+00:00:39,910 --> 00:00:44,310
+عشانها ساعة، ومقدمة في الهندسة، الهندسة مرة واحدة.
+
+10
+00:00:44,310 --> 00:00:48,370
+اللقاء يكون هكذا، هذه معناه ثلاث ساعات معتمدة، احنا
+
+11
+00:00:48,370 --> 00:00:51,910
+هنكون إن شاء الله، سبت، وإثنين، وأربعة، في نفس
+
+12
+00:00:51,910 --> 00:00:57,670
+الموعد، من الـ 12 للواحدة، في هذه القاعة بإذن الله.
+
+13
+00:00:57,670 --> 00:01:03,050
+وهنغطي فيزياء عامة ألف، معناته في فيزياء عامة، باء،
+
+14
+00:01:03,700 --> 00:01:07,780
+فيزياء عامة ألف بتحكي عن علم الميكانيكا، علم
+
+15
+00:01:07,780 --> 00:01:10,720
+الميكانيكا اللي أخذتوها في عاشر، وحادي عشر، وثاني عشر،
+
+16
+00:01:10,720 --> 00:01:16,680
+بمواضيع مختلفة، وبالتالي المواضيع اللي هنشرحها،
+
+17
+00:01:16,680 --> 00:01:21,260
+كعنوان، هتكون هي نفس العناوين اللي مرت علينا في
+
+18
+00:01:21,260 --> 00:01:28,440
+المدرسة، لكن هناخدها بمنظور مختلف، منظور أوسع، وغالبا
+
+19
+00:01:28,440 --> 00:01:33,020
+المنظور بنوسعه لأنه في الثانوية كان الـ Calculus أو
+
+20
+00:01:33,020 --> 00:01:38,020
+الرياضيات اللي عندكم قاصرة، وبالتالي في بعض
+
+21
+00:01:38,020 --> 00:01:40,900
+المواضيع ما بيقدروش يتوسعوا فيها في المدارس، لأن
+
+22
+00:01:40,900 --> 00:01:44,180
+الطالب لسه مداركه في الرياضيات بتكون بسيطة.
+
+23
+00:01:44,180 --> 00:01:48,180
+وبالتالي بتاخدوا مرات عنوان، أو قشرة من الموضوع.
+
+24
+00:01:48,180 --> 00:01:52,040
+احنا بنفرض، بنركن فكرة أن الطالب أصلًا ما شاء الله
+
+25
+00:01:52,040 --> 00:01:59,710
+عليه نضج، وبعدين بياخد الـ Calculus معانا بالجامعة،
+
+26
+00:01:59,710 --> 00:02:04,630
+وبالتالي بيكون جاهز نتوسع في المواضيع بصورة أوسع.
+
+27
+00:02:04,630 --> 00:02:10,850
+هذا هو الـ Mobile رقمي، عشان الـ WhatsApp، طبعًا احنا
+
+28
+00:02:10,850 --> 00:02:17,190
+هيكون لنا مجموعة، مجموعة WhatsApp، وهتقدروا تنضموا
+
+29
+00:02:17,190 --> 00:02:20,950
+إليها. في عندنا في الجامعة حاجة بنسميها الـ Moodle، إذا
+
+30
+00:02:20,950 --> 00:02:25,050
+سمعتوا فيه، هذا الـ Moodle، اليوم يعني خلينا نقول
+
+31
+00:02:25,050 --> 00:02:29,130
+الواجب تبعنا اليوم، بدي يكون أنه نروح نلعب شوية على
+
+32
+00:02:29,130 --> 00:02:34,710
+الكمبيوتر، تمام؟ تخشوا على موقع الجامعة، تعرفوا اللي
+
+33
+00:02:34,710 --> 00:02:38,930
+سجلتوا منه، وقدمتوا طلب الالتحاق، وصلتكم كلمة السر
+
+34
+00:02:38,930 --> 00:02:43,310
+ولا لأ، من قبل، والتسجيل، لما تفوتوا في موقع الجامعة،
+
+35
+00:02:43,310 --> 00:02:47,450
+في تحت حاجة بيسموها التعليم الإلكتروني، أو الـ Moodle،
+
+36
+00:02:47,450 --> 00:02:52,940
+تمام؟ بتفوتوا، ويقول لكم دخلوا رقمكم الجامعي، وكلمة
+
+37
+00:02:52,940 --> 00:02:58,220
+السر، هيجيكم تفعيل للمساقات اللي مسجلينها، لما
+
+38
+00:02:58,220 --> 00:03:03,980
+تدعسوا على زر فيزياء عامة ألف، تمام، بتفوتوا على صفحة
+
+39
+00:03:03,980 --> 00:03:08,660
+هذه، فيها شغلات كتيرة جوا، بتخص المادة، من ضمنها هذا
+
+40
+00:03:08,660 --> 00:03:13,320
+اللي أنتم شايفينه، بيكون موجود كملف PDF File، تمام؟
+
+41
+00:03:13,320 --> 00:03:17,340
+شغلة ثانية، فيها رابط مجموعة الـ WhatsApp، عشان تنضموا
+
+42
+00:03:17,340 --> 00:03:24,630
+إليها، تمام؟ هذا الـ WhatsApp، أنا باتواصل معاكم من
+
+43
+00:03:24,630 --> 00:03:28,770
+خلاله، يعني أي معلومة بدي إياكم تعرفوها، أو أي خبر
+
+44
+00:03:28,770 --> 00:03:32,770
+عن طريق الـ WhatsApp، طبعًا، بس ما يكونش أحاديث، لأنه
+
+45
+00:03:32,770 --> 00:03:36,450
+بيصير تواصل، لما البنات يحكوا، بيصير تواصل بين بعض، يعني
+
+46
+00:03:36,450 --> 00:03:41,810
+وبالتالي، أنا حاضر الكلام، أنا بدي التعليمات عنها.
+
+47
+00:03:41,810 --> 00:03:47,110
+وبالتالي، و مرات بلزم الطالب يحكي معايا على الخاص
+
+48
+00:03:47,110 --> 00:03:53,380
+WhatsApp، عشان كده هذا هو الـ Mobile تبعي، تمام، زي ما
+
+49
+00:03:53,380 --> 00:04:00,280
+حكينا، إيش بدنا نشرح في فيزياء عامة ألف، الجامعة في
+
+50
+00:04:00,280 --> 00:04:06,650
+الفصل الدراسي، معمولة 15 أسبوع دراسي يا بنات، عادةً
+
+51
+00:04:06,650 --> 00:04:11,190
+احنا بناخد منه 14، وبنخلي الأسبوع الأخير فيه
+
+52
+00:04:11,190 --> 00:04:15,510
+امتحانات للمعامل، والمراسيم، والشغلات اللي زي هذا.
+
+53
+00:04:15,510 --> 00:04:23,790
+فاحنا غالبًا هنشرح 14 أسبوع كامل، في هذا الـ 14 أسبوع،
+
+54
+00:04:23,790 --> 00:04:29,630
+هنغطي إما 11 أو 12 شابتر، شابتر يعني باب في
+
+55
+00:04:29,630 --> 00:04:34,760
+الكتاب، تمام، هيك؟ وبالتالي في هذه الشباتر، إيش فيها؟
+
+56
+00:04:34,760 --> 00:04:39,820
+ابتداءً من Chapter رقم واحد، هلاقي فيه حاجة اسمها
+
+57
+00:04:39,820 --> 00:04:44,320
+Measurements and Units، هذا Chapter خفيف، دم بسيط،
+
+58
+00:04:44,320 --> 00:04:48,680
+للتسخين، كلكم بتعرفوا عنه، أخذتوها بصورة أو بأخرى.
+
+59
+00:04:48,680 --> 00:04:52,520
+احنا بنعرف في الفيزياء، بنقيس، ولا لأ؟ بنقيس إيش؟
+
+60
+00:04:52,520 --> 00:04:56,620
+بنقيس مسافات، وبالتالي المسافة لها وحدة، ولا لأ؟
+
+61
+00:04:56,620 --> 00:05:03,360
+متر، ولا قدم، ولا ياردة، ولا إنش، ولا ميل، ولا كيلومتر.
+
+62
+00:05:03,360 --> 00:05:08,500
+هذه أنظمة، وبنقيس الكتل، صحيح ولا لأ؟ وبنقيس
+
+63
+00:05:08,500 --> 00:05:14,200
+الزمن، إذًا الطول، والكتلة، والزمن، هذه هي الوحدات
+
+64
+00:05:14,200 --> 00:05:19,000
+الأساسية لعلم الميكانيكا، تمام، كيف بنقيسها؟ لها
+
+65
+00:05:19,000 --> 00:05:24,260
+أنظمة، هنحكي عنها، تمام؟ وزي لما نقول بالله، في
+
+66
+00:05:24,260 --> 00:05:26,680
+الرياضيات، بيقولوا X بتساوي خمسة، ما حد بيقولهم إيش
+
+67
+00:05:26,680 --> 00:05:30,240
+اللي سويتوا، X بتساوي خمسة، خلاص، معلومة كاملة، في
+
+68
+00:05:30,240 --> 00:05:32,700
+الفيزياء، لما واحد يقول X بتساوي خمسة، بيقول له خمسة
+
+69
+00:05:32,700 --> 00:05:38,000
+إيش؟ خمسة كيلومتر، ولا خمسة جول؟ هل الـ Joule زي
+
+70
+00:05:38,000 --> 00:05:41,780
+الـ Kilometer؟ لأ، ولا الـ Newton، إذًا معناته أنت
+
+71
+00:05:41,780 --> 00:05:45,760
+عشان تديني المعلومة كاملة، بعد خمسة، حط لي حاجة
+
+72
+00:05:45,760 --> 00:05:50,480
+عشان أفهم عليك، أنت عن إيش بتتحدث، فالوحدة هي الـ
+
+73
+00:05:50,480 --> 00:05:55,760
+Top الفيزيائي، اللي بنلبسه للكمية، عشان نفهم عن إيش
+
+74
+00:05:55,760 --> 00:05:59,140
+بنحكي، هذه معناتها Measurements and Units، طب أنتم
+
+75
+00:05:59,140 --> 00:06:03,380
+شايفين، أنا بحكي عربي ولا لأ؟ والكلام؟ ما تخافوش من
+
+76
+00:06:03,380 --> 00:06:06,840
+الإنجليزي، احنا هنضل نحكي مع بعض عربي، لكن
+
+77
+00:06:06,840 --> 00:06:11,160
+امتحاناتنا بالإنجليزي، والكتاب بالإنجليزي، الـ
+
+78
+00:06:11,160 --> 00:06:14,060
+Slides بالإنجليزي، كله بالإنجليزي، لكن أنتم بكرة
+
+79
+00:06:14,060 --> 00:06:16,820
+بصيروا أشهر من تعاون بريطانيا بالإنجليزي، اتخافوش.
+
+80
+00:06:16,820 --> 00:06:20,980
+يعني هذه المشكلة بتاعت الإنجليزي، بتنتهي معاكم، بس
+
+81
+00:06:20,980 --> 00:06:25,020
+مجرد أسبوع، بعدين بصيروا خبرة بالإنجليزي، وبالشغلات
+
+82
+00:06:25,020 --> 00:06:27,880
+اللي بتلزمنا، يعني احنا بالأخير، مش عشان نكون شكسبير
+
+83
+00:06:27,880 --> 00:06:31,980
+في الإنجليزي، لأ، شغلات بسيطة، وأنتم بتعرفوا أغلبها.
+
+84
+00:06:31,980 --> 00:06:37,380
+يعني لما أقول، إيش...إيش رمز القوة في الفيزياء؟
+
+85
+00:06:37,380 --> 00:06:41,420
+F، من وين اجت؟ من Force، من بدل ما نقول قوة، من
+
+86
+00:06:41,420 --> 00:06:46,160
+الصين، نقول Force، السرعة، كنا بنرمز لها V، جاية من كلمة
+
+87
+00:06:46,160 --> 00:06:49,560
+Velocity، حتسمعوها مني Velocity، بس هذه هي، ولما
+
+88
+00:06:49,560 --> 00:06:53,260
+تسمعوها مرتين، ثلاث، مش بتحفظوها، فتخافوش من الـ
+
+89
+00:06:53,260 --> 00:06:56,440
+English، يعني، وهذا ما بنحفظوش، ولا حاجة، ميجرمنس
+
+90
+00:06:56,440 --> 00:07:04,590
+من قياس Units، وحدات، تمام؟ حلو، هذا العنوان، Chapter واحد.
+
+91
+00:07:04,590 --> 00:07:08,010
+احنا بنعوِّد، هناخده يوم الإثنين، ويوم الأربعاء، و
+
+92
+00:07:08,010 --> 00:07:11,270
+نتخلص منه، هذا مقدم، وزي ما أقول، بكون كـ تسخين،
+
+93
+00:07:11,270 --> 00:07:15,890
+بنتعرفوش، بس هيك عشان نتعرف على بعض، ونشجع بعض، و
+
+94
+00:07:15,890 --> 00:07:19,970
+نشوف إن المادة سهلة، وشغلات بسيطة، كده من السنة
+
+95
+00:07:19,970 --> 00:07:25,900
+اللي جاي، بنخش بالجد، Linear Motion، Linear من Line،
+
+96
+00:07:25,900 --> 00:07:31,640
+إيش يعني Line؟ خط، Motion حركة، فالحركة الخطية، يعني
+
+97
+00:07:31,640 --> 00:07:36,120
+إيش؟ حركة خطية، حركة في اتجاه واحد، اتجاه واحد، يعني
+
+98
+00:07:36,120 --> 00:07:40,960
+Line، طبعًا، لما نيجي نذكر بعض يا بنات، ذاكرين هذا
+
+99
+00:07:40,960 --> 00:07:47,940
+القانون، ذاكرينه.
+
+100
+00:07:47,940 --> 00:07:54,930
+هنا هذا قانون، بيحكم الحركة في خط مستقيم، بس بشرط
+
+101
+00:07:54,930 --> 00:07:58,130
+أن تكون التسارع ثابت، الشيء هو التسارع، هي
+
+102
+00:07:58,130 --> 00:08:03,110
+Acceleration، Acceleration، عشان كده يا ماخد الـ a، والـ
+
+103
+00:08:03,110 --> 00:08:07,730
+t، الـ Time، والـ v، Velocity، Final، و Initial، نهائي،
+
+104
+00:08:07,730 --> 00:08:11,530
+وابتدائي، فبدأنا ناخده بالتفصيل، ونحل عليه بعض
+
+105
+00:08:11,530 --> 00:08:15,870
+الأسئلة، زي السقوط الحر، ذاكرينه، السقوط الحر، حركة
+
+106
+00:08:15,870 --> 00:08:21,350
+باتجاه واحد، بس عمودي، السيارة بتمشي أفقي، صح ولا لأ؟
+
+107
+00:08:21,350 --> 00:08:28,310
+إذًا هذا خط، وهذا خط، صارت كده، بقول لك لما تخش تتوسع
+
+108
+00:08:28,310 --> 00:08:33,990
+عن حركة الخطية، وبتحكي عن حركة في أكثر من خط، بلزمك
+
+109
+00:08:33,990 --> 00:08:41,680
+شغلة، بلزمك إنه في كميات تعتبر مش كميات، زي الزمن، زي
+
+110
+00:08:41,680 --> 00:08:45,720
+السرعة، وزي القوة، متجهة، وبالتالي لما تيجي تتعامل
+
+111
+00:08:45,720 --> 00:08:50,240
+معاها، بدك تنتبه، خمسة زائد خمسة، بيساوي عشرة، صحيح
+
+112
+00:08:50,240 --> 00:08:53,600
+ولا لأ؟ يعني أربعة زائد ثلاثة، ممكن تصير خمسة، بطلت
+
+113
+00:08:53,600 --> 00:08:58,190
+سبعة، وبالتالي هذه الكميات، طب كل الكميات الفيزيائية
+
+114
+00:08:58,190 --> 00:09:02,690
+هيك بقول له، لأ، في كميات عادية، زي الزمن، زي الطاقة، هذه
+
+115
+00:09:02,690 --> 00:09:07,230
+كميات قياسية، لكن في كميات ما بتجمعهاش، بدك تنتبه، طب
+
+116
+00:09:07,230 --> 00:09:10,490
+كيف بدنا نعمل؟ بدنا نتعلمها، إيش هي الكميات اللي
+
+117
+00:09:10,490 --> 00:09:15,860
+بدها انتباه؟ بنسميها كميات متجهة، وتانية كميات قياسية.
+
+118
+00:09:15,860 --> 00:09:20,380
+Vectors يعني كميات متجهة، Scalars يعني كميات قياسية.
+
+119
+00:09:20,380 --> 00:09:24,540
+هنتعلم كيف نجمعها، كيف نطرحها، كيف نضربها، كل هذه
+
+120
+00:09:24,540 --> 00:09:29,540
+الشغلات هنتعلمها في Chapter كامل، Chapter ثلاثة، بعد
+
+121
+00:09:29,540 --> 00:09:33,200
+كده، بعد ما نصير خبرة بها، كده أمور، بيقول لي هنجت من
+
+122
+00:09:33,200 --> 00:09:37,770
+نفوت على الحركة المستوية، أو بالـ Two Dimensions، Two
+
+123
+00:09:37,770 --> 00:09:41,990
+Dimensions يعني بعدين، سينوسايد، تمام؟ بعدين Two
+
+124
+00:09:41,990 --> 00:09:45,870
+Dimension، هذه اختصار هذه Two، وهذه Dimension، يعني
+
+125
+00:09:45,870 --> 00:09:51,470
+بعدين، بعدين، سينوسايد، Motion، هي Motion مرت هنا، و
+
+126
+00:09:51,470 --> 00:09:54,750
+Motion مرت هنا، ما نقولش معنى Motion خلاص،
+
+127
+00:09:54,750 --> 00:10:00,510
+ماعرفش معنى Motion بالإنجليزي، مش معضلة، تمام يا
+
+128
+00:10:00,510 --> 00:10:03,920
+بنات؟ Two Dimensional Motion، الـ Two Dimensional
+
+129
+00:10:03,920 --> 00:10:09,880
+Motion، فيه حركتين مشهورتين، حركة المقذوفات، سمعتوا فيها؟
+
+130
+00:10:09,880 --> 00:10:13,280
+هذه الـ Two Dimensional Motion، مش فيه سينوسايد، و
+
+131
+00:10:13,280 --> 00:10:18,360
+الحركة الدائرية، سمعتوا فيها برضه؟ حركة مستوية، هناخدها
+
+132
+00:10:18,360 --> 00:10:23,040
+تفصيلًا، إذًا الـ Projectile Motion، حركة المقذوفات،
+
+133
+00:10:23,040 --> 00:10:28,800
+هناخدها بالتفصيل، لأنها أشهر أنواع الحركة في بعدين، هي
+
+134
+00:10:28,800 --> 00:10:31,880
+والحركة الدائرية، بس الدائرية أنواعها كتيرة.
+
+135
+00:10:31,880 --> 00:10:35,940
+Relative Motion، شوفوا كلمة Motion، قادرة بتتكرر،
+
+136
+00:10:35,940 --> 00:10:40,480
+طبعًا، معظم ميكانيكا حركة، Relative Motion، الحركة
+
+137
+00:10:40,480 --> 00:10:44,880
+النسبية، وأنتم جايين من البيت على الجامعة، و
+
+138
+00:10:44,880 --> 00:10:48,160
+بتطلعوا من شباك السيارة، وسرحانين، بتلاقوا الشجرة
+
+139
+00:10:48,160 --> 00:10:52,320
+قاعدة بتجري، صح ولا لأ؟ بتجري وراكم، بتحسها
+
+140
+00:10:52,320 --> 00:10:56,280
+المعاكس، مع أن الشجرة واقفة، لكنها واقفة بالنسبة لواحد
+
+141
+00:10:56,280 --> 00:10:59,120
+واقف على الأرض، لكن بالنسبة لواحد بيتحرك في
+
+142
+00:10:59,120 --> 00:11:02,760
+السيارة، صارت تتحرك، إذًا هذه ما بنسميها سرعة نسبية،
+
+143
+00:11:02,760 --> 00:11:08,000
+إذًا الراصد، إذا اتغير، بتتغير كمية الفيزيائية، السرعة
+
+144
+00:11:08,000 --> 00:11:14,940
+بصير لها قيمة، تمام؟ هذه ما بنسميها حركة نسبية، تمام؟
+
+145
+00:11:14,940 --> 00:11:22,140
+بعد كده، جاية الميكانيكا، لها أب، The Father of
+
+146
+00:11:22,140 --> 00:11:27,340
+Mechanics، مين أبوها؟ نيوتن، لنيوتن له قوانين، كم
+
+147
+00:11:27,340 --> 00:11:33,180
+واحد؟ ثلاثة، هدول الثلاثة بدنا نعيدهم، وطبعًا مش
+
+148
+00:11:33,180 --> 00:11:37,720
+هنقول لكم اذكروا قوانين نيوتن، هنقول لكم افهموا قوانين
+
+149
+00:11:37,720 --> 00:11:43,460
+نيوتن، وكيف تطبقوها، تمام؟ فـ Newton's Laws of Motion،
+
+150
+00:11:43,460 --> 00:11:47,280
+قوانين نيوتن الثلاثة، لهم Chapter كامل، من أهم
+
+151
+00:11:47,280 --> 00:11:52,160
+الشباتر، لأنه هو أبو الميكانيكا، بدون هذه القوانين
+
+152
+00:11:52,160 --> 00:11:57,340
+فهمها، الواحد ما يكونش أخد ميكانيكا، تمام؟ بعد كده
+
+153
+00:11:57,340 --> 00:12:02,920
+هناخد نوع من أنواع القوة المهمة، وهي قوة الاحتكاك،
+
+154
+00:12:02,920 --> 00:12:10,300
+سمعتوها؟ وهنا ما هناخدهاش بالتفصيل، بعد كده هناخد الـ
+
+155
+00:12:10,300 --> 00:12:14,860
+Circular Motion، السيارة لما بتكون ماشية، لما بتكون ماشية حركة
+
+156
+00:12:14,860 --> 00:12:20,810
+خطية، تخش دوار، بتاع في الدوار، بتصير حركة دائرية، لها
+
+157
+00:12:20,810 --> 00:12:26,530
+أنظمة وقوانين مختلفة، في تسارع مركزي، سمعتوا فيه؟ وقوة
+
+158
+00:12:26,530 --> 00:12:31,370
+مركزية، هذا تابع للقوة الدائرية، أو الدورانية،
+
+159
+00:12:31,370 --> 00:12:37,510
+Circular Motion، بعدين Work، شغل، سمعتوا فيه؟ Kinetic
+
+160
+00:12:37,510 --> 00:12:42,630
+Energy، طاقة حركة، إيش وحدة الشغل؟ إيش وحدة طاقة
+
+161
+00:12:42,630 --> 00:12:46,390
+الحركة؟ Bravo، ما زال، هذا جول، وهذا جول، يعني أهمهم
+
+162
+00:12:46,390 --> 00:12:50,830
+واحد، ولا لأ؟ لهم نفس الوحدة، ما زال، أهمهم واحدة، إذًا
+
+163
+00:12:50,830 --> 00:12:55,230
+لازم يكون بينهم علاقة، في نظرية مشهورة، بتربط الشغل
+
+164
+00:12:55,230 --> 00:12:59,410
+
+223
+00:18:06,360 --> 00:18:14,420
+نسميها إيش وكأنه كتلة دورانية، آخر حاجة هدي وتاول
+
+224
+00:18:14,420 --> 00:18:18,250
+عزم، بيقول لي طب بينهم علاقات، بقول له بينهم علاقات، و
+
+225
+00:18:18,250 --> 00:18:22,930
+بنشتقهم، فبالتالي Angular يعني زاوية من Angle، Angle
+
+226
+00:18:22,930 --> 00:18:27,850
+زاوية، Angular زاوية، الـ Translational هي الانتقالية
+
+227
+00:18:27,850 --> 00:18:31,250
+أو الخطية، تقدر تقول له الـ Quantities بيقول لي إيش
+
+228
+00:18:31,250 --> 00:18:38,110
+العلاقة بين الكميات الخطية والكميات الزاوية، تمام؟
+
+229
+00:18:38,110 --> 00:18:43,590
+هنأخذهم ونشتقهم مع بعض، وأغلبكم عارفينهم أنتم الـ
+
+230
+00:18:43,590 --> 00:18:47,830
+Torque اللي تاوي، قلت عنه تاوأه مهوتة، وهذا شغلة
+
+231
+00:18:47,830 --> 00:18:52,850
+مهمة لأن المسبب للحركة في الحركة الخطية هي F
+
+232
+00:18:52,850 --> 00:18:58,550
+والمسبب للحركة الدورانية هي Torque، تمام؟ بعدين قال
+
+233
+00:18:58,550 --> 00:19:02,650
+لي قوانين الحركة الدورانية، بدك تشتق لي إياها من أول وجديد
+
+234
+00:19:02,650 --> 00:19:08,430
+dynamics كيف تتحرك كل حركة دورانية، هنأخذها الـ
+
+235
+00:19:08,430 --> 00:19:12,790
+moment of inertia لها تفصيل، اللي هي I، هذه moment of
+
+236
+00:19:12,790 --> 00:19:16,370
+inertia وكيف نحسبها، لها قوانين بدنا نأخذها
+
+237
+00:19:16,370 --> 00:19:21,770
+بالتفصيل، مثل كتلة تمشي، تمام، rotational kinetic
+
+238
+00:19:21,770 --> 00:19:24,670
+energy قال لي الـ kinetic energy بنعرف أنها نص MV
+
+239
+00:19:24,670 --> 00:19:30,290
+تربيع، صح؟ طب الـ kinetic قال لي لأ، لها قانون مختلف لأنه
+
+240
+00:19:30,290 --> 00:19:34,450
+دورانية، مظبوط ولا لأ؟ طبعا، بعدين بنشوف قوانين، إحنا
+
+241
+00:19:34,450 --> 00:19:37,630
+ما بدنا نجيب قوانين دلوقتي، بيقولوا طب مبدأ الطاقة
+
+242
+00:19:37,630 --> 00:19:43,470
+في الحركة الدورانية، عدله بدنا نعيده، تمام؟ Angular
+
+243
+00:19:43,470 --> 00:19:50,230
+momentum زخم زاوي، زخم زاوي اللي هو L، هنأخذه، قال طب
+
+244
+00:19:50,230 --> 00:19:53,910
+هذه مرات بيكون preserved يعني محفوظ، Conservation
+
+245
+00:19:53,910 --> 00:19:58,350
+of angular momentum وقت إيش بيكون محفوظ وإيش تطبيقات
+
+246
+00:19:58,350 --> 00:20:05,250
+حفظ كمية التحرك، تمام؟ بعدين قال لي الاتزان
+
+247
+00:20:05,250 --> 00:20:10,330
+الاستاتيكي، اتزان، وطبعا الاتزان هو أساس علم
+
+248
+00:20:10,330 --> 00:20:15,780
+الهندسة المدنية، هم لما يعملوا جسر، بينفع يجي، لأ لما
+
+249
+00:20:15,780 --> 00:20:20,840
+يعملوا مبنى، هبت ريح يروح، فبالتالي لازم يعملوا يكون
+
+250
+00:20:20,840 --> 00:20:24,400
+فيه توازن في كل شيء، فهذا علم كبير إحنا بناخد شبطر
+
+251
+00:20:24,400 --> 00:20:29,120
+هم بياخذوا مواد في هذا العلم، تمام، center of
+
+252
+00:20:29,120 --> 00:20:34,240
+gravity بتشبه center of mass، بيجي لها تفصيل، elastic
+
+253
+00:20:34,240 --> 00:20:37,740
+properties of solids قال لي المهندس بدي أستخدم
+
+254
+00:20:37,740 --> 00:20:43,270
+الحديد والنحاس والألمنيوم، طب هذه بتظل زي ما هي في
+
+255
+00:20:43,270 --> 00:20:48,070
+الحرارة، بتتغير في مع الشد ولا مع الضغط بتتغير، طب
+
+256
+00:20:48,070 --> 00:20:54,350
+كيف تتغير، ووقت إيش بتتغير، هذه لها قوانينها لحد
+
+257
+00:20:54,350 --> 00:20:59,070
+الآن، أكيد هنأخذ هذا الـ chapter الأخير، اللي مرات
+
+258
+00:20:59,070 --> 00:21:04,070
+بنقول مرات بنلحقهوش، عن إيش بحكي، الـ fluid mechanics
+
+259
+00:21:04,070 --> 00:21:09,310
+ميكانيكا السوائل أو الموائع، إيش فيها؟ اللي في حاجة
+
+260
+00:21:09,310 --> 00:21:13,710
+بيسموها pressure الضغط، تمام؟ كل ما نزلته تحت في
+
+261
+00:21:13,710 --> 00:21:18,830
+الماء ضغط، مزيد، تمام؟ قال لي في حاجة بيسموها مبدأ
+
+262
+00:21:18,830 --> 00:21:23,770
+Pascal، سمعتوا فيه؟ تمام، وقال لي في حاجة بيسموها الـ
+
+263
+00:21:23,770 --> 00:21:29,360
+buoyant force أو قوة الطفو أو الدفع تبع الماء، تمام
+
+264
+00:21:29,360 --> 00:21:35,000
+وهذه  بإختصار Archimedes principle، صح ولا لأ؟ وبرضه
+
+265
+00:21:35,000 --> 00:21:40,500
+بيلخصها بنفس الموضوع، continuity equation معادلة
+
+266
+00:21:40,500 --> 00:21:45,460
+الاستمرارية، معادلة مشهورة، تمام، وفي Bernoulli
+
+267
+00:21:45,460 --> 00:21:49,160
+equation، معادلة Bernoulli، Bernoulli اسم عالي، إن
+
+268
+00:21:49,160 --> 00:21:54,420
+شاء الله نقدر نلحقها، تمام، هذا course objectives
+
+269
+00:21:57,520 --> 00:22:03,700
+المطلوب من هذا الـ Chapter مش مهم كتير تقرأوه، وهذا
+
+270
+00:22:03,700 --> 00:22:09,080
+القالب أو إيش اللي بنحققه، نيجي للمهم، إحنا بندرس من
+
+271
+00:22:09,080 --> 00:22:13,220
+كتاب مشهور، ولما أقول مشهور يعني مشهور في كل
+
+272
+00:22:13,220 --> 00:22:17,860
+العالم، مش في غزة، يعني بتلاقي أنت الطالب اللي بتدرس
+
+273
+00:22:17,860 --> 00:22:21,400
+في جامعة أسيوط في غزة، وطالب بتدرس في Los Angeles
+
+274
+00:22:21,400 --> 00:22:27,300
+وطالب بتدرس في Tokyo ولا واحدة في بكين، كلهم تقريبا
+
+275
+00:22:27,300 --> 00:22:31,800
+من نفس الكتاب بتدرسه تقريبا، وهذا الكتاب يمكن أكثر
+
+276
+00:22:31,800 --> 00:22:35,660
+من 60% من جامعات العالم اعتمدوا هذا الكتاب، هذا
+
+277
+00:22:35,660 --> 00:22:40,400
+كتاب عالمي موجود طول عمره، من أيام أنا كنت بأدرسكم
+
+278
+00:22:40,400 --> 00:22:45,940
+physics اسمه for scientists and engineers، هذا اسم
+
+279
+00:22:45,940 --> 00:22:50,520
+الكتاب، مؤلفينه Sir Wayne Jewett وهذه الطبعة
+
+280
+00:22:50,520 --> 00:22:54,960
+التاسعة، إحنا أيامنا كانت الطبعة الثانية، أنا كنت في
+
+281
+00:22:54,960 --> 00:23:00,540
+الجامعة، جات لكم سنة 1980، أمكم ما كانتش مولودة، مظبوط
+
+282
+00:23:00,540 --> 00:23:06,700
+ليها، تمام، فسنة 1980 كان هذا الكتاب موجود بس النسخة
+
+283
+00:23:06,700 --> 00:23:11,350
+الثانية،  هجرت صارت تسعة، لأ صار في عشرة كمان، تمام، فهذا
+
+284
+00:23:11,350 --> 00:23:14,710
+من أشهر الكتب وما زال موجود، زمان كان Serway لحاله
+
+285
+00:23:14,710 --> 00:23:19,250
+انضم له Jewett  يساعده، ممكن خطير Serway فبدأوا واحد شاب
+
+286
+00:23:19,250 --> 00:23:26,670
+يتنشط معه، تمام، دائما في كل مادة بيقولوا أنه لازم
+
+287
+00:23:26,670 --> 00:23:31,930
+تعطي كتاب، وتعطي بعض المراجع، تمام، هذه المراجع برضه
+
+288
+00:23:32,590 --> 00:23:37,710
+عالمية ومشهورة، من المراجع، طبعا إحنا لما نقول مرجع
+
+289
+00:23:37,710 --> 00:23:45,670
+يعني بيشرح نفس المواضيع لكن بترتيبات معينة، و
+
+290
+00:23:45,670 --> 00:23:50,150
+بتفصيل معين، هذا لكتاب الـ reference اسمه
+
+291
+00:23:50,150 --> 00:23:53,670
+fundamentals of physics أساسيات علم الفيزياء
+
+292
+00:23:54,610 --> 00:23:58,550
+المؤلفين تبعه Halliday, Resnick and Walker، برضه
+
+293
+00:23:58,550 --> 00:24:02,170
+أيامنا كان Halliday and Resnick بس، يعني كان مشهور
+
+294
+00:24:02,170 --> 00:24:04,830
+إيش الكتاب اللي درست منه؟ يقول Serway، إيش الكتاب
+
+295
+00:24:04,830 --> 00:24:07,630
+اللي درست منه؟ يقول Halliday and Resnick، هيك كانوا
+
+296
+00:24:07,630 --> 00:24:11,370
+مشهورين، يبقى نضيف لهم هذا الشاب اللي معه، و Walker
+
+297
+00:24:11,370 --> 00:24:15,540
+نضيف لهم، وفي كتاب ثالث اسمه university physics
+
+298
+00:24:15,540 --> 00:24:20,800
+مؤلفينه Sears, Zemansky and Young، هدول ممكن أشهر
+
+299
+00:24:20,800 --> 00:24:24,800
+ثلاثة كتب، هدول اثنين أشهر شوية من هذا، لكن هدول
+
+300
+00:24:24,800 --> 00:24:28,760
+موجودين ومنتشرين في كل العالم، ولو أنتم دخلتوا على
+
+301
+00:24:28,760 --> 00:24:33,080
+جوجل وكتبتوا بس أسماء المؤلفين، هيجيكم، ويمكنكم
+
+302
+00:24:33,080 --> 00:24:37,140
+تنزلوهم، أنتم عارفين جوجل، منتشرة، الكتاب لما يكون
+
+303
+00:24:37,140 --> 00:24:41,420
+قديم بيكون متاح في الإنترنت، موجود يعني، وبيمكنكم
+
+304
+00:24:41,420 --> 00:24:47,040
+تنزلوهم، طبعا إحنا مش طماعين، إحنا واقعيين، إحنا بهمنا
+
+305
+00:24:47,040 --> 00:24:53,800
+هذا الكتاب، هدول مرجعتوا لهم؟ نعم، به مارجعتوش مش
+
+306
+00:24:53,800 --> 00:25:02,440
+كتير يعني مهم، لكن أحيانا بيلزم ترجعوا لهم، نيجي نشوف
+
+307
+00:25:02,440 --> 00:25:06,820
+هالـ Grade،  ياسيتنا في المادة، إحنا كلنا ما شاء
+
+308
+00:25:06,820 --> 00:25:10,500
+الله علينا شاطرين وطموحين، وبدنا علامة عالية، صح ولا
+
+309
+00:25:10,500 --> 00:25:15,800
+لأ؟ عشان نحصل على العلامة العالية بدنا نفهم كيف إحنا
+
+310
+00:25:15,800 --> 00:25:19,800
+بندي العلامة، طبعا إحنا ما بتطلعش عوجوكم، نحط علامات
+
+311
+00:25:19,800 --> 00:25:26,800
+لأ، في نشاط بنعمله، وبناء عليه بنقيمكم، إحنا ماذا
+
+312
+00:25:26,800 --> 00:25:29,920
+ثانوية، توجيهي، في امتحان واحد، لأ، ياب لأسود، صح ولا
+
+313
+00:25:29,920 --> 00:25:34,860
+لأ، لأ، إحنا عندنا في الجامعة في عدة محاولات بتخليك
+
+314
+00:25:34,860 --> 00:25:40,380
+تقيم الطالب، وغالبا بتقيمه صح، علامة كل المواد في
+
+315
+00:25:40,380 --> 00:25:44,670
+الجامعة يا بنات بتكون من 100، كلها من 100، بس إلها
+
+316
+00:25:44,670 --> 00:25:49,490
+كلها وزن واحد، بقول لك لأ، بصير علامة بيك تضربها في
+
+317
+00:25:49,490 --> 00:25:53,810
+عدد الساعات، يعني الفيزياء لو جبتي فيها 90، تنضرب
+
+318
+00:25:53,810 --> 00:25:58,750
+في ثلاثة بصير 270، القرآن لو جبتي 100، بيضلها 100،
+
+319
+00:25:58,750 --> 00:26:02,030
+لأنها لو بتضربيها في، قديش؟ واحد، مقدمة في الهندسة
+
+320
+00:26:02,030 --> 00:26:06,830
+100، بتضربيها في 100، وبتجمعي وبتضربي بقى كم ساعة،
+
+321
+00:26:06,830 --> 00:26:11,990
+مساقين، 16، بتقسموا على 16 في الآخر، بيطلع معدلكم،
+
+322
+00:26:12,380 --> 00:26:17,660
+الفصلي اللي إن شاء الله كله يكون امتياز، تمام، هجرة
+
+323
+00:26:17,660 --> 00:26:21,180
+حملة، تديكم علامة من مئة إن شاء الله بعد ما تخلصوا
+
+324
+00:26:21,180 --> 00:26:24,160
+الامتحانات، تبدأ تطلع العلامات بعد صلاة العشاء
+
+325
+00:26:24,160 --> 00:26:29,580
+تديكم رسالة حلوة، علامتك في المادة الفلانية كذا، أول
+
+326
+00:26:29,580 --> 00:26:33,880
+ما تشوفوا إن الجوال  يجيب لكم إياه، والله علامة  ممتازة
+
+327
+00:26:33,880 --> 00:26:37,360
+بتروحوا تزغرتوها عندكم، تقولوا علامتنا حلوة، وإن شاء
+
+328
+00:26:37,360 --> 00:26:42,220
+الله تكون كلها علامات حلوة، بتجيء رسائل، علامة
+
+329
+00:26:42,220 --> 00:26:47,340
+الطالب، كل علامة بعلامتها حسب، كيف نعتمد، كيف  بنحنا
+
+330
+00:26:47,340 --> 00:26:53,140
+نعمل علامات، إحنا هيكون عندنا ثلاثة أنشطة رئيسية بتحدد
+
+331
+00:26:53,140 --> 00:27:00,720
+العلامات، أول نشاط هذا هو Quizzes، يعني فرصة
+
+332
+00:27:00,720 --> 00:27:05,420
+كلنا نجيب 20 من 20 منها، هذه عليها 20 درجة، 20% من
+
+333
+00:27:05,420 --> 00:27:12,000
+العلامة، كيف؟ قال أنا بدي أعطيك 11 quiz، quiz إيش
+
+334
+00:27:12,000 --> 00:27:17,460
+معنى quiz؟ اختبار قصير، ليش Quizzes؟ لأنه هتعملوه
+
+335
+00:27:17,460 --> 00:27:23,060
+في البيت، تعملوه في البيت، وأمك وأبوك وأخوك
+
+336
+00:27:23,060 --> 00:27:27,840
+حواليك، وشايك وجاهزتك اللي عندك وكتابك ودفترك
+
+337
+00:27:27,840 --> 00:27:34,890
+برضه حواليك، تمام؟ و calculator؟ وورقة فاضية وقلم
+
+338
+00:27:34,890 --> 00:27:39,790
+بتفوت  أو غرفتك وبتقول له بدي أعمل امتحان، تمام؟ كيف
+
+339
+00:27:39,790 --> 00:27:42,970
+الامتحان هذا؟ امتحان على الكمبيوتر أو على الجوال
+
+340
+00:27:42,970 --> 00:27:47,150
+الـ Moodle اللي تاوي حكيت عنه، تمام؟ اللي هتفوتوا عليه اليوم
+
+341
+00:27:47,150 --> 00:27:50,210
+عليه وتشوفوه، هتلاقي فيه quiz واحد، quiz اثنين،
+
+342
+00:27:50,210 --> 00:27:53,990
+quiz ثلاثة، هذا الـ quiz أنا بافتحه، بقول لكم ما كانش بدي
+
+343
+00:27:53,990 --> 00:27:59,910
+أفتحه، متاح، غالبا بعمل يوم خميس، بافتحه بعد صلاة
+
+344
+00:27:59,910 --> 00:28:04,130
+الفجر، الساعة ستة، بيضلوا ماشي مفتوح لساعة 12 في
+
+345
+00:28:04,130 --> 00:28:08,290
+الليل، بس مش مفتوح كل هذه الفترة، كل واحد بيجي بفوت
+
+346
+00:28:08,290 --> 00:28:13,730
+بيعطيه عشر دقائق أو ثمان دقائق، بحيث فيهم خمس أسئلة
+
+347
+00:28:13,730 --> 00:28:18,990
+كل سؤال تقريبا بده دقيقة، السؤال الإقرائي بتلاقي
+
+348
+00:28:18,990 --> 00:28:22,250
+أربع إجابات بتجي تختاري واحد، كيف إحنا عاملين
+
+349
+00:28:22,250 --> 00:28:27,230
+الكمبيوتر يعمل هذا الـ quiz، عاملين كمبيوتر منشئين
+
+350
+00:28:27,230 --> 00:28:33,370
+خمس صناديق، خمس صناديق، هي واحد، اثنين، ثلاثة، أربعة،
+
+351
+00:28:33,370 --> 00:28:38,490
+خمسة، كل Chapter قسمناه خمسة مواضيع، في هذا
+
+352
+00:28:38,490 --> 00:28:41,850
+الموضوع الأول حطينا فيه حوالي ثلاثين، أربعين سؤال.
+
+353
+00:28:42,510 --> 00:28:46,390
+وهذا موضوع ثاني، وهذا موضوع ثالث، وهذا رابع، وهذا
+
+354
+00:28:46,390 --> 00:28:51,630
+خامس، قسمناهم حسب المواضيع، بتيجي فاطمة أنت تعمل
+
+355
+00:28:51,630 --> 00:28:56,830
+الامتحان على طول، بقول الكمبيوتر متاح، لأنه أنا يوم
+
+356
+00:28:56,830 --> 00:28:59,490
+الخميس بجيء، الكمبيوتر يوم الخميس بده يبدأ الساعة ستة
+
+357
+00:28:59,490 --> 00:29:02,950
+ودقيقة بقول لك متاح، بيجي من داخل الكمبيوتر، من داخل
+
+358
+00:29:02,950 --> 00:29:07,500
+الكمبيوتر، يطلع لفاطمة سؤال من هذا الصندوق بس، السؤال
+
+359
+00:29:07,500 --> 00:29:10,140
+التالي، ما نوع يجيبه من هنا، يجيبه من هنا، السؤال
+
+360
+00:29:10,140 --> 00:29:12,920
+الثالث من هنا، السؤال الرابع من هنا، والسؤال الخامس
+
+361
+00:29:12,920 --> 00:29:16,220
+من هنا، عشان ما يجيء طالب تقول، والكمبيوتر حاطط ضده
+
+362
+00:29:16,220 --> 00:29:20,560
+جاب لكل الخمس أسئلة من الموضوع الصعب، مستحيل، مستحيل
+
+363
+00:29:20,560 --> 00:29:24,240
+إذا هذا سهل، كلكم هيجيكم سؤال زيه، وغالبا عشان
+
+364
+00:29:24,240 --> 00:29:27,900
+العدالة، الحمد لله، نحط الأسئلة متشابهة، يعني مغيرين برقم
+
+365
+00:29:27,900 --> 00:29:34,140
+مغيرين فكرة، بيطلع لكم خمس أسئلة، سؤال وهي أربع خيارات
+
+366
+00:29:34,140 --> 00:29:39,150
+زي من سيربح المليون، وبتختاري بقى، الساعة بقى كله
+
+367
+00:29:39,150 --> 00:29:46,170
+اختيار، هذا هيك مصمم، تعمل click وبتختاري، تطلعي على
+
+368
+00:29:46,170 --> 00:29:49,010
+الساعة وبتقولي الساعة جديد قدامك، إن هو الله ده ليه
+
+369
+00:29:49,010 --> 00:29:51,750
+يجيئ لك اثنين، ده ليه ثلاث دقائق، بعدين بيقول لي خلصتي
+
+370
+00:29:51,750 --> 00:29:56,570
+بيقول لي خلصت، بيقول لك Submit، يعني سلم، بيقول لي سلمت، خلصت
+
+371
+00:29:56,570 --> 00:30:00,250
+أول ما تقولي سلمت، العلامة بتظهر عندك، الساعة اثنتا عشرة
+
+372
+00:30:00,250 --> 00:30:04,950
+في الليل ودقيقة، بتظهر عندك علامتك بتأخذيها، بنضل
+
+373
+00:30:04,950 --> 00:30:09,570
+نجمع، كل نهاية شهر، يعني الأسبوع هذا لأ طبعا
+
+374
+00:30:09,570 --> 00:30:12,650
+الأسبوع هذا لسه نتعرف على بعض، الخميس هذا ما فيه
+
+375
+00:30:12,650 --> 00:30:15,550
+quiz، إن شاء الله الخميس اللي وراه غالبا بيكون فيه
+
+376
+00:30:15,550 --> 00:30:19,570
+عندنا quiz، تمام؟ وإحنا بنذكر، وفي الـ whatsapp أنا
+
+377
+00:30:19,570 --> 00:30:22,730
+بكتب إن الـ quiz بدي يفتح، دير بالكم الساعة 6، وبدي
+
+378
+00:30:22,730 --> 00:30:26,970
+يسكر الساعة 12، يعني بنتواصل بأكثر من طريقة، واللي
+
+379
+00:30:26,970 --> 00:30:30,090
+بدي يفتح الساعة 6 يفتح الساعة 12 الظهر يفتح
+
+380
+00:30:30,090 --> 00:30:35,230
+الساعة 11 في الليل، يفتح بس بعد 12 ممنوع، بتسكيرو، جيت
+
+381
+00:30:35,230 --> 00:30:41,490
+هدول Quizzes سهلين، لأنه في داري وكل وقتي وكل أهلي
+
+382
+00:30:41,490 --> 00:30:45,070
+حواليا، يعني ما فيه امتحان وخايفة وجالسة، بدي هم لأ
+
+383
+00:30:45,070 --> 00:30:48,550
+امتحان عادي، وبالتالي لازم نجيب فيه علامة كاملة
+
+384
+00:30:48,550 --> 00:30:52,150
+وعاملين Quizzes أخرى، بنقول يمكن الطالب يصير في عنده
+
+385
+00:30:52,150 --> 00:30:56,850
+ظرف، في
+
+445
+00:35:27,160 --> 00:35:29,920
+حقيقية لزمان كنت تكتب يعني V بالعربي؟ إيش ممكن
+
+446
+00:35:29,920 --> 00:35:32,400
+تكتب بالإنترنت؟  V بالصورة الخمسة كيف ممكن تكتبها
+
+447
+00:35:32,400 --> 00:35:35,200
+بالعربي؟ هي مش حقيقية لزمان كده، أنا قلت لكم ما
+
+448
+00:35:35,200 --> 00:35:38,180
+تخافوش من الإنجليزي، ما تخافوش من الإنجليزي بالمرة
+
+449
+00:35:38,180 --> 00:35:40,660
+أنتم أول مرة تفكروا في شيء، لا أنتم في العالم
+
+450
+00:35:40,660 --> 00:35:44,980
+دخلتوا علوم أو هندسة، أكملوا بدا، ما هم كان أمك أو
+
+451
+00:35:44,980 --> 00:35:50,100
+أبوك، أخذوا ومشي، الأمور سهلة سهلة كتير، أقصد من ما
+
+452
+00:35:50,100 --> 00:35:55,870
+تتوقعي وأنا بحكي فهماني يعني؟ آه ما بكذب إنجليزي، و
+
+453
+00:35:55,870 --> 00:36:02,250
+هيك عندكم تمام؟ حلو طبعاً، إحنا عشان أنتم
+
+454
+00:36:02,250 --> 00:36:08,910
+نساعدكم إنكم تدرسوا وتفهموا، عاملين للمادة مناقشة
+
+455
+00:36:08,910 --> 00:36:12,990
+شفتوها في الجدول، في لقاء أسبوعي، هذه المناقشة
+
+456
+00:36:12,990 --> 00:36:16,730
+بيجيب لكم معيدة، وهذه المعيدة هي الأولى على القسم
+
+457
+00:36:16,730 --> 00:36:19,790
+يعني من أولى القسم بنجيبهم، ليش؟ عشان يحلوا معاكم
+
+458
+00:36:19,790 --> 00:36:23,960
+بعض الأسئلة، لأن الأسئلة وأنتم بتحلوها عندما نحكي عن
+
+459
+00:36:23,960 --> 00:36:29,140
+الأسئلة، ممكن سؤال ما يظبطش معاكم، بدكم حد يساعدكم،
+
+460
+00:36:29,140 --> 00:36:32,580
+بيجي المعيد يحل بعض الأسئلة، هذا برضه المعيد
+
+461
+00:36:32,580 --> 00:36:37,300
+ما يكفيش، بدكم إياي أنا، فإحنا حاطين ساعات مكتبية
+
+462
+00:36:38,360 --> 00:36:45,120
+اللي بدها أستاذ يشوف ويستأنسله، أنا بالنسبة لكم حاط
+
+463
+00:36:45,120 --> 00:36:49,300
+يوم السبت من الـ 11 للـ 12 إن شاء الله يكون متاح
+
+464
+00:36:49,300 --> 00:36:53,960
+يعني أنتم فاضيين، ما فيش عندكم محاضرات، وهي غرفتي
+
+465
+00:36:53,960 --> 00:37:01,620
+C236، واحدة عندها شيء تعالوا على المكتب، مزال أنا
+
+466
+00:37:01,620 --> 00:37:07,870
+موجود في المكتب وفاضي، أهلاً وسهلاً فيكم بأي وقت، تمام؟
+
+467
+00:37:07,870 --> 00:37:16,050
+هذا وقت رسمي، أحكي الأسئلة
+
+468
+00:37:16,050 --> 00:37:20,350
+اللي إحنا محددين، هي إليك اتسانى شوية، هاي زيكم
+
+469
+00:37:20,350 --> 00:37:26,230
+تلاقوا من هذا الـ emails، ههه الكتاب اللي توي حكيت
+
+470
+00:37:26,230 --> 00:37:30,330
+عنه، أنا اللي موجود في مكتبة الطالب في كل نهاية
+
+471
+00:37:30,330 --> 00:37:34,990
+chapter فيه أسئلة كتير، فيه مرات بصلمية وكذا سؤال
+
+472
+00:37:34,990 --> 00:37:44,000
+تمام؟ المنطقي أو الـ Ideal أو الشغلة الميثالية إن
+
+473
+00:37:44,000 --> 00:37:47,360
+واحد يحلهم كلهم، إحنا بنقول لكم إحنا مش طماعين، ما بدناش
+
+474
+00:37:47,360 --> 00:37:55,560
+تحلهم كلهم، مختارين لكم جزء منهم، إيش مسميينهم الأسئلة
+
+475
+00:37:55,560 --> 00:37:59,320
+الموصى بحلها، الأسئلة الموصى بحلها، هي recommenders
+
+476
+00:37:59,320 --> 00:38:02,920
+إذا بتسموها recommendation letter، رسالة توصية، إذا
+
+477
+00:38:02,920 --> 00:38:06,020
+اسمها توصية، recommended problems اللي إحنا بنوصي
+
+478
+00:38:06,020 --> 00:38:09,480
+إنكم تحلوها، إيش يعني؟ يعني هذا الحد الأدنى اللي
+
+479
+00:38:09,480 --> 00:38:14,060
+لازم تحلوه، هذا الحد الأدنى لازم تحلوه، هذه أقام
+
+480
+00:38:14,060 --> 00:38:17,600
+الأسئلة، شوفوا أنتم لو تطلعوا تعدوا من المية يمكن
+
+481
+00:38:17,600 --> 00:38:21,500
+مختارين إحنا، إما الثلث أو الربع بس، عشان تحلوهم
+
+482
+00:38:21,500 --> 00:38:25,440
+ما كانش ممكن تحلوهم، هدول حاجات إحنا امتحان نص يوم
+
+483
+00:38:25,440 --> 00:38:31,780
+ثمانية، ثلاث عشرة، أحد عشر، صح ولا ثلاث عشرة أحد عشر؟ مش يوم
+
+484
+00:38:31,780 --> 00:38:38,210
+اثنا عشر، نبدأ نحل، ما نخلصش، ما نفعش، وقت الحل يجي جبل
+
+485
+00:38:38,210 --> 00:38:41,130
+ما يبدأ السبت، اللي بدي يخش chapter جديد، بدي أكون خلص
+
+486
+00:38:41,130 --> 00:38:45,650
+الـ chapter اللي جابله، فهمتوا عليّ كده؟ يعني أنا غالباً
+
+487
+00:38:45,650 --> 00:38:49,970
+يوم سبت بنبدأ chapter جديد، بكون خلال الأسبوع اللي
+
+488
+00:38:49,970 --> 00:38:53,190
+جابله، بدي أحل الجمعة، بدي أكون خلصت الـ chapter اللي
+
+489
+00:38:53,190 --> 00:38:58,450
+جابله، خلاص حليته، إذا حليته، هدول بعضلاتكم لحالكم
+
+490
+00:38:58,450 --> 00:39:02,610
+بضمن لكم العلامة الكاملة، لأن غالباً أسئلة امتحانات
+
+491
+00:39:02,610 --> 00:39:07,470
+بتكون منهم، غالباً بتكون من هذه الأسئلة، هذه
+
+492
+00:39:07,470 --> 00:39:10,970
+الـ recommended problems، والمعيد بدي أحل منهم طبعاً
+
+493
+00:39:10,970 --> 00:39:14,390
+هدول كتابة، ما أقدرش أحلهم كلهم، ياريت لو أنتم تكونوا
+
+494
+00:39:14,390 --> 00:39:17,930
+مستعدين وحليتوه وعرفتوا إيش الصعب، تختاروا من المعيد
+
+495
+00:39:17,930 --> 00:39:23,160
+بدل ما هو لما يدرجنا، ما حليتُ، ما فتحنا، ما حلّينا
+
+496
+00:39:23,160 --> 00:39:26,940
+حاجة، ساعتها بيختار لحاله، مظبوط ولا لأ؟ لكن لما
+
+497
+00:39:26,940 --> 00:39:28,940
+نقول له لأ والله السؤال الفلاني أنا حاولت أحله في
+
+498
+00:39:28,940 --> 00:39:32,600
+الدار، ما عرفش أحله، بحاول أحلكم إياه، أفضل،
+
+499
+00:39:32,600 --> 00:39:38,720
+أتفاهم؟ هذه أرقام الأسئلة اللي لازم تحلوها، لازم
+
+500
+00:39:38,720 --> 00:39:43,540
+تحلوها، حد الأدنى اللي لازم ينحل، عشان نجيب علامة
+
+501
+00:39:43,540 --> 00:39:46,360
+حلوة، تمام يا بنات؟ حلو
+
+502
+00:39:48,820 --> 00:39:56,860
+الآن، هذه هي المقدمة تبعتنا، إحنا محاضرتنا مصورة
+
+503
+00:39:56,860 --> 00:40:04,220
+يعني فضيحة جلاجل بتتوزع، تمام؟ إيش بدي منكم؟ كل
+
+504
+00:40:04,220 --> 00:40:10,180
+طالبة عندها سؤال، ما ترفعش أيدها، تسأل، قد ما بدكم
+
+505
+00:40:10,180 --> 00:40:14,800
+اسألوا، وقت ما شعرتوا إني أنا بحكي حاجة صراحة، و
+
+506
+00:40:14,800 --> 00:40:18,780
+بطلتوا تستوعبوا، واجفوني، طول ما أنتم بتهزوا رأسكم
+
+507
+00:40:18,780 --> 00:40:23,980
+أنا بأعتبركم فاهمين، حتى لو بتهزوا رأسكم كذب، تمام
+
+508
+00:40:23,980 --> 00:40:26,820
+لأنهم مرة بطيجة عينها في عين واحدة بتعمل هيك، خلاص
+
+509
+00:40:27,640 --> 00:40:32,600
+ما هي حرة، تمام؟ طبعاً يا بنات، أنتم لازم تعرفوا إحنا
+
+510
+00:40:32,600 --> 00:40:36,960
+طبيعتنا كبشر مختلفين عن بعض، في ناس بخجلوا، وفي ناس
+
+511
+00:40:36,960 --> 00:40:39,500
+عندهم الجرأة ما شاء الله عليهم، أنا بحب أشجعهم في
+
+512
+00:40:39,500 --> 00:40:45,700
+الأسئلة، اللي بسميهم مشاغب إيجابي، ليش؟ لأنه أنتم لما
+
+513
+00:40:45,700 --> 00:40:48,520
+تسألوا سؤال، بيكون واحد ثاني بيقول يا هو، رضيني، الحمد
+
+514
+00:40:48,520 --> 00:40:51,660
+لله اللي سأله، كنت بدي أسأله بس خجول، أنتم بتاخذوا
+
+515
+00:40:51,660 --> 00:40:56,140
+ثواب، بتاخذوا ثواب إنكم سألتم، و... وظبطها، وفي أحد
+
+516
+00:40:56,140 --> 00:40:57,280
+بيكره ياخذ ثواب
+
+517
+00:41:00,000 --> 00:41:03,140
+طول ما أنتم شايفين إني أنا بحكي حاجة أنتم مش
+
+518
+00:41:03,140 --> 00:41:07,560
+فاهمينها، حقكم تسألوا، ما تترددوش، ومش واحدة تقول
+
+519
+00:41:07,560 --> 00:41:10,460
+والله أنا سألت سؤالين، خلاص بدي أخجل، أنتم سألوا
+
+520
+00:41:10,460 --> 00:41:16,680
+حوشوا حسنات داركم، اسألوا، لما تزهجوا، طول ما أن
+
+521
+00:41:16,680 --> 00:41:21,480
+أنتم مش فاهمين، وزي ما إحنا بنقول دائماً، ما فيش سؤال
+
+522
+00:41:21,480 --> 00:41:26,160
+بسيط ولا بايخ، السؤال البايخ فقط لسؤال اللي بسأله
+
+523
+00:41:26,160 --> 00:41:30,210
+وأنا عارف إجابته، حاجة دي بيكون بسأل عشان أضيع وقت
+
+524
+00:41:30,210 --> 00:41:33,990
+أما كل سؤال، حتى لو اتنين في تلاتة بيستوي ستة، كيف
+
+525
+00:41:33,990 --> 00:41:38,390
+اجت وأنتم مش عارفينه، بتقولوا تمام؟ لأنه إحنا
+
+526
+00:41:38,390 --> 00:41:42,050
+هنشرح الشغلات، مرت عليكم في المدرسة، صح ولا لأ؟
+
+527
+00:41:42,050 --> 00:41:45,410
+وبالتالي، ممكن تكون دخلة المعلومة غلط، والله أنا كنت
+
+528
+00:41:45,410 --> 00:41:50,810
+فاهمها هيك، أنتم بتقولوا كلام غلط، نفترض نحكي صوت عالي
+
+529
+00:41:50,810 --> 00:41:55,950
+ونصل لشغلة، نتفقين عليها، عشان تفوت المعلومة صح، و
+
+530
+00:41:55,950 --> 00:42:00,110
+إحنا بنركز وبنقول، دير بالكم، هذا موضوع مهم، بنركز
+
+531
+00:42:00,110 --> 00:42:03,130
+عليه، لما أقول موضوع مهم، يعني معناته موضوع أسئلة
+
+532
+00:42:03,130 --> 00:42:09,050
+لأنه إحنا في الآخر بنشرح، موضوع مهم، موضوع فرعي، و
+
+533
+00:42:09,050 --> 00:42:15,280
+إحنا لما نيجي نحط الامتحان، بنحط امتحان عساس إنه
+
+534
+00:42:15,280 --> 00:42:19,880
+بنشوف الطالب طلع بالأساسيات تبعت المادة ولا لأ
+
+535
+00:42:19,880 --> 00:42:25,480
+ما بنروحش على ما بين السطور، وبنجيب أسئلة لأ قوانين
+
+536
+00:42:25,480 --> 00:42:30,640
+نيوتن، أبو الميكانيكا، بدنا الطالب يفهمهم، بسأل فيهم
+
+537
+00:42:31,380 --> 00:42:35,240
+بسأل فيهم، وبالتالي بنركز على الشغلات الأساسية، وهذه
+
+538
+00:42:35,240 --> 00:42:39,140
+الشغلات الأساسية بنحكيها صراحة قدامكم، عشان كده
+
+539
+00:42:39,140 --> 00:42:42,000
+حضور المحاضرة مهم، لأن أنا بحكي دلوقت هذا موضوع
+
+540
+00:42:42,000 --> 00:42:47,400
+جداً مهم، وهذه الأسئلة بتيجي زيها، هذه الـ tricks
+
+541
+00:42:47,400 --> 00:42:53,260
+بتيجي زيها، فبنكون إحنا وياكم، لو أنتم انتبهتوا، إيه
+
+542
+00:42:53,260 --> 00:42:56,240
+كانت بتيجي الامتحان اللي كنتوا عارفين، يعني مثلاً
+
+543
+00:42:56,240 --> 00:42:59,830
+الـ quiz، لما تخشوا على الـ moodle اللي بتتفرجوا الليلة
+
+544
+00:42:59,830 --> 00:43:04,310
+هتلاقوا كل أسئلة الـ quizzes موجودة جوا، بـ df file
+
+545
+00:43:04,310 --> 00:43:10,110
+زيها، يعني chapter واحد بتلاقوا فيه quizzes مكتوب
+
+546
+00:43:10,110 --> 00:43:14,810
+folder، ملاقاش مثلاً، ومجلد folder اسمه quizzes، فوتوا
+
+547
+00:43:14,810 --> 00:43:17,550
+بتلاقي chapter واحد، chapter اتنين، chapter تلاتة، chapter أربعة
+
+548
+00:43:17,550 --> 00:43:20,950
+خشوا على chapter اتنين، نفترض، بتلاقوا لكم مثلاً خمسين
+
+549
+00:43:20,950 --> 00:43:27,290
+سؤال، هدول الخمسين سؤال هيجيكم زيهم في الـ moodle، يعني
+
+550
+00:43:27,290 --> 00:43:31,290
+إن تحلوهم، بتفوتوا، بتحلوا، بدل ما تاخدوا خمس دقائق
+
+551
+00:43:31,290 --> 00:43:35,650
+بدقيقتين بتحلوا، وبتطلعوا، فبالتالي حتى هذه الأسئلة
+
+552
+00:43:35,650 --> 00:43:42,190
+بنعطيينكم نماذج منها، عشان ما تفوتوش، تصدموا بطبيعة
+
+553
+00:43:42,190 --> 00:43:46,110
+الأسئلة، لأ الطالب اللي بده يشوف هذه الأسئلة موجودة
+
+554
+00:43:46,110 --> 00:43:51,090
+بين إيديه، هذه الـ slides، إحنا بكرة مثلاً نفترض يوم
+
+555
+00:43:51,090 --> 00:43:55,270
+الاثنين، مش يوم الاثنين، بنا نبدأ يوم الاثنين، إما
+
+556
+00:43:55,270 --> 00:43:59,330
+بتفوتوا على chapter واحد وبتطبعوا، بتلاقوا PDF
+
+557
+00:43:59,330 --> 00:44:03,650
+file، chapter واحد بتطبعوا، بدل ما تكتبوا ورايا
+
+558
+00:44:03,650 --> 00:44:07,710
+ما فيش دفتر للتذكير، الـ slides هي الدفتر، الـ slides
+
+559
+00:44:07,710 --> 00:44:10,590
+بتكون مطبوعة قدامكم، عشان بس تطلعوا على اللوحة، تطلعوا
+
+560
+00:44:10,590 --> 00:44:14,690
+عليها، عشان تفضوا تسألوني، ما تديش شرك هي، وأنتم تكتبوا
+
+561
+00:44:15,160 --> 00:44:19,160
+تمام؟ كل اللي أنا بأشرحه موجود بين إيديكم مكتوب
+
+562
+00:44:19,160 --> 00:44:24,480
+اللي عليه، هيكون موجود، يعني هذه الصفحة موجودة نفسها
+
+563
+00:44:24,480 --> 00:44:29,600
+وكل اللي عرضته موجود تحت، band outlines، يعني... إيش
+
+564
+00:44:29,600 --> 00:44:33,320
+الـ outlines معنى بالعربي يعني؟ عناوين أو... مش...
+
+565
+00:44:33,320 --> 00:44:37,640
+مش... راحت من... من بالي، إيش ال... الاسم الرسمي
+
+566
+00:44:37,640 --> 00:44:44,380
+تبعت، بعد كده بتلاقي chapter واحد، بتطبعوه، أو أظن في
+
+567
+00:44:44,380 --> 00:44:48,560
+مكتب بتاعة الطالب، طبعينه، مجاهزين، إذا بدكم
+
+568
+00:44:48,560 --> 00:44:51,700
+تاخدوهم، يعني أنا مش عارف، هيك اللي فهمته يعني
+
+569
+00:44:51,700 --> 00:44:54,220
+بتطبعوهم، أو كل واحدة بتطبع، إذا عندها طابعة في
+
+570
+00:44:54,220 --> 00:44:57,800
+الدار، بتطبعهم كلهم، منها كام ورقة، وبيجيبوهم، بيصير كل
+
+571
+00:44:57,800 --> 00:45:00,940
+chapter بـ chapter، وهذا هو دفترنا، بالإضافة إلى
+
+572
+00:45:00,940 --> 00:45:04,180
+الكتاب، كل مادة لها كتاب ودفتر، فدفترنا هي الـ slides
+
+573
+00:45:04,180 --> 00:45:08,040
+أو إيش رايحين نسميها، هذا PowerPoint، ما أنتم
+
+574
+00:45:08,040 --> 00:45:12,120
+عارفين الـ PowerPoint هو عبارة عن شرايح، هذه شريحة، وهذه شريحة
+
+575
+00:45:12,120 --> 00:45:15,120
+وهذه شريحة، تمام؟ فهذه اللي بنطبعه
+
+576
+00:45:15,120 --> 00:45:19,340
+بيتحولوا لـ PDF file، وبيصيروا بالإيديكم، حكيات كلمة
+
+577
+00:45:19,340 --> 00:45:22,240
+مش مكتوبة، بتضيفوها برصاص ولا بجلم، يعني بيكون هو
+
+578
+00:45:22,240 --> 00:45:26,860
+دفتركم، تمام يا بنات؟ فالعملية كتير سهلة، طبعاً الـ
+
+579
+00:45:26,860 --> 00:45:31,220
+slides هي اللي بتكتب على اللوح، هو الـ slides، زي كل
+
+580
+00:45:31,220 --> 00:45:35,540
+مادة في كتاب، وفيه المدرس بيخصّص، فإحنا ما بنخصّصش على
+
+581
+00:45:35,540 --> 00:45:39,780
+اللوح، طبعاً هنكتب على اللوح، لأنه هنشرح وهنقشر، و
+
+582
+00:45:39,780 --> 00:45:46,720
+نخربش، ونعمل، ونجاوب، و نغوّش، يعني معركة فيه، تمام؟
+
+583
+00:45:46,720 --> 00:45:53,240
+الشغل، الاثنين اللي لازم تتعلموهم، إن الساعة في
+
+584
+00:45:53,240 --> 00:45:56,960
+الجامعة هي خمسين دقيقة، يعني إحنا الساعة اثنا عشر
+
+585
+00:45:56,960 --> 00:46:01,860
+خافوش، ما هو ده الأخ سامح، يقول خلصت، بدون ما لأنه في
+
+586
+00:46:01,860 --> 00:46:04,520
+وراها كمان محاضرة، فالمهم أنتم لما يكون في عينكم
+
+587
+00:46:04,520 --> 00:46:09,280
+محاضرة، الصوت للعشر، ويقول للدكتور، خلصت المحاضرة، أنا
+
+588
+00:46:09,280 --> 00:46:12,720
+هجيت واحد وخمسين، خدت منكم دقيقة، تمام؟ بس إحنا في
+
+589
+00:46:12,720 --> 00:46:16,160
+البداية، فبالتالي الساعة ونص، بصير الساعة وربع، يعني
+
+590
+00:46:16,160 --> 00:46:22,320
+بكرا مثلاً، عينكم من ثمانية لتسع ونص، تسع وربع بخلص
+
+591
+00:46:22,320 --> 00:46:26,640
+تمام؟ إذا اللي بنتقابل إن شاء الله يوم الاثنين
+
+592
+00:46:26,640 --> 00:46:32,940
+الساعة اثنا عشر، شرح حقيقي، وإن كان بسيط، يعطيكم
+
+593
+00:46:32,940 --> 00:46:33,380
+العافية
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Gsr87nrM9VY_postprocess.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Gsr87nrM9VY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f237229f768df3e88b9e189612c18a00e92f1041
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Gsr87nrM9VY_postprocess.srt
@@ -0,0 +1,2372 @@
+1
+00:00:05,280 --> 00:00:08,640
+تمام بعد ما نسمي باسم الله الرحمن الرحيم انتوا
+
+2
+00:00:08,640 --> 00:00:13,360
+عارفين انه انا هكون معاكم في مساق المادة بنسميها
+
+3
+00:00:13,360 --> 00:00:17,000
+مساق في الجامعة ال calculus مساق و الفيزيا مساق و
+
+4
+00:00:17,000 --> 00:00:22,710
+ما يقدم في الهندسة مساق مساق الفيزيا عامة ألفهنكون
+
+5
+00:00:22,710 --> 00:00:27,170
+مع بعض اسبوعيا تلت مرات زي ما هو محطوط في الجدول
+
+6
+00:00:27,170 --> 00:00:31,530
+وهذا معناه تلت ساعات معتمدة دير بالكم ساعة معتمدة
+
+7
+00:00:31,530 --> 00:00:35,230
+يعني اسبوعيا أكم ساعة يعني المادة اللي تلت ساعات
+
+8
+00:00:35,230 --> 00:00:39,910
+معتمدة هتشوفه في الجدول تلت مرات القرآن الكريم
+
+9
+00:00:39,910 --> 00:00:44,310
+عشانه ساعة ومقدمة في الهندسة الهندسة مرة واحدة
+
+10
+00:00:44,310 --> 00:00:48,370
+اللقاء تكونوهكذا هذه معناه تلت ساعات معتمدة احنا
+
+11
+00:00:48,370 --> 00:00:51,910
+هنكون ان شاء الله سبت و اتنين و اربعة في نفس
+
+12
+00:00:51,910 --> 00:00:57,670
+الموعد من الاتنعاش للوحدة في هذه القاعة بإذن الله
+
+13
+00:00:57,670 --> 00:01:03,050
+و هنغطي فيزيا عامة ألف معناته في فيزيا عامة باع
+
+14
+00:01:03,700 --> 00:01:07,780
+فيزيا عامة ألف بتحكي عن علم الميكانيكا علم
+
+15
+00:01:07,780 --> 00:01:10,720
+الميكانيكا اللي أخدته في عاشر وحد عشر وثاني عشر
+
+16
+00:01:10,720 --> 00:01:16,680
+بمواضيع مختلفة وبالتالي المواضيع اللي هنشرحها
+
+17
+00:01:16,680 --> 00:01:21,260
+كعنوين هتكون هي نفس العنوين اللي مرت علينا في
+
+18
+00:01:21,260 --> 00:01:28,440
+المدرسة لكن هناخدها بمنظور مختلف منظور أوسع وغالبا
+
+19
+00:01:28,440 --> 00:01:33,020
+المنظور بنوسع لإنهفي الثانوية كان ال calculus أو
+
+20
+00:01:33,020 --> 00:01:38,020
+الرياضيات اللي عندكم قاصرة وبالتالي في بعض
+
+21
+00:01:38,020 --> 00:01:40,900
+المواضيع بيقدروش يتوسعوا فيها في المدارس لأن
+
+22
+00:01:40,900 --> 00:01:44,180
+الطالب لسه مداركه في الرياضيات بتكون بسيطة
+
+23
+00:01:44,180 --> 00:01:48,180
+وبالتالي بتاخدوا مرات عنوان أو قشرة من الموضوع
+
+24
+00:01:48,180 --> 00:01:52,040
+احنا بنفوت بنكون ركننا ان الطالب اصلا ما شاء الله
+
+25
+00:01:52,040 --> 00:01:59,710
+علينا نضج وبعدين بياخد calculus معانا بالبالجامعة
+
+26
+00:01:59,710 --> 00:02:04,630
+وبالتالي بكون جاهز نتوسع في المواضيع بصورة عامة
+
+27
+00:02:04,630 --> 00:02:10,850
+هذا هو ال mobile رقمي عشان ال watts طبعا احنا
+
+28
+00:02:10,850 --> 00:02:17,190
+هيكون لنا مجموعة مجموعة watts و هتقدروا تنضموا
+
+29
+00:02:17,190 --> 00:02:20,950
+إليها في عندنا في الجامعة حاجة نسميها ال model إذا
+
+30
+00:02:20,950 --> 00:02:25,050
+سمعتوا فيههذا الـ model اليوم يعني خلّيني نقول
+
+31
+00:02:25,050 --> 00:02:29,130
+الواجب تبعنا اليوم بدي يكون أنه نروح نلعب شوية على
+
+32
+00:02:29,130 --> 00:02:34,710
+الكمبيوتر تمام؟ تخشوا على موقع الجامعة تعرفوا اللي
+
+33
+00:02:34,710 --> 00:02:38,930
+سجلتوا منه و جدّمتوا طلب الاتحاق وصلتكم كلمة السر
+
+34
+00:02:38,930 --> 00:02:43,310
+ولا لأ من قبل و التسجيل لما تفوتوا في موقع الجامعة
+
+35
+00:02:43,310 --> 00:02:47,450
+في تحت حاجة بيسميها التعليم الإلكتروني أو ال model
+
+36
+00:02:47,450 --> 00:02:52,940
+تمام؟بتفوتوا ويقولكم دخلوا رقمكم الجامعي وكلمة
+
+37
+00:02:52,940 --> 00:02:58,220
+السر هيجيكم تفعيل للمساقات اللي مسجلينها لما
+
+38
+00:02:58,220 --> 00:03:03,980
+تدعسوا على زر فيزيا عام ألف تمام بتفوتوا على صفحة
+
+39
+00:03:03,980 --> 00:03:08,660
+هذه فيها شغلات كتيرة جوا بتخص المادة من ضمنها هذا
+
+40
+00:03:08,660 --> 00:03:13,320
+اللي انتوا شايفينه بيكون موجود كملف PDF file تمام؟
+
+41
+00:03:13,320 --> 00:03:17,340
+شغلتانية فيها رابط مجموعة الـ WhatsApp عشان تنضموا
+
+42
+00:03:17,340 --> 00:03:24,630
+إلها تمام؟هذا الـ What's Upأنا باتواصل معاكم من
+
+43
+00:03:24,630 --> 00:03:28,770
+خلاله يعني أي معلومة بدي إياكم تعرفوها أو أي خبر
+
+44
+00:03:28,770 --> 00:03:32,770
+عن طريق الـ WhatsApp طبعا بس ماكنوش أحكوا لأنه
+
+45
+00:03:32,770 --> 00:03:36,450
+بصير تواش لما البنات يحكوا بصير تواش بين بعض يعني
+
+46
+00:03:36,450 --> 00:03:41,810
+وبالتالي أنا حاضر الكلام أنا بدي التعليمات عنها
+
+47
+00:03:41,810 --> 00:03:47,110
+وبالتالي و مرات بلزم الطالب يحكي معايا على الخاص
+
+48
+00:03:47,110 --> 00:03:53,380
+WhatsApp عشان كده هذا هو ال mobile تبعي تمامزي ما
+
+49
+00:03:53,380 --> 00:04:00,280
+حكينا إيش بدنا نشرح في فيزيا عامة ألف الجامعة في
+
+50
+00:04:00,280 --> 00:04:06,650
+الفصل الدراسيامعملاه 15 أسبوع دراسي يا بنات عادة
+
+51
+00:04:06,650 --> 00:04:11,190
+احنا بناخد منه 14 و بنخلي الأسبوع الأخير فيه
+
+52
+00:04:11,190 --> 00:04:15,510
+امتحانات للمعامل و المراسم و الشغلات اللي زي هذا
+
+53
+00:04:15,510 --> 00:04:23,790
+فاحنا غالبا هنشرح 14 أسبوع كامل في هذا ال 14 أسبوع
+
+54
+00:04:23,790 --> 00:04:29,630
+هنغطي اما 11 او 12 شعبطار شعبطار يعني باب في
+
+55
+00:04:29,630 --> 00:04:34,760
+الكتاب تمام هيك؟وبالتالي في هذه الشباتر إيش فيها
+
+56
+00:04:34,760 --> 00:04:39,820
+ابتداء من chapter رقم واحد هلاجي فيه حاجة اسمها
+
+57
+00:04:39,820 --> 00:04:44,320
+measurements and units هذا chapter خفيف دم بسيطة
+
+58
+00:04:44,320 --> 00:04:48,680
+للتسخين كلكم بتعرفوا عنه أخدتوا بصورة أو باخرى
+
+59
+00:04:48,680 --> 00:04:52,520
+احنا بنعرف في الفيزيا بننجيس ولا لأ بننجيس ايش
+
+60
+00:04:52,520 --> 00:04:56,620
+بننجيس مسافاتوبالتالي المسافة إليها وحدة ولا لأ
+
+61
+00:04:56,620 --> 00:05:03,360
+متر ولا قدم ولا ياردة ولا انش ولا ميل ولا كيلومتر
+
+62
+00:05:03,360 --> 00:05:08,500
+هذه أنظمة وبينا نجيس الكتل صحيح ولا لأ وبينا نجيس
+
+63
+00:05:08,500 --> 00:05:14,200
+الزمن إذا الطول والكتلة والزمن هذه هي الوحدات
+
+64
+00:05:14,200 --> 00:05:19,000
+الأساسية لعلم الميكانيكا تمام كيف بنجيسها إليها
+
+65
+00:05:19,000 --> 00:05:24,260
+أنظمة هنحكي عنهاتمام؟ و زي لما نقول بالله في
+
+66
+00:05:24,260 --> 00:05:26,680
+الرياضيات بيقولوا X بتساوي خمسة ماحد بيقولهم إيش
+
+67
+00:05:26,680 --> 00:05:30,240
+اللي سويته X بتساوي خمسة خلاص معلومة كاملة في
+
+68
+00:05:30,240 --> 00:05:32,700
+الفيزيا لما واحد يقول X بتساوي خمسة بيقوله خمسة
+
+69
+00:05:32,700 --> 00:05:38,000
+إيش؟ خمسة كيلومتر ولا خمسة جيول؟هل الـ Joule زي
+
+70
+00:05:38,000 --> 00:05:41,780
+الـ Kilometer؟ لأ و لا لـ Newton إذا معناته أنت
+
+71
+00:05:41,780 --> 00:05:45,760
+عشان تديني المعلومة الكاملة بعد خمسة حطلي حاجة
+
+72
+00:05:45,760 --> 00:05:50,480
+عشان أفهم عليك أنت عن إيش بتتحدث فالوحدة هي الـ
+
+73
+00:05:50,480 --> 00:05:55,760
+Top الفيزيائي اللي بنلبسه للكمية عشان نفهم عن إيش
+
+74
+00:05:55,760 --> 00:05:59,140
+بنحكي هذه معناتها Measurements and Units طب أنتوا
+
+75
+00:05:59,140 --> 00:06:03,380
+شايفين أنا بحكي عربي ولا لأ؟ والكلام؟ ما تخافوش من
+
+76
+00:06:03,380 --> 00:06:06,840
+الإنجليزياحنا هنضلنا نحكي مع بعض عربي لكن
+
+77
+00:06:06,840 --> 00:06:11,160
+امتحاناتنا بالإنجليزي والكتابنا بالإنجليزي ال
+
+78
+00:06:11,160 --> 00:06:14,060
+slides بالإنجليزي كله بالإنجليزي لكن انتوا بكرا
+
+79
+00:06:14,060 --> 00:06:16,820
+بصيروا أشهر من تعاون بريطانيا بالإنجليزي اتخافوش
+
+80
+00:06:16,820 --> 00:06:20,980
+يعني هذه المشكلة تبعت الإنجليزي بتنظي معاكم بس
+
+81
+00:06:20,980 --> 00:06:25,020
+مجرد أسبوع بعدين بصيروا خبرة بالإنجليزي و بالشغلات
+
+82
+00:06:25,020 --> 00:06:27,880
+اللي بتلزمنا يعني احنا بالأخر من عشان نكون شيكسبير
+
+83
+00:06:27,880 --> 00:06:31,980
+في الإنجليزيلأ شغلات بسيطة و انتوا بتعرفوا أغلبها
+
+84
+00:06:31,980 --> 00:06:37,380
+يعني لما أقول ايش .. ايش رمز القوة في التوجيه كان؟
+
+85
+00:06:37,380 --> 00:06:41,420
+F من وين اجدها؟ من Force من بدل ان نقول قوة من
+
+86
+00:06:41,420 --> 00:06:46,160
+الصين نقول Forceالسرعة كنت برمز V جاي من كلمة
+
+87
+00:06:46,160 --> 00:06:49,560
+Velocity حتسمعوا مني Velocity بس هاد هي و لما
+
+88
+00:06:49,560 --> 00:06:53,260
+تسمعوها مرتين تلاتة مش بتحفظوها فتخافوش من ال
+
+89
+00:06:53,260 --> 00:06:56,440
+English يعني و هذا مابناش نحفظه ولا حاجة ميجارمنس
+
+90
+00:06:56,440 --> 00:07:04,590
+من قياس units وحدات تمام؟ حلوهذا العنوان شبتر واحد
+
+91
+00:07:04,590 --> 00:07:08,010
+احنا بنعدوش هناخده يوم التنين و يوم الأربعة و
+
+92
+00:07:08,010 --> 00:07:11,270
+نتخلص منه هدى مقدم و زي ما اقول بكون كسخين
+
+93
+00:07:11,270 --> 00:07:15,890
+بنتبرهوش بس هيك عشان نتعرف على بعض و نشجع بعض و
+
+94
+00:07:15,890 --> 00:07:19,970
+نشوف ان المادة سهلة و شغلات بسيطة كده من السنة
+
+95
+00:07:19,970 --> 00:07:25,900
+اللي جاي بنخش بالجدlinear motion linear من line
+
+96
+00:07:25,900 --> 00:07:31,640
+ايش يعني line خط motion حركة فالحركة الخطية يعني
+
+97
+00:07:31,640 --> 00:07:36,120
+ايش حركة خطية حركة في اتجاه واحد اتجاه واحد يعني
+
+98
+00:07:36,120 --> 00:07:40,960
+line طبعا لما نيجي نذكر بعض يا بنات ذاكرين هذا
+
+99
+00:07:40,960 --> 00:07:47,940
+القانون ذاكره
+
+100
+00:07:47,940 --> 00:07:54,930
+هنا هذا قانونبتحكم في الحركة في خط مستقيم بس بشرط
+
+101
+00:07:54,930 --> 00:07:58,130
+ان تكون التسارق ثابت الشي هو التسارق هي
+
+102
+00:07:58,130 --> 00:08:03,110
+acceleration acceleration عشان كده يا ماخد ال a و
+
+103
+00:08:03,110 --> 00:08:07,730
+ال t ال time و ال v velocity final و initial نهائي
+
+104
+00:08:07,730 --> 00:08:11,530
+و ابتدائي فبدأنا ناخده بالتفصيل و نحل عليه بعض
+
+105
+00:08:11,530 --> 00:08:15,870
+الأسئلة زي السقوط الحر ذاكرينه السقوط الحر حركة
+
+106
+00:08:15,870 --> 00:08:21,350
+بتجه واحدبس عمودي الصيارة بتمشي أفقي صح ولا لأ؟
+
+107
+00:08:21,350 --> 00:08:28,310
+إذا هذه خط وهذا خط تمى بقت كده بقولي لما تخش توسع
+
+108
+00:08:28,310 --> 00:08:33,990
+عن حركة الخطية و بتحكي عن حركة في أكتر من خط بلزمك
+
+109
+00:08:33,990 --> 00:08:41,680
+شغلة بلزمك إنه في كمياتتعتبر مش كميات زي الزمن زي
+
+110
+00:08:41,680 --> 00:08:45,720
+السرعة و زي القوة متجهة وبالتالي لما تيجي تتعامل
+
+111
+00:08:45,720 --> 00:08:50,240
+معاها بدك تنتبه خمسة زائد خمسة بيساويش عشرة صحيح
+
+112
+00:08:50,240 --> 00:08:53,600
+ولا لأ؟ يعني أربعة زائد تلاتة ممكن تصيل خمسة بطلت
+
+113
+00:08:53,600 --> 00:08:58,190
+سبعةوبالتالي هذه الكميات طب كل الكميات الفيزيائية
+
+114
+00:08:58,190 --> 00:09:02,690
+هيك بقوله لأ في كميات عادية زي الزمن زي الطاقة هذه
+
+115
+00:09:02,690 --> 00:09:07,230
+كميات قياسية لكن في كميات ما تجمعها بدك تنتبه طب
+
+116
+00:09:07,230 --> 00:09:10,490
+كيف بدنا نعمل؟ بدنا نتعلمها إيش هي الكميات اللي
+
+117
+00:09:10,490 --> 00:09:15,860
+بدها انتباه؟ بسميها كميات متجهةوتانية كميات قياسية
+
+118
+00:09:15,860 --> 00:09:20,380
+vectors يعني كميات متجهة scalars يعني كميات قياسية
+
+119
+00:09:20,380 --> 00:09:24,540
+هنتعلم كيف نجمحها كيف نطرحها كيف نضربها كل هذه
+
+120
+00:09:24,540 --> 00:09:29,540
+الشغلات هنتعلمها في chapter كامل chapter تلاتة بعد
+
+121
+00:09:29,540 --> 00:09:33,200
+كده بعد ما نصير خبرة بها كده أمور بيقولي هجت من
+
+122
+00:09:33,200 --> 00:09:37,770
+فوتك على الحركةالمستوية او بالـ two dimensions two
+
+123
+00:09:37,770 --> 00:09:41,990
+dimensions يعني بعدين سينوساد تمام؟ بعدين two
+
+124
+00:09:41,990 --> 00:09:45,870
+dimension هذه اقتصار هذه two و هذه dimension يعني
+
+125
+00:09:45,870 --> 00:09:51,470
+بعدين بعدين سينوساد motion هي motion مرت هنا و
+
+126
+00:09:51,470 --> 00:09:54,750
+motion مرت هنا مقرب مانقولش معنى motion خلاص
+
+127
+00:09:54,750 --> 00:10:00,510
+ماعرفش معنى motion فالإنجليزي مش معضل تمام يا
+
+128
+00:10:00,510 --> 00:10:03,920
+بنات؟ two dimensional motionالـ Two Dimensional
+
+129
+00:10:03,920 --> 00:10:09,880
+Motion فيه حركتين مشهورات حركة المقذوفات سمعت فيها
+
+130
+00:10:09,880 --> 00:10:13,280
+هذه الـ Two Dimensional Motion مش فيه سينوساط و
+
+131
+00:10:13,280 --> 00:10:18,360
+الحركة الدائرية سمعت فيها برضه حركة مستوية حناخدها
+
+132
+00:10:18,360 --> 00:10:23,040
+تفصيلاإذن الـ Projectile Motion حركة المقضوفات
+
+133
+00:10:23,040 --> 00:10:28,800
+هنخدها بالتفصيل لأنه أشهر أنواع الحركة في بعدين هي
+
+134
+00:10:28,800 --> 00:10:31,880
+والحركة الدائرية بس الدائرية أنواع الصحة كتير
+
+135
+00:10:31,880 --> 00:10:35,940
+Relative Motion شوفوا كلمة motion قادرة بتتكرر
+
+136
+00:10:35,940 --> 00:10:40,480
+طبعا محنى ميكانيكا حركة Relative Motion الحركة
+
+137
+00:10:40,480 --> 00:10:44,880
+النسبية وانتوا جايين من الدار على الجامعة و
+
+138
+00:10:44,880 --> 00:10:48,160
+بتطلعوا من شبّاك السيارة وسرحين بتلاقيوا الشجرة
+
+139
+00:10:48,160 --> 00:10:52,320
+قاعدة بيجريصح ولا لأ؟ بتجري وراكم، بتشتيها
+
+140
+00:10:52,320 --> 00:10:56,280
+المعاكس، مع أن الشجر واقف، لكن هو واقف بالنسبة لو
+
+141
+00:10:56,280 --> 00:10:59,120
+واحد واقف الأرض، لكن بالنسبة لو واحد بتحرك في
+
+142
+00:10:59,120 --> 00:11:02,760
+السيارة، صار يتحرك، إذا دي ما تسميها سرعة نسبية،
+
+143
+00:11:02,760 --> 00:11:08,000
+إذا الراصد إذا تتغير، تتغير كمية الفيزاقية، السفر
+
+144
+00:11:08,000 --> 00:11:14,940
+بصله قيمة، تمام؟ هذه ما تسميها حركة نسبية، تمام؟
+
+145
+00:11:14,940 --> 00:11:22,140
+بعد كده،جالوا الميكانيكا إلها أبوه The father of
+
+146
+00:11:22,140 --> 00:11:27,340
+mechanics مين أبوها؟ نيوتن النيوتن له قوانين ها
+
+147
+00:11:27,340 --> 00:11:33,180
+كام واحد؟ تلاتة هدول التلاتة بدنا نعيدهم وطبعا مش
+
+148
+00:11:33,180 --> 00:11:37,720
+هنقولكم اذكروا قوانين نيوتن هنقولكم افهموا قوانين
+
+149
+00:11:37,720 --> 00:11:43,460
+نيوتن بكوا تطبقوهاتمام؟ فـNewton's laws of motion
+
+150
+00:11:43,460 --> 00:11:47,280
+قوانين نيوتن التلاتة لهم chapter كامل من أهم
+
+151
+00:11:47,280 --> 00:11:52,160
+الشباتر لأنه هو أبو الميكانيكا بدون هذه القوانين
+
+152
+00:11:52,160 --> 00:11:57,340
+فهمها الواحد مايكونش أخد ميكانيكا تمام؟ بعد كده
+
+153
+00:11:57,340 --> 00:12:02,920
+هناخد نوع من أنواع القوة المهمة وهي قوة الاحتكاك
+
+154
+00:12:02,920 --> 00:12:10,300
+سمعتوها؟وهنا ما هناخدها بالتفصيل بعد كده هناخد الـ
+
+155
+00:12:10,300 --> 00:12:14,860
+Circular Motion السيارة هي ماشية ايدي الماشية حركة
+
+156
+00:12:14,860 --> 00:12:20,810
+خطية خشة دوار بتاع في الدوار تصير حركة دائريةالها
+
+157
+00:12:20,810 --> 00:12:26,530
+أنظمة وقوانين مختلفة في تسارع مركز سمعت فيه وقوة
+
+158
+00:12:26,530 --> 00:12:31,370
+مركزية هذا تابع للقوة الدائرية او الدورانية
+
+159
+00:12:31,370 --> 00:12:37,510
+circular motion بعدين work شغل سمعت فيه كيناتك
+
+160
+00:12:37,510 --> 00:12:42,630
+energy طاقة حركة ايش واحدة الشغل؟ ايش واحدة طاقة
+
+161
+00:12:42,630 --> 00:12:46,390
+الحركة؟ Bravo ما زال هاد جول و هاد جول يعني امهم
+
+162
+00:12:46,390 --> 00:12:50,830
+واحد ولا لأ؟الهم نفس الجنس ماذال امهم واحدة اذا
+
+163
+00:12:50,830 --> 00:12:55,230
+لازم يكون بينهم علاقة في نظرية مشهورة بتربط الشغل
+
+164
+00:12:55,230 --> 00:12:59,410
+مع طاقة الحركة مظهرته لا ؟ هذه هناخدها تفصيلة
+
+165
+00:12:59,410 --> 00:13:03,290
+بعدين بيقول في كمان نوع سمعنا فيه عن الطاقة طاقة
+
+166
+00:13:03,290 --> 00:13:09,870
+الوضع ايش قانونها؟مجي اتش potential energy طاقة
+
+167
+00:13:09,870 --> 00:13:14,390
+الرضيع هناخده شوف انا جيت لحد الان في عنوان مارش
+
+168
+00:13:14,390 --> 00:13:20,580
+علينا الحمد لله كل مواضيع مارت عليناتمام؟ بعد كده
+
+169
+00:13:20,580 --> 00:13:24,880
+هناخد قانون عالمي مهم واسمعنا فيه زمان و ما زلنا
+
+170
+00:13:24,880 --> 00:13:30,300
+بنسمع فيه مبدأ حفظ الطاقة conservation of energy
+
+171
+00:13:30,300 --> 00:13:36,400
+مبدأ حفظ الطاقة مبدأ عالمي يطبق عليه شغلات كتيرة و
+
+172
+00:13:36,400 --> 00:13:40,420
+يستخدم في حلول كتير من مسائل بعدين سمعتوا في كلمة
+
+173
+00:13:40,420 --> 00:13:45,930
+زخمLinear Momentum زخم يعني Momentum Linear خطي
+
+174
+00:13:45,930 --> 00:13:52,610
+الزخم الخطي مظبوط ولا إيش رمزه برافع عليكم P تمام
+
+175
+00:13:52,610 --> 00:13:59,970
+حلو هناخده بعدين قال ليه في كل جن تصادم أكمنه برق
+
+176
+00:13:59,970 --> 00:14:02,850
+ليه؟
+
+177
+00:14:03,550 --> 00:14:08,450
+التالت فرعيه؟ فيه marine و غير marine و بس هل جيت
+
+178
+00:14:08,450 --> 00:14:13,010
+الغير marine نوعين بيهمش بس هو غير marine فالنوعين
+
+179
+00:14:13,010 --> 00:14:17,030
+هم الأساسيين بين ال marine و غير ال marine فيه
+
+180
+00:14:17,030 --> 00:14:20,350
+خلاف ان هاي القيانت ال energy محفوظة ولا لأ صح ولا
+
+181
+00:14:20,350 --> 00:14:29,850
+لأ عشان كده بنقول نوعين فقط حلو الدفع impulse ال
+
+182
+00:14:29,850 --> 00:14:35,000
+impulse والزخمجرايب ولا لأ؟ جرايب تمام؟ هايكم
+
+183
+00:14:35,000 --> 00:14:41,940
+شاطري؟ Center of Mass مركز الكتلة كيف يعني؟ قاللي
+
+184
+00:14:41,940 --> 00:14:46,200
+هذه الإجزازة لو إيديك بقى كتعلجها و تتزن مش
+
+185
+00:14:46,200 --> 00:14:50,660
+بتتعلجها من نقطة مش بالضرورة تكون من النص لأنها دي
+
+186
+00:14:50,660 --> 00:14:54,780
+متكونش في النص ليش؟ لأنها دي أخف منها دي وبالتالي
+
+187
+00:14:54,780 --> 00:14:58,800
+عند نقطة تم تتزن طب هذه كيف تحسبها؟ بنتعلم كيف
+
+188
+00:14:58,800 --> 00:15:02,740
+تحسبهاتمام يا بنات؟ كيف نجيب؟ يعني نفترض أنه في
+
+189
+00:15:02,740 --> 00:15:11,000
+عندى حشبة زي هيك تتوقعوا تتزل من النص؟ لأ بتكون
+
+190
+00:15:11,000 --> 00:15:14,300
+أقرب للتجول صح ولا .. يعني لو كان هاي النص بتتقع
+
+191
+00:15:14,300 --> 00:15:18,080
+هنا طبعا في الآخر في قوانين كيف أجيبها بالظبط هذا
+
+192
+00:15:18,080 --> 00:15:22,800
+من أن تتعلموا تمام؟ احنا ماشيين دلوقت chapter ..
+
+193
+00:15:22,800 --> 00:15:26,640
+chapter .. chapter تقريبا يعني احنا هنا وصلنا لأخر
+
+194
+00:15:26,640 --> 00:15:32,600
+فصل الحاجات شوي شوي تمام؟هناخد many particle
+
+195
+00:15:32,600 --> 00:15:36,560
+systems يعني بيقول لي في مرات عندك system نظام
+
+196
+00:15:36,560 --> 00:15:40,880
+متكون مش مش مجسم واحد من عدة عيسام كيبك تتعامل معه
+
+197
+00:15:40,880 --> 00:15:46,000
+هذا اللي بدنا نتعلمه بعدين برجع للحركة الدورانية
+
+198
+00:15:46,000 --> 00:15:51,720
+الهواية بتعرفوها تتحركو ولا تتحركش بتصري الشجعية
+
+199
+00:15:52,360 --> 00:15:56,240
+بيضلها الدور بيضلها الدور مظبوطا لأ لكن حركة هذه
+
+200
+00:15:56,240 --> 00:16:00,480
+بيسميها حركة دورانية الها قوانينها و الها شغلاتها
+
+201
+00:16:00,480 --> 00:16:05,820
+بإننا نتعلمها تمام جالي طيب ما زال في انت حكيت
+
+202
+00:16:05,820 --> 00:16:10,600
+حركة دائرية أو حركة دورانية وسمعون بالسرعة الزاوية
+
+203
+00:16:10,600 --> 00:16:14,820
+سمعتوا فيها؟ ايش رمزها؟ يا عزيزي مش بتقولوا كلكم W
+
+204
+00:16:14,820 --> 00:16:19,600
+يا الله Omega Omega هي عشان تشبه ال W خلونا نطلع
+
+205
+00:16:19,600 --> 00:16:27,850
+ال W هذه مظبوطا لأهاجد هاد ايش؟ هاجم شطر ايه؟ هاي
+
+206
+00:16:27,850 --> 00:16:33,910
+Alpha هي أول حرف في اللغة اليونانية وهادي Omega
+
+207
+00:16:33,910 --> 00:16:39,710
+تمام؟ وهادي؟
+
+208
+00:16:39,710 --> 00:16:47,230
+علي صوتك هادي Omega؟ بس capital Omega نشوف تاريخها
+
+209
+00:16:47,230 --> 00:16:54,210
+هاجد هدي واحدية ايش هادي؟نوتن؟ جيبناها من مين؟ من
+
+210
+00:16:54,210 --> 00:17:00,190
+اسمه صح ولا لا؟ او متكرمه قالوا بدنا ندي المقاومة
+
+211
+00:17:00,190 --> 00:17:04,630
+وحدة او إذا قالوا يلّا بنقول زي نوتن ناخد أول حرف
+
+212
+00:17:04,630 --> 00:17:11,170
+في كلمة او إيش لجوها؟ او بشعة دويرة حرف مش حلو
+
+213
+00:17:11,170 --> 00:17:14,110
+قالوا شوفوا حرف تاني راحوا دوروا على اللغة
+
+214
+00:17:14,110 --> 00:17:17,550
+اليونانية قالوا إيش المناظر للأو في اللغة
+
+215
+00:17:17,550 --> 00:17:23,430
+اليونانية؟ قالوا Omegaفأخدوا Omega فهذه أوم لما
+
+216
+00:17:23,430 --> 00:17:26,990
+تكتبوا أوم باليوناني هتكون هذه أول حرف أوم اسم
+
+217
+00:17:26,990 --> 00:17:30,290
+عالم ولا لأ؟ و هذه Omega بس هذه Small و هذه
+
+218
+00:17:30,290 --> 00:17:34,610
+Capital هذه Omega و هذه Omega تمام ارجعنا هذه سرعة
+
+219
+00:17:34,610 --> 00:17:41,490
+و هذه ال V سرعة بس هذه سرعة خطية و هذه سرعة زوية
+
+220
+00:17:41,490 --> 00:17:48,900
+صح ولا لأ طيب هذه إيش؟ و هذه إيش؟هدي زخم و هدي زخم
+
+221
+00:17:48,900 --> 00:17:55,980
+صح ولا لا؟ بس هدا زاوي و هدا خطي طيب هدي إيه؟ و
+
+222
+00:17:55,980 --> 00:18:06,360
+هدي ألفة صح؟ طيب هدي و هدي اللي هي بالظبط ممكن
+
+223
+00:18:06,360 --> 00:18:14,420
+نسميها إيش و كأنه كتلة دورانية أخر حاجة هدي و تاول
+
+224
+00:18:14,420 --> 00:18:18,250
+عزمبيقولي طب بينهم علاقات بقوله بينهم علاقات و
+
+225
+00:18:18,250 --> 00:18:22,930
+بنشتقهم فبالتالي Angular يعني زاوية من Angle Angle
+
+226
+00:18:22,930 --> 00:18:27,850
+زاوية Angular زاوية ال Translational هي الانتقالية
+
+227
+00:18:27,850 --> 00:18:31,250
+أو الخطية تقدر تقوله ال Quantities بيقوللي ايش
+
+228
+00:18:31,250 --> 00:18:38,110
+العلاقة بين الكميات الخطية و الكميات الزاوية تمام؟
+
+229
+00:18:38,110 --> 00:18:43,590
+هناخدهم و نشتقهم مع بعض و أغلبهم عارفينهم انتوا ال
+
+230
+00:18:43,590 --> 00:18:47,830
+Torque اللي تاوي قلت عنه تاوأه مهوتة و هدا شغلة
+
+231
+00:18:47,830 --> 00:18:52,850
+مهمة لأن المسبب للحركة في الحركة الخطية هي F
+
+232
+00:18:52,850 --> 00:18:58,550
+والمسبب للحركة الدورانية هي torque تمام؟ بعدين قال
+
+233
+00:18:58,550 --> 00:19:02,650
+لي قوانين الحركة الدورانية بدك تشتقليها من أول و
+
+234
+00:19:02,650 --> 00:19:08,430
+جديد dynamics كيف تتحرك كل حركة دورانية هناخدها ال
+
+235
+00:19:08,430 --> 00:19:12,790
+moment of inertia لها تفصيل اللي هي Iهذه moment of
+
+236
+00:19:12,790 --> 00:19:16,370
+inertia وكيف نحسبها لها قوانين بدنا ناخدها
+
+237
+00:19:16,370 --> 00:19:21,770
+بالتفصيل مثل كتلة تمشي تمام rotational kinetic
+
+238
+00:19:21,770 --> 00:19:24,670
+energy قاللي ال kinetic energy بنعرف أنها نص MV
+
+239
+00:19:24,670 --> 00:19:30,290
+تربيع صح؟ طب الهواية قاللي لأ لها قانون مختلف لأنه
+
+240
+00:19:30,290 --> 00:19:34,450
+دورانية مظبوط ولا لأ؟ طبعا بعدين بنشوف قوانين احنا
+
+241
+00:19:34,450 --> 00:19:37,630
+مابناش نجيب قوانين دلوقتي بيقولوا طب مبدأ الطاقة
+
+242
+00:19:37,630 --> 00:19:43,470
+في الحركة الدورانية عدلية بدنا نعيده تمام؟Angular
+
+243
+00:19:43,470 --> 00:19:50,230
+momentum زخم زاوي زخم زاوي اللي هو L هناخده قال طب
+
+244
+00:19:50,230 --> 00:19:53,910
+هذه مرات بيكون preserved يعني محفوظ Conservation
+
+245
+00:19:53,910 --> 00:19:58,350
+of angular momentum وقتيش بيكون محفوظ وإيش تطبيقات
+
+246
+00:19:58,350 --> 00:20:05,250
+حفظ كمية التحرك تمام؟بعدين قال لي الاتزان
+
+247
+00:20:05,250 --> 00:20:10,330
+الاستاتيكي اتزان و طبعا الاتزان هو أساس علم
+
+248
+00:20:10,330 --> 00:20:15,780
+الهندسة المدنية هم لما يعملوا جسر بينفع يجلبلأ لما
+
+249
+00:20:15,780 --> 00:20:20,840
+يعملوا مبنى هبّت ريح يروح فالتالي لازم يعملوا يكون
+
+250
+00:20:20,840 --> 00:20:24,400
+فيه توازن في كل إشي فهذا علم كبير احنا بناخد شبطر
+
+251
+00:20:24,400 --> 00:20:29,120
+هم بياخدوا مواد في هذا العلم تمام center of
+
+252
+00:20:29,120 --> 00:20:34,240
+gravity بتشبه center of mass بيجيها تفصيلا elastic
+
+253
+00:20:34,240 --> 00:20:37,740
+properties of solids قاللي المهندس بدي استخدم
+
+254
+00:20:37,740 --> 00:20:43,270
+الحديد وانحاس والألمنيوم طب هذهبتظل زي ما هي في
+
+255
+00:20:43,270 --> 00:20:48,070
+الحرارة بتتغير في مع الشد ولا مع الضغط بتتغير طب
+
+256
+00:20:48,070 --> 00:20:54,350
+كيف تتغير و وقت إيش بتتغير هذه إلها قوانينها لحد
+
+257
+00:20:54,350 --> 00:20:59,070
+الآن أكيد هناخده هذا ال chapter الأخير اللي مرات
+
+258
+00:20:59,070 --> 00:21:04,070
+بنقول مرات بنلحقهوش عن إيش بحكي ال fluid mechanics
+
+259
+00:21:04,070 --> 00:21:09,310
+ميكانيكا السوائل أو المواعع إيش فيها اللي في حاجة
+
+260
+00:21:09,310 --> 00:21:13,710
+بيسموها pressure الضغطتمام؟ كل ما نزلته تحت في
+
+261
+00:21:13,710 --> 00:21:18,830
+الميّه ضغط مزيد تمام؟ جاللي في حاجة بيسموها مبدأ
+
+262
+00:21:18,830 --> 00:21:23,770
+Pascal سمعتوا فيه؟ تمام و جاللي في حاجة بيسموها ال
+
+263
+00:21:23,770 --> 00:21:29,360
+buoyant force أو قوة الطفوأو الدفع تبع الميّه تمام
+
+264
+00:21:29,360 --> 00:21:35,000
+وهذه بالحجها Archimedes principle صح ولا لأ و برضه
+
+265
+00:21:35,000 --> 00:21:40,500
+بيلحجها بنفس الموضوع continuity equation معادلة
+
+266
+00:21:40,500 --> 00:21:45,460
+الاستمرارية معادلة مشهورة تمام وفي Bernoulli
+
+267
+00:21:45,460 --> 00:21:49,160
+equation معادلة Bernoulli Bernoulli اسم عالي ان
+
+268
+00:21:49,160 --> 00:21:54,420
+شاء الله نقدر نلحجها تمام هذا course objectives
+
+269
+00:21:57,520 --> 00:22:03,700
+المطلوب من هذا الـ Chapter مش مهم كتير تقرأوه وهذا
+
+270
+00:22:03,700 --> 00:22:09,080
+القالع أو إيش اللي بنحققه نيجي للمهم إحنا بندرس من
+
+271
+00:22:09,080 --> 00:22:13,220
+كتاب مشهور ولمّا أقول مشهور يعني مشهور في كل
+
+272
+00:22:13,220 --> 00:22:17,860
+العالم مش في غزة يعنيبتلاقي انت الطالب اللي بتدرس
+
+273
+00:22:17,860 --> 00:22:21,400
+في جامعة أسامية في غزة وطالب بتدرس في Los Angeles
+
+274
+00:22:21,400 --> 00:22:27,300
+وطالب بتدرس في Tokyo ولا واحدة في بكين كلهم تقريبا
+
+275
+00:22:27,300 --> 00:22:31,800
+من نفس الكتاب بتدرسه تقريبا وهذا الكتاب يمكن أكتر
+
+276
+00:22:31,800 --> 00:22:35,660
+من 60% من جامعة العالم باعتمدوا هذا الكتاب هذا
+
+277
+00:22:35,660 --> 00:22:40,400
+كتاب عالمي موجود طول عمره من أيام انا كنت جادكم
+
+278
+00:22:40,400 --> 00:22:45,940
+physics اسمه for scientists and engineersهذا اسم
+
+279
+00:22:45,940 --> 00:22:50,520
+الكتاب مؤلفينه Sir Wayne Jewett وهذه الطبعة
+
+280
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+fundamentals of physics أساسيات علم الفيزيا
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+100، بتضربها في 100، وبتجمع وبتضرب بقى كام ساعة،
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+321
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+329
+00:26:42,220 --> 00:26:47,340
+الطالب كل علامة بعلامتها حسب كيف تعتمد كيف بينا
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+كلنا نجيب 20 من 20 منها هذه عليها 20 درجة 20% من
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+335
+00:27:17,460 --> 00:27:23,060
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+افتحه متاح غالبا بعمل يوم خميس بافتحه بعد صلاة
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+الفجر الساعة ستةبيضلوا ماشي مفتوح لساعة 12 في
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+الليل بس مش مفتوح كل هذه الفترة كل واحد بيجي بفوت
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+346
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+خمس سنديك خمس سنديكهي واحد، تنين، تلاتة، أربعة،
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+خمسة. كل Chapter انجسمينه خمس مواضيع. في هذا
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+الموضوع الأول حطين فيه حوالي تلاتين، أربعين سؤال.
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+التالي مانوع يجيبه من هنا يجيبه من هنا السؤال
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+361
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+إذا هذا سهل كلكم هيجيكم سؤال زيه و غالبا عشان
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+هدولي Quizات سهلين لأنه في داري وكل وقتي وكل حبابي
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+حواليا يعني مافيش امتحان وخايفة وجالبي بدهم لأ
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+quizzes one at the end of each chapter كل chapter
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+عليه quiz each quiz كل quiz contains five multiple
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+electronically by moodleعلى الجهاز the best eight
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+محدد من اليوم 13.11 شفته في الجدول سمعتوا ايش او
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+لجميع الطالبات اللي بياخدوا نفس المادةهتلاقوا الـ
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+Calculus إليه موعد و الفيزيا إليها موعد بنقولكم
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+عنه برضه بنثبت إيش المواد اللي هتنزل هذا امتحان
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+فيه مراقبين و ورقة و تعملوا الامتحان و بنقولكم أكم
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+415
+00:33:05,720 --> 00:33:10,100
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+416
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+417
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+الآخر احنا بالحديد احنا وياكم بنشوف باقى المدرسين
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+418
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+419
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+420
+00:33:25,710 --> 00:33:30,230
+بعلامته وإن شاء الله تكون كلها حلوة هذه عالية 30%
+
+421
+00:33:30,230 --> 00:33:34,990
+من الدرجة وهذا برضه باعتبره أنا فرصة طالب يجيب فيه
+
+422
+00:33:34,990 --> 00:33:39,910
+علامات ليش؟ كلهم خمس شباتر وكنا متابعين أول بأول
+
+423
+00:33:39,910 --> 00:33:45,710
+وبالتالي بنقدر عليه تمام يا بنات؟ هاي صار 50% نجي
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+424
+00:33:45,710 --> 00:33:53,980
+للـFinal Final عليه 50%و هذا بتدخل فيه كل الشباتر
+
+425
+00:33:53,980 --> 00:33:59,200
+من أول ما أخدنا لما خلصنا و بيكون هذا مدته ساعة
+
+426
+00:33:59,200 --> 00:34:03,880
+one hour exam هذا two hour exam مائة و عشرين
+
+427
+00:34:03,880 --> 00:34:09,880
+minutes ساعتين طبعا لأنه بيشمل كل المادة وبالتالي
+
+428
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+برضه بيكون في نهاية شهر واحد مكتوب تاريخه عندكم
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+429
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+اظن تمانية واحد مكتوب عندكم في الجدول تطلعت على
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+430
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+جدولكمأعمل واحد و واحد بتطلع أول ما أخد الشدوى ليش
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+431
+00:34:21,100 --> 00:34:23,660
+ورا .. بيولدوا بتطلع إيش هال .. هالخرابيش
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+432
+00:34:23,660 --> 00:34:32,020
+المكتوبين .. كل شيء إله معنى .. بيحكي .. إلى وقت
+
+433
+00:34:32,020 --> 00:34:37,300
+أفرج .. تاني شي .. بعدين .. تمام .. إنت سنة تانية
+
+434
+00:34:37,300 --> 00:34:42,360
+.. أه .. تمام .. إلى وقت أفرج .. القصة ده نبتثلت
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+435
+00:34:42,360 --> 00:34:43,780
+كلمة في عمال الصلاة والأولى لسه بيعرفوش هذه
+
+436
+00:34:43,780 --> 00:34:46,120
+المصطلحات .. خلينا .. بيحكي يا بنتين ..
+
+437
+00:34:50,030 --> 00:34:56,650
+أصابعك طول واحد لأ في شبتر طويل وشبتر قصير احنا هو
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+438
+00:34:56,650 --> 00:34:59,570
+انت بتفكر انهم جاذبوا عيد ولا ممكن يكونوا جاذبوا
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+439
+00:34:59,570 --> 00:35:02,610
+عيد فبالتالي انا مش حافظك على كام صفحة فيه بقولك
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+440
+00:35:02,610 --> 00:35:05,730
+شبتر طويل وشبتر قصير يعني الشبتر الأول اللي بنسخن
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+441
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+فيه قصير أما شبتر طبعا يوتن اللي هو أقولها طويل
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+442
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+443
+00:35:17,910 --> 00:35:19,710
+تمام أحكيها
+
+444
+00:35:23,720 --> 00:35:27,160
+Okay مكتوبة بالإنجليزي تحكي بالعربي؟ احكي مش
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+445
+00:35:27,160 --> 00:35:29,920
+حقيقية لزمان كنت تكتب يعني V بالعربي؟ ايش ممكن
+
+446
+00:35:29,920 --> 00:35:32,400
+تكتب بالإنترنت؟ V بالصورة الخمسة كيف ممكن تكتبها
+
+447
+00:35:32,400 --> 00:35:35,200
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+448
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+تخافوش من الإنجليزي ما تخافوش من الإنجليزي بالمرة
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+449
+00:35:38,180 --> 00:35:40,660
+انتوا اول مرة تفكروا في شيء لا انتوا في العالم
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+450
+00:35:40,660 --> 00:35:44,980
+دخلتوا علوم او هندسة اكملوا بدا ماهم كان امك او
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+451
+00:35:44,980 --> 00:35:50,100
+ابوك اخدوا ومشي الامور سهلة سهلة كتير اقصد من ما
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+452
+00:35:50,100 --> 00:35:55,870
+تتوقعي وانا بحكفاهماني يعني؟ اه مابكيش انجليزي و
+
+453
+00:35:55,870 --> 00:36:02,250
+هيك عند الله تمام؟ حلو طبعا احنا عشان انتوا
+
+454
+00:36:02,250 --> 00:36:08,910
+نساعدكم انكم تدرسوا و تفهموا عاملين للمادة مناقشة
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+455
+00:36:08,910 --> 00:36:12,990
+شفتوها في الجدول في لقاء أسبوعي هذه المناقشة
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+456
+00:36:12,990 --> 00:36:16,730
+بيجيبكم معيدة وهذه المعيدة هي الأولى على القسم
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+457
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+458
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+459
+00:36:23,960 --> 00:36:29,140
+الأسئلة ممكن سؤال مايظبطش معاكم، بدكم حد يساعدكم،
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+460
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+بيجي المعيد بحل بعض الأسئلة، هذا برضه المعيد
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+461
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+ماكفاش، بدكم إياني أنا، فإحنا حاطين ساعات مكتبية
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+462
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+اللي بدها أستاذ يشوف ويستسأله انا بالنسبة لكم حاط
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+463
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+يوم السبت من ال 11 ال 12 ان شاء الله يكون متاح
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+464
+00:36:49,300 --> 00:36:53,960
+يعني انتوا فاضين مافيش عندكم محاضرات وهي غرفتي
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+465
+00:36:53,960 --> 00:37:01,620
+C236 واحدة عندها اشي تعالوا على المكتب مزال أنا
+
+466
+00:37:01,620 --> 00:37:07,870
+موجود في المكتب وفاضي أهلا وسهلا فيكم بأي وقتتمام؟
+
+467
+00:37:07,870 --> 00:37:16,050
+هذا وقت رسمي احكي الاسئلة
+
+468
+00:37:16,050 --> 00:37:20,350
+اللي احنا محددين هي اليك اتسانى شوية هاي زيكم
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+469
+00:37:20,350 --> 00:37:26,230
+فلتقوا من هذا ال emails هه الكتاب اللي توي حكيت
+
+470
+00:37:26,230 --> 00:37:30,330
+عنه انا اللي موجود في مكتبة الطالب في كل نهاية
+
+471
+00:37:30,330 --> 00:37:34,990
+chapter فيه اسئلة كتير فيه مرات بصلمية وكذا سؤال
+
+472
+00:37:34,990 --> 00:37:44,000
+تمام؟المنطقي أو الـ Ideal أو الشغلة الميثالية ان
+
+473
+00:37:44,000 --> 00:37:47,360
+واحد يحلهم كلهم احنا بتقوله احنا مش طمعين بدناش
+
+474
+00:37:47,360 --> 00:37:55,560
+تحلهم كلهممختارينكم جزء منهم ايش مسميينهم الاسئلة
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+475
+00:37:55,560 --> 00:37:59,320
+الموصى بحلها الاسئلة الموصى بحلها هي recommenders
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+476
+00:37:59,320 --> 00:38:02,920
+اذا بتسموها recommendation letter رسالة توصية اذا
+
+477
+00:38:02,920 --> 00:38:06,020
+اسمها توصية recommended problems اللي احنا بنوصي
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+478
+00:38:06,020 --> 00:38:09,480
+انكم تحلوها ايش يعني؟ يعني هذا الحد الأدنى اللي
+
+479
+00:38:09,480 --> 00:38:14,060
+لازم تحلوههذه الحد الأدنى لازم اتحلوه هذه أقام
+
+480
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+الأسئلة شوفوا انت لو تطلعوا تعدوا من المية يمكن
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+481
+00:38:17,600 --> 00:38:21,500
+مختارين احنا اما التلت او الربع بس عشان اتحلوهم
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+482
+00:38:21,500 --> 00:38:25,440
+ماكنتش ممكن اتحلهم هدول حاجات احنا امتحانا نصي يوم
+
+483
+00:38:25,440 --> 00:38:31,780
+تمانية تلتاش احد عاش صح ولا تلتاش احد عاش مش يوم
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+484
+00:38:31,780 --> 00:38:38,210
+اتناش نبدأ نحالبتخلصوش، بنفعش، هوقتش الحل جالي جبل
+
+485
+00:38:38,210 --> 00:38:41,130
+ما يبدأ السبت اللي بدي يخش شبطر جديد بدي أكون خلص
+
+486
+00:38:41,130 --> 00:38:45,650
+الشبطر اللي جابله فهمتوا عليا كده؟ يعني أنا غالبا
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+487
+00:38:45,650 --> 00:38:49,970
+يوم سبت بنبدأ شبطر جديد بكون خلال الأسبوع اللي
+
+488
+00:38:49,970 --> 00:38:53,190
+جابله بدي أتحل الجمعة بدي أكون شطبط الشبطر اللي
+
+489
+00:38:53,190 --> 00:38:58,450
+جابلهخلاص حليته إذا حليته هدول بعضلاتكم لحالكم
+
+490
+00:38:58,450 --> 00:39:02,610
+بضمنلكم العلمة الكاملة لأن غالبا أسئلة امتحانات
+
+491
+00:39:02,610 --> 00:39:07,470
+بتكون منهم غالبا بتكون من هذه الأسئلة هذه
+
+492
+00:39:07,470 --> 00:39:10,970
+الـrecommended problems والمعيد بدي أحل منهم طبعا
+
+493
+00:39:10,970 --> 00:39:14,390
+هدول كتابة بقدرش أحلهم كلهم ياريت لو أنتوا تكونوا
+
+494
+00:39:14,390 --> 00:39:17,930
+مستعدين وحليته وعرفتوا إيش الصعب تختاروا من المعيد
+
+495
+00:39:17,930 --> 00:39:23,160
+بدل ما هو لما يدرجوناش حليته نفتحتهمناماحللناش
+
+496
+00:39:23,160 --> 00:39:26,940
+حاجة، ساعته بيختار لحاله، مظبط ولا لأ؟ لكن لما
+
+497
+00:39:26,940 --> 00:39:28,940
+نقول له لأ والله السؤال الفلاني أنا حاولت أحله في
+
+498
+00:39:28,940 --> 00:39:32,600
+الدار، ماعرفش أحله، بحاول أحلكم إياه، أفضل،
+
+499
+00:39:32,600 --> 00:39:38,720
+اتفجنا؟ هذه أرقام الأسئلة اللي لازم تحلوها، لازم
+
+500
+00:39:38,720 --> 00:39:43,540
+تحلوها، حد الأدنى اللي لازم ينحل، عشان نجيب علامة
+
+501
+00:39:43,540 --> 00:39:46,360
+حلوة، تمام يا بنات؟ حلو
+
+502
+00:39:48,820 --> 00:39:56,860
+الآن هذه هي المقدمة تباعتنا احنا محاضرتنا مصورة
+
+503
+00:39:56,860 --> 00:40:04,220
+يعني فضيحة جلاجل بتتوزع تمام؟ ايش بدي منكم؟ كل
+
+504
+00:40:04,220 --> 00:40:10,180
+طالبة عندها سؤال ما ترفعش أصبحها تسألقد ما بدكم
+
+505
+00:40:10,180 --> 00:40:14,800
+اسأله وقت ما شعرتوا اني انا بحكي حاجة صراحته و
+
+506
+00:40:14,800 --> 00:40:18,780
+بطلتوا تستوعبوا واجفونى طول ما انتوا بتهزوا راسكم
+
+507
+00:40:18,780 --> 00:40:23,980
+انا بعتبركم فاهمين حتى لو بتهزوا راسكم كذب تمام
+
+508
+00:40:23,980 --> 00:40:26,820
+لأنهم مرة بطيجة عينها في عين واحدة بتعمل هيك خلاص
+
+509
+00:40:27,640 --> 00:40:32,600
+ما هي حرة تمام؟ طبعا يا بنات انت لازم تعرفوا احنا
+
+510
+00:40:32,600 --> 00:40:36,960
+طبيعتنا كبشر مختلفين عن بعض في ناس بخجلوا و في ناس
+
+511
+00:40:36,960 --> 00:40:39,500
+عندهم الجرقة ما شاء الله عليهم انا بحب اشجاري في
+
+512
+00:40:39,500 --> 00:40:45,700
+الأسئلة اللي بسميه مشاغب إيجابي ليش؟ لأنه انت لما
+
+513
+00:40:45,700 --> 00:40:48,520
+تسألت سؤال بيكون واحد تاني بيقول ياهو رضيني الحمد
+
+514
+00:40:48,520 --> 00:40:51,660
+لله اللي سأله كنت بدي اسأله بس خجلان انت بتاخد
+
+515
+00:40:51,660 --> 00:40:56,140
+ثواب بتاخد ثواب انك سألته و .. وظبطها وفي حدا
+
+516
+00:40:56,140 --> 00:40:57,280
+بيكره ياخد ثواب
+
+517
+00:41:00,000 --> 00:41:03,140
+طول ما انتوا شعرين اني انا بحكي حاجة انتوا مش
+
+518
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+فاهمينها حقكم تسألوا ما تترددوش ومش واحدة تقول
+
+519
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+والله أنا سألت سؤالين بخلاص بدي أخجل انت سألوش
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+520
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+حوشوا حسنات داركم اسألوا لما تزهجوا طول ما ان
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+521
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+522
+00:41:21,480 --> 00:41:26,160
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+523
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+وانا عارف إجابتهحاجة دي بيكون بسأل عشان اضيع وجد
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+524
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+اما كل سؤال حتى لو اتنين في تلاتة بيستوى ستة كيف
+
+525
+00:41:33,990 --> 00:41:38,390
+اجت وانتوا مش عارفينه بتقولوا تمام؟ لأنه احنا
+
+526
+00:41:38,390 --> 00:41:42,050
+هنشرع الشغلات مرت عليكم في المدرسة صح ولا لأ؟
+
+527
+00:41:42,050 --> 00:41:45,410
+وبالتالي ممكن تكون دخلة المعلومة غلط والله انا كنت
+
+528
+00:41:45,410 --> 00:41:50,810
+فاهمها هيك انت بتقولش كلام غلط نفترض نحكي صوت عالي
+
+529
+00:41:50,810 --> 00:41:55,950
+ونصل لشغلةبالتفقين عليها عشان تفوت المعلومة صح و
+
+530
+00:41:55,950 --> 00:42:00,110
+احنا بنركز و بنقول دير باكم هذا موضوع مهم بنركز
+
+531
+00:42:00,110 --> 00:42:03,130
+عليه لما أقول موضوع مهم يعني معناته موضوع أسئلة
+
+532
+00:42:03,130 --> 00:42:09,050
+لأنه احنا في الآخر بنشرح موضوع مهمة موضوع فرعية و
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+533
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+احنا لما نيجي نحط الامتحانبنحط امتحان عساس انه
+
+534
+00:42:15,280 --> 00:42:19,880
+بنشوف الطالب طلع بالاساسيات تبعتي المادة ولا لأ
+
+535
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+مابنروحش على ما بين السطور و بنجيب أسئلة لأ قانوني
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+536
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+نيوتل أبو الميكانيكا بد الطالب يفهمهم بسأل فيهم
+
+537
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+بسأل فيهم وبالتالي بنركز على الشغلات الأساسية وهذه
+
+538
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+الشغلات الأساسية بنحكيها صراحة قدامكم عشان كده
+
+539
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+حضور المحاضرة مهمة لإن أنا بحكي دلوقت هذا موضوع
+
+540
+00:42:42,000 --> 00:42:47,400
+جدا مهم وهذه الأسئلة بتيجي زيها هذه ال tricks
+
+541
+00:42:47,400 --> 00:42:53,260
+بتيجي زيها فبنكون احنا وياكم لو انتوا انتبهتوا ايه
+
+542
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+كانت بتيجي الامتحان اللي كنتوا عارفين يعني مثلا
+
+543
+00:42:56,240 --> 00:42:59,830
+الـ quizلما تخشوا على المودي اللي بتتفرجوا الليلة
+
+544
+00:42:59,830 --> 00:43:04,310
+هتلاقوا كل أسلة الـ quizzes موجودة جوا بـdf file
+
+545
+00:43:04,310 --> 00:43:10,110
+زيها يعني شبطر واحد بتلاقوا فيه quizzes مكتوب
+
+546
+00:43:10,110 --> 00:43:14,810
+folder ملاقاش مثلا ومجلد folder اسمه quizzes فوتوا
+
+547
+00:43:14,810 --> 00:43:17,550
+بتلاقي شبطر واحد شبطر اتنين شبطر تلاتة شبطر اربعة
+
+548
+00:43:17,550 --> 00:43:20,950
+خشوا على شبطر اتنين نفترض بتلاقوا لكم مثلا خمسين
+
+549
+00:43:20,950 --> 00:43:27,290
+سؤالهدول الخمسين سؤال هيجيكم زيهم في الموديل يعني
+
+550
+00:43:27,290 --> 00:43:31,290
+ان تحلوهم بتفوتوا بتحلوا بدل ما تاخدوا خمس دقايق
+
+551
+00:43:31,290 --> 00:43:35,650
+بيدجكتين بتحلوا و بتطلعوا فبالتالي حتى هذه الأسئلة
+
+552
+00:43:35,650 --> 00:43:42,190
+نعطيينكم نمازج منها عشان ما تفوتوش تصدموا بطبيعة
+
+553
+00:43:42,190 --> 00:43:46,110
+الأسئلة لأ الطالب اللي بده يشوف هذه الأسئلة موجودة
+
+554
+00:43:46,110 --> 00:43:51,090
+بين إيديههذه الـ Slides احنا بكره مثلا نفترض يوم
+
+555
+00:43:51,090 --> 00:43:55,270
+التنين مش يوم التنين بنا نبدأ يوم التنين إما
+
+556
+00:43:55,270 --> 00:43:59,330
+بتفوتوا على chapter واحد و بتطبعوا بتلاقوا PDF
+
+557
+00:43:59,330 --> 00:44:03,650
+file chapter واحد بتطبعوا بدل ما تكتبوا ورايا
+
+558
+00:44:03,650 --> 00:44:07,710
+مافيش دفتر للتيزيا ال slides هي الدفتر ال slides
+
+559
+00:44:07,710 --> 00:44:10,590
+بتكون مطبعة قدامكم عشان بس تطلعوا على اللحة تطلعوا
+
+560
+00:44:10,590 --> 00:44:14,690
+عليها عشان تفضوا تسألوني مديش شركهي و انتوا تكتبوا
+
+561
+00:44:15,160 --> 00:44:19,160
+تمام؟ كل اللي انا بأشرحه موجود بين إيديكوا مكتوب
+
+562
+00:44:19,160 --> 00:44:24,480
+اللي علّه هيكون موجود يعني هذه الصفحة موجودة نفسها
+
+563
+00:44:24,480 --> 00:44:29,600
+وكل اللي عرضته موجود تحت band outlines يعني .. إيش
+
+564
+00:44:29,600 --> 00:44:33,320
+ال outlines معنى بالعربي يعني؟ عنوين أو .. مش ..
+
+565
+00:44:33,320 --> 00:44:37,640
+مش .. راحت من .. من بالي إيش ال .. الاسم الرسمي
+
+566
+00:44:37,640 --> 00:44:44,380
+تبعت بعد كده بتلاقي شطر واحدبتطبعوه او اظن في
+
+567
+00:44:44,380 --> 00:44:48,560
+المكتب بتاعة الطالب طبعينه مجاهزين اذا بدكم
+
+568
+00:44:48,560 --> 00:44:51,700
+تاخدوهم يعني انا مش عارف هيك اللي فهمته يعني
+
+569
+00:44:51,700 --> 00:44:54,220
+بتطبعوهم او كل واحدة بتطبح اذا عندها طابعة في
+
+570
+00:44:54,220 --> 00:44:57,800
+الدار بتطبحهم كلهم منها كام ورقة وبيجيبوهم بصير كل
+
+571
+00:44:57,800 --> 00:45:00,940
+chapter ب chapter و هذا هو دفترنا بالاضافة الى
+
+572
+00:45:00,940 --> 00:45:04,180
+الكتاب كل مادة الى كتاب و دفتر فدفترنا هي ال slide
+
+573
+00:45:04,180 --> 00:45:08,040
+او اش رايحزي ما بنسميها هذا PowerPoint ما انتوا
+
+574
+00:45:08,040 --> 00:45:12,120
+عارفين ال PowerPoint هو عبارة عن شرايح هذه شريحة و
+
+575
+00:45:12,120 --> 00:45:15,120
+هذه شريحة و هذه شريحة تمام فهذه اللي بنطبعه
+
+576
+00:45:15,120 --> 00:45:19,340
+بيتحولوا ل PDF file و بيصيروا بالإيديكم حكيات كلمة
+
+577
+00:45:19,340 --> 00:45:22,240
+مش مكتوبة بتضيفوها بارصاص ولا بجلم يعني بيكون هو
+
+578
+00:45:22,240 --> 00:45:26,860
+دفتركمتمام يا بنات؟ فالعملية كتير سهلة طبعا ال
+
+579
+00:45:26,860 --> 00:45:31,220
+slides هي اللي بتكتبه على اللوح هو ال slides زي كل
+
+580
+00:45:31,220 --> 00:45:35,540
+مادة في كتاب وفيه المدرس بلخص فاحنا بلخصش على
+
+581
+00:45:35,540 --> 00:45:39,780
+اللوح طبعا هنكتب على اللوح لأنه هنشرح و هنقشر و
+
+582
+00:45:39,780 --> 00:45:46,720
+نخربش و نعمل و نجاتر و نغوّش يعني معركة فيها تمام
+
+583
+00:45:46,720 --> 00:45:53,240
+الشغل الأثنان اللي لازم تتعلموها انهالساعة في
+
+584
+00:45:53,240 --> 00:45:56,960
+الجامعة هي خمسين دقيقة يعني إحنا الساعة أتناش
+
+585
+00:45:56,960 --> 00:46:01,860
+خافوش ما هو ده الأخ سامح يقول خلصت بدون لأنه في
+
+586
+00:46:01,860 --> 00:46:04,520
+وراها كمان محاضرة فالمهم أنتوا لما يكون في عينكم
+
+587
+00:46:04,520 --> 00:46:09,280
+محاضرة صوت للعشر ويقول للدكتور خلصت المحاضرة أنا
+
+588
+00:46:09,280 --> 00:46:12,720
+هجيت واحد وخمسين خدت منكم دقيقة تمام؟ بس أحنا في
+
+589
+00:46:12,720 --> 00:46:16,160
+البداية فبالتالي الساعة ونص بصي الساعة وربع يعني
+
+590
+00:46:16,160 --> 00:46:22,320
+بكرا مثلا عينكم من تمانية لتسعة ونصتسعة و ربع بخلص
+
+591
+00:46:22,320 --> 00:46:26,640
+تمام؟ اذا اللي بنتقابل ان شاء الله يوم التنين
+
+592
+00:46:26,640 --> 00:46:32,940
+الساعة اتنعاش شرح حقيقي و ان كان بسيط يعطيكوا
+
+593
+00:46:32,940 --> 00:46:33,380
+العافية
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/H4drweiMiJA.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/H4drweiMiJA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..48b820a5ec06f455d0ea388bc2b012794582c645
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/H4drweiMiJA.srt
@@ -0,0 +1,1979 @@
+
+1
+00:00:05,150 --> 00:00:11,190
+تمام يا بنات، نستكمل وقفنا بعد ما أخذنا الـ velocity
+
+2
+00:00:11,190 --> 00:00:18,850
+وقلنا الـ velocity هي كمية فيزيائية تعني أن
+
+3
+00:00:18,850 --> 00:00:23,830
+الـ position بتغير مع الزمن، وعندي average velocity
+
+4
+00:00:23,830 --> 00:00:28,790
+وعندي instantaneous velocity. الـ Average Velocity
+
+5
+00:00:28,790 --> 00:00:34,070
+عرفناها على أنها V Average = ΔX / Δ
+
+6
+00:00:34,070 --> 00:00:39,750
+T، والـ Instantaneous Velocity = Limit  تبع الـ
+
+7
+00:00:39,750 --> 00:00:49,530
+ΔX / ΔT. تمام، نجي لها الـ quiz نشوف كنا
+
+8
+00:00:49,530 --> 00:00:53,950
+نحكي عربي ولا لأ. Consider the one-dimensional
+
+9
+00:00:53,950 --> 00:00:59,980
+motion. إيش هي؟ بقول: A ball is thrown vertically
+
+10
+00:00:59,980 --> 00:01:04,180
+upward.  دي كرة، رميناها لأعلى. تمام، سقوط حر ولا
+
+11
+00:01:04,180 --> 00:01:11,140
+لا؟ تمام. Rises to a highest point and falls back
+
+12
+00:01:11,140 --> 00:01:15,580
+into the thrower's hand. ورجعت على إيده. انطلقت من
+
+13
+00:01:15,580 --> 00:01:18,460
+إيده ورجعت على إيده. مين يقول لي جديش الـ average
+
+14
+00:01:18,460 --> 00:01:23,360
+velocity؟ صفر، صح ولا لأ؟ الـ average velocity صفر.
+
+15
+00:01:23,360 --> 00:01:26,940
+تمام، معلومة خزنتها جوا.  في هذه الحركة، الـ average
+
+16
+00:01:26,940 --> 00:01:33,420
+velocity صفر. A car or a race car. سيارة
+
+17
+00:01:33,420 --> 00:01:37,840
+سباق. تمام. الـ car starts from rest. بدأت من السكون
+
+18
+00:01:37,840 --> 00:01:44,180
+وضلت تمشي and speeds up  وصلت سرعة 100 متر per
+
+19
+00:01:44,180 --> 00:01:49,200
+second. وصلت طبعا ما وصلتش مرة واحدة، ضلت تتزيد، صح
+
+20
+00:01:49,200 --> 00:01:53,280
+ولا لأ؟ لو أجيت بدي أخذ جديش الـ average velocity
+
+21
+00:01:53,280 --> 00:01:57,980
+تبعها؟ خمسين، ستين، أربعين، مظبوط ولا لأ؟ رقم من
+
+22
+00:01:57,980 --> 00:02:02,520
+هالأرقام، اتفاجأنا؟ إذا زيادة منتظمة، بتكون السرعة
+
+23
+00:02:02,520 --> 00:02:06,410
+المتوسطة من النص بالظبط. إذا منتظمة، إذا مش منتظمة
+
+24
+00:02:06,410 --> 00:02:10,230
+بتكون إما قيمة واحدة أو أكثر، مش مشكلة، إنما رقم ما بين
+
+25
+00:02:10,230 --> 00:02:16,610
+الصفر والـ 100، صح ولا لأ؟ تمام. A space craft. سفينة فضاء
+
+26
+00:02:17,190 --> 00:02:21,890
+ماشي في الفضاء، drifts through space. بتمشي في
+
+27
+00:02:21,890 --> 00:02:25,710
+الـ space. الـ space يعني فراغ. At constant velocity.
+
+28
+00:02:25,710 --> 00:02:31,170
+سرعتها ثابتة. مين يقول لي إيش بتكون قيمة الـ instantaneous velocity لما تكون السرعة
+
+29
+00:02:31,170 --> 00:02:36,590
+ثابتة؟  الـ instantaneous velocity = الـ average، نفسها، نفسها.
+
+30
+00:02:36,590 --> 00:02:43,220
+صح ولا لأ؟ نفسها. يعني لو كانت بتمشي بسرعة ثابتة
+
+31
+00:02:43,220 --> 00:02:46,760
+مقدارها مائة كيلومتر في الساعة، الـ average مائة، والـ
+
+32
+00:02:46,760 --> 00:02:49,440
+instantaneous هو مائة ... مائة ... مائة ... مائة ... مائة ...
+
+33
+00:02:49,440 --> 00:02:51,100
+مائة ... مائة ... مائة ... مائة ... مائة ... مائة ...
+
+34
+00:02:51,100 --> 00:02:51,120
+مائة ... مائة ... مائة ... مائة ... مائة ... مائة ...
+
+35
+00:02:51,120 --> 00:02:51,180
+مائة ... مائة ... مائة ... مائة ... مائة ... مائة ...
+
+36
+00:02:51,180 --> 00:02:53,140
+مائة ... مائة ... مائة ... مائة ... مائة ... مائة ...
+
+37
+00:02:53,140 --> 00:02:54,360
+مائة ... مائة ... مائة ... مائة ... مائة ... مائة ...
+
+38
+00:02:54,360 --> 00:02:57,840
+مائة ... مائة ... مائة ... مائة ... مائة ... مائة ...
+
+39
+00:02:57,840 --> 00:03:01,090
+مائة ... مائة ... Are there any points... في نقطة
+
+40
+00:03:01,090 --> 00:03:05,510
+أثناء الحركة at which the instantaneous velocity
+
+41
+00:03:05,510 --> 00:03:09,230
+has the same value as the average velocity over
+
+42
+00:03:09,230 --> 00:03:13,050
+the entire motion. إيش يعني؟ بقول: في الثلاث حركات
+
+43
+00:03:13,050 --> 00:03:18,350
+إنتِ خزنتِ السرعة المتوسطة ولا لأ؟ الأولى قلنا zero.
+
+44
+00:03:18,350 --> 00:03:24,110
+و الثانية قلنا حوالي من أربعين، خمسين، ستين.
+
+45
+00:03:24,110 --> 00:03:27,770
+و الثالثة ما هي نفس المقدار. بيقول: لمين من هذول
+
+46
+00:03:27,770 --> 00:03:32,630
+بتكون السرعة اللحظية عند لحظة ما تساوي السرعة
+
+47
+00:03:32,630 --> 00:03:39,070
+المتوسطة؟ طيب، نشوف الأولى، جديش السرعة المتوسطة، في
+
+48
+00:03:39,070 --> 00:03:42,330
+الأولى، في لحظة من اللحظات في سقوط الحر بتكون
+
+49
+00:03:42,330 --> 00:03:47,220
+السرعة اللحظية صفر، عند أقصى ارتفاع، لذا فيه؟ إذن
+
+50
+00:03:47,220 --> 00:03:53,080
+حيثُ خلصنا. عند لحظة... طيب ما في تم السؤال. الثانية وهو
+
+51
+00:03:53,080 --> 00:03:57,400
+ماشي، لما يصل الـ 100، مرّ على الـ 10، والـ 20، والـ 30
+
+52
+00:03:57,400 --> 00:04:00,800
+والـ 40، والـ 50، والـ 60، ولا لأ؟ إذا في لحظة من
+
+53
+00:04:00,800 --> 00:04:04,120
+اللحظات كانت سرعته خمسين، وفي لحظة من اللحظات كانت
+
+54
+00:04:04,120 --> 00:04:07,260
+أربعين، وفي لحظة من اللحظات كانت ستين، إذا الـ
+
+55
+00:04:07,260 --> 00:04:10,180
+average خمسين، في نقطة وصلت خمسين، إذا الـ average
+
+56
+00:04:10,180 --> 00:04:13,900
+ستين، في نقطة وصلت ستين، صح ولا لأ؟ إذا برضه صحيحة.
+
+57
+00:04:14,050 --> 00:04:18,990
+و الثالثة ما هي واضحة إنها صحيحة، إذا معناته في
+
+58
+00:04:18,990 --> 00:04:22,050
+الأولى ولا في الثانية ولا في الثالثة ولا في كلهم؟
+
+59
+00:04:22,050 --> 00:04:27,730
+في كلهم، تمام، الآن
+
+60
+00:04:27,730 --> 00:04:34,690
+بدنا نحكي عن الـ acceleration، تسارع. طبعا، نرجع دائما
+
+61
+00:04:34,690 --> 00:04:39,110
+نقول: لكل مسمى من اسمه نصيب. سموه تسارع لأنه مش سرعة.
+
+62
+00:04:39,110 --> 00:04:43,890
+تسارع لغويا يعني تسارع، زيادة. فيه السرعة بتتغير...
+
+63
+00:04:43,890 --> 00:04:51,130
+بتتغير. هنا بشتق X بالنسبة للـ T، يعني اللي بتغير X
+
+64
+00:04:51,130 --> 00:04:57,630
+طلع سرعة.  لو أجيت X وحطيت V، تطلع تسارع. تمام؟
+
+65
+00:04:57,630 --> 00:05:01,630
+لأن إيش اللي بده يتغير؟ السرعة. إذا لو تغيرت...
+
+66
+00:05:01,630 --> 00:05:05,690
+بالنسبة للزمن... لو تغيرت السرعة، بنقول الجسم له
+
+67
+00:05:05,690 --> 00:05:09,350
+تسارع. اتفقنا هيك؟ إذا هيك، عرفنا الـ acceleration
+
+68
+00:05:09,350 --> 00:05:14,150
+when the velocity of a particle... velocity عرفناها
+
+69
+00:05:14,150 --> 00:05:18,650
+معناها varies with time أو changes with time.
+
+70
+00:05:18,650 --> 00:05:22,390
+بتتغير مع الزمن. The particle is said to be
+
+71
+00:05:22,390 --> 00:05:29,130
+accelerating. بمعنى
+
+72
+00:05:29,130 --> 00:05:34,310
+آخر has an acceleration. لما تكون السرعة ثابتة
+
+73
+00:05:34,310 --> 00:05:41,310
+ما بتتغير، جديش تسارعها؟ صفر، صح ولا لأ؟ إيش معناته؟ بيقول لي
+
+74
+00:05:41,310 --> 00:05:46,430
+معناته حيكون في عندك كميتين، جديش إيش هي؟ بيقول لي
+
+75
+00:05:46,430 --> 00:05:51,630
+A average = ΔV / ΔT. شوف إيش اللي
+
+76
+00:05:51,630 --> 00:05:57,750
+اتغير؟ V اتغيرت. الآن، A instantaneous =
+
+77
+00:05:57,750 --> 00:06:04,620
+اشتقاق مين؟ ΔV / ΔT. إذا بدل ما تتغير الـ position
+
+78
+00:06:04,620 --> 00:06:09,100
+اتغيرت الآن السرعة. اتغيرت السرعة، صار في عندي
+
+79
+00:06:09,100 --> 00:06:12,960
+acceleration. اتفقنا يا بنات؟ إذا الـ acceleration
+
+80
+00:06:12,960 --> 00:06:16,940
+في عندك average وفي عندك instantaneous.
+
+81
+00:06:19,500 --> 00:06:25,860
+اللي هو ده الاشتقاق. طيب، اشتقاق الـ V ما بعرف اشتقها، طب
+
+82
+00:06:25,860 --> 00:06:29,540
+هي الـ V مش جاية من اشتقاق الـ X؟ إذا لو اشتققت الـ X
+
+83
+00:06:29,540 --> 00:06:33,660
+مرتين، بتطلع تسارع ولا لأ؟ إذا هذا التسارع ممكن
+
+84
+00:06:33,660 --> 00:06:37,200
+أقول هي الاشتقاق الثاني لـ X بالنسبة للزمن. أه، أول
+
+85
+00:06:37,200 --> 00:06:40,770
+مرة أشتق بتطلع سرعة، أشتق مرة ثانية بتطلع تسارع. صحيح
+
+86
+00:06:40,770 --> 00:06:46,290
+ولا لأ؟ تمام. التسارع كمية فيزيائية، مشهورة، جديدة،
+
+87
+00:06:46,290 --> 00:06:50,650
+لا هي L ولا هي M ولا هي T، لكن هي L / T تربيع، ولا
+
+88
+00:06:50,650 --> 00:06:53,870
+لا؟ L / T تربيع. معناته وحداتها متر per second
+
+89
+00:06:53,870 --> 00:06:57,290
+تربيع، أو centimeter per second تربيع، أو foot per
+
+90
+00:06:57,290 --> 00:07:01,770
+second تربيع. الوحدة الـ SI unit في النظام العالمي
+
+91
+00:07:01,770 --> 00:07:06,770
+متر per second تربيع. لاحظتِ أننا حكينا حاجة جديدة؟
+
+92
+00:07:06,770 --> 00:07:15,120
+سهلة، تمام، جالي حلو، جالي الاشتقاق. ربطيلي يا ميل
+
+93
+00:07:15,120 --> 00:07:22,640
+ولا لأ؟ مشهور، اشتقاق ميل، حلو. طيب، هيدي ميل، وهيدي ميل.
+
+94
+00:07:22,640 --> 00:07:26,600
+هيدي ميل الخط الواصل ما بين نقطتي البداية
+
+95
+00:07:26,600 --> 00:07:33,640
+والنهاية، ولا لأ؟ أو هذا ميل الخط المماس للرسم عند
+
+96
+00:07:33,640 --> 00:07:39,080
+نقطة ما، صح؟ إذا بيقول لي: in the velocity... لما يكون
+
+97
+00:07:39,080 --> 00:07:44,840
+عندك رسمة بين الـ V والـ T، لأن مش الـ X والـ T، الـ V
+
+98
+00:07:44,840 --> 00:07:49,720
+والـ T. In the velocity-time graph. أي رسمة هذه
+
+99
+00:07:49,720 --> 00:07:54,270
+بنسميها velocity-time graph، graph، رسمة. بيقول لي: the
+
+100
+00:07:54,270 --> 00:07:59,630
+average acceleration is the slope of the
+
+101
+00:07:59,630 --> 00:08:05,840
+line connecting... هاي بداية، وهاي نهاية. أعمل خط، جيب
+
+102
+00:08:05,840 --> 00:08:09,400
+ميله. هذه هي الـ average acceleration. الـ average
+
+103
+00:08:09,400 --> 00:08:12,720
+acceleration. إذا the average acceleration is the
+
+104
+00:08:12,720 --> 00:08:17,620
+slope، ميل، of the line connecting the initial and
+
+105
+00:08:17,620 --> 00:08:20,800
+the final points. اللي بربط من نقطتي البداية
+
+106
+00:08:20,800 --> 00:08:26,910
+والنهاية. While بينما the instantaneous acceleration
+
+107
+00:08:26,910 --> 00:08:31,750
+at any time is the slope of the tangent at that
+
+108
+00:08:31,750 --> 00:08:36,450
+time. هو ميل المماس. يعني أنا بدي عند النقطة هادي
+
+109
+00:08:36,450 --> 00:08:42,890
+عند هذه النقطة، بقول بسيطة، بدي أعمل مماس، صح؟ و بدي
+
+110
+00:08:42,890 --> 00:08:46,570
+بميله. كان أفقيا، صفر، كانت عند النقطة هادي، بعمل هيك
+
+111
+00:08:46,570 --> 00:08:50,790
+صح ولا لأ؟ و بدي بميله. هذه مفهومة ومعروفة، بس
+
+112
+00:08:50,790 --> 00:08:54,270
+بنذكر بعض فيها. أحكي يا بنتي.
+
+113
+00:09:01,430 --> 00:09:05,450
+مثل البرسكين التربيع. الـ acceleration. الـ velocity
+
+114
+00:09:05,450 --> 00:09:10,350
+المكتوب هنا velocity بخطأ، هذه خطأ مطبعي، وهنا شوف
+
+115
+00:09:10,350 --> 00:09:13,890
+آه، هذه acceleration. ما احنا نحكي عن الـ acceleration
+
+116
+00:09:13,890 --> 00:09:17,470
+مفهومة، بس هذه خطأ مطبعي. هذه كلمة acceleration.
+
+117
+00:09:17,470 --> 00:09:18,190
+كلامك صحيح.
+
+118
+00:09:23,530 --> 00:09:28,690
+إذن هذه نقطة بداية، وهذه نقطة نهاية.  بتخط جيب
+
+119
+00:09:28,690 --> 00:09:31,730
+هذا. The slope of the line connecting A and B is
+
+120
+00:09:31,730 --> 00:09:36,530
+the average acceleration between A and B. بدي السرعة
+
+121
+00:09:36,530 --> 00:09:42,930
+عند النقطة B، لحظة، باخذ tangent وبأخذ ميله. معروفة.
+
+122
+00:09:42,930 --> 00:09:48,410
+تكرار للكلام اللي حكيناه. تمام. هلّأ جيت الـ velocity،
+
+123
+00:09:48,410 --> 00:09:51,690
+قلنا بتختلف عن الـ speed، ولا لأ؟ الـ velocity اللي
+
+124
+00:09:51,690 --> 00:09:55,600
+لها direction. وعشان احنا في chapter 2، لسه ما خلصناش
+
+125
+00:09:55,600 --> 00:09:59,760
+chapter 3، قلنا الـ direction بدنا نستعيض عنه بموجب و
+
+126
+00:09:59,760 --> 00:10:04,780
+سالب. وقلنا الحركة العمودية لأعلى موجب، ولأسفل
+
+127
+00:10:04,780 --> 00:10:10,100
+سالب، والحركة الأفقية يمين موجب، ويسار سالب. تمام، و
+
+128
+00:10:10,100 --> 00:10:14,340
+قال لي هذه ممكن تغيرها حسب إنتِ إيش بدك، لكن هذا الـ
+
+129
+00:10:14,340 --> 00:10:18,020
+default. حلو. قال لي الـ acceleration جاية من الـ
+
+130
+00:10:18,020 --> 00:10:21,980
+velocity. فهمتوا علي؟ يعني معناته إلها direction.
+
+131
+00:10:21,980 --> 00:10:26,360
+لأن الـ velocity إلها direction. جالي حلو، جالي.
+
+132
+00:10:26,360 --> 00:10:28,640
+معناته الـ acceleration ممكن تكون موجبة وممكن تكون
+
+133
+00:10:28,640 --> 00:10:32,920
+سالبة، مش حسب الـ direction... حسب الـ direction. تمام،
+
+134
+00:10:32,920 --> 00:10:39,040
+جالي: The acceleration is positive... اتجاهها positive
+
+135
+00:10:39,040 --> 00:10:43,980
+موجب، يعني باتجاه يمين أو يسار حسب موجبك، when the
+
+136
+00:10:43,980 --> 00:10:49,140
+velocity is increasing. لما تكون السرعة متزايدة in
+
+137
+00:10:49,140 --> 00:10:54,620
+the positive x direction، speeding up. بزيادة السرعة.
+
+138
+00:10:54,620 --> 00:10:58,540
+أعطيكم trick أخذتوها في الـ calculus. أعطيكم سؤال في
+
+139
+00:10:58,540 --> 00:11:03,440
+التوجيهي. أعطيكم دالة، وقال لكم هادي الدالة... دالة بتعرفوها
+
+140
+00:11:03,440 --> 00:11:07,800
+دالة، function، بتاخدوها. متزايدة ولا متناقصة؟ كيف
+
+141
+00:11:07,800 --> 00:11:09,580
+تعملوا؟ كنتوا تشتقوها.
+
+142
+00:11:12,570 --> 00:11:17,530
+إذا موجبة تقولوا عنها متزايدة، مظبوط ولا لا؟ حلو،
+
+143
+00:11:17,530 --> 00:11:21,990
+هاي نقعد نطبق. أنا مش اللي... التسارع اشتقاق الـ
+
+144
+00:11:21,990 --> 00:11:26,710
+velocity، إذا الـ velocity بتزيد،  ده اللي ما هي،
+
+145
+00:11:26,710 --> 00:11:30,570
+بتتوقع الـ acceleration تكون موجبة ولا لا؟ صحيح؟ طب
+
+146
+00:11:30,570 --> 00:11:35,750
+وإذا بتتناقص، تطلع سالبة؟ بهذه الحالة، إيش بيقول
+
+147
+00:11:35,750 --> 00:11:38,410
+ليه؟ Velocity and acceleration are in the same
+
+148
+00:11:38,410 --> 00:11:43,110
+direction. لما تكون السرعة بتزيد. ها انتبهولي، دخلوا
+
+149
+00:11:43,110 --> 00:11:47,330
+المعلومة في مخكم. إذا السرعة بتزيد، التسارع والسرعة
+
+150
+00:11:47,330 --> 00:11:54,210
+بنفس الاتجاه. تمام. مش هنتناقش. اتجاه السرعة بتزيد،
+
+151
+00:11:54,210 --> 00:12:00,390
+هجيت. أعطيكم trick. واحد رايح على انصرات، كيف بدك تعرف
+
+152
+00:12:00,390 --> 00:12:07,070
+سرعته؟ تجاه انصرات. سرعته بتزيد، كيف التسارع اتجاهه؟
+
+153
+00:12:07,070 --> 00:12:13,070
+انصرات، انصرات، انصرات. اتفقنا هيك؟ حلو. طلعوا الواحدة
+
+154
+00:12:13,070 --> 00:12:17,950
+الثانية. بيقول لي: The acceleration is negative when
+
+155
+00:12:17,950 --> 00:12:22,770
+the velocity is decreasing. بتتناقص in the positive
+
+156
+00:12:22,770 --> 00:12:25,070
+x direction. أنا ماخذ الـ positive x direction، الـ
+
+157
+00:12:25,070 --> 00:12:29,830
+default. تمام. Slowing down. Velocity and
+
+158
+00:12:29,830 --> 00:12:33,530
+acceleration are in opposite direction. بيكونوا عكس
+
+159
+00:12:33,530 --> 00:12:39,330
+بعض. يعني نرجع سيارة رايحة عنصرات وقاعدة بتتباطأ.
+
+160
+00:12:39,330 --> 00:12:43,970
+بدأت توقف في الآخر. هجيت هي وين رايحة؟ عنصرات،
+
+161
+00:12:43,970 --> 00:12:49,310
+سرعتها كيف اتجاهها؟ عنصرات. تسارعها؟ ع جباليا، ع
+
+162
+00:12:49,310 --> 00:12:55,250
+جباليا، العكس. فهمتوا علي؟ إذا إذا السرعة تتزايد،
+
+163
+00:12:55,250 --> 00:13:00,730
+السرعة والتسارع مع بعض. إذا السرعة بتتناقص، السرعة
+
+164
+00:13:00,730 --> 00:13:04,430
+والتسارع عكس بعض. دخلت المعلومة. هلّأ positive ولا
+
+165
+00:13:04,430 --> 00:13:08,770
+negative؟ حاجة ثانية، حسب الـ positive تبعي، تمام؟ حسب إنتِ
+
+166
+00:13:08,770 --> 00:13:12,210
+إيش ماخذة الـ positive، ماخذة الشرق ولا الغرب. أما
+
+167
+00:13:12,210 --> 00:13:15,350
+لازم يكونوا مع بعض إذا السرعة بتزيد، ولازم يكونوا
+
+168
+00:13:15,350 --> 00:13:21,610
+ضد بعض إذا كانت تتناقص. تمام يا بنات؟ أي استفسار؟
+
+169
+00:13:21,610 --> 00:13:29,110
+دخلنا المعلومة. هذه الـ quiz، نشوف إيش ك
+
+223
+00:17:53,430 --> 00:17:57,510
+الجملة، بدي أطلع لفوق، إيش التصارع تبعه؟ تصارع
+
+224
+00:17:57,510 --> 00:18:01,150
+جاذبية ولا لا؟ ثابت ولا مش ثابت التصارع، الجاذبية؟
+
+225
+00:18:01,150 --> 00:18:06,330
+بده يضلوا واصل السماء؟ لأ، عند ضغط معين بده يجف، صح؟
+
+226
+00:18:06,330 --> 00:18:10,190
+ولا .. إذا هذا غلط، الكلمة أنه هو تصارع ثابت لكن
+
+227
+00:18:10,190 --> 00:18:14,970
+واجف، نجي للأخيرة، بيقول لي طيب ممنوع يجف، يضل واقف
+
+228
+00:18:14,970 --> 00:18:17,670
+بيقول له اه هذا بيجف، بيضل شوية ولا بيحرض وبيقول
+
+229
+00:18:17,670 --> 00:18:23,030
+بديش هيدا، بديش، هنزل، صح اللو؟ لأ، بعد برجع، إذا هو بيجف
+
+230
+00:18:23,030 --> 00:18:28,610
+لكن ما ضلش واقف، مزال فيه تسارع، بدي أرجعه، فيمتى عليه؟
+
+231
+00:18:28,610 --> 00:18:29,330
+احكي يا بنات
+
+232
+00:18:33,160 --> 00:18:37,040
+يعني واحدة مكملة للتانية، أنه لازم الجسم لما يوصل
+
+233
+00:18:37,040 --> 00:18:40,780
+لنقطة معينة، يابا يعني بنزل بيكمل، لأن التصارع ما
+
+234
+00:18:40,780 --> 00:18:45,360
+زال ثابت، بيبقى موجود، طبعا هو تصارع، بيبقى يأثّر، مش
+
+235
+00:18:45,360 --> 00:18:48,820
+مظبوط ولا .. فبيرجعه، فلازم يرجعه، لو أجينا
+
+236
+00:18:48,820 --> 00:18:52,080
+بالامتحان نفس السؤال، الـ C و D نفس ما هما هانت من
+
+237
+00:18:52,080 --> 00:18:58,200
+أصلكِ؟ لأ، ما نالَش، عدلتها، لأ، هي الـ D اه، بس الصح
+
+238
+00:18:58,200 --> 00:19:01,360
+الأكتر حاجة دي، تمام، وأنا عدلتها، يعني في الآخر
+
+239
+00:19:01,360 --> 00:19:03,780
+طلعت عملي، مهام عدل عينكم، حلو
+
+240
+00:19:06,320 --> 00:19:09,660
+نجي للمثال، هذا مثال سهل، فيه كتير أمثلة سهلة
+
+241
+00:19:09,660 --> 00:19:12,660
+The velocity of a particle يا بنات moving along
+
+242
+00:19:12,660 --> 00:19:17,400
+the X-axis varies with time، بتتغير مع الزمن، ماذا
+
+243
+00:19:17,400 --> 00:19:19,940
+بتتغير مع الزمن؟ زي في acceleration ولا لا؟ في
+
+244
+00:19:19,940 --> 00:19:22,980
+acceleration، قال لي كيف بتتغير؟ قلت له تبع لي
+
+245
+00:19:22,980 --> 00:19:27,220
+المعادلة اللي أنتِ شايفة، أربعين ناقص خمسة ت تربيع
+
+246
+00:19:27,220 --> 00:19:32,290
+شايفين المعادلة؟ شايفينها، with z in meter per
+
+247
+00:19:32,290 --> 00:19:34,930
+second and t in second، يعني أنا بستخدم الـ SI
+
+248
+00:19:34,930 --> 00:19:41,470
+system، تمام؟ إيش بدك؟ حاجة بتحصل حاليا، Find the
+
+249
+00:19:41,470 --> 00:19:46,330
+average acceleration for the interval من 0 ل 2
+
+250
+00:19:46,330 --> 00:19:49,870
+second، بدي الـ average acceleration في فترة زمنية
+
+251
+00:19:49,870 --> 00:19:54,550
+معروفة من 0 ل 2 second، تمام؟ والمطلوب الثاني ..
+
+252
+00:19:54,550 --> 00:19:57,470
+شكرا يا سامي، determine the acceleration، الـ T
+
+253
+00:19:57,470 --> 00:20:01,030
+بتساوي 2 second، ماذا تلك اللحظة، معينة، مع أننا نتحدث
+
+254
+00:20:01,030 --> 00:20:09,310
+عن التسارع اللحظي، تمه .. ها .. هنا هنا، هذه القوانين
+
+255
+00:20:09,310 --> 00:20:16,570
+صحّح ولا لأ؟ Delta V معناته V لما T بتساوي 2 ناقص V
+
+256
+00:20:16,570 --> 00:20:23,770
+لما T بتساوي 0، ولا لأ؟ على 2 ناقص 0، صحيح، تمام، هذه
+
+257
+00:20:23,770 --> 00:20:28,150
+بدنا نجيبها من أين؟ نجيبها هذه وهذه من المعادلة
+
+258
+00:20:28,150 --> 00:20:35,850
+يلا، إيه average بتساوي؟ منى، أجلني، يلا، أربعين ناقص
+
+259
+00:20:35,850 --> 00:20:41,910
+خمسة في أربعة، خمسة في أربعة، أربعين ناقص عشرين، إذا
+
+260
+00:20:41,910 --> 00:20:44,930
+هذه عشرين، ناقص
+
+261
+00:20:46,370 --> 00:20:50,910
+صفر، يعني ناقص أربعين، اه بالظبط، ناقص أربعين، لأنه
+
+262
+00:20:50,910 --> 00:20:57,030
+عوضتِ  بصفر، فـ ناقص أربعين على اتنين، ناقص عشرين
+
+263
+00:20:57,030 --> 00:21:05,270
+على اتنين، minus 10، إيه يا بنات؟ واضح شو سويت؟ سهلة
+
+264
+00:21:05,270 --> 00:21:11,170
+تمام، سهلة جدا، احكي يا بنتي كيف
+
+265
+00:21:16,980 --> 00:21:26,360
+علي صوتكِ، اه، لأ، بتعطيكي التصارع اللحظي، وهو بدّوش
+
+266
+00:21:26,360 --> 00:21:32,700
+التصارع اللحظي، ما ينفعش، لما يقول لي التصارع المتوسط
+
+267
+00:21:32,700 --> 00:21:38,760
+ما ينفعش أشتق، لأ، التعريف، شوفوا التعريف، بيقول لي A
+
+268
+00:21:38,760 --> 00:21:42,800
+average بيساوي DV على DT، ولا Delta V على Delta T
+
+269
+00:21:42,800 --> 00:21:48,050
+Delta و Delta مش اشتقاق، فهمتوا عليّ؟  دلوقت أنا بركز
+
+270
+00:21:48,050 --> 00:21:53,470
+بهيدا، لأن هذا خطأ شائع بيجي، ما ينفعش تشتقي، أنا مش
+
+271
+00:21:53,470 --> 00:21:56,890
+طالبة التصارع، التسارع اللحظي، أنا بدي التسارع
+
+272
+00:21:56,890 --> 00:22:02,070
+المتوسط، التسارع المطلوب الثاني هالجيبة، إيش بده؟
+
+273
+00:22:02,070 --> 00:22:07,150
+التسارع عند لحظة، تمام، هاي هاي، يعني بدك هادي،
+
+274
+00:22:07,150 --> 00:22:11,230
+بقول له يلا، هالجيبة تبقى متشاطرة على الاشتقاق،
+
+275
+00:22:11,230 --> 00:22:18,370
+اشتقّي، أربعين ناقص خمسة T، يعني ناقص عشرة T، هيجيك بدك وعند
+
+276
+00:22:18,370 --> 00:22:22,190
+أي زمان، عند T بتساوي 2 second، بقول له إذا إيه عند T
+
+277
+00:22:22,190 --> 00:22:27,890
+بتساوي 2 second بتساوي ناقص عشرين، تمام
+
+278
+00:22:27,890 --> 00:22:33,310
+يا بنات، تمام، حلّينا
+
+279
+00:22:33,310 --> 00:22:40,710
+السؤال، وهينطلع، لما يقول لي بدي average، لا تشتقي، انتبهي
+
+280
+00:22:40,710 --> 00:22:46,270
+بدي عوض في المعادلة، تمام، عوضنا وجبنا، تمام، ولما
+
+281
+00:22:46,270 --> 00:22:51,070
+جبنا الـ instantaneously، روحت اشتقيت وطلعتها، تمام
+
+282
+00:22:56,070 --> 00:23:00,190
+في acceleration، في acceleration، إيش تعرفي الـ acceleration؟
+
+283
+00:23:00,190 --> 00:23:03,670
+معدّل تغير السرعة بالنسبة للزمن، فيه متوسط وفيه
+
+284
+00:23:03,670 --> 00:23:07,830
+منه لحظي، نجي للتسارع اللحظي، أحيانا التسارع يا بنات
+
+285
+00:23:07,830 --> 00:23:12,930
+بيكون ثابت، زي مثلا نفترض عندي هذه الأرقام، شوفولي
+
+286
+00:23:12,930 --> 00:23:17,860
+كيف يزيد هذه الأرقام، سرعات، تمام؟ اتنين، أربعة، ستة،
+
+287
+00:23:17,860 --> 00:23:21,180
+ثمانية، عشرة، زادت ولا نقصت؟ إيه قيمة الزيادة هذه؟
+
+288
+00:23:21,180 --> 00:23:24,320
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+289
+00:23:24,320 --> 00:23:24,580
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+290
+00:23:24,580 --> 00:23:25,200
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+291
+00:23:25,200 --> 00:23:27,340
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+292
+00:23:27,340 --> 00:23:34,600
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+293
+00:23:34,600 --> 00:23:39,920
+اتنين، عندك معادلات تستطيع اشتقاقها، إذا بيقول
+
+294
+00:23:39,920 --> 00:23:44,200
+particle under constant acceleration، إذا أنتِ عندك
+
+295
+00:23:44,200 --> 00:23:50,840
+معطى أن إيه مالها constant، a is constant، طبعا
+
+296
+00:23:50,840 --> 00:23:57,120
+وياكم، هيك نجرب الجملة، ونكتب مع بعض، ونجرب، في حدا
+
+297
+00:23:57,120 --> 00:24:04,440
+منكم ما خلّصش صف رابع، وصف ثامن، وصلنا هنا، إذا أنا
+
+298
+00:24:04,440 --> 00:24:07,980
+ممكن تبهدلوني، مازال خلصت رابع وثامن، أثبتولي هال
+
+299
+00:24:07,980 --> 00:24:15,900
+gate، تمام، a is constant، بيعطيكم
+
+300
+00:24:15,900 --> 00:24:20,600
+أرقام، تجيبوا لي متوسطهم، تعرفوا تجيبوا المتوسطات، 5 5 5 5
+
+301
+00:24:20,600 --> 00:24:21,200
+5 5
+
+302
+00:24:25,340 --> 00:24:30,440
+خمسة، مظبوط ولا لا؟ لما يكون الشيء ثابت، اه، أروح أجمعه
+
+303
+00:24:30,440 --> 00:24:33,780
+وأقسم على عددهم، وأرخم حالتي، ما يوم أنت ما غيرت شيء
+
+304
+00:24:33,780 --> 00:24:41,060
+طيب، إيه الـ constant، بقدر أقول أن إيه average هي
+
+305
+00:24:41,060 --> 00:24:47,360
+نفسها إيه؟ اه، مازال constant، اه، نفسها، نفسها، والله
+
+306
+00:24:47,360 --> 00:24:52,100
+هاي ها، ده ما قلت لكم، هاي خمسة، هاي خمسة، هاي خمسة، هاي
+
+307
+00:24:52,100 --> 00:24:58,710
+خمسة، أي قيمة منهم، جيد، والمتوسط إذا، اللحظة هذه
+
+308
+00:24:58,710 --> 00:25:03,890
+والمتوسط زي بعض، صح ولا لأ؟ طب، أمين، جالي هادي لها
+
+309
+00:25:03,890 --> 00:25:08,110
+قانون ولا لأ، اللي توسّطت عنه، مش اشتقاق، جالي هادي
+
+310
+00:25:08,110 --> 00:25:12,810
+والله، جالولي V final ناقص V initial على T final ناقص
+
+311
+00:25:12,810 --> 00:25:16,290
+T initial، اعتبر T initial صفر يا سيدي، ما أنتَ دائما
+
+312
+00:25:16,290 --> 00:25:21,130
+بتشغل الساعة من بداية، فبتعتبر T initial صفر، وما
+
+313
+00:25:21,130 --> 00:25:24,790
+زال بطل في عندك T initial، فبضلّ T واحدة مضاجعة
+
+314
+00:25:24,790 --> 00:25:31,090
+final، تمام، بتساوي إيه؟ وين اللي قال خلّص رابع؟ نضرب
+
+315
+00:25:31,090 --> 00:25:37,130
+ضرب تبادلي، نضرب ضرب تبادلي، imply that، أو هذا يعني
+
+316
+00:25:37,130 --> 00:25:43,610
+The final ناقص V initial برضه
+
+317
+00:25:43,610 --> 00:25:47,210
+في صف رابع، حد بيحطها بالشجرة الثانية، فصار V final
+
+318
+00:25:47,210 --> 00:25:48,750
+بتساوي V initial
+
+319
+00:25:53,650 --> 00:25:58,210
+شفتوها؟ بتعرفوها؟ وحفظناها زي السمن، صح ولا لأ؟ هاي
+
+320
+00:25:58,210 --> 00:26:01,770
+أول قانون، أهل الاشتقاق، مش كتير مهم، بس يعني احنا ما
+
+321
+00:26:01,770 --> 00:26:05,870
+زال رابع وثامن، مخلصينه، مستقي، يعني هاي أول ..
+
+322
+00:26:05,870 --> 00:26:11,950
+فيها إيه سفسار يا بنات؟ تمام، حلو، الـ gate، A is
+
+323
+00:26:11,950 --> 00:26:17,730
+constant، هذا شرط، لأنه علاقة هذا، دائما شرط، صح ولا لأ؟
+
+324
+00:26:17,730 --> 00:26:22,670
+حلو، اطلعوا لي على هذه السرعات، بتعطيكم، أهم أنتم كتبتوا
+
+325
+00:26:22,670 --> 00:26:27,950
+خمسات، كانت تسارعّات، سرعة، اتنين، أربعة، ستة، ثمانية
+
+326
+00:26:27,950 --> 00:26:35,050
+عشرة، كيف الزيادة، مش ثابتة، بتتغير، من يجيب لي الـ
+
+327
+00:26:35,050 --> 00:26:41,150
+average، المعدّل، إيش كيف نجيب المعدّل؟ احنا معكِ، يلا
+
+328
+00:26:41,150 --> 00:26:48,550
+اجمعي لي اتنين وأربعة، اتنين وأربعة، ستة، وستة وثمانية
+
+329
+00:26:48,550 --> 00:26:52,270
+وعشرة، واحد على اتنين، تلقى اتة، أربعة، خمسة، تلاتين على
+
+330
+00:26:52,270 --> 00:26:57,110
+خمسة، ستة، الـ average، جالي يطلع هدول، لو مليون، ده
+
+331
+00:26:57,110 --> 00:27:00,630
+تجمع المليون، وتقسم على مليون، يطلع هالـ trick، إذا
+
+332
+00:27:00,630 --> 00:27:07,390
+الزيادة ثابتة، آخذي الأول والأخير، واجمعي على اتنين، اتنين
+
+333
+00:27:07,390 --> 00:27:12,540
+وعشرة، على اتنين، إيه؟ ولا طلعت ستة، نفس الجواب، بشرط
+
+334
+00:27:12,540 --> 00:27:14,960
+أن تكون الزيادة ثابتة، وأنا عندي الـ acceleration
+
+335
+00:27:14,960 --> 00:27:20,320
+مالها ثابتة، ده اللي في هذه الحالة، هذه سرعات، V
+
+336
+00:27:20,320 --> 00:27:25,860
+average،  الأولى زائد الأخيرة على اتنين
+
+337
+00:27:28,600 --> 00:27:31,200
+فده القانون اللي أخذناه في المدرسة، ما أعرفش أخذته هو
+
+338
+00:27:31,200 --> 00:27:36,040
+إيه، صفر، بلاش أتعذب عليكم، أقول رابع، لأ، مش رابع، تمام
+
+339
+00:27:36,040 --> 00:27:39,720
+أعلى شوية من رابع، أنتم اكتشفتوا الحكاية دي، المعدل
+
+340
+00:27:39,720 --> 00:27:43,780
+ومش المعدل، تمام؟ اه تمام، يعني إذا أنجزت رابع، تمام
+
+341
+00:27:43,780 --> 00:27:50,660
+عشان كده، تمام، حلّوا لي، طيب، مين يذكرني في average
+
+342
+00:27:50,660 --> 00:27:58,340
+قانونها؟ إيش؟ X final ناقص X initial، إذا X final ناقص
+
+343
+00:27:58,340 --> 00:28:02,320
+X initial على T final ناقص T initial، بتقولنا T
+
+344
+00:28:02,320 --> 00:28:10,960
+بتساوي V initial زائد V final على 2، ضرب تبادلي، وتبقى
+
+345
+00:28:10,960 --> 00:28:19,430
+صف رابع، من هنا خلينا نقول، بقول X final ناقص X initial
+
+346
+00:28:19,430 --> 00:28:29,150
+بتساوي نص V initial زائد V final في T، هاي كمان
+
+347
+00:28:29,150 --> 00:28:36,790
+معادلة، تمام؟ حلو، قال لي طيب، رجعنا للهادي، لسه قال
+
+348
+00:28:36,790 --> 00:28:45,620
+لي، هادي، ما ينفعش، حتة منها مش هي نفسها، اه، شحّتني، يلا
+
+349
+00:28:45,620 --> 00:28:51,200
+نشحت، بقول له
+
+350
+00:28:51,200 --> 00:28:59,080
+X final ناقص X initial على T بتساوي V initial زائد
+
+351
+00:28:59,080 --> 00:29:07,620
+V final زائد V initial زائد AT،  عطيني متابعين
+
+352
+00:29:07,620 --> 00:29:15,900
+معايا؟ V initial زائد V initial، إذن هذه صارت اتنين
+
+353
+00:29:15,900 --> 00:29:21,440
+V initial، صح ولا لأ؟ تمام، جالي هيك، بترتب لي إياها، بقول
+
+354
+00:29:21,440 --> 00:29:28,080
+X final ناقص X initial على T بتساوي V initial زائد نص
+
+355
+00:29:28,080 --> 00:29:32,220
+AT، صح
+
+356
+00:29:32,220 --> 00:29:40,620
+صحّح، متابعين، حلو، يلا، ضرب تبادلي، ضرب تبادلي، بتصير
+
+357
+00:29:40,620 --> 00:29:47,530
+هاتي هيك، هاتي، وهاتي تربيع، وهي القانون الحلو تبعنا
+
+358
+00:29:47,530 --> 00:29:51,930
+X final ناقص X initial بيساوي V initial في T زائد نص
+
+359
+00:29:51,930 --> 00:30:00,790
+AT تربيع، ام صح؟ صحّحين، هاي كمان قانون، طيب، نرجع
+
+360
+00:30:00,790 --> 00:30:11,490
+لصف رابع، بدي T من هنا، أنتَ اه، ما هو، قوليلي، أجلّيلي T
+
+361
+00:30:13,150 --> 00:30:20,630
+حلو، إذا T بتساوي V final ناقص V initial على إيه؟ صحّحية
+
+362
+00:30:20,630 --> 00:30:27,330
+تمام؟ اه، كنا بنعرف، قال لي حلو، بنفهم دي T، نعوّض عليها؟
+
+363
+00:30:28,300 --> 00:30:31,720
+بدي أعوّضها، أشوف إيش بتطلع معايا، بصحّح ولا بصحّح
+
+364
+00:30:31,720 --> 00:30:38,960
+إيش؟ بصحّح، بقول x final ناقص x initial بتساوي v
+
+365
+00:30:38,960 --> 00:30:44,240
+initial، بدل t بدي أحط v final ناقص v initial على a
+
+366
+00:30:44,240 --> 00:30:52,040
+زائد نص a، بدي أربّح هذه v final ناقص v initial تربيع
+
+367
+00:30:52,040 --> 00:30:56,420
+على a تربيع، صح ولا لأ؟ لأنه بدي أربّح هذه وبدي
+
+368
+00:30:56,420 --> 00:31:01,330
+أربّح هذه، طيب، أما علمتكم أنكم في صف رابع، ثلث وخمس
+
+369
+00:31:01,330 --> 00:31:07,890
+كيف تجيبوه؟ ثلث وخمس، كيف كنتوا تجيبوه؟
+
+370
+00:31:07,890 --> 00:31:11,130
+جمع
+
+371
+00:31:11,130 --> 00:31:17,050
+الكسور العادية، أنسيتوها، مش من عامل مشترك، ثلث
+
+372
+00:31:17,050 --> 00:31:24,870
+وخمس، بنحط إيش في المقام؟ خلاص، إيه بالدقيقة، وصلت
+
+373
+00:31:26,590 --> 00:31:29,610
+أخذت الخمسة عشر، لأنه جيت أنا، المفروض آخذ الكبير
+
+374
+00:31:29,610 --> 00:31:32,290
+بس الكبير ما ظلطش معايا، اللي هو ثلاثة أو خمسة، روح
+
+375
+00:31:32,290 --> 00:31:36,270
+اتكبر أكثر وأكثر، دي بتطلع خمسة، لكن خمسة زائد عشرة
+
+376
+00:31:36,270 --> 00:31:40,550
+إيش، هيأخذتها عامل مشترك؟ عشرة، عشرة، صح ولا لأ؟
+
+377
+00:31:40,550 --> 00:31:44,550
+يطلع إيه، إيش بدي أسوي؟ بيقول لي أنتِ إيش عملتِ؟
+
+378
+00:31:44,550 --> 00:31:52,880
+وين أنا وصلت هنا؟ هـ .. هذي .. هذي، هي، شفتوها؟ صح؟
+
+379
+00:31:52,880 --> 00:31:56,220
+صارت اتنين إيه، وهنا إيه؟ إيش أخذ عامل مشترك؟
+
+380
+00:31:56,220 --> 00:31:58,240
+إيه؟ اتنين إيه؟ اتنين إيه؟ اتنين إيه؟ اتنين إيه؟
+
+381
+00:31:58,240 --> 00:32:00,280
+اتنين إيه؟ اتنين إيه؟ اتنين إيه؟ اتنين إيه؟ اتنين
+
+382
+00:32:00,280 --> 00:32:04,320
+إيه؟ اتنين إيه؟ اتنين إيه؟ اتنين إيه؟ اتنين إيه؟
+
+383
+00:32:04,32
+
+445
+00:37:42,120 --> 00:37:46,780
+متر per second بيقول لي what is its acceleration؟
+
+446
+00:37:46,780 --> 00:37:52,870
+بده إيه؟ assume constant عشان أستخدم الأربع معادلات
+
+447
+00:37:52,870 --> 00:37:57,430
+تمام، هيك بيقول لي if it stops in two seconds
+
+448
+00:37:57,430 --> 00:38:02,110
+بيقول لي إذا الطائرة وقفت بعد ثانيتين من ساعت ما
+
+449
+00:38:02,110 --> 00:38:07,910
+لمست الأرض، وقفت، قديش التسارع النهائي بالسرعة
+
+450
+00:38:07,910 --> 00:38:13,090
+الابتدائية ثلاثة وستين، والزمن؟ التسارع، التسارع بده
+
+451
+00:38:13,090 --> 00:38:15,790
+التسارع، ذاكروني بالقانون الأول
+
+452
+00:38:21,190 --> 00:38:26,530
+Vfinal بتساوي Vinitial زائد AT، Vfinal معطى ولا
+
+453
+00:38:26,530 --> 00:38:30,030
+مش معطى؟ معطى، Vfinal معطى ولا مش معطى؟
+
+454
+00:38:30,030 --> 00:38:30,130
+Vfinal معطى ولا مش معطى؟ Vfinal معطى ولا مش
+
+455
+00:38:30,130 --> 00:38:30,850
+معطى ولا مش معطى؟ Vfinal معطى ولا مش معطى؟
+
+456
+00:38:30,850 --> 00:38:38,650
+معطى؟ Vfinal  بيقول if the jet touches down at
+
+457
+00:38:38,650 --> 00:38:46,800
+a position x initial، يعني قال لي الـ position أول ما
+
+458
+00:38:46,800 --> 00:38:50,080
+لمست الأرض هي ما رجعتك، بدي x final، يعني قداش
+
+459
+00:38:50,080 --> 00:38:54,040
+المسافة اللي اجتعتها لما وقفت، بسيطة، مثلاً أنت جبتي
+
+460
+00:38:54,040 --> 00:38:57,120
+الزمن و الـ acceleration، قاعد في أي معادلة تجيب x
+
+461
+00:38:57,120 --> 00:39:01,180
+المعادلة الأخيرة اللي هو x final ناقص x initial
+
+462
+00:39:01,180 --> 00:39:05,080
+بيساوي v initial في t زائد نص AT تربيع، وإيه جبتها؟
+
+463
+00:39:05,080 --> 00:39:09,580
+خلصنا، إذن بيقول لي The initial point is the point at
+
+464
+00:39:09,580 --> 00:39:15,400
+which the jet hits the ground، X initial هي المسافة
+
+465
+00:39:15,400 --> 00:39:18,900
+At this point, the initial بتساوي ثلاثة و ستين متر
+
+466
+00:39:18,900 --> 00:39:23,060
+per second، و أنتو قولتوا لي، و the final قولتوا لي المسافة
+
+467
+00:39:23,060 --> 00:39:26,580
+لأنها عبارة عن stop، قال لي هذا القانون الحلو
+
+468
+00:39:26,580 --> 00:39:31,080
+بتطلع لي أول مطلوب، طلعنا، طلعت ناقص ثلاثين متر per
+
+469
+00:39:31,080 --> 00:39:37,060
+second تربيع، slowing down، مظبوط ولا لأ؟ قطع لأنه في
+
+470
+00:39:37,060 --> 00:39:41,810
+الآخر بدي أوقف، تمام، هالجيت لو الطائرة ماشية هيك اتجاه
+
+471
+00:39:41,810 --> 00:39:49,530
+التسارع؟ برافو عليكم، عكس، لأنها بتتناقص، هذه المعلومة
+
+472
+00:39:49,530 --> 00:39:54,530
+اللي عندي حلو، بجيب الـ DX، قولت له هذا القانون إيه
+
+473
+00:39:54,530 --> 00:39:59,790
+هذا ممكن أستخدمه؟ لأن أنت بديك X، V initial
+
+474
+00:39:59,790 --> 00:40:03,970
+مديتني إياها ولا لأ؟ و V final مديتني إياها ولا لأ؟ بعوض
+
+475
+00:40:03,970 --> 00:40:08,170
+هذا، هي طالع الـ 63، إيش بيقول لي، آه هنا واحد بيقول لي
+
+476
+00:40:09,850 --> 00:40:16,010
+طب لو استخدمت القانون الثاني اللي هو X final ناقص X
+
+477
+00:40:16,010 --> 00:40:20,090
+initial، يساوي V initial في T زائد نص AT تربيع
+
+478
+00:40:20,090 --> 00:40:24,250
+بتطلع جواب مختلف، نفس الجواب، طريقتين بيؤدوا إلى نفس
+
+479
+00:40:24,250 --> 00:40:30,010
+روما، هدول القانونين، هدا أنا بحبه أكتر، بس الكتاب
+
+480
+00:40:30,010 --> 00:40:34,010
+مستخدم هذا القانون، وأنا دائماً بربط الحمار زي ما
+
+481
+00:40:34,010 --> 00:40:42,850
+بده صاحبه، فهو هيك بده المثال، فخطط في الـ slides، لكن
+
+482
+00:40:42,850 --> 00:40:46,770
+أنا لو بده حوالي بحلبه هدا لإنه هدا القانون أنا
+
+483
+00:40:46,770 --> 00:40:50,890
+حافظه أكتر لإنه هدا أساسي و هداك فرعي، تمام، مش
+
+484
+00:40:50,890 --> 00:40:54,630
+مشكلة، لكن في الآخر أنا ب… أحكي، بنفع نجيب مثلاً
+
+485
+00:40:54,630 --> 00:41:01,300
+من قانون الـ DP و الـ… اللي هي delta x و delta t
+
+486
+00:41:01,300 --> 00:41:06,920
+بتعطيك سرعة متوسطة، بتعرفوا السرعة المتوسطة؟ لأ، بس
+
+487
+00:41:06,920 --> 00:41:08,980
+هو ما أعطاني السرعة الابتدائية و السرعة اللي هي هي
+
+488
+00:41:08,980 --> 00:41:14,380
+كذا، لها سحر، يعني معناته… آه بيجيبها؟ غالباً، لكن
+
+489
+00:41:14,380 --> 00:41:18,820
+صح تفكيرك، صح، تمام، بس دائماً واحد بيخش على الطريق
+
+490
+00:41:18,820 --> 00:41:25,800
+السهل، آه يا بنات، صحصحولي، بدنا نرجع أول
+
+491
+00:41:30,500 --> 00:41:35,380
+بتعرفوا،  a traveling at a constant speed of
+
+492
+00:41:35,380 --> 00:41:40,460
+40 meter per second، السيارة ماشية عدل وبسرعة ثابتة
+
+493
+00:41:40,460 --> 00:41:43,180
+والسيارة عشان تطلع بسرعة ثابتة لازم الطريق يكون
+
+494
+00:41:43,180 --> 00:41:48,140
+فاضي، و لا مطبات ولا حاجة، تمام هيك؟ في نص الليل
+
+495
+00:41:48,140 --> 00:41:52,580
+السيارة ماشية في شارع عامل مختار، وعند مفترق
+
+496
+00:41:52,580 --> 00:41:57,410
+السراية في… لوحة إعلانات كبيرة، بتعرفوها اللي
+
+497
+00:41:57,410 --> 00:42:00,930
+بيعلقوا عليها شغلات كتيرة، بيقول لي هناك متخبي شرطي
+
+498
+00:42:00,930 --> 00:42:07,750
+متخبي شرطي، السيارة وهي ماشية بأمان الله بسرعة 45
+
+499
+00:42:07,750 --> 00:42:12,330
+متر per second، باصّة، يعني مرت عن الـ trooper، الـ
+
+500
+00:42:12,330 --> 00:42:17,010
+trooper معناته شرطي متنقل أو جوال أو على موتوسيكل
+
+501
+00:42:17,010 --> 00:42:22,150
+هذا بنسميه trooper، شرطي، الـ trooper on a motorcycle
+
+502
+00:42:22,150 --> 00:42:26,810
+على موتور، وهو قاعد طافي الموتور وقاعد ومتخبي و
+
+503
+00:42:26,810 --> 00:42:30,730
+بده يصيد للسيارات اللي بتخالف، حلوة، هذه مرت بأمان
+
+504
+00:42:30,730 --> 00:42:33,730
+والدنيا ليه؟ وإيش فيه قاعد يرفض إنه في شوفت قاعد
+
+505
+00:42:33,730 --> 00:42:40,440
+متخبي؟ ماشية بسرعة كبيرة، 45 متر per second، قال لي
+
+506
+00:42:40,440 --> 00:42:44,620
+hidden behind a billboard، هذا الشرطي، hidden يعني
+
+507
+00:42:44,620 --> 00:42:49,280
+متخبي خلف billboard يعني لوحة إعلانات اللي قلت
+
+508
+00:42:49,280 --> 00:42:53,580
+عنها توي في الصراية، حلو، بيقول لي بعد ما اكتشف أن
+
+509
+00:42:53,580 --> 00:42:57,280
+هذه قاعدة ماشية بسرعة كبيرة، أكبر من السرعة
+
+510
+00:42:57,280 --> 00:43:02,220
+المسموح تمشي فيها، قال لي، قبل ما يفكر وشغل كانت مرة
+
+511
+00:43:02,220 --> 00:43:05,680
+ثانية، ثانية مش كتير، لكن الثانية كانت في السيارة
+
+512
+00:43:05,680 --> 00:43:11,010
+جنبه ولا مشيت، ماشية، بيقول لي one second
+
+513
+00:43:11,010 --> 00:43:15,790
+بعد ثانية، after the speeding car passes the
+
+514
+00:43:15,790 --> 00:43:19,630
+billboard، بعد ثانية ما مرت السيارة عن الـ billboard
+
+515
+00:43:19,630 --> 00:43:23,250
+اللي هي اللوحة، وهو الشرطي نفسه ما هناك كان واقف
+
+516
+00:43:23,250 --> 00:43:27,250
+قال لي the trooper sits out from the billboard
+
+517
+00:43:27,250 --> 00:43:32,070
+انطلق من الـ billboard وراح يلحق السيارة، اتفجنا يا
+
+518
+00:43:32,070 --> 00:43:38,610
+بنات؟ بعد ثانية من مرور السيارة، تم out of from the
+
+519
+00:43:38,610 --> 00:43:41,550
+billboard to catch the car accelerating، كان واقف
+
+520
+00:43:41,550 --> 00:43:45,430
+التروبر، إيه تسارع التروبر ابتدائي، لأنه كان واقف
+
+521
+00:43:45,430 --> 00:43:51,650
+تسارع التروبر ثانياً ثلاثة متر per second، حلو، how
+
+522
+00:43:51,650 --> 00:43:55,830
+long does it take، قديش للتروبر أخذ زمن عشان يمسك
+
+523
+00:43:55,830 --> 00:44:00,970
+السيارة، يلحقها، فاهم السؤال، أول بالعربي، بعدين
+
+524
+00:44:00,970 --> 00:44:05,750
+بنترجمه علمياً، الآن، واحدة واحدة، هالجيت بتطلع لي على
+
+525
+00:44:05,750 --> 00:44:10,750
+الـ car، كلمة constant speed إيش يعني؟ قديش
+
+526
+00:44:10,750 --> 00:44:16,190
+تسارعه؟ صفر، مظبوط ولا لأ؟ هو بيقول لي الـ car
+
+527
+00:44:16,190 --> 00:44:22,370
+كانت تمشي بسرعة ثابتة، يعني تسارعها يساوي صفر، بدي
+
+528
+00:44:22,370 --> 00:44:27,310
+أعمل هيك وأعمل هيك وأقول هذا الـ car وهذا الـ
+
+529
+00:44:27,310 --> 00:44:34,810
+trooper، إيش trooper يعني؟ الشرطي، أول حاجة، إيه للـ
+
+530
+00:44:34,810 --> 00:44:39,710
+car بتساوي صفر؟ من أين عرفت؟ من الـ constant speed
+
+531
+00:44:39,710 --> 00:44:46,410
+إذا هو اللي قال لي، إيه للـ trooper بتساوي ثلاثة متر
+
+532
+00:44:46,410 --> 00:44:49,930
+per second تربيع؟ هيه أعطاني إياها ولا ما أعطاني إياها؟
+
+533
+00:44:49,930 --> 00:44:56,190
+تمام؟ إيش بده؟ قال لي بده الزمن اللي أخذه الشرطي
+
+534
+00:44:56,190 --> 00:45:00,570
+إذا أنا بدي أشغل ساعة الإيقاف أول ما يتحرك الشرطي
+
+535
+00:45:01,400 --> 00:45:06,460
+مظبوط ولا لأ؟ لأنه بدي الزمن اللي بيستغرقه الشرطي، حلو، هالجيت
+
+536
+00:45:06,460 --> 00:45:10,800
+هما مروا على بعض عند وين؟ عند السراية، وهو ماشي
+
+537
+00:45:10,800 --> 00:45:15,960
+هالجيت، بدهم يمسكوا بعض، في مجال إنهم يمسكوا بعض يكون
+
+538
+00:45:15,960 --> 00:45:21,070
+الشرطي عند السامر والسيارة عند الساحة؟ لازم يكونوا
+
+539
+00:45:21,070 --> 00:45:24,310
+في نفس المكان، ولا لأ؟ إذا أنت عشان بتقول لي بيبقوا
+
+540
+00:45:24,310 --> 00:45:28,190
+يمسكوا بعض، لازم X final للشرطي تساوي X final
+
+541
+00:45:28,190 --> 00:45:31,990
+للسيارة، ولا لأ؟ هذه فكرة السؤال، طب إيش بقى كنت
+
+542
+00:45:31,990 --> 00:45:35,410
+تسوي؟ قال لي جيب X final للسيارة و X final للتروبر
+
+543
+00:45:35,410 --> 00:45:39,910
+وسويهم ببعض، صح ولا لأ؟ بتطلع إيه اللي بدك إياه، طيب
+
+544
+00:45:39,910 --> 00:45:46,190
+نرجع، قال لي V للـ car بتساوي 45 متر per second، مش أنت
+
+545
+00:45:46,190 --> 00:45:53,300
+قلت لي هيها، V initial لـ trooper بتساوي صفر؟ فح؟
+
+546
+00:45:53,300 --> 00:46:00,580
+هذه معطى؟ تمام؟ بقول له يلا نشتغل، بقول له X initial
+
+547
+00:46:00,580 --> 00:46:04,920
+للسيارة، إيش يعني initial، أول ما يتحرك الشرطي؟ كانت
+
+548
+00:46:04,920 --> 00:46:09,480
+جنبه؟ كيف بدي أعرف قديش وين كانت؟ بقول له مش أنت أعطيتني
+
+549
+00:46:09,480 --> 00:46:14,540
+سرعتها؟ 45 في قديش؟ في واحد، لأن واحد ثانية
+
+550
+00:46:16,660 --> 00:46:21,940
+initial للـ car بتساوي V initial للـ car في T اللي
+
+551
+00:46:21,940 --> 00:46:26,360
+هو واحد second، ولا لأ؟ هتتهادي initial للـ car هي
+
+552
+00:46:26,360 --> 00:46:30,920
+نفسها، ما هو ما بتتغيرش، بتساوي خمسة وأربعين متر
+
+553
+00:46:30,920 --> 00:46:39,200
+هذه X initial للـ car، مظبوط ولا لأ؟ تمام، اتحرك
+
+554
+00:46:39,200 --> 00:46:44,240
+الشرطي، هذه السيارة هنا وصلت هنا، هذه المسافة 45 متر
+
+555
+00:46:44,240 --> 00:46:52,180
+بدأ يبدأ يجري، حلو، بقول X final ناقص X initial للـ
+
+556
+00:46:52,180 --> 00:46:58,160
+car بتساوي V initial للـ car في T زائد نصف A للـ
+
+557
+00:46:58,160 --> 00:47:01,680
+car في T تربيع، سمعتوا بالقانون هذا؟ طيب الـ A للـ
+
+558
+00:47:01,680 --> 00:47:05,120
+car قد إيش؟ إذا هذه ما كانت دعوة فيها يا ابني، هذه
+
+559
+00:47:05,120 --> 00:47:13,080
+صفر، ماهي مش صفر، تم، X final للـ car ناقص خمسة
+
+560
+00:47:13,080 --> 00:47:19,180
+وأربعين، بتساوي خمسة وأربعين T، ولا لأ؟ وقف
+
+561
+00:47:19,180 --> 00:47:25,760
+هنا، خلاص، اجت هذه، تمام؟ حلو، نيجي للشرطي حبيبنا
+
+562
+00:47:25,760 --> 00:47:33,090
+بقول له X final ناقص X initial للـ trooper بتساوي V
+
+563
+00:47:33,090 --> 00:47:39,490
+initial للتروبر في T زائد نص A للتروبر في T تربيع، مش
+
+564
+00:47:39,490 --> 00:47:45,670
+هذا قانون، قديش V initial للتروبر؟ برافو عليكم، هذه
+
+565
+00:47:45,670 --> 00:47:50,630
+كانت صفر، ولا ما صفر، إذا X final للتروبر بتساوي نص
+
+566
+00:47:50,630 --> 00:47:59,290
+في ثلاثة في T تربيع، ثلاثة في نص… واحد ونص… ثلاثة
+
+567
+00:47:59,290 --> 00:48:02,190
+في اثنين… مظبوط… واحد ونص… أجيب هذه وأحط
+
+568
+00:48:02,190 --> 00:48:06,870
+واحد ونص… قعد واحد يقول ليش اللي عملته… واحد
+
+569
+00:48:06,870 --> 00:48:09,250
+و نص… مهو كان… إذا هيسرح… مهو يقول كانت ثلاثة
+
+570
+00:48:09,250 --> 00:48:12,850
+في اثنين، إيش اللي ودّيتها… صارت… تمام… حلو…
+
+571
+00:48:12,850 --> 00:48:18,050
+هالجيت مسكوا بعض، إذا قطعاً هذه بتساوي هذه، صح
+
+572
+00:48:18,050 --> 00:48:21,290
+…إذا مازال بتقول لي واكتشف، يعني مسكوا بعض، إذا
+
+573
+00:48:21,290 --> 00:48:25,630
+قطعاً مسكوا بعض عند السامر أو عند الساحة… احكي…
+
+574
+00:48:35,740 --> 00:48:44,860
+خمسة وأربعين، المسافة بتساوي السرعة في الزمن، السرعة
+
+575
+00:48:44,860 --> 00:48:47,880
+خمسة وأربعين، والزمن واحد، اضربي
+
+576
+00:48:55,000 --> 00:49:00,140
+بس طبعاً مهما خلوها تسأل، أنا بدي أنا أتسأل، طلع one
+
+577
+00:49:00,140 --> 00:49:05,020
+second، إذا الـ one second أنا اخترعت اختراع؟ تمام
+
+578
+00:49:05,800 --> 00:49:10,940
+حلو، برافو عليكي، تمام يا بنات، اتطلعوا يا بنات، بقول
+
+579
+00:49:10,940 --> 00:49:16,420
+عشان الشرطي يمسك السيارة لازم X للشرطي تساوي X
+
+580
+00:49:16,420 --> 00:49:22,160
+للسيارة final، إذا معناته لازم يكون خمسة و
+
+581
+00:49:22,160 --> 00:49:27,120
+أربعين، آه بدي أجيب هذه هنا يا بنات، خمسة و
+
+582
+00:49:27,120 --> 00:49:31,400
+أربعين زائد خمسة وأربعين T تساوي واحد ونص T تربيع
+
+583
+00:49:31,400 --> 00:49:37,740
+سويت هذه بهذه، مظبوط هيك ولا لأ؟ بدي أرتب المعادلة
+
+584
+00:49:37,740 --> 00:49:42,280
+أرتبها، أجيب هدول الاثنين الحلوين هنا، صارت واحد و
+
+585
+00:49:42,280 --> 00:49:47,860
+نصف T تربيع زائد خمسة وأربعين T زائد خمسة وأربعين
+
+586
+00:49:47,860 --> 00:49:55,180
+بتساوي صفر، هذه معادلة من الدرجة الثانية، بتديك حل…
+
+587
+00:49:55,180 --> 00:50:00,960
+أكم حل؟ حل، ليه؟ حل… حلو، هذه معادلة رياضية جبرية
+
+588
+00:50:00,960 --> 00:50:04,440
+أخدتها زمان أنا، بالنسبة للفيزياء، بيقص اللي عندنا أخد
+
+589
+00:50:04,440 --> 00:50:09,160
+عشرة من عشرة، والباقي ما بديش إياه، ليش؟ لأن طب و
+
+590
+00:50:09,160 --> 00:50:12,980
+قلت لكم مين مش مخلّص رابع، وقلت لكم، وخلصنا رابع، و
+
+591
+00:50:12,980 --> 00:50:16,800
+خلصتوا تامين، إذا خلاص أنا متأكد، ما بدي تحلّوا رابع و
+
+592
+00:50:16,800 --> 00:50:21,440
+تامين، هالجيت من هنا لما إجيت حلت يا بنات، طلعت T
+
+593
+00:50:21,440 --> 00:50:26,170
+بتساوي واحد وثلاثين second، صدّقنا الكتاب، احنا بدنا
+
+594
+00:50:26,170 --> 00:50:29,750
+نرجع لرقم 48، صدّقنا الكتاب، طبعاً كده بتتأكد أنه صح
+
+595
+00:50:29,750 --> 00:50:33,850
+ولا لأ، بروح بعوض، بتتحقق المعادلة، معناته أكيد صادق
+
+596
+00:50:33,850 --> 00:50:39,670
+طيب، طلعت الزمن زي ما بدك، لو إيه سألني وين مسكه
+
+597
+00:50:39,670 --> 00:50:44,390
+بعض، معناته مش بالـ position، ولا لأ؟ طب أعوّض هلّأ ولا
+
+598
+00:50:44,390 --> 00:50:44,770
+هلّأ
+
+599
+00:50:48,110 --> 00:50:54,010
+ما هما زي بعض، عوّض هنا ولا عوّض هنا، هتطلع عندك نفس
+
+600
+00:50:54,010 --> 00:50:58,930
+الإجابة، ولا لأ؟ طلعت حوالي one point أربعة أربعة
+
+601
+00:50:58,930 --> 00:51:02,950
+في عشرة أس ثلاثة متر، يعني حوالي واحد ونصف كيلو
+
+602
+00:51:02,950 --> 00:51:06,730
+ألف وأربعمائة وأربعين متر، يعني حوالي واحد ونصف
+
+603
+00:51:06,730 --> 00:51:11,750
+كيلو، واحنا قلنا من عند الصراية للسامر يدوب كيلو
+
+604
+00:51:11,750 --> 00:51:16,200
+يدوب للساحة، تكون هذه المسافة، عشان نضلنا نجدر
+
+605
+00:51:16,200 --> 00:51:20,760
+المسافات، مش الواحد يفكر حاله يمشي من الصراية
+
+606
+00:51:20,760 --> 00:51:24,120
+للساحة، يقول أمي والله مشيت اليوم كتير، ويقول
+
+607
+00:51:24,120 --> 00:51:28,740
+ما مشيت… مش كيلو، نص وكيلو، لما يجوا يعملوا
+
+608
+00:51:28,740 --> 00:51:31,620
+برامج الرياضة، بيقول لك بيجي تمشي لك خمسة ستة كيلو
+
+609
+00:51:31,620 --> 00:51:36,360
+عقل شيء، مش تمشي كيلو ونص
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/H4drweiMiJA_postprocess.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/H4drweiMiJA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7f45de1f4f580a00b53d9360f37d44ea076b632c
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/H4drweiMiJA_postprocess.srt
@@ -0,0 +1,2444 @@
+1
+00:00:05,150 --> 00:00:11,190
+تمام يا بنات نستكمل وقفنا بعد ما أخدنا ال velocity
+
+2
+00:00:11,190 --> 00:00:18,850
+وقلنا ال velocity هي كمية فيزيائية بتعني أن ال
+
+3
+00:00:18,850 --> 00:00:23,830
+position بتغير مع الزمن وعنا average velocity
+
+4
+00:00:23,830 --> 00:00:28,790
+وعندي instantaneous velocityالـ Average Velocity
+
+5
+00:00:28,790 --> 00:00:34,070
+عرفناها على إنها V Average بيسوى Delta X على Delta
+
+6
+00:00:34,070 --> 00:00:39,750
+T وال Instantaneous Velocity بتسوى Limit تبع الـ
+
+7
+00:00:39,750 --> 00:00:49,530
+DT يعني DX على DT تمهى نجي لها ال quiz نشوف كنا
+
+8
+00:00:49,530 --> 00:00:53,950
+نحكي عربي ولا لأ consider the one dimensional
+
+9
+00:00:53,950 --> 00:00:59,980
+motion إيش هي؟بقول a ball is thrown vertically
+
+10
+00:00:59,980 --> 00:01:04,180
+upward دي بتكرة و رامتها لأعلى تمام سخوط حر ولا
+
+11
+00:01:04,180 --> 00:01:11,140
+لا؟ تمامRises to a highest point and falls back
+
+12
+00:01:11,140 --> 00:01:15,580
+into the thrower's hand ورجعت على إيده انطلقت من
+
+13
+00:01:15,580 --> 00:01:18,460
+إيده ورجعت على إيده مين يقول ليه جديش ال average
+
+14
+00:01:18,460 --> 00:01:23,360
+velocity؟ سفر صح ولا لأ ال average velocity سفر
+
+15
+00:01:23,360 --> 00:01:26,940
+تمام معلومة خزنتها جوا هذه الحركة ال average
+
+16
+00:01:26,940 --> 00:01:33,420
+velocity ليه جديش؟ سفر A car or a race car سيارة
+
+17
+00:01:33,420 --> 00:01:37,840
+سباق تمام الـ Stars fall from rest بدأت من السكون
+
+18
+00:01:37,840 --> 00:01:44,180
+وضلت تمشي and the speeds up ووصلت سرعة 100 متر per
+
+19
+00:01:44,180 --> 00:01:49,200
+second وصلت طبعا ماوصلتش مرة واحدة ضلها تتزيد صح
+
+20
+00:01:49,200 --> 00:01:53,280
+ولا لأ؟ لو إتيت بدي أخذ انجداش ال average velocity
+
+21
+00:01:53,280 --> 00:01:57,980
+تبعتها خمسين ستين أربعين مظبوط ولا لأ؟ رقم من
+
+22
+00:01:57,980 --> 00:02:02,520
+هالأرقام اتفاجنا؟ إذا زيادة منتظمة بتكون السرعة
+
+23
+00:02:02,520 --> 00:02:06,410
+المتوسطة من النص بالظبطإذا منتظمة إذا مش منتظمة
+
+24
+00:02:06,410 --> 00:02:10,230
+بتكون إما انقلة أو أكتر مش مشكلة إنما رقم ما بين
+
+25
+00:02:10,230 --> 00:02:16,610
+صفر اللامية صح ولا لأ تمام space craft سفينة فضاء
+
+26
+00:02:17,190 --> 00:02:21,890
+ماشي في الفضاء drift through space بتمشي في ال
+
+27
+00:02:21,890 --> 00:02:25,710
+space ال space يعني فراغة ال constant velocity
+
+28
+00:02:25,710 --> 00:02:31,170
+سرعتها ثابتة مين يقولي إيش بتفرج لما تكون السرعة
+
+29
+00:02:31,170 --> 00:02:36,590
+ثابتة سرعة ثابت الحظية عن ال average نفسها نفسها
+
+30
+00:02:36,590 --> 00:02:43,220
+صح ولا لا نفسها يعني لو كانت بتمشي بسرعةثابتة
+
+31
+00:02:43,220 --> 00:02:46,760
+مقدارها مائة كيلومتر في الساعة ال average مية وال
+
+32
+00:02:46,760 --> 00:02:49,440
+instant هو مائة .. مائة .. مائة .. مائة .. مائة ..
+
+33
+00:02:49,440 --> 00:02:51,100
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+34
+00:02:51,100 --> 00:02:51,120
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+35
+00:02:51,120 --> 00:02:51,180
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+36
+00:02:51,180 --> 00:02:53,140
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+37
+00:02:53,140 --> 00:02:54,360
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+38
+00:02:54,360 --> 00:02:57,840
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+39
+00:02:57,840 --> 00:03:01,090
+مائة .. مائة .. مThere are any points في نقطة
+
+40
+00:03:01,090 --> 00:03:05,510
+أثناء الحركة at which the instantaneous velocity
+
+41
+00:03:05,510 --> 00:03:09,230
+has the same value as the average velocity over
+
+42
+00:03:09,230 --> 00:03:13,050
+the entire motion. إيش يعني؟ بقول في التلت حركات
+
+43
+00:03:13,050 --> 00:03:18,350
+أنت خزنت السرعة المتوسطة ولا لأ؟الأولى قلنا zero
+
+44
+00:03:18,350 --> 00:03:24,110
+والتانية قلنا حوالي من اربعين، خمسين، ستين
+
+45
+00:03:24,110 --> 00:03:27,770
+والتالتة ما هي نفس المقدار بيقول لمين من هدول
+
+46
+00:03:27,770 --> 00:03:32,630
+بتكون السرعة اللحظية عند لحظة ما تساوي السرعة
+
+47
+00:03:32,630 --> 00:03:39,070
+المتوسطةطب يشوف الأولى، جديش السرعة المتوسطة، في
+
+48
+00:03:39,070 --> 00:03:42,330
+الأولى، في لحظة من اللحظات في سقوط الحر بتكون
+
+49
+00:03:42,330 --> 00:03:47,220
+السرعة اللحظية سفر، عند أقصى ارتفاع، لذا فيه؟أذن
+
+50
+00:03:47,220 --> 00:03:53,080
+حيثي خلصنا عند لحظة طيب مافي تم السؤال التانية وهو
+
+51
+00:03:53,080 --> 00:03:57,400
+ماشي لما يصل المية مر على العشرة والعشين والتلاتين
+
+52
+00:03:57,400 --> 00:04:00,800
+والاربعين والخمسين والستين ولا لأ اذا في لحظة من
+
+53
+00:04:00,800 --> 00:04:04,120
+اللحظات كان سرعته خمسين وفي لحظة من اللحظات كانت
+
+54
+00:04:04,120 --> 00:04:07,260
+اربعين وفي لحظة من اللحظات كانت ستين اذا ال
+
+55
+00:04:07,260 --> 00:04:10,180
+average خمسين في نقطة وصلة خمسين اذا ال average
+
+56
+00:04:10,180 --> 00:04:13,900
+ستين في نقطة وصلة ستين صح ولا لأ اذا برضه صحيحة
+
+57
+00:04:14,050 --> 00:04:18,990
+والتالتة ما هي واضحة إنها صحيحة إذا معناته في
+
+58
+00:04:18,990 --> 00:04:22,050
+الأولى ولا في التانية ولا في التالتة ولا في كلهم
+
+59
+00:04:22,050 --> 00:04:27,730
+في كلهم تمام الآن
+
+60
+00:04:27,730 --> 00:04:34,690
+بدي نحكي عن ال acceleration تسارعطبعا نرجع دايما
+
+61
+00:04:34,690 --> 00:04:39,110
+نقول لكل مسمى من اسمه نصيب سموه تسارع لأنه مش سرعة
+
+62
+00:04:39,110 --> 00:04:43,890
+تسارع لغويا يعني تسارعة جاعة بيه السرعة بتتغير ..
+
+63
+00:04:43,890 --> 00:04:51,130
+بتتغير هنا بشتق X بالنسبالتي يعني اللي بتغير X
+
+64
+00:04:51,130 --> 00:04:57,630
+طلعت سرعة جالي لو جمت X وحطيت V تطلع تسارعةتمام؟
+
+65
+00:04:57,630 --> 00:05:01,630
+لأن إيش اللي بدى يتغير؟ السرعة إذا لو تغيرت ..
+
+66
+00:05:01,630 --> 00:05:05,690
+بالنسبالي الزمن .. لو تغيرت السرعة بنقول الجسم له
+
+67
+00:05:05,690 --> 00:05:09,350
+تسارع اتفجنا هيك؟ إذا هيك عارف الـ acceleration
+
+68
+00:05:09,350 --> 00:05:14,150
+when the velocity of a particle velocity عارفناش
+
+69
+00:05:14,150 --> 00:05:18,650
+معناتها varies with time أو changes with time
+
+70
+00:05:18,650 --> 00:05:22,390
+بتتغير مع الزمنThe particle is said to be
+
+71
+00:05:22,390 --> 00:05:29,130
+accelerating بمعنى
+
+72
+00:05:29,130 --> 00:05:34,310
+آخر has an acceleration لما تكون السرعة ثابتة
+
+73
+00:05:34,310 --> 00:05:41,310
+تتغير جدش تسرعه سفرصح ولا لأ؟ إيش معناته؟ بيقوللي
+
+74
+00:05:41,310 --> 00:05:46,430
+معناته حيكون في عندك كميتين إجداد إيش هي؟ بيقوللي
+
+75
+00:05:46,430 --> 00:05:51,630
+A average بتسوي delta V على delta T شوف إيش اللي
+
+76
+00:05:51,630 --> 00:05:57,750
+اتغير؟ V اتغيرت الآن و A instantaneous بتسوي
+
+77
+00:05:57,750 --> 00:06:04,620
+مستقلة مين؟ DV على DTإذا بدل ما تتغير ال position
+
+78
+00:06:04,620 --> 00:06:09,100
+اتغير الآن السرعة اتغيرت السرعة صار في عندي
+
+79
+00:06:09,100 --> 00:06:12,960
+acceleration اتفقنا يا بنات؟ إذا ال acceleration
+
+80
+00:06:12,960 --> 00:06:16,940
+في عندك average وفي عندك instantaneous
+
+81
+00:06:19,500 --> 00:06:25,860
+اللي هو ده المشطقة طيب مشطقة ال V ماعرف اشطقها طب
+
+82
+00:06:25,860 --> 00:06:29,540
+هي ال V مش جاية من اشتقاق ال X إذا لو أشطقت ال X
+
+83
+00:06:29,540 --> 00:06:33,660
+مرتين بتطلع تسارع ولا لأ؟ إذا هذه التسارع ممكن
+
+84
+00:06:33,660 --> 00:06:37,200
+أقول هي المشطقة التانية ل X بالنسبة للزمن أه أول
+
+85
+00:06:37,200 --> 00:06:40,770
+مرة أشطق بتطلع سرعة أشطق مرة مرة بتطلع تسارعصحيح
+
+86
+00:06:40,770 --> 00:06:46,290
+ولا لا؟ تمام التسارعة كمية فيزيائية مشهورة، جديدة،
+
+87
+00:06:46,290 --> 00:06:50,650
+لا هي L ولا هي M ولا هي T لكن هي L على T تربيع ولا
+
+88
+00:06:50,650 --> 00:06:53,870
+لا؟ L على T تربيع معناته وحداتها متر per second
+
+89
+00:06:53,870 --> 00:06:57,290
+تربية أو centimeter per second تربية أو foot per
+
+90
+00:06:57,290 --> 00:07:01,770
+second تربية الوحدة الـ SI unit في النظام العالمي
+
+91
+00:07:01,770 --> 00:07:06,770
+متر per second تربية لاحظت أننا حكينا حاجة جديدة؟
+
+92
+00:07:06,770 --> 00:07:15,120
+سهلة، تمامجالي حلو جالي الاشتقاق ربطيلي يا ب ميل
+
+93
+00:07:15,120 --> 00:07:22,640
+ولا لأ مشهور اشتقاق ميل حلو طيب هدي ميل و هدي ميل
+
+94
+00:07:22,640 --> 00:07:26,600
+هدي ميل الخط الواصل ما بين النقطتي البداية
+
+95
+00:07:26,600 --> 00:07:33,640
+والنهاية ولا لأو هذه ميل الخط المماس للرسم عند
+
+96
+00:07:33,640 --> 00:07:39,080
+نقطة ما صح؟ اذا بقوللي in the velocity لما يكون
+
+97
+00:07:39,080 --> 00:07:44,840
+عندك رسمة بين ال V و ال T لان مش ال X و ال T ال V
+
+98
+00:07:44,840 --> 00:07:49,720
+و ال T in the velocity time graph اي رسمة هذه
+
+99
+00:07:49,720 --> 00:07:54,270
+بنسميها velocity time graph graph رسمةبقول لي the
+
+100
+00:07:54,270 --> 00:07:59,630
+average acceleration if the slope هو الميل of the
+
+101
+00:07:59,630 --> 00:08:05,840
+line connecting هاي بداية و هاي نهايةأعمل خط جيب
+
+102
+00:08:05,840 --> 00:08:09,400
+ميله هذه هي ال average acceleration ال average
+
+103
+00:08:09,400 --> 00:08:12,720
+acceleration اذا the average acceleration is the
+
+104
+00:08:12,720 --> 00:08:17,620
+slope ميل of the line connecting the initial and
+
+105
+00:08:17,620 --> 00:08:20,800
+the final points اللي بربط من نقطتي البداية
+
+106
+00:08:20,800 --> 00:08:26,910
+والنهاية while بينماThe instantaneous acceleration
+
+107
+00:08:26,910 --> 00:08:31,750
+at any time is the slope of the tangent at that
+
+108
+00:08:31,750 --> 00:08:36,450
+time هو ميلي المماس يعني أنا بدي عند النقطة هادي
+
+109
+00:08:36,450 --> 00:08:42,890
+عند هذه النقطة بقوله بسيطة بدي أعمل مماس صح؟ و بدي
+
+110
+00:08:42,890 --> 00:08:46,570
+بميله كان أفق السفر كانت عند النقطة هادي بعمل هيك
+
+111
+00:08:46,570 --> 00:08:50,790
+صح ولا لأ؟ و بدي بميله هذه مفهومة و معروفة بس
+
+112
+00:08:50,790 --> 00:08:54,270
+بنذكر بعض فينا هيا أحكي يا بنتي
+
+113
+00:09:01,430 --> 00:09:05,450
+مثل البرسكين التربيع ال acceleration ال velocity
+
+114
+00:09:05,450 --> 00:09:10,350
+المكتوب هنا velocity بخطأ هذه خطأ مطبعي و هنا شوف
+
+115
+00:09:10,350 --> 00:09:13,890
+اه هذه acceleration ماحنا نحكي عن ال acceleration
+
+116
+00:09:13,890 --> 00:09:17,470
+مفهومة بس هذه خطأ مطبعي هذه كلمة acceleration
+
+117
+00:09:17,470 --> 00:09:18,190
+كلامك صحية
+
+118
+00:09:23,530 --> 00:09:28,690
+إذن هذه نقطة بداية وهذه نقطة نهاية بت الخط جالي
+
+119
+00:09:28,690 --> 00:09:31,730
+هادى the slope of the line connecting A and B is
+
+120
+00:09:31,730 --> 00:09:36,530
+the average acceleration between A and B بد الصرعة
+
+121
+00:09:36,530 --> 00:09:42,930
+عند النقطة B لحظة باخد tangent و باخد ميلو معروفة
+
+122
+00:09:42,930 --> 00:09:48,410
+تكرار للكلام اللي حاكيناه تمام هلجيت ال velocity
+
+123
+00:09:48,410 --> 00:09:51,690
+قولنا بتختلف عن ال speed ولا لأ ال velocity اللي
+
+124
+00:09:51,690 --> 00:09:55,600
+لها directionو عشان احنا في chapter 2 لسه ماخلصناش
+
+125
+00:09:55,600 --> 00:09:59,760
+chapter 3 قلنا ال direction بدنا نستعيد عنه موجب و
+
+126
+00:09:59,760 --> 00:10:04,780
+سالب و قلنا الحركة العمودية لأعلى موجب و لأسفل
+
+127
+00:10:04,780 --> 00:10:10,100
+سالب و الحركة الأفقية يمين موجب و يسار سالب تمه و
+
+128
+00:10:10,100 --> 00:10:14,340
+قاللي هذه ممكن تغيرها حسب انت ايش بدك لكن هذا ال
+
+129
+00:10:14,340 --> 00:10:18,020
+default حلو قاللي ال acceleration جاية من ال
+
+130
+00:10:18,020 --> 00:10:21,980
+velocityفهمتوا عليا؟ يعني معناته إيها direction
+
+131
+00:10:21,980 --> 00:10:26,360
+لأن ال velocity إيها direction جالي حلو جالي
+
+132
+00:10:26,360 --> 00:10:28,640
+معناته ال acceleration ممكن تكون موجبة وممكن تكون
+
+133
+00:10:28,640 --> 00:10:32,920
+سالبة مش حسب ال direction حسب ال direction تمه
+
+134
+00:10:32,920 --> 00:10:39,040
+جالي the acceleration is positive اتجاهها positive
+
+135
+00:10:39,040 --> 00:10:43,980
+موجب يعني باتجاه يمين أو يسار حسب موجبك when the
+
+136
+00:10:43,980 --> 00:10:49,140
+velocity is increasing لما تكون السرعة متزايدةin
+
+137
+00:10:49,140 --> 00:10:54,620
+the positive x direction speeding up بزيادة السرعة
+
+138
+00:10:54,620 --> 00:10:58,540
+أديكم trick أخدتهوا في ال calculus أديكم سؤال في
+
+139
+00:10:58,540 --> 00:11:03,440
+توجيهي أديكم دالة وقالكم هادي الدالة دالة بتعرف ما
+
+140
+00:11:03,440 --> 00:11:07,800
+دالة function بتاخدوها متزايدة ولا متنقصة كيف
+
+141
+00:11:07,800 --> 00:11:09,580
+تعملوا كنتوا تشتقوها
+
+142
+00:11:12,570 --> 00:11:17,530
+إذا موجبة تقولوا عنها متزايدة، مظبوط ولا لا؟ حلو،
+
+143
+00:11:17,530 --> 00:11:21,990
+هاي نقعد نتطبق، أنا مش اللي تسارع اشتقاق ال
+
+144
+00:11:21,990 --> 00:11:26,710
+velocity، إذا ال velocity بتزيد، ده اللي ما هي،
+
+145
+00:11:26,710 --> 00:11:30,570
+تتوقع ال acceleration تكون موجبة ولا لا؟ صحيح؟ طب
+
+146
+00:11:30,570 --> 00:11:35,750
+وإذا بتتناقص، تطلع سالبة؟بهذه الحالة إيش بيقول
+
+147
+00:11:35,750 --> 00:11:38,410
+ليه؟ Velocity and acceleration are in the same
+
+148
+00:11:38,410 --> 00:11:43,110
+direction لما تكون السرعة بتزيد ها انتبهولي دخلوا
+
+149
+00:11:43,110 --> 00:11:47,330
+المعلومة في مخكم إذا السرعة بتزيد التصارع والسرعة
+
+150
+00:11:47,330 --> 00:11:54,210
+بنفس الاتجاه تمام مش هنتنقلهم اتجاه السرعة بتزيد
+
+151
+00:11:54,210 --> 00:12:00,390
+هجيت هديكم trick واحد رايح على انصرات كيف تجه
+
+152
+00:12:00,390 --> 00:12:07,070
+سرعته؟تجاه انصرات سرعته بتزيد كيف التسارع اتجاهه
+
+153
+00:12:07,070 --> 00:12:13,070
+انصرات انصرات انصرات اتفقنا هيك حلو طلعوا الواحدة
+
+154
+00:12:13,070 --> 00:12:17,950
+التانية بيقولني the acceleration is negativewhen
+
+155
+00:12:17,950 --> 00:12:22,770
+the velocity is decreasing بتتناقص in the positive
+
+156
+00:12:22,770 --> 00:12:25,070
+x direction أنا ماخد ال positive x direction ال
+
+157
+00:12:25,070 --> 00:12:29,830
+default تمام slowing down velocity and
+
+158
+00:12:29,830 --> 00:12:33,530
+acceleration are in opposite direction بيكونوا عكس
+
+159
+00:12:33,530 --> 00:12:39,330
+بعض يعني نرجع سيارة رايحة عنصرات و قاعدة بتتباطع
+
+160
+00:12:39,330 --> 00:12:43,970
+بدأت توقف في الآخرهيجيت هي وين رايحة؟ عن صراط،
+
+161
+00:12:43,970 --> 00:12:49,310
+صرعتها كيف اتجاهها؟ عن صراط، تساروحها؟ ع جباليا، ع
+
+162
+00:12:49,310 --> 00:12:55,250
+جباليا، العكس، فهمتوا عليا؟ إذا إذا الصرعة تتزايد،
+
+163
+00:12:55,250 --> 00:13:00,730
+الصرعة والتسارع مع بعض، إذا الصرعة بتتناقص، الصرعة
+
+164
+00:13:00,730 --> 00:13:04,430
+والتسارع عكس بعض، دخلة المعلومة، هجيت positive ولا
+
+165
+00:13:04,430 --> 00:13:08,770
+negative جثة تانية، حسب positive تبعيتمام؟ حسب انت
+
+166
+00:13:08,770 --> 00:13:12,210
+ايش ماخده الـ positive ماخده الشرق ولا الغرب أما
+
+167
+00:13:12,210 --> 00:13:15,350
+لازم يكونوا مع بعض إذا السرعة بتزيد و لازم يكونوا
+
+168
+00:13:15,350 --> 00:13:21,610
+ضد بعض إذا كانت تتناقص تمام يا بنات؟ أي استفسار؟
+
+169
+00:13:21,610 --> 00:13:29,110
+دخلنا المعلومة هذه quiz نشوف إيش كنا نحكي صيني ولا
+
+170
+00:13:29,110 --> 00:13:37,170
+عربي؟ تماميقولني if a car is travelling eastward
+
+171
+00:13:37,170 --> 00:13:42,290
+رايحة شرق، اتجاه السرعة كيف؟ شرق، هو هذي معطى،
+
+172
+00:13:42,290 --> 00:13:49,350
+مبينةواضحة وصريحة and slowing down تتباطى تباطى
+
+173
+00:13:49,350 --> 00:14:01,870
+تباطى
+
+174
+00:14:01,870 --> 00:14:09,010
+تباطى تباطى تباطى
+
+175
+00:14:09,010 --> 00:14:11,770
+تباطى تباطى تباطى تباطى تباطى تباطى تباطى تباطى
+
+176
+00:14:11,770 --> 00:14:11,910
+تباطى تباطى تباطى تباطى تباطى تباطى تباطى تباطى
+
+177
+00:14:11,910 --> 00:14:14,730
+تباطى تباطى تباطى تباطى تباطى تباطى تباطEast نعب
+
+178
+00:14:14,730 --> 00:14:18,430
+عيد بس بيقول Slow down إذا عكس بعيد إيش عكس ال
+
+179
+00:14:18,430 --> 00:14:23,490
+East؟ West إذا ال West طلع هنا لا هيك ولا هيك وها
+
+180
+00:14:23,490 --> 00:14:27,370
+دي زيك زاك مرة رايح و مرة جاه مفهوم مظبوط ولا لأ
+
+181
+00:14:27,370 --> 00:14:33,010
+إذا الخيار الصح إذا استوعبته كلمتي معناته Westward
+
+182
+00:14:33,010 --> 00:14:38,820
+ولا لأ Westward حلو كان لك إيه ماني quiz نكملWhich
+
+183
+00:14:38,820 --> 00:14:43,240
+of the following statements is true؟ قال بيدي تديك
+
+184
+00:14:43,240 --> 00:14:50,960
+جمال و تقولي مين منها صح ومين منها غلط تمام If a
+
+185
+00:14:50,960 --> 00:14:57,760
+car is traveling eastward سيارة رايحة east its
+
+186
+00:14:57,760 --> 00:15:03,730
+acceleration must be eastحلو هيكم شطرين شايفوا ما
+
+187
+00:15:03,730 --> 00:15:07,250
+اشتركوا لأنه قلتلي انت ايش بعرفني ما حقه لو انت
+
+188
+00:15:07,250 --> 00:15:12,090
+كملتيلي معطيات لأ ممكن تكون عكسه ولا لأ اذا حسب
+
+189
+00:15:12,090 --> 00:15:18,010
+السرعة متزايدة او مش متزايدة تمام ازاي جت الكهربا
+
+190
+00:15:18,010 --> 00:15:25,690
+ارحمنا يا سان ماشيتش تمام if a car is slowing down
+
+191
+00:15:25,690 --> 00:15:32,110
+تمام هجيت غشتشني جالي بتتباطأX acceleration must
+
+192
+00:15:32,110 --> 00:15:37,230
+be negative يا الله أعلم كيف ال negative تبعي انت
+
+193
+00:15:37,230 --> 00:15:42,030
+ما جابتليش لسه مادتنيش معطيات كافية انا بقولك
+
+194
+00:15:42,030 --> 00:15:45,430
+slowing down لو قلتلي السرعة والتسارع ضد بعض بقولك
+
+195
+00:15:45,430 --> 00:15:49,550
+اه لكن انت بتقوللي negative و positive حسب اتجاهي
+
+196
+00:15:49,550 --> 00:15:56,630
+صحيح تمام حلو يعني مثلا هيك السرعة معناته التسارع
+
+197
+00:15:56,630 --> 00:16:00,060
+هيك ولا لأ طب يمكن انا هيك هو موجه بيهفهمتوا
+
+198
+00:16:00,060 --> 00:16:04,400
+عليها؟ اذا حسب ال direction وانت ماقلتليش .. انت
+
+199
+00:16:04,400 --> 00:16:09,760
+ماقلتليش حلو a particle with constant acceleration
+
+200
+00:16:09,760 --> 00:16:13,480
+هنا في خطوة مش عارف انا عند الشباب لجته صح او في
+
+201
+00:16:13,480 --> 00:16:17,560
+شعب هن هنا can never stop can never .. عندكم
+
+202
+00:16:17,560 --> 00:16:21,180
+never؟ bravo عليكم طبعا .. طبعا الشعب اللي جابلكم
+
+203
+00:16:21,180 --> 00:16:25,220
+كانت never موجودة can never stop بيقولي واحد
+
+204
+00:16:25,220 --> 00:16:29,400
+constant acceleration اديكم مثال لها السقوط الحر
+
+205
+00:16:30,480 --> 00:16:34,420
+constant acceleration ولا لأ الجسم لما تضربه بجفش
+
+206
+00:16:34,420 --> 00:16:40,860
+بالمرة بجف بس لحظيا إذا ممكن يجف ممكن يجف إذا هذه
+
+207
+00:16:40,860 --> 00:16:46,130
+برضه مش صحيحة نشوف الأخيرةa particle with constant
+
+208
+00:16:46,130 --> 00:16:51,090
+acceleration can never stop and stay stop مش ممكن
+
+209
+00:16:51,090 --> 00:16:55,270
+يجف يظل واقف لازم يعود يرجع ويتحرك اللي هو بيعمل
+
+210
+00:16:55,270 --> 00:17:00,250
+reversing بنعكس إذا الأخيرة هي الغلط ولا ممكن يجف
+
+211
+00:17:00,250 --> 00:17:05,650
+يظل واقف بيجف فاصل حظيا صح عشان يرجع هي الصح مانعش
+
+212
+00:17:05,650 --> 00:17:10,550
+قولت؟ تمام يعني هو الخيار اللي بدي أخده إذا الخيار
+
+213
+00:17:10,550 --> 00:17:16,620
+إيش هو؟أه يا بنات أي سفسار احنا متفجين جاريقين مما
+
+214
+00:17:16,620 --> 00:17:19,920
+فيه الكفاية أنه نسأل بدون تردد أنا إيه جاني الشاب
+
+215
+00:17:19,920 --> 00:17:22,740
+الصبحيات بعد ما خلصت من العهد و الله قليل تسأل بدي
+
+216
+00:17:22,740 --> 00:17:27,440
+أسألك رحت الحسنات منه لإنه ماثبتش غيره أنا صرت
+
+217
+00:17:27,440 --> 00:17:33,990
+أجاوبه إله لحاله احكيالـ C و D هال gate بيقولي
+
+218
+00:17:33,990 --> 00:17:36,970
+constant acceleration تمام؟ ال constant
+
+219
+00:17:36,970 --> 00:17:41,030
+acceleration بيقولي و لا ممكن يجف بقوله لأ انا
+
+220
+00:17:41,030 --> 00:17:45,370
+افترض ان ال acceleration ها دي بتباطع فيها ايش
+
+221
+00:17:45,370 --> 00:17:49,530
+بتباطع يعني؟ في الآخر ايش بيصير فيه؟ و دي جف صح؟
+
+222
+00:17:49,530 --> 00:17:53,430
+يظن ان دي غلط و اديتك مثال السقوط الحُرف هذا
+
+223
+00:17:53,430 --> 00:17:57,510
+الجلمةبدي اطلع الى فوق، ايش التصارع تبعه؟ تصارع
+
+224
+00:17:57,510 --> 00:18:01,150
+جاذبية ولا لا؟ ثابت ولا مش ثابت التصارع الجاذبية؟
+
+225
+00:18:01,150 --> 00:18:06,330
+بده يضلوا واصل السماء؟لأ عند ضغطة معينة بدي يجف صح
+
+226
+00:18:06,330 --> 00:18:10,190
+ولا .. اذا هذا غلط الكلمة انه هي تسارق ثابت لكن
+
+227
+00:18:10,190 --> 00:18:14,970
+واجف نجي للاخيرة بيقولي طيب ممنوع يجف يظل واقف
+
+228
+00:18:14,970 --> 00:18:17,670
+بيقوله اه هذا بيجف بيظل شويه ولا بيحرض و بيقول
+
+229
+00:18:17,670 --> 00:18:23,030
+بديش ها بديش هنزل صح اللو؟ لأ بعد برجع اذا هو بيجف
+
+230
+00:18:23,030 --> 00:18:28,610
+لكن مضلش واقف مزال في تسارع بدي رجعه فيمتى عليها؟
+
+231
+00:18:28,610 --> 00:18:29,330
+احكي يا بنتين
+
+232
+00:18:33,160 --> 00:18:37,040
+يعني واحدة مكملة للتانية انه لازم الجسم لما يوصل
+
+233
+00:18:37,040 --> 00:18:40,780
+لنقطة معينة يابي يعني بنزل بيكمل لإن التصارع ما
+
+234
+00:18:40,780 --> 00:18:45,360
+زال ثابت بيبقى موجود طبعا هو تصارع بيبقى يأكسه مش
+
+235
+00:18:45,360 --> 00:18:48,820
+مظبوط ولا .. فبيرجعه فلازم يرجعه لو أجينا
+
+236
+00:18:48,820 --> 00:18:52,080
+بالامتحان نفس السؤال الـC وD نفس ما هما هانت من
+
+237
+00:18:52,080 --> 00:18:58,200
+أصحتك؟ لأ مانالش عدلتها لأ هي الـDأه بس الصح
+
+238
+00:18:58,200 --> 00:19:01,360
+الأكتر حاجة دي تمام و أنا عدلتها يعني في الآخر
+
+239
+00:19:01,360 --> 00:19:03,780
+طلعت عملي مهام عدل عينكم حلو
+
+240
+00:19:06,320 --> 00:19:09,660
+نجيها المثال، هذا مثال سهل، فيه كتير أمثلة سهلة
+
+241
+00:19:09,660 --> 00:19:12,660
+The velocity of a particle يا بنات moving along
+
+242
+00:19:12,660 --> 00:19:17,400
+the X-axis varies with time بتتغير مع الزمن، ماذا
+
+243
+00:19:17,400 --> 00:19:19,940
+بتتغير مع الزمن؟ زي في acceleration ولا لا؟ في
+
+244
+00:19:19,940 --> 00:19:22,980
+acceleration قاللي كيف بتتغير؟ قولتله تبعلي
+
+245
+00:19:22,980 --> 00:19:27,220
+المعادلة اللي أنت شايفها أربعين ناقص خمسة تتربيع
+
+246
+00:19:27,220 --> 00:19:32,290
+شايفين المعادلة؟ شايفينهاwith z in meter per
+
+247
+00:19:32,290 --> 00:19:34,930
+second and t in second يعني أنا بستخدم الـ SI
+
+248
+00:19:34,930 --> 00:19:41,470
+system تمام؟ إيش بدك؟ حاجة بتحصل حالي Find the
+
+249
+00:19:41,470 --> 00:19:46,330
+average acceleration for the interval من 0 ل 2
+
+250
+00:19:46,330 --> 00:19:49,870
+second بدي ال average acceleration في فترة زمنية
+
+251
+00:19:49,870 --> 00:19:54,550
+معروفة من 0 ل 2 second تمام؟والمطلوب التاني ..
+
+252
+00:19:54,550 --> 00:19:57,470
+شكرا يا سامي determine the acceleration ال T
+
+253
+00:19:57,470 --> 00:20:01,030
+بتساوي 2 second ماذا ذاك اللحظة معينة مع اننا نتود
+
+254
+00:20:01,030 --> 00:20:09,310
+التسارع اللحظي تمه .. ها .. هنا هنا هذه القوانين
+
+255
+00:20:09,310 --> 00:20:16,570
+صحيك ولا لأ؟ Delta V معناته V لما T بتساوي 2 نقص V
+
+256
+00:20:16,570 --> 00:20:23,770
+لما T بتساوي 0 ولا لأ؟ على 2 نقص 0صحيحيك تمام هذه
+
+257
+00:20:23,770 --> 00:20:28,150
+بدنا نجيبها من اين نجيبها هذه و هذه من المعادلة
+
+258
+00:20:28,150 --> 00:20:35,850
+يلا ايه average بتساوي منى نجلني يلا اربعين ناقص
+
+259
+00:20:35,850 --> 00:20:41,910
+خمسة في اربعة خمسة في اربعة اربعين ناقص عشرين اذا
+
+260
+00:20:41,910 --> 00:20:44,930
+هذه عشرين ناقص
+
+261
+00:20:46,370 --> 00:20:50,910
+سفر يعني ناقص اربعين اه بالظبط ناقص اربعين لإنه
+
+262
+00:20:50,910 --> 00:20:57,030
+عوضت بحالك بسفر فناقص اربعين ع اتنين ناقص عشرين
+
+263
+00:20:57,030 --> 00:21:05,270
+على اتنين minus 10 ايه يا بنات واضح شو سويته سهلة
+
+264
+00:21:05,270 --> 00:21:11,170
+تمام سهلة جدا احكي يا بنتى كيف
+
+265
+00:21:16,980 --> 00:21:26,360
+علي صوتك اه لأ بتديكي الصراع اللحظية و هو بدوش
+
+266
+00:21:26,360 --> 00:21:32,700
+الصراع اللحظية مينفعش لما يقولي الصراع المتوسطة
+
+267
+00:21:32,700 --> 00:21:38,760
+مينفع أستقل لأ التعريف شفاه التعريف بيقولي A
+
+268
+00:21:38,760 --> 00:21:42,800
+average بيسوي DV على DT ولا Delta V على Delta T
+
+269
+00:21:42,800 --> 00:21:48,050
+Delta و Delta مش اشتقاقفهمتوا عليّ؟ دلوقت أنا بركز
+
+270
+00:21:48,050 --> 00:21:53,470
+بيش لإن هذا خطأ شائع بيجي، مينفعش، تشتاق، أنا مش
+
+271
+00:21:53,470 --> 00:21:56,890
+طالب الصراع للتسارع اللحظي، أنا بدي التسارع
+
+272
+00:21:56,890 --> 00:22:02,070
+المتوسط، التسارع المطلوب التاني هالجهة، إيش بده؟
+
+273
+00:22:02,070 --> 00:22:07,150
+التسارع عند لحظة تمام، هاي هاي يعني بدك هادي،
+
+274
+00:22:07,150 --> 00:22:11,230
+بقوله يلّا، هالجهة تبقى متشاطرة على الاستقاب،
+
+275
+00:22:11,230 --> 00:22:18,370
+اشتقىاربعين نقص خمسة T يعني نقص عشرة T هيجيك بدك و
+
+276
+00:22:18,370 --> 00:22:22,190
+عند أي زمان عندتي اتنين second بقوله اذا ايه عندتي
+
+277
+00:22:22,190 --> 00:22:27,890
+بتسوى اتنين second بتسوى نقص عشرين تمام
+
+278
+00:22:27,890 --> 00:22:33,310
+يا بنات تمام حلنا
+
+279
+00:22:33,310 --> 00:22:40,710
+السؤال وهينطلع لما يقولي بدي average اشتقلأ انتبه
+
+280
+00:22:40,710 --> 00:22:46,270
+بدي أوض في المعاجلة تمام أوضنا و جيبنا تمام و لما
+
+281
+00:22:46,270 --> 00:22:51,070
+جيبنا ال instantaneously روحت اشتقت و طلعتها تمام
+
+282
+00:22:56,070 --> 00:23:00,190
+في اكسليراشن في اكسليراشن ايش تعرفي الاكسليراشن
+
+283
+00:23:00,190 --> 00:23:03,670
+معدل تغير سرعة بالنسبة للزمن في منطقة متوسط وفي
+
+284
+00:23:03,670 --> 00:23:07,830
+منها لعبة نجي للتسارع جلي أحيانا التسارع يا بنات
+
+285
+00:23:07,830 --> 00:23:12,930
+بيكون ثابت زي مثلا نفترض عندي هذه الأرقام تشوفولي
+
+286
+00:23:12,930 --> 00:23:17,860
+كيف يزيد هذه الأرقام سرعاتتمام؟ اتنين، اربعة، ستة،
+
+287
+00:23:17,860 --> 00:23:21,180
+تمانية، عشرة، زادت ولا زاق؟ ايه كيب الزيادة ده؟
+
+288
+00:23:21,180 --> 00:23:24,320
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+289
+00:23:24,320 --> 00:23:24,580
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+290
+00:23:24,580 --> 00:23:25,200
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+291
+00:23:25,200 --> 00:23:27,340
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+292
+00:23:27,340 --> 00:23:34,600
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+293
+00:23:34,600 --> 00:23:39,920
+اتنفي عندك معادلات تستطيع اشتقاقها اذا بيقول
+
+294
+00:23:39,920 --> 00:23:44,200
+particle under constant acceleration اذا انت عندك
+
+295
+00:23:44,200 --> 00:23:50,840
+معطى ان ايه مالها constant a is constant طبعا
+
+296
+00:23:50,840 --> 00:23:57,120
+وياكم هيك نجرب الجلم و نكتب مع بعض و نجرب في حدا
+
+297
+00:23:57,120 --> 00:24:04,440
+منكم ماخلصش صف رابع و صف تامنووصلنا هنا اذا انا
+
+298
+00:24:04,440 --> 00:24:07,980
+ممكن تبهولي مازال خلصته رابع وتامن اثبتولي هال
+
+299
+00:24:07,980 --> 00:24:15,900
+gate تمام a is constant بيديكم
+
+300
+00:24:15,900 --> 00:24:20,600
+ألقام تجيبولي متوسطهم تعرف تجيب المتوسطات 5 5 5 5
+
+301
+00:24:20,600 --> 00:24:21,200
+5 5
+
+302
+00:24:25,340 --> 00:24:30,440
+خمسة مظبوط او لا لما يكون الشغل ثابت اه اروح اجمحه
+
+303
+00:24:30,440 --> 00:24:33,780
+و اجلس مع عددهم و ارخم حالت مايوم انت ماغيرتش اشي
+
+304
+00:24:33,780 --> 00:24:41,060
+طيب ايه ال constant بقدر اقول ان ايه average هي
+
+305
+00:24:41,060 --> 00:24:47,360
+نفسها ايه اه مازال constant اه نفسها نفسها والله
+
+306
+00:24:47,360 --> 00:24:52,100
+هاي ها ده ما قلتلكم هاي خمسة هاي خمسة هاي خمسة هاي
+
+307
+00:24:52,100 --> 00:24:58,710
+خمسةأي قيمة منهم جديش والمتوسط اذا اللحظة دي
+
+308
+00:24:58,710 --> 00:25:03,890
+والمتوسط زي بعض صح ولا لأ طب آمين جالي هادي لها
+
+309
+00:25:03,890 --> 00:25:08,110
+قانون ولا لأ اللي توسأت عنه مش اشتقاق جالي هادي
+
+310
+00:25:08,110 --> 00:25:12,810
+والله جالولي V final نقص V initial على T final نقص
+
+311
+00:25:12,810 --> 00:25:16,290
+T initial اعتبر T initial سفر يا سيدي مانت دايما
+
+312
+00:25:16,290 --> 00:25:21,130
+بتشغل الساعة من بداية فبتعتبر Tinitial السفر وما
+
+313
+00:25:21,130 --> 00:25:24,790
+زال بطل في عندك T initial فشلة T واحدة مضاجين
+
+314
+00:25:24,790 --> 00:25:31,090
+final تمام بتساوي ايه؟ وين اللي جال خلص رابع؟ نضرب
+
+315
+00:25:31,090 --> 00:25:37,130
+درب تبادلي نضرب درب تبادلي imply that او هذا يعني
+
+316
+00:25:37,130 --> 00:25:43,610
+The final ماقس V initial برضه
+
+317
+00:25:43,610 --> 00:25:47,210
+في صف رابع حد بيدحطها الشجرة التانية فصار V final
+
+318
+00:25:47,210 --> 00:25:48,750
+بتساوي V initial
+
+319
+00:25:53,650 --> 00:25:58,210
+شوفتهوا؟ بتعرفوه؟ وخفظينه زي سمنه صح ولا لأ؟ هاي
+
+320
+00:25:58,210 --> 00:26:01,770
+أول قانون أهل الشتقاق مش كتير مهم بس يعني احنا ما
+
+321
+00:26:01,770 --> 00:26:05,870
+زال رابعه و تامين مخلصينه مستقى يعني هاي أول ..
+
+322
+00:26:05,870 --> 00:26:11,950
+فيها إيه سفسار يا بنات؟ تمام حلو ال gate A is
+
+323
+00:26:11,950 --> 00:26:17,730
+constant هذا شرط لأنه علوان هذادائما شرط صح ولا لأ
+
+324
+00:26:17,730 --> 00:26:22,670
+حلو اطلعولي على هذه سرعات بتديكم يهم انتوا كتبتم
+
+325
+00:26:22,670 --> 00:26:27,950
+خمسات كانت تسارعات سرعة اتنين اربعة ستة تمانية
+
+326
+00:26:27,950 --> 00:26:35,050
+عشرة كيف الزيادة مش ثابت بتغير من يجيبلي ال
+
+327
+00:26:35,050 --> 00:26:41,150
+average المعدل ايش كيف نجيب المعدل احنا معاكي يلا
+
+328
+00:26:41,150 --> 00:26:48,550
+اجمعيلي اتنين واربعةاتنين واربعة ستة وستة و تمانية
+
+329
+00:26:48,550 --> 00:26:52,270
+و عشرة واحد ع اتنين تلقى اتة اربع خمسة تلاتين ع
+
+330
+00:26:52,270 --> 00:26:57,110
+خمسة ستة ال average جالي يطلع هدول لو مليون ده
+
+331
+00:26:57,110 --> 00:27:00,630
+تجمع المليون و تجسم ع مليون يطلع هال trick إذا
+
+332
+00:27:00,630 --> 00:27:07,390
+زيادة ثابت أخودي الأول و الأخر و جسم ع اتنين اتنين
+
+333
+00:27:07,390 --> 00:27:12,540
+و عشرةع تمين ايه؟ و لا طلعت ستة نفس الجواب بس بشرط
+
+334
+00:27:12,540 --> 00:27:14,960
+ان تكون الزيادة ثابتة و انا عندي ال acceleration
+
+335
+00:27:14,960 --> 00:27:20,320
+مالها ثابتة ده اللي في هذه الحالة هذه سرعات V
+
+336
+00:27:20,320 --> 00:27:25,860
+average قطعا الأولى زائد الأخيرة عتنين
+
+337
+00:27:28,600 --> 00:27:31,200
+فده القانون اللي خدناه في المدرسة ماعرفش اخدت هو
+
+338
+00:27:31,200 --> 00:27:36,040
+اي صفر بلاش اتبل عليكم اقول رابع لأ مش رابع تمام
+
+339
+00:27:36,040 --> 00:27:39,720
+اعلى شوية من رابع انتوا اكتشفتوا الاحصة دي المعدل
+
+340
+00:27:39,720 --> 00:27:43,780
+و مش المعدل تمام اه تمام يعني اذا انجليت رابع تمام
+
+341
+00:27:43,780 --> 00:27:50,660
+عشان كده تمام حلوجيلي طيب مين يذكرني في average
+
+342
+00:27:50,660 --> 00:27:58,340
+قانونها إيش X final نقص X initial إذا X final نقص
+
+343
+00:27:58,340 --> 00:28:02,320
+X initial على T final نقص T initial بتقولنا T
+
+344
+00:28:02,320 --> 00:28:10,960
+بتساوي V initial زي V final على 2 ضرب تبادي و تبقى
+
+345
+00:28:10,960 --> 00:28:19,430
+صفرابع من هنا خلينا نقولبقول X final مقص X initial
+
+346
+00:28:19,430 --> 00:28:29,150
+بتساوي نص V initial زي V final في T هاي كمان
+
+347
+00:28:29,150 --> 00:28:36,790
+معادلة تمام؟ حلو قال لي طيب رجعنا للهادي لسه قال
+
+348
+00:28:36,790 --> 00:28:45,620
+لي هادي مينفعش حتة منها مش هي نفسها اهشحتني يلّا
+
+349
+00:28:45,620 --> 00:28:51,200
+نشحت بقوله
+
+350
+00:28:51,200 --> 00:28:59,080
+X final مقص X initial على T بتساوي V initial زائد
+
+351
+00:28:59,080 --> 00:29:07,620
+V final زائد V initial زائد AT عطني متابعين
+
+352
+00:29:07,620 --> 00:29:15,900
+معايا؟ V initial زائد V initial إذن هذه صارتاتنين
+
+353
+00:29:15,900 --> 00:29:21,440
+V initial صح ولا لأ تمام جالي هيك بترتب ليها بقول
+
+354
+00:29:21,440 --> 00:29:28,080
+X final نقص X initial على T بتسوي V initial زي نص
+
+355
+00:29:28,080 --> 00:29:32,220
+A T صح
+
+356
+00:29:32,220 --> 00:29:40,620
+صحته متابعين حلو يلا درب تبادلي درب تبادلي بتصير
+
+357
+00:29:40,620 --> 00:29:47,530
+هاتي هيك هاتي و هاتي تربيةوهي القانون الحلو تبعنا
+
+358
+00:29:47,530 --> 00:29:51,930
+X final نقص X initial بيسوا V initial في T زي نص
+
+359
+00:29:51,930 --> 00:30:00,790
+AT تربية ام صح صحين هاي كمان قانون طيب نرجع
+
+360
+00:30:00,790 --> 00:30:11,490
+لصف رابع بدي T من هنا انت اه ما هو قوليلي نجليلي T
+
+361
+00:30:13,150 --> 00:30:20,630
+حلو إذا T بتساوي Vfinal نقص Vinitial على إيه؟ صحية
+
+362
+00:30:20,630 --> 00:30:27,330
+تمام؟ أه كنا بنعرف قال لي حلو بنفهدي T تعوض علينا؟
+
+363
+00:30:28,300 --> 00:30:31,720
+بدي أعوضها، هشوف إيش بتطلع معايا بصحلي ولا بصحلي
+
+364
+00:30:31,720 --> 00:30:38,960
+إيش؟ بصحلي بقول x final نقص x initial بتساوي v
+
+365
+00:30:38,960 --> 00:30:44,240
+initial بدل t بدي أحط v final نقص v initial على a
+
+366
+00:30:44,240 --> 00:30:52,040
+زاد نص a بدي أربح هذه v final نقص v initial تربيع
+
+367
+00:30:52,040 --> 00:30:56,420
+على a تربيع صح ولا لأ؟ لأنه بدي أربح هذه و بدي
+
+368
+00:30:56,420 --> 00:31:01,330
+أربح هذهطيب اما علمتكم انكم في صفرابيع تلت و خمس
+
+369
+00:31:01,330 --> 00:31:07,890
+كيف تجيبوه؟ تلت و خمس كيف كنتوا تجيبوه؟
+
+370
+00:31:07,890 --> 00:31:11,130
+جمع
+
+371
+00:31:11,130 --> 00:31:17,050
+الكثور اللي عتيادية انسيتوها مش من عامل مشتراك تلت
+
+372
+00:31:17,050 --> 00:31:24,870
+و خمس بنحط فيش في المقام؟ خلاص ايه بالدقيقة وصلت
+
+373
+00:31:26,590 --> 00:31:29,610
+أخدت الخمسة عشر لإنه لجيت انا المفروض أخد الكبير
+
+374
+00:31:29,610 --> 00:31:32,290
+بس الكبير بظلطش معايا اللي هو تلاتة أو خمسة روح
+
+375
+00:31:32,290 --> 00:31:36,270
+اتكبرت أكتر و أكتر دي بتال خمسة لكن خمس زائد عشر
+
+376
+00:31:36,270 --> 00:31:40,550
+إيش هيخدتها عاملهم الشراك؟ عشرة عشرة صح ولا لأ؟
+
+377
+00:31:40,550 --> 00:31:44,550
+اتطلع ايه إيش بدي أسوي؟ بيقوللي أنت إيش لعملته؟
+
+378
+00:31:44,550 --> 00:31:52,880
+وين أنا وصلت هنا؟ ه .. هذي .. هذي هي شفينهاصح؟
+
+379
+00:31:52,880 --> 00:31:56,220
+صارت اتنين ايه و هنا ايه؟ ايش اخد عالم المشارك؟
+
+380
+00:31:56,220 --> 00:31:58,240
+ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟
+
+381
+00:31:58,240 --> 00:32:00,280
+اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين
+
+382
+00:32:00,280 --> 00:32:04,320
+ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟
+
+383
+00:32:04,320 --> 00:32:08,360
+اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين
+
+384
+00:32:08,360 --> 00:32:12,780
+ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟
+
+385
+00:32:12,780 --> 00:32:18,240
+اتنين ايه؟ اتنين
+
+386
+00:32:20,710 --> 00:32:26,550
+وحدنا المقام ايش احطشيه في المقام هداشيه اضربوه في
+
+387
+00:32:26,550 --> 00:32:31,950
+اتنين اذا اضربولي هدي اتنين V initial V final نقص
+
+388
+00:32:31,950 --> 00:32:43,430
+اتنين V initial تربيع اه صح صح تمام زائد مين
+
+389
+00:32:43,430 --> 00:32:51,600
+يربعلي هدي ربع V final تربيعنقص اتنين V initial V
+
+390
+00:32:51,600 --> 00:32:58,460
+final زائد V initial تربيع تمام هيك؟ طلعولي الأول
+
+391
+00:32:58,460 --> 00:33:09,160
+و الأخير يا عيني عليكم اتطلعي ناقص V initial تربيع
+
+392
+00:33:09,160 --> 00:33:14,800
+زائد V initial تربيع ناقص V initial تربيع صحيح؟
+
+393
+00:33:14,800 --> 00:33:21,210
+اذا هذه متساويها بالأصمر المرة هذه هاي المقام
+
+394
+00:33:21,210 --> 00:33:26,970
+اتنين ايه ناقص
+
+395
+00:33:26,970 --> 00:33:33,250
+V initial تربيع تبعين
+
+396
+00:33:33,250 --> 00:33:37,150
+معاه؟ قال لي ها دي ايش مش ساوي كله X final ناقص X
+
+397
+00:33:37,150 --> 00:33:43,250
+initial هاي ها X final ناقص X initial اضرب ضرب
+
+398
+00:33:43,250 --> 00:33:55,050
+تبادلي ضربناصار X final نقص X initial في 2A بتساوي
+
+399
+00:33:55,050 --> 00:34:00,730
+V initial تربيع بالسالب زي V final تربيع رطب
+
+400
+00:34:00,730 --> 00:34:04,810
+المعادلة زي ما علمونا حطل ال V initial ع الشجة
+
+401
+00:34:04,810 --> 00:34:12,590
+التانيةهي كانت سلبش بتصير V final تربيع بتساوي V
+
+402
+00:34:12,590 --> 00:34:16,870
+initial تربيع زي اتنين A X final نقص X initial
+
+403
+00:34:16,870 --> 00:34:23,870
+المعادلة الأخيرة هاي الأربع معادلات والحمد لله
+
+404
+00:34:23,870 --> 00:34:28,970
+الاشتقاق بجيب هشي انا بأنها معلومة رابع تامة
+
+405
+00:34:31,190 --> 00:34:34,030
+ماصدقتوا انت بتقولوا ماصدقنا ننجح من الرابع اننا
+
+406
+00:34:34,030 --> 00:34:38,370
+ننجح على الرابع تمام اه يا بنات تمام اذا في عندي
+
+407
+00:34:38,370 --> 00:34:43,430
+اربع معادلات اهم معادلتين اللي بتمنى تحفظوهم الاول
+
+408
+00:34:43,430 --> 00:34:47,930
+والتاني الاول والتاني وين الاول اللي محيته والتاني
+
+409
+00:34:47,930 --> 00:34:52,930
+هذاالأول Vfinal بيسوي Vinitial زي a2 والتاني
+
+410
+00:34:52,930 --> 00:34:56,490
+Xfinal نقص Xinitial بيسوي Vinitial في T زي نص aT
+
+411
+00:34:56,490 --> 00:34:59,890
+تربيع والتانين التالت والرابع بشتقهم من التانين
+
+412
+00:34:59,890 --> 00:35:06,090
+الأولانين تفرجش معايا أول والتاني هو المهمإذن لما
+
+413
+00:35:06,090 --> 00:35:08,970
+تكون التسارع ثابت في عندى أربع معادلات ممكن
+
+414
+00:35:08,970 --> 00:35:13,830
+نستخدمهم ولا لأ إذا قيمي ثابت أصلا مينفعش أشتقهم
+
+415
+00:35:13,830 --> 00:35:21,290
+مفشله من البداية حلو إذا هذا كل الكلام عملته هي
+
+416
+00:35:21,290 --> 00:35:27,290
+أول واحدة طلعناها بعدين جبنا و عوضناه خليني نلعب
+
+417
+00:35:27,290 --> 00:35:32,350
+شوية بال power point يعني نسليكم شوية تمام تبعنا و
+
+418
+00:35:32,350 --> 00:35:36,960
+عملنا طلعنا التانيةتمام؟ و جالي برضه نفس العملية
+
+419
+00:35:36,960 --> 00:35:43,500
+طلعت التالتة جالي substituting for T عوض من T from
+
+420
+00:35:43,500 --> 00:35:47,420
+the first equation اللي ادتنينياها انت من المعادلة
+
+421
+00:35:47,420 --> 00:35:51,300
+الأولى في المعادلة التانية التانية اللي كانت هي
+
+422
+00:35:51,300 --> 00:35:56,120
+هذه جالي عملتها و اشتغلت اللي اشتغلتوا معايا فيها
+
+423
+00:35:56,120 --> 00:35:59,740
+فطلعت الرابعة تمام يا بنات؟ حلو
+
+424
+00:36:02,580 --> 00:36:06,120
+two samurais عشان .. راح أحطهم تحت بعض بس عشان
+
+425
+00:36:06,120 --> 00:36:16,840
+يرتبلي يوم حلوين هيك أسهللي تمام هيك؟ حلو example
+
+426
+00:36:16,840 --> 00:36:22,400
+a jet جت يعني طيارة حربية تمام اسمعتوا في حاجة اسم
+
+427
+00:36:22,400 --> 00:36:28,890
+حامل الطائرات؟ Shiaسفينة .. سفينة كبيرة بتحمل
+
+428
+00:36:28,890 --> 00:36:32,710
+طيارات والطيارات بتطير منها و بترجعلها و طبعا
+
+429
+00:36:32,710 --> 00:36:35,690
+انتوا بتعرفوا الطيارة لما بدها تنزل على الأرض على
+
+430
+00:36:35,690 --> 00:36:39,450
+السفينة ولا على الأرض العادية بدها مضرش لأنه أول
+
+431
+00:36:39,450 --> 00:36:43,190
+ما تلمس الأرض بتجافلأ بتاخد وجهة عبارة عن المتجاف
+
+432
+00:36:43,190 --> 00:36:46,790
+عشان كده فيه مدرجات طويلة في المطارات عشان كده
+
+433
+00:36:46,790 --> 00:36:51,170
+المطارات غالبا بيحطوها في اماكن اما صحراء او جنب
+
+434
+00:36:51,170 --> 00:36:55,790
+بحار عشان مايكونش فيه عمارات تمام؟ بيقوللي ها دي
+
+435
+00:36:56,550 --> 00:37:02,650
+طائرة حربية Jet Lance بديها تفبط on an aircraft
+
+436
+00:37:02,650 --> 00:37:07,550
+carrier حامل الطائرات carrier من carry بتعرفش
+
+437
+00:37:07,550 --> 00:37:11,550
+معاناة carry بيحمل اذا aircraft carrier حامل
+
+438
+00:37:11,550 --> 00:37:15,090
+الطائرات aircraft برضه طيارة بقى مائة الف نوع
+
+439
+00:37:15,090 --> 00:37:19,170
+طيارة ما أنتم بتعرفوا و planes برضه طائرات هذا هي
+
+440
+00:37:19,170 --> 00:37:25,240
+يلابقول لي أول ما لمست أرض السفينة اللي حاملة
+
+441
+00:37:25,240 --> 00:37:29,080
+الطائرات كانت سرعتها 140 ميل بال hour قال لي أنا
+
+442
+00:37:29,080 --> 00:37:32,480
+ال chapter واحد اللي قلتلك كيف اتحول بدي رايحك منه
+
+443
+00:37:32,480 --> 00:37:36,800
+انا بحولك و خالص 63 متر per second ايه رايحنا،
+
+444
+00:37:36,800 --> 00:37:42,120
+مظبط او لا؟ اذا ان اول ما لمس الأرض كانت سرعة 63
+
+445
+00:37:42,120 --> 00:37:46,780
+متر per second بيقول لي what is its acceleration؟
+
+446
+00:37:46,780 --> 00:37:52,870
+بده ايه؟assume constant عشان أستخدم الأربع حوارين
+
+447
+00:37:52,870 --> 00:37:57,430
+تمام هيك بيقوللي if it stops in two seconds
+
+448
+00:37:57,430 --> 00:38:02,110
+بيقوللي إذا الطيارة وكفت بعد ثانيتين من ساعت ما
+
+449
+00:38:02,110 --> 00:38:07,910
+لمست الأرض وكفت جديش التسارع النهائية بالسرعة
+
+450
+00:38:07,910 --> 00:38:13,090
+التدائية تلاتة وستين والزمن؟ تسارع تسارع بده
+
+451
+00:38:13,090 --> 00:38:15,790
+التسارع ذاكروني في القانون الأول
+
+452
+00:38:21,190 --> 00:38:26,530
+Vfinal بتساوي Vinitial زايد AT Vfinal مُعطَى ولا
+
+453
+00:38:26,530 --> 00:38:30,030
+مش مُعطَى؟ مُعطَى Vfinal مُعطَى ولا مش مُعطَى؟
+
+454
+00:38:30,030 --> 00:38:30,130
+Vfinal مُعطَى ولا مش مُعطَى؟ Vfinal مُعطَى ولا مش
+
+455
+00:38:30,130 --> 00:38:30,850
+مُعطَى ولا مش مُعطَى؟ Vfinal مُعطَى ولا مش مُعطَى؟
+
+456
+00:38:30,850 --> 00:38:38,650
+Vfinal مُعطَى ولا مش مُعطَى؟ Vfinal مُعطَى ولا مش
+
+457
+00:38:38,650 --> 00:38:46,800
+مُعطَى؟ Vfinal مُبقول if the jets touches down at
+
+458
+00:38:46,800 --> 00:38:50,080
+a position x initial يعني قاللي ال position أول ما
+
+459
+00:38:50,080 --> 00:38:54,040
+لمست الأرض هي ما رجعتك بدي x final يعني قداش
+
+460
+00:38:54,040 --> 00:38:57,120
+المسافر اللي جتعتها لما وقفت بسيطة مثلا إنت جيبتي
+
+461
+00:38:57,120 --> 00:39:01,180
+الزمان و ال acceleration قاعد في أي معادلة تجيب x
+
+462
+00:39:01,180 --> 00:39:05,080
+المعادلة الأخيرة اللي هو x final نقص x initial
+
+463
+00:39:05,080 --> 00:39:09,580
+بيسوا v initial في t زي نص AT تربيع و إيه جبتها؟
+
+464
+00:39:09,580 --> 00:39:15,400
+خلصنا إذن بيقولليThe initial point is the point at
+
+465
+00:39:15,400 --> 00:39:18,900
+which the jet hits the ground X initial هي السفر
+
+466
+00:39:18,900 --> 00:39:23,060
+At this point, the initial بتسوى تلاتة و ستين متر
+
+467
+00:39:23,060 --> 00:39:26,580
+per second و انتوا قولتولي و the final قولتولي سفر
+
+468
+00:39:26,580 --> 00:39:31,080
+لأنها عبارة عن stop قاللي هذا القانون الحلو
+
+469
+00:39:31,080 --> 00:39:37,060
+بتطلعلي أول مطلوب طلعنا طلعت ناقص تلاتين متر per
+
+470
+00:39:37,060 --> 00:39:41,810
+second تربية slowing downمظبوط ولا لا؟ قطع لأنه في
+
+471
+00:39:41,810 --> 00:39:49,530
+الآخر بدي اجف تمام هلجيت لو الطيارة ماشي هيك اتجاه
+
+472
+00:39:49,530 --> 00:39:54,530
+التصالح؟ براو عليكم عكس لأنها بتتناقص هذه المعلومة
+
+473
+00:39:54,530 --> 00:39:59,790
+اللي عندي حلو بجلب ال DX قولتله هاي القانون ايه
+
+474
+00:39:59,790 --> 00:40:03,970
+هذا ممكن استخدمه؟ لإن انت بديك XYX V initial
+
+475
+00:40:03,970 --> 00:40:08,170
+مديتنيها ولا لا؟ و V final مديتنيها ولا لا؟ بعوض
+
+476
+00:40:09,850 --> 00:40:16,010
+هذا هى طالع الـ 63 ايش بيقولى اه هنا واحد بيقولى
+
+477
+00:40:16,010 --> 00:40:20,090
+طب لو استخدمت القانون التانى اللى هو X final نقص X
+
+478
+00:40:20,090 --> 00:40:24,250
+initial يه سفر V initial في T زائد نص AT تربيع
+
+479
+00:40:24,250 --> 00:40:30,010
+بتطلع جواب مختلف نفس الجوابطريقين بيأدوا إلى نفس
+
+480
+00:40:30,010 --> 00:40:34,010
+روما هدوا القانونين هدى أنا بحب هدى أكتر بس الكتاب
+
+481
+00:40:34,010 --> 00:40:37,830
+مستخدم هداك القانون و أنا دايما بربط الحمار زي ما
+
+482
+00:40:37,830 --> 00:40:42,850
+بده صاحبه فهو هيك بده المثال فخطط في ال slides لكن
+
+483
+00:40:42,850 --> 00:40:46,770
+انا لو بده حوالي بحلب هدى لإنه هدى القانون انا
+
+484
+00:40:46,770 --> 00:40:50,890
+حافظه أكتر لإنه هدى أساسي و هداك فرعية تمام مش
+
+485
+00:40:50,890 --> 00:40:54,630
+مشكلة لكن في الآخر انا ب .. أحكي بإنفع نجيب مثلا
+
+486
+00:40:54,630 --> 00:41:01,300
+من قانون ال DP و الأه اللي هي delta x و delta t
+
+487
+00:41:01,300 --> 00:41:06,920
+شهدك بيعطيك سرعة متوسطة تعرفيها سرعة متوسطة؟ لأ بس
+
+488
+00:41:06,920 --> 00:41:08,980
+هو ماعطيلي السرعة الابتدائية و السرعة اللي هي هي
+
+489
+00:41:08,980 --> 00:41:14,380
+كده لها سحر يعني معناته .. اه بيجيبيها؟ غالبا لكن
+
+490
+00:41:14,380 --> 00:41:18,820
+صح تفكيرك صح تمام بس دايما واحد بيخش على الطريق
+
+491
+00:41:18,820 --> 00:41:25,800
+السهل اه يا بنات صحصحولي بدنا ترجم اول
+
+492
+00:41:30,500 --> 00:41:35,380
+بتعرفوش مانعتها a traveling at a constant speed of
+
+493
+00:41:35,380 --> 00:41:40,460
+40 meter per second السيارة ماشية عدل وبسرعة ثابتة
+
+494
+00:41:40,460 --> 00:41:43,180
+والسيارة عشان تطلع بسرعة ثابتة لازم الطريق يكون
+
+495
+00:41:43,180 --> 00:41:48,140
+فاضي و لا مطبات ولا حاجة تمام هيك؟ في نص الليل
+
+496
+00:41:48,140 --> 00:41:52,580
+السيارة ماشية في شارع عمال مختار وعند مفترج
+
+497
+00:41:52,580 --> 00:41:57,410
+السراية في ..لوحة إعلانات كبيرة بتعرفوها اللي
+
+498
+00:41:57,410 --> 00:42:00,930
+بيعلقوا عليها شغلات كتيرة بيقوللي هناك متخبي شرطي
+
+499
+00:42:00,930 --> 00:42:07,750
+متخبي شرطيالسيارة و هي ماشية بأمان الله بسرعة 45
+
+500
+00:42:07,750 --> 00:42:12,330
+متر per second باسيز يعني مرت عن ال trooper ال
+
+501
+00:42:12,330 --> 00:42:17,010
+trooper معناته شرطي متنقل او جوال او على موتوسيكل
+
+502
+00:42:17,010 --> 00:42:22,150
+هذا بنسميه trooper شرطي ال trooper on a motorcycle
+
+503
+00:42:22,150 --> 00:42:26,810
+على مطير و هو قاعد طافه الموتور و قاعد و متخبي و
+
+504
+00:42:26,810 --> 00:42:30,730
+بده يتصيد للسيارات اللي بتخالفحلوة فهذه مرت بأمان
+
+505
+00:42:30,730 --> 00:42:33,730
+والدنيا ليه؟ وإيش في قاعد رفها إنه في شوفت قاعد
+
+506
+00:42:33,730 --> 00:42:40,440
+متخبي؟ ماشية بسرعة كبيرة 45 متر per secondجاللي
+
+507
+00:42:40,440 --> 00:42:44,620
+hidden behind a billboard هذا الشرطي hidden يعني
+
+508
+00:42:44,620 --> 00:42:49,280
+متخبي خلف billboard يعني لوحة إعلانات اللي قلت
+
+509
+00:42:49,280 --> 00:42:53,580
+عنها توي في الصلاية حلو بقوللي بعد ما اكتشف ان
+
+510
+00:42:53,580 --> 00:42:57,280
+هادي قاعدة ماشية بسرعة كبيرة أكبر من السرعة
+
+511
+00:42:57,280 --> 00:43:02,220
+المسموح تمشي فيها جاللي عبل ما فكر وشغل كانت مرة
+
+512
+00:43:02,220 --> 00:43:05,680
+ثانية ثانية مش كتير لكن الثانية كانت في السيارة
+
+513
+00:43:05,680 --> 00:43:11,010
+جنبه ولا مشيتماشيت ما هي ماشية بيقول لي one second
+
+514
+00:43:11,010 --> 00:43:15,790
+بعد ثانية after the speeding car passes the
+
+515
+00:43:15,790 --> 00:43:19,630
+billboard بعد ثانية ما مرت السيارة عن ال billboard
+
+516
+00:43:19,630 --> 00:43:23,250
+اللي هي اللوحة و هو الشرطي نفسه ما هناك كان واقف
+
+517
+00:43:23,250 --> 00:43:27,250
+قال لي the trooper sits out from the billboard
+
+518
+00:43:27,250 --> 00:43:32,070
+انطلق من ال billboard و راح يلحق السيارة اتفجنا يا
+
+519
+00:43:32,070 --> 00:43:38,610
+بنات؟ بعد ثانية من مرور السيارة تمout of from the
+
+520
+00:43:38,610 --> 00:43:41,550
+billboard to catch the car accelerating كان واقف
+
+521
+00:43:41,550 --> 00:43:45,430
+لتروبر ايه تصارع التروبر ابتدائية لأنه كان واقف
+
+522
+00:43:45,430 --> 00:43:51,650
+تصارع لتروبر أطانيا تلاتة متر per second حلو how
+
+523
+00:43:51,650 --> 00:43:55,830
+long does it take جديش لتروبر أخذ زمن عشان يمسك
+
+524
+00:43:55,830 --> 00:44:00,970
+السيارة يلحقها فاهم السؤال أول بالعربي بعدين
+
+525
+00:44:00,970 --> 00:44:05,750
+بنترجمه علميا الآنواحدة واحدة هالجيث بتطلعولي على
+
+526
+00:44:05,750 --> 00:44:10,750
+ال car كلمة constant speed إيش يعني؟ جدّيش
+
+527
+00:44:10,750 --> 00:44:16,190
+تصالحها؟ proud مظبوط ولا لأ؟ هو بيقوللي ال car
+
+528
+00:44:16,190 --> 00:44:22,370
+كانت تمشي بسرعة ثابتة يعني تصالحه ماله سفر بدي
+
+529
+00:44:22,370 --> 00:44:27,310
+أعمل هيك و أعمل هيك و أقول هذا ال car وهذا ال
+
+530
+00:44:27,310 --> 00:44:34,810
+trooper إيش trooper يعني؟ الشرطيأول حاجة ايه لل
+
+531
+00:44:34,810 --> 00:44:39,710
+car بتساوي سفر؟ من أين عرفت؟ من ال constant speed
+
+532
+00:44:39,710 --> 00:44:46,410
+اذا هو اللي قاللي ايه لل Etrober بتساوي تلاتة متر
+
+533
+00:44:46,410 --> 00:44:49,930
+per second تربيه؟ هيه أطانيها ولا ما أطانيشها؟
+
+534
+00:44:49,930 --> 00:44:56,190
+تمام؟ إيش بدك؟ قاللي بدي الزمن اللي أخده الشرطي
+
+535
+00:44:56,190 --> 00:45:00,570
+إذا أنا بدي أشغل ساعة الإيقاف أول ما اتحرك الشرطي
+
+536
+00:45:01,400 --> 00:45:06,460
+مظبوطك ولا لا؟ لأنه بدي زمان يستخرخ الشرطي حلو هجت
+
+537
+00:45:06,460 --> 00:45:10,800
+هم مروا على بعض عند وين؟ عند السراية و هو ماشي
+
+538
+00:45:10,800 --> 00:45:15,960
+هلجيك بدهم يمسكوا بعض في مجال انهم يمسكوا بعض يكون
+
+539
+00:45:15,960 --> 00:45:21,070
+الشرطي عند السامر و السيارة عند الساحة؟لازم يكونوا
+
+540
+00:45:21,070 --> 00:45:24,310
+في نفس الموضوع ولا لأ؟ إذا انت عشان بتقوللي بيبقوا
+
+541
+00:45:24,310 --> 00:45:28,190
+يمسكوا بعض لازم X final للشرطي تسوي X final
+
+542
+00:45:28,190 --> 00:45:31,990
+للسيارة ولا لأ؟ هاي ترك السؤال طب إيش بقى كنت
+
+543
+00:45:31,990 --> 00:45:35,410
+تسوي؟ قاللي جيب X final للسيارة و X final للتروبر
+
+544
+00:45:35,410 --> 00:45:39,910
+و سويهم بعض صح ولا لأ؟ بتطلع أيه اللي بدك إيه طيب
+
+545
+00:45:39,910 --> 00:45:46,190
+نرجع قاللي V لل car بتسوي 45 متر per second مش انت
+
+546
+00:45:46,190 --> 00:45:53,300
+قلتلي هيهاV initial لـ Retrober بتساوي سفر؟ فح؟
+
+547
+00:45:53,300 --> 00:46:00,580
+هذي معطة؟ تمى؟ بقوله يلّا نشتغل بقوله X initial
+
+548
+00:46:00,580 --> 00:46:04,920
+للسيارة إيش يعني initial أول ما اتحرك الشرطي؟ كانت
+
+549
+00:46:04,920 --> 00:46:09,480
+جنبه؟ كيف بدي أعرف جدي وين كانت؟ بقوله مش أنت دتني
+
+550
+00:46:09,480 --> 00:46:14,540
+صراعتها؟ 45 في جدي إيش؟ في واحد لإن واحد سكنت
+
+551
+00:46:16,660 --> 00:46:21,940
+initial للـ car بتساوي V initial للـ car في T اللي
+
+552
+00:46:21,940 --> 00:46:26,360
+هو واحد second ولا لأ هتتهادي initial للـ car هي
+
+553
+00:46:26,360 --> 00:46:30,920
+نفسها ما هو ما بتتغيرش بتساوي خمسة و أربعين متر
+
+554
+00:46:30,920 --> 00:46:39,200
+هذه X initial للـ car مظبوطك ولا لأ تم اتحرك
+
+555
+00:46:39,200 --> 00:46:44,240
+الشرطي هذه السيارة هناوصلت هنا هذه المسافة 45 متر
+
+556
+00:46:44,240 --> 00:46:52,180
+بدأ يبدأ يجري حلو بقول X final نقص X initial لل
+
+557
+00:46:52,180 --> 00:46:58,160
+car بتسوي V initial لل car في T زي اجمال اصفر A لل
+
+558
+00:46:58,160 --> 00:47:01,680
+car في T تربيع سمعتوا في القانون هذا طيب ال A لل
+
+559
+00:47:01,680 --> 00:47:05,120
+car قد ياش اذا هذه ماكنتش دعوة فيها يا ابني هذه
+
+560
+00:47:05,120 --> 00:47:13,080
+سفر ماهي مش سفرتم اكس final لل car نقص خمسة
+
+561
+00:47:13,080 --> 00:47:19,180
+واربعين مشانية بتساوي خمسة واربعين T ولا لأ؟ وقف
+
+562
+00:47:19,180 --> 00:47:25,760
+هنا خلاص اجيبت هذه تمام؟ حلو نيجي للشرطة حبيبنا
+
+563
+00:47:25,760 --> 00:47:33,090
+بقوله اكس final نقص اكس initial لل Etroberبتساوي V
+
+564
+00:47:33,090 --> 00:47:39,490
+initial للتروبر في T زي نص A للتروبر في T تربيع مش
+
+565
+00:47:39,490 --> 00:47:45,670
+هذا قانون جديش V initial للتروبر براو عليكم وها دي
+
+566
+00:47:45,670 --> 00:47:50,630
+كان لسفر ولا مالسفر اذا X final للتروبر بتساوي نص
+
+567
+00:47:50,630 --> 00:47:59,290
+في تلاتة في T تربيع تلاتة في نصواحد و نص .. تلاتة
+
+568
+00:47:59,290 --> 00:48:02,190
+اتنين .. مظبوط .. واحد و نص .. اجيب مهادي و احط
+
+569
+00:48:02,190 --> 00:48:06,870
+واحد و نص .. قعد واحد يقول ليش اللي عملته .. واحد
+
+570
+00:48:06,870 --> 00:48:09,250
+و نص .. مهو كان .. اذا هسرح .. مهو يقول كانت تلاتة
+
+571
+00:48:09,250 --> 00:48:12,850
+اتنين ايش اللي وديها .. صارت .. تمام .. حلو ..
+
+572
+00:48:12,850 --> 00:48:18,050
+هجيت مسكوا بعض .. اذا قطعا هادي بتسوي هادي .. صح
+
+573
+00:48:18,050 --> 00:48:21,290
+.. اذا مزال بتقولي واكتشف دمي مسكوا بعض .. اذا
+
+574
+00:48:21,290 --> 00:48:25,630
+قطعا مسكوا بعض عند السامر او عند الساحة .. احكي ..
+
+575
+00:48:35,740 --> 00:48:44,860
+خمس واربعين المسافة بيساوي الصلعة في الزمن الصلعة
+
+576
+00:48:44,860 --> 00:48:47,880
+خمس واربعين والزمن واحد اضربي
+
+577
+00:48:55,000 --> 00:49:00,140
+بس طبعا مهما خلوها تسأل انا بدي انا اتسأل طلعي one
+
+578
+00:49:00,140 --> 00:49:05,020
+second اذا ال one second انا اخترعت اختراع؟ تمام
+
+579
+00:49:05,800 --> 00:49:10,940
+حلو براه عليكي تمام يا بنات اتطلعوا يا بنات بقول
+
+580
+00:49:10,940 --> 00:49:16,420
+عشان الشرط يمسك السيارة لازم X للشرط تسوي X
+
+581
+00:49:16,420 --> 00:49:22,160
+للسيارة final اذا معناته لازم بالأصمر خمسة و
+
+582
+00:49:22,160 --> 00:49:27,120
+أربعين او اه بدي اجيب هدي هنا يا بنات خمسة و
+
+583
+00:49:27,120 --> 00:49:31,400
+أربعين زائد خمسة و أربعين T تسوي واحد و نص T تربية
+
+584
+00:49:31,400 --> 00:49:37,740
+سويت هدي بهديمظبوط هيك ولا لأ؟ بدي أرطب المعادلة
+
+585
+00:49:37,740 --> 00:49:42,280
+أرطبها أجيب هدول الاتنين الحلوين هنا صارت واحد و
+
+586
+00:49:42,280 --> 00:49:47,860
+نص T تربيع زائد خمسة و أربعين T زائد خمسة و أربعين
+
+587
+00:49:47,860 --> 00:49:55,180
+بتساوي سفر هذه معادلة من درجة التانية بتديك حل ..
+
+588
+00:49:55,180 --> 00:50:00,960
+أكم حل؟ حل ليه؟ حل .. حلوهذه معادلة رياضية جبرية
+
+589
+00:50:00,960 --> 00:50:04,440
+أخدتها زمان أنا بالنسبة للفيزيا يقص اللي عندنا أخد
+
+590
+00:50:04,440 --> 00:50:09,160
+عشرة من عشرة والباقي بديش إياه لإيش؟ لأن طب و
+
+591
+00:50:09,160 --> 00:50:12,980
+قلتلكم مين مش مخلص رابع و قلتكم و خلصنا رابع و
+
+592
+00:50:12,980 --> 00:50:16,800
+خلصتوا تامين إذا خلاص أنا متأكد بديش تحلولي رابع و
+
+593
+00:50:16,800 --> 00:50:21,440
+تامين هل جيت من هنا لما إجيت حلت يا بنات طلعت T
+
+594
+00:50:21,440 --> 00:50:26,170
+بتساوي واحد و تلاتين secondصدقنا الكتاب احنا بدنا
+
+595
+00:50:26,170 --> 00:50:29,750
+نرجع لرقم 48 صدقين الكتاب طبعا كده بتتأكد انه صح
+
+596
+00:50:29,750 --> 00:50:33,850
+ولا لأ بروح بعود تتحقق المعادل معناته أكيد صادق
+
+597
+00:50:33,850 --> 00:50:39,670
+طيب طلعت الزمن زي ما تبدك لو إيه ساقلني وين مسكه
+
+598
+00:50:39,670 --> 00:50:44,390
+بعض معناته مش بال Deposition ولا لأ طب أعود هل ولا
+
+599
+00:50:44,390 --> 00:50:44,770
+هل
+
+600
+00:50:48,110 --> 00:50:54,010
+ما هما زبايا عوّض هنا و لا عوّض هنا هتطلع عندك نفس
+
+601
+00:50:54,010 --> 00:50:58,930
+الإجابة و لا لأ طلعت حوالي one point اربعة اربعة
+
+602
+00:50:58,930 --> 00:51:02,950
+في عشرة أُس ثلاثة متر يعني حوالي واحد و نص كيلو
+
+603
+00:51:02,950 --> 00:51:06,730
+ألف و أربعمية و أربعين متر يعني حوالي واحد و نص
+
+604
+00:51:06,730 --> 00:51:11,750
+كيلو و احنا قلنا من عند الصراية للسامر يدوب كيلو
+
+605
+00:51:11,750 --> 00:51:16,200
+يدوب لساحة تكون هذه المسافةعشان نضلنا نجدر
+
+606
+00:51:16,200 --> 00:51:20,760
+المسافات مش الواحد يفكر حاله يمشي من الصرايا
+
+607
+00:51:20,760 --> 00:51:24,120
+للساحة يقول أمي والله مشيت اليوم كتير ويقول
+
+608
+00:51:24,120 --> 00:51:28,740
+مامشيشيشي مشيله كيلو نص وكيلو نص لما ييجوا يعملوا
+
+609
+00:51:28,740 --> 00:51:31,620
+برامج الرياضة بيقولك بيجي تمشي لك خمسة ستة كيلو
+
+610
+00:51:31,620 --> 00:51:36,360
+عقل شيء مش تمشي كيلو نص تتحملوا جميلة كل الناس لأ
+
+611
+00:51:36,360 --> 00:51:37,420
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/H4drweiMiJA_raw.json b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/H4drweiMiJA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a2ceab40106dd8dae5dafdbebf94b6833ae5489c
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/H4drweiMiJA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2593, "start": 5.15, "end": 25.93, "text": "تمام يا بنات نستكمل وقفنا بعد ما أخدنا ال velocity وقلنا ال velocity هي كمية فيزيائية بتعني أن ال position بتغير مع الزمن وعنا average velocity وعندي instantaneous velocity", "tokens": [39237, 10943, 35186, 4724, 8315, 2655, 8717, 14851, 24793, 1211, 4032, 4587, 5172, 8315, 39182, 19446, 5551, 9778, 3215, 8315, 2423, 9269, 4032, 4587, 1211, 8315, 2423, 9269, 39896, 9122, 2304, 10632, 8978, 11622, 1829, 16373, 10632, 39894, 3615, 22653, 14739, 2423, 2535, 39894, 17082, 13546, 20449, 6024, 110, 27842, 4032, 3615, 8315, 4274, 9269, 4032, 3615, 1863, 16254, 45596, 9269], "avg_logprob": -0.19405241526903644, "compression_ratio": 1.5421686746987953, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 5.15, "end": 5.55, "word": "تمام", "probability": 0.387603759765625}, {"start": 5.55, "end": 5.63, "word": " يا", "probability": 0.81005859375}, {"start": 5.63, "end": 6.01, "word": " بنات", "probability": 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0.9853515625}], "temperature": 1.0}, {"id": 22, "seek": 47286, "start": 448.2, "end": 472.86, "text": "و هذه ميل الخط المماس للرسم عند نقطة ما صح؟ اذا بقوللي in the velocity لما يكون عندك رسمة بين ال V و ال T لان مش ال X و ال T ال V و ال T in the velocity time graph اي رسمة هذه بنسميها velocity time graph graph رسمة", "tokens": [2407, 29538, 3714, 26895, 33962, 9566, 9673, 15042, 3794, 5296, 1211, 2288, 38251, 43242, 8717, 47432, 3660, 19446, 20328, 5016, 22807, 1975, 15730, 4724, 39648, 20292, 294, 264, 9269, 5296, 15042, 7251, 30544, 43242, 4117, 12602, 38251, 3660, 49374, 2423, 691, 4032, 2423, 314, 5296, 7649, 37893, 2423, 1783, 4032, 2423, 314, 2423, 691, 4032, 2423, 314, 294, 264, 9269, 565, 4295, 1975, 1829, 12602, 38251, 3660, 29538, 44945, 38251, 1829, 11296, 9269, 565, 4295, 4295, 12602, 38251, 3660], "avg_logprob": -0.23164062332361937, "compression_ratio": 1.7597765363128492, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 448.2, "end": 448.46, "word": "و", 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0.55322265625}, {"start": 457.78, "end": 458.04, "word": " the", "probability": 0.923828125}, {"start": 458.04, "end": 458.6, "word": " velocity", "probability": 0.85693359375}, {"start": 458.6, "end": 458.88, "word": " لما", "probability": 0.89990234375}, {"start": 458.88, "end": 459.08, "word": " يكون", "probability": 0.93798828125}, {"start": 459.08, "end": 459.52, "word": " عندك", "probability": 0.846923828125}, {"start": 459.52, "end": 460.18, "word": " رسمة", "probability": 0.8118489583333334}, {"start": 460.18, "end": 460.86, "word": " بين", "probability": 0.91796875}, {"start": 460.86, "end": 461.18, "word": " ال", "probability": 0.82177734375}, {"start": 461.18, "end": 461.62, "word": " V", "probability": 0.73974609375}, {"start": 461.62, "end": 462.12, "word": " و", "probability": 0.7001953125}, {"start": 462.12, "end": 462.2, "word": " ال", "probability": 0.382568359375}, {"start": 462.2, "end": 462.38, "word": " T", "probability": 0.89306640625}, {"start": 462.38, "end": 462.9, "word": " لان", "probability": 0.5653076171875}, {"start": 462.9, "end": 463.3, "word": " مش", "probability": 0.9013671875}, {"start": 463.3, "end": 463.46, "word": " ال", "probability": 0.9365234375}, {"start": 463.46, "end": 463.68, "word": " X", "probability": 0.96533203125}, {"start": 463.68, "end": 463.84, "word": " و", "probability": 0.955078125}, {"start": 463.84, "end": 463.92, "word": " ال", "probability": 0.5419921875}, {"start": 463.92, "end": 464.1, "word": " T", "probability": 0.9677734375}, {"start": 464.1, "end": 464.66, "word": " ال", "probability": 0.7333984375}, {"start": 464.66, "end": 464.84, "word": " V", "probability": 0.9736328125}, {"start": 464.84, "end": 465.02, "word": " و", "probability": 0.99072265625}, {"start": 465.02, "end": 465.1, "word": " ال", "probability": 0.865234375}, {"start": 465.1, "end": 465.34, "word": " T", "probability": 0.98046875}, {"start": 465.34, "end": 466.14, "word": " in", "probability": 0.86376953125}, {"start": 466.14, "end": 466.38, "word": " the", "probability": 0.9375}, {"start": 466.38, "end": 466.94, "word": " velocity", "probability": 0.8056640625}, {"start": 466.94, "end": 467.5, "word": " time", "probability": 0.60693359375}, {"start": 467.5, "end": 468.12, "word": " graph", "probability": 0.939453125}, {"start": 468.12, "end": 468.56, "word": " اي", "probability": 0.678955078125}, {"start": 468.56, "end": 469.36, "word": " رسمة", "probability": 0.9845377604166666}, {"start": 469.36, "end": 469.72, "word": " هذه", "probability": 0.65087890625}, {"start": 469.72, "end": 470.24, "word": " بنسميها", "probability": 0.920166015625}, {"start": 470.24, "end": 470.68, "word": " velocity", "probability": 0.90869140625}, {"start": 470.68, "end": 471.18, "word": " time", "probability": 0.83740234375}, {"start": 471.18, "end": 471.76, "word": " graph", "probability": 0.9677734375}, {"start": 471.76, "end": 472.38, "word": " graph", "probability": 0.59521484375}, {"start": 472.38, "end": 472.86, "word": " رسمة", "probability": 0.9903971354166666}], "temperature": 1.0}, {"id": 23, "seek": 48331, "start": 473.51, "end": 483.31, "text": "بقول لي the average acceleration if the slope هو الميل of the line connecting هاي بداية و هاي نهاية", "tokens": [3555, 39648, 32239, 264, 4274, 17162, 498, 264, 13525, 31439, 9673, 26895, 295, 264, 1622, 11015, 8032, 47302, 4724, 28259, 10632, 4032, 8032, 47302, 8717, 11296, 10632], "avg_logprob": -0.3563057950564793, "compression_ratio": 1.2169811320754718, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 473.51, "end": 473.99, "word": "بقول", "probability": 0.46240234375}, {"start": 473.99, "end": 474.15, "word": " لي", "probability": 0.228515625}, {"start": 474.15, "end": 474.27, "word": " the", "probability": 0.403564453125}, {"start": 474.27, "end": 474.77, "word": " average", "probability": 0.72998046875}, {"start": 474.77, "end": 476.11, "word": " acceleration", "probability": 0.87939453125}, {"start": 476.11, "end": 476.81, "word": " if", "probability": 0.375732421875}, {"start": 476.81, "end": 477.07, "word": " the", "probability": 0.875}, {"start": 477.07, "end": 477.61, "word": " slope", "probability": 0.95068359375}, {"start": 477.61, "end": 478.09, "word": " هو", "probability": 0.89697265625}, {"start": 478.09, "end": 478.71, "word": " الميل", "probability": 0.650146484375}, {"start": 478.71, "end": 479.39, "word": " of", "probability": 0.92724609375}, {"start": 479.39, "end": 479.63, "word": " the", "probability": 0.82177734375}, {"start": 479.63, "end": 480.19, "word": " line", "probability": 0.970703125}, {"start": 480.19, "end": 481.59, "word": " connecting", "probability": 0.91796875}, {"start": 481.59, "end": 481.87, "word": " هاي", "probability": 0.4666748046875}, {"start": 481.87, "end": 482.35, "word": " بداية", "probability": 0.947265625}, {"start": 482.35, "end": 482.47, "word": " و", "probability": 0.650390625}, {"start": 482.47, "end": 482.69, "word": " هاي", "probability": 0.827392578125}, {"start": 482.69, "end": 483.31, "word": " نهاية", "probability": 0.9384765625}], "temperature": 1.0}, {"id": 24, "seek": 50324, "start": 484.28, "end": 503.24, "text": "أعمل خط جيب ميله هذه هي ال average acceleration ال average acceleration اذا the average acceleration is the slope ميل of the line connecting the initial and the final points اللي بربط من نقطتي البداية والنهاية while بينما", "tokens": [10721, 25957, 1211, 16490, 9566, 10874, 1829, 3555, 3714, 26895, 3224, 29538, 39896, 2423, 4274, 17162, 2423, 4274, 17162, 1975, 15730, 264, 4274, 17162, 307, 264, 13525, 3714, 26895, 295, 264, 1622, 11015, 264, 5883, 293, 264, 2572, 2793, 13672, 1829, 4724, 25513, 9566, 9154, 8717, 47432, 31371, 29739, 28259, 10632, 16070, 1863, 11296, 10632, 1339, 49374, 15042], "avg_logprob": -0.2550317887532509, "compression_ratio": 1.632183908045977, "no_speech_prob": 1.8537044525146484e-05, "words": [{"start": 484.28, "end": 484.66, "word": "أعمل", "probability": 0.6795247395833334}, {"start": 484.66, "end": 485.04, "word": " خط", "probability": 0.98046875}, {"start": 485.04, "end": 485.84, "word": " جيب", "probability": 0.70556640625}, {"start": 485.84, "end": 486.24, "word": " ميله", "probability": 0.69384765625}, {"start": 486.24, "end": 486.76, "word": " هذه", "probability": 0.505859375}, {"start": 486.76, "end": 486.98, "word": " هي", "probability": 0.8232421875}, {"start": 486.98, "end": 487.08, "word": " ال", "probability": 0.82421875}, {"start": 487.08, "end": 487.44, "word": " average", "probability": 0.465576171875}, {"start": 487.44, "end": 488.28, "word": " acceleration", "probability": 0.84130859375}, {"start": 488.28, "end": 489.0, "word": " ال", "probability": 0.58740234375}, {"start": 489.0, "end": 489.4, "word": " average", "probability": 0.7197265625}, {"start": 489.4, "end": 490.2, "word": " acceleration", "probability": 0.88623046875}, {"start": 490.2, "end": 490.92, "word": " اذا", "probability": 0.56024169921875}, {"start": 490.92, "end": 491.14, "word": " the", "probability": 0.20751953125}, {"start": 491.14, "end": 491.46, "word": " average", "probability": 0.74560546875}, {"start": 491.46, "end": 492.16, "word": " acceleration", "probability": 0.86572265625}, {"start": 492.16, "end": 492.48, "word": " is", "probability": 0.77734375}, {"start": 492.48, "end": 492.72, "word": " the", "probability": 0.66650390625}, {"start": 492.72, "end": 493.22, "word": " slope", "probability": 0.947265625}, {"start": 493.22, "end": 493.74, "word": " ميل", "probability": 0.8525390625}, {"start": 493.74, "end": 494.3, "word": " of", "probability": 0.83154296875}, {"start": 494.3, "end": 494.54, "word": " the", "probability": 0.7822265625}, {"start": 494.54, "end": 494.96, "word": " line", "probability": 0.962890625}, {"start": 494.96, "end": 496.22, "word": " connecting", "probability": 0.880859375}, {"start": 496.22, "end": 497.04, "word": " the", "probability": 0.857421875}, {"start": 497.04, "end": 497.38, "word": " initial", "probability": 0.84912109375}, {"start": 497.38, "end": 497.62, "word": " and", "probability": 0.92431640625}, {"start": 497.62, "end": 497.74, "word": " the", "probability": 0.85986328125}, {"start": 497.74, "end": 498.06, "word": " final", "probability": 0.93505859375}, {"start": 498.06, "end": 498.86, "word": " points", "probability": 0.822265625}, {"start": 498.86, "end": 499.42, "word": " اللي", "probability": 0.9384765625}, {"start": 499.42, "end": 499.76, "word": " بربط", "probability": 0.9124348958333334}, {"start": 499.76, "end": 499.86, "word": " من", "probability": 0.8828125}, {"start": 499.86, "end": 500.22, "word": " نقطتي", "probability": 0.9226888020833334}, {"start": 500.22, "end": 500.8, "word": " البداية", "probability": 0.9723307291666666}, {"start": 500.8, "end": 501.52, "word": " والنهاية", "probability": 0.8812255859375}, {"start": 501.52, "end": 501.84, "word": " while", "probability": 0.8173828125}, {"start": 501.84, "end": 503.24, "word": " بينما", "probability": 0.959228515625}], "temperature": 1.0}, {"id": 25, "seek": 53427, "start": 504.49, "end": 534.27, "text": "The instantaneous acceleration at any time is the slope of the tangent at that time هو ميلي المماس يعني أنا بدي عند النقطة هادي عند هذه النقطة بقوله بسيطة بدي أعمل مماس صح؟ و بدي بميله كان أفق السفر كانت عند النقطة هادي بعمل هيك صح ولا لأ؟ و بدي بميله هذه مفهومة و معروفة بس بنذكر بعض فينا هيا أحكي يا بنتي", "tokens": [2278, 45596, 17162, 412, 604, 565, 307, 264, 13525, 295, 264, 27747, 412, 300, 565, 31439, 3714, 1829, 20292, 9673, 15042, 3794, 37495, 22653, 41850, 4724, 16254, 43242, 28239, 47432, 3660, 8032, 995, 16254, 43242, 29538, 28239, 47432, 3660, 4724, 39648, 3224, 4724, 3794, 1829, 9566, 3660, 4724, 16254, 5551, 25957, 1211, 3714, 15042, 3794, 20328, 5016, 22807, 4032, 4724, 16254, 4724, 2304, 26895, 3224, 25961, 5551, 5172, 4587, 21136, 5172, 2288, 25961, 2655, 43242, 28239, 47432, 3660, 8032, 995, 16254, 4724, 25957, 1211, 39896, 4117, 20328, 5016, 49429, 5296, 10721, 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"probability": 0.81982421875}, {"start": 509.57, "end": 510.01, "word": " slope", "probability": 0.9306640625}, {"start": 510.01, "end": 510.31, "word": " of", "probability": 0.9833984375}, {"start": 510.31, "end": 510.59, "word": " the", "probability": 0.8828125}, {"start": 510.59, "end": 511.17, "word": " tangent", "probability": 0.9228515625}, {"start": 511.17, "end": 511.55, "word": " at", "probability": 0.62646484375}, {"start": 511.55, "end": 511.75, "word": " that", "probability": 0.94091796875}, {"start": 511.75, "end": 512.21, "word": " time", "probability": 0.88134765625}, {"start": 512.21, "end": 512.77, "word": " هو", "probability": 0.72265625}, {"start": 512.77, "end": 513.25, "word": " ميلي", "probability": 0.7987467447916666}, {"start": 513.25, "end": 514.13, "word": " المماس", "probability": 0.7906901041666666}, {"start": 514.13, "end": 514.69, "word": " يعني", "probability": 0.87060546875}, {"start": 514.69, "end": 514.89, "word": " أنا", "probability": 0.7099609375}, {"start": 514.89, "end": 515.17, "word": " بدي", "probability": 0.76025390625}, {"start": 515.17, "end": 515.43, "word": " عند", "probability": 0.81494140625}, {"start": 515.43, "end": 515.97, "word": " النقطة", "probability": 0.9596354166666666}, {"start": 515.97, "end": 516.45, "word": " هادي", "probability": 0.7958984375}, {"start": 516.45, "end": 517.47, "word": " عند", "probability": 0.85498046875}, {"start": 517.47, "end": 517.67, "word": " هذه", "probability": 0.63623046875}, {"start": 517.67, "end": 518.09, "word": " النقطة", "probability": 0.9884440104166666}, {"start": 518.09, "end": 518.41, "word": " بقوله", "probability": 0.7335611979166666}, {"start": 518.41, "end": 519.07, "word": " بسيطة", "probability": 0.9859375}, {"start": 519.07, "end": 519.77, "word": " بدي", "probability": 0.8525390625}, {"start": 519.77, "end": 520.33, "word": " أعمل", "probability": 0.8916015625}, {"start": 520.33, "end": 521.09, "word": " مماس", "probability": 0.9684244791666666}, {"start": 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{"start": 638.18, "end": 639.04, "word": " positive", "probability": 0.9228515625}, {"start": 639.04, "end": 639.9, "word": " موجب", "probability": 0.90283203125}, {"start": 639.9, "end": 640.36, "word": " يعني", "probability": 0.93896484375}, {"start": 640.36, "end": 640.78, "word": " باتجاه", "probability": 0.934814453125}, {"start": 640.78, "end": 641.12, "word": " يمين", "probability": 0.9734700520833334}, {"start": 641.12, "end": 641.3, "word": " أو", "probability": 0.8037109375}, {"start": 641.3, "end": 641.56, "word": " يسار", "probability": 0.9617513020833334}, {"start": 641.56, "end": 641.82, "word": " حسب", "probability": 0.95361328125}, {"start": 641.82, "end": 642.4, "word": " موجبك", "probability": 0.9830322265625}, {"start": 642.4, "end": 643.74, "word": " when", "probability": 0.794921875}, {"start": 643.74, "end": 643.98, "word": " the", "probability": 0.9267578125}, {"start": 643.98, "end": 644.4, "word": " velocity", "probability": 0.81396484375}, {"start": 644.4, "end": 644.74, "word": " is", "probability": 0.95654296875}, {"start": 644.74, "end": 645.58, "word": " increasing", "probability": 0.96044921875}, {"start": 645.58, "end": 645.88, "word": " لما", "probability": 0.876220703125}, {"start": 645.88, "end": 646.18, "word": " تكون", "probability": 0.993408203125}, {"start": 646.18, "end": 646.66, "word": " السرعة", "probability": 0.8152669270833334}, {"start": 646.66, "end": 647.86, "word": " متزايدة", "probability": 0.9548828125}], "temperature": 1.0}, {"id": 30, "seek": 66958, "start": 648.84, "end": 669.58, "text": "in the positive x direction speeding up بزيادة السرعة أديكم trick أخدتهوا في ال calculus أديكم سؤال في توجيهي أديكم دالة وقالكم هادي الدالة دالة بتعرف ما دالة function بتاخدوها متزايدة ولا متنقصة كيف تعملوا كنتوا تشتقوها", "tokens": [259, 264, 3353, 2031, 3513, 35593, 493, 4724, 11622, 1829, 18513, 3660, 21136, 2288, 27884, 5551, 16254, 24793, 4282, 5551, 9778, 3215, 47395, 14407, 8978, 2423, 33400, 5551, 16254, 24793, 8608, 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speeding", "probability": 0.2374267578125}, {"start": 651.48, "end": 652.28, "word": " up", "probability": 0.958984375}, {"start": 652.28, "end": 654.2, "word": " بزيادة", "probability": 0.681689453125}, {"start": 654.2, "end": 654.62, "word": " السرعة", "probability": 0.9295247395833334}, {"start": 654.62, "end": 655.52, "word": " أديكم", "probability": 0.6040852864583334}, {"start": 655.52, "end": 656.4, "word": " trick", "probability": 0.39697265625}, {"start": 656.4, "end": 656.82, "word": " أخدتهوا", "probability": 0.8365234375}, {"start": 656.82, "end": 656.9, "word": " في", "probability": 0.9189453125}, {"start": 656.9, "end": 656.98, "word": " ال", "probability": 0.90771484375}, {"start": 656.98, "end": 657.36, "word": " calculus", "probability": 0.49658203125}, {"start": 657.36, "end": 658.16, "word": " أديكم", "probability": 0.5459798177083334}, {"start": 658.16, "end": 658.42, "word": " سؤال", "probability": 0.9949544270833334}, {"start": 658.42, "end": 658.54, "word": " 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"word": " بتاخدوها", "probability": 0.87763671875}, {"start": 665.46, "end": 666.9, "word": " متزايدة", "probability": 0.9693359375}, {"start": 666.9, "end": 667.02, "word": " ولا", "probability": 0.88720703125}, {"start": 667.02, "end": 667.66, "word": " متنقصة", "probability": 0.8046875}, {"start": 667.66, "end": 667.8, "word": " كيف", "probability": 0.901611328125}, {"start": 667.8, "end": 668.38, "word": " تعملوا", "probability": 0.7216796875}, {"start": 668.38, "end": 669.12, "word": " كنتوا", "probability": 0.8099772135416666}, {"start": 669.12, "end": 669.58, "word": " تشتقوها", "probability": 0.96923828125}], "temperature": 1.0}, {"id": 31, "seek": 69357, "start": 672.57, "end": 693.57, "text": "إذا موجبة تقولوا عنها متزايدة، مظبوط ولا لا؟ حلو، هاي نقعد نتطبق، أنا مش اللي تسارع اشتقاق ال velocity، إذا ال velocity بتزيد، ده اللي ما هي، تتوقع ال acceleration تكون موجبة ولا لا؟ صحيح؟ طب وإذا بتتناقص، تطلع سالبة؟", "tokens": [28814, 15730, 3714, 29245, 49401, 6055, 39648, 14407, 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are in opposite direction بيكونوا عكس بعض يعني نرجع سيارة رايحة عنصرات و قاعدة بتتباطع بدأت توقف في الآخر", "tokens": [18822, 264, 9269, 307, 23223, 39894, 2655, 8315, 4587, 9381, 294, 264, 3353, 2031, 3513, 41850, 3714, 47283, 3215, 2423, 3353, 2031, 3513, 2423, 7576, 46811, 10943, 26958, 760, 9269, 293, 17162, 366, 294, 6182, 3513, 4724, 1829, 30544, 14407, 6225, 4117, 3794, 45030, 11242, 37495, 22653, 8717, 47341, 3615, 8608, 1829, 9640, 3660, 12602, 47302, 5016, 3660, 18871, 9381, 2288, 9307, 4032, 12174, 995, 22488, 3660, 39894, 2655, 3555, 41193, 3615, 47525, 10721, 2655, 6055, 30543, 5172, 8978, 6024, 95, 34740], "avg_logprob": -0.2083960843373494, "compression_ratio": 1.5, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 737.59, "end": 737.95, "word": "when", "probability": 0.2490234375}, {"start": 737.95, "end": 738.23, "word": " the", "probability": 0.86572265625}, {"start": 738.23, "end": 738.59, "word": " velocity", "probability": 0.74072265625}, {"start": 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following statements is true؟ قال بيدي تديك جمال و تقولي مين منها صح ومين منها غلط تمام If a car is traveling eastward سيارة رايحة east its acceleration must be east", "tokens": [33785, 295, 264, 3480, 12363, 307, 2074, 22807, 50239, 4724, 1829, 16254, 6055, 16254, 4117, 10874, 2304, 6027, 4032, 6055, 39648, 1829, 3714, 9957, 9154, 11296, 20328, 5016, 4032, 2304, 9957, 9154, 11296, 32771, 1211, 9566, 46811, 10943, 759, 257, 1032, 307, 9712, 10648, 1007, 8608, 1829, 9640, 3660, 12602, 47302, 5016, 3660, 10648, 1080, 17162, 1633, 312, 10648], "avg_logprob": -0.3046875109275182, "compression_ratio": 1.3295454545454546, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 878.38, "end": 878.82, "word": "Which", "probability": 0.269287109375}, {"start": 878.82, "end": 879.86, "word": " of", "probability": 0.92138671875}, {"start": 879.86, "end": 880.1, "word": " the", "probability": 0.91943359375}, {"start": 880.1, "end": 880.54, "word": " following", "probability": 0.8623046875}, 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"probability": 0.796875}, {"start": 896.14, "end": 897.76, "word": " its", "probability": 0.281982421875}, {"start": 897.76, "end": 898.72, "word": " acceleration", "probability": 0.88037109375}, {"start": 898.72, "end": 899.34, "word": " must", "probability": 0.88720703125}, {"start": 899.34, "end": 899.64, "word": " be", "probability": 0.96240234375}, {"start": 899.64, "end": 900.08, "word": " east", "probability": 0.90673828125}], "temperature": 1.0}, {"id": 41, "seek": 92927, "start": 901.21, "end": 929.27, "text": "حلو هيكم شطرين شايفوا ما اشتركوا لأنه قلتلي انت ايش بعرفني ما حقه لو انت كملتيلي معطيات لأ ممكن تكون عكسه ولا لأ اذا حسب السرعة متزايدة او مش متزايدة تمام ازاي جت الكهربا ارحمنا يا سان ماشيتش تمام if a car is slowing down تمام هجيت غشتشني جالي بتتباطأ", "tokens": [5016, 1211, 2407, 39896, 24793, 13412, 9566, 2288, 9957, 13412, 995, 33911, 14407, 19446, 1975, 8592, 2655, 31747, 14407, 5296, 33456, 3224, 12174, 1211, 2655, 20292, 16472, 2655, 1975, 1829, 8592, 45030, 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new file mode 100644
index 0000000000000000000000000000000000000000..5e0041cb00b656fe6834ae5a80366b397e116f8f
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/H4drweiMiJA_raw.srt
@@ -0,0 +1,2468 @@
+1
+00:00:05,150 --> 00:00:11,190
+تمام يا بنات نستكمل وقفنا بعد ما أخدنا ال velocity
+
+2
+00:00:11,190 --> 00:00:18,850
+وقلنا ال velocity هي كمية فيزيائية بتعني أن ال
+
+3
+00:00:18,850 --> 00:00:23,830
+position بتغير مع الزمن وعنا average velocity
+
+4
+00:00:23,830 --> 00:00:28,790
+وعندي instantaneous velocityالـ Average Velocity
+
+5
+00:00:28,790 --> 00:00:34,070
+عرفناها على إنها V Average بيسوى Delta X على Delta
+
+6
+00:00:34,070 --> 00:00:39,750
+T وال Instantaneous Velocity بتسوى Limit تبع الـ
+
+7
+00:00:39,750 --> 00:00:49,530
+DT يعني DX على DT تمهى نجي لها ال quiz نشوف كنا
+
+8
+00:00:49,530 --> 00:00:53,950
+نحكي عربي ولا لأ consider the one dimensional
+
+9
+00:00:53,950 --> 00:00:59,980
+motion إيش هي؟بقول a ball is thrown vertically
+
+10
+00:00:59,980 --> 00:01:04,180
+upward دي بتكرة و رامتها لأعلى تمام سخوط حر ولا
+
+11
+00:01:04,180 --> 00:01:11,140
+لا؟ تمامRises to a highest point and falls back
+
+12
+00:01:11,140 --> 00:01:15,580
+into the thrower's hand ورجعت على إيده انطلقت من
+
+13
+00:01:15,580 --> 00:01:18,460
+إيده ورجعت على إيده مين يقول ليه جديش ال average
+
+14
+00:01:18,460 --> 00:01:23,360
+velocity؟ سفر صح ولا لأ ال average velocity سفر
+
+15
+00:01:23,360 --> 00:01:26,940
+تمام معلومة خزنتها جوا هذه الحركة ال average
+
+16
+00:01:26,940 --> 00:01:33,420
+velocity ليه جديش؟ سفر A car or a race car سيارة
+
+17
+00:01:33,420 --> 00:01:37,840
+سباق تمام الـ Stars fall from rest بدأت من السكون
+
+18
+00:01:37,840 --> 00:01:44,180
+وضلت تمشي and the speeds up ووصلت سرعة 100 متر per
+
+19
+00:01:44,180 --> 00:01:49,200
+second وصلت طبعا ماوصلتش مرة واحدة ضلها تتزيد صح
+
+20
+00:01:49,200 --> 00:01:53,280
+ولا لأ؟ لو إتيت بدي أخذ انجداش ال average velocity
+
+21
+00:01:53,280 --> 00:01:57,980
+تبعتها خمسين ستين أربعين مظبوط ولا لأ؟ رقم من
+
+22
+00:01:57,980 --> 00:02:02,520
+هالأرقام اتفاجنا؟ إذا زيادة منتظمة بتكون السرعة
+
+23
+00:02:02,520 --> 00:02:06,410
+المتوسطة من النص بالظبطإذا منتظمة إذا مش منتظمة
+
+24
+00:02:06,410 --> 00:02:10,230
+بتكون إما انقلة أو أكتر مش مشكلة إنما رقم ما بين
+
+25
+00:02:10,230 --> 00:02:16,610
+صفر اللامية صح ولا لأ تمام space craft سفينة فضاء
+
+26
+00:02:17,190 --> 00:02:21,890
+ماشي في الفضاء drift through space بتمشي في ال
+
+27
+00:02:21,890 --> 00:02:25,710
+space ال space يعني فراغة ال constant velocity
+
+28
+00:02:25,710 --> 00:02:31,170
+سرعتها ثابتة مين يقولي إيش بتفرج لما تكون السرعة
+
+29
+00:02:31,170 --> 00:02:36,590
+ثابتة سرعة ثابت الحظية عن ال average نفسها نفسها
+
+30
+00:02:36,590 --> 00:02:43,220
+صح ولا لا نفسها يعني لو كانت بتمشي بسرعةثابتة
+
+31
+00:02:43,220 --> 00:02:46,760
+مقدارها مائة كيلومتر في الساعة ال average مية وال
+
+32
+00:02:46,760 --> 00:02:49,440
+instant هو مائة .. مائة .. مائة .. مائة .. مائة ..
+
+33
+00:02:49,440 --> 00:02:51,100
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+34
+00:02:51,100 --> 00:02:51,120
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+35
+00:02:51,120 --> 00:02:51,180
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+36
+00:02:51,180 --> 00:02:53,140
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+37
+00:02:53,140 --> 00:02:54,360
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+38
+00:02:54,360 --> 00:02:57,840
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+39
+00:02:57,840 --> 00:02:57,840
+مائة .. مائة .. مائة .. مائة .. مائة .. مائة ..
+
+40
+00:02:57,840 --> 00:03:01,090
+مائة .. مائة .. مThere are any points في نقطة
+
+41
+00:03:01,090 --> 00:03:05,510
+أثناء الحركة at which the instantaneous velocity
+
+42
+00:03:05,510 --> 00:03:09,230
+has the same value as the average velocity over
+
+43
+00:03:09,230 --> 00:03:13,050
+the entire motion. إيش يعني؟ بقول في التلت حركات
+
+44
+00:03:13,050 --> 00:03:18,350
+أنت خزنت السرعة المتوسطة ولا لأ؟الأولى قلنا zero
+
+45
+00:03:18,350 --> 00:03:24,110
+والتانية قلنا حوالي من اربعين، خمسين، ستين
+
+46
+00:03:24,110 --> 00:03:27,770
+والتالتة ما هي نفس المقدار بيقول لمين من هدول
+
+47
+00:03:27,770 --> 00:03:32,630
+بتكون السرعة اللحظية عند لحظة ما تساوي السرعة
+
+48
+00:03:32,630 --> 00:03:39,070
+المتوسطةطب يشوف الأولى، جديش السرعة المتوسطة، في
+
+49
+00:03:39,070 --> 00:03:42,330
+الأولى، في لحظة من اللحظات في سقوط الحر بتكون
+
+50
+00:03:42,330 --> 00:03:47,220
+السرعة اللحظية سفر، عند أقصى ارتفاع، لذا فيه؟أذن
+
+51
+00:03:47,220 --> 00:03:53,080
+حيثي خلصنا عند لحظة طيب مافي تم السؤال التانية وهو
+
+52
+00:03:53,080 --> 00:03:57,400
+ماشي لما يصل المية مر على العشرة والعشين والتلاتين
+
+53
+00:03:57,400 --> 00:04:00,800
+والاربعين والخمسين والستين ولا لأ اذا في لحظة من
+
+54
+00:04:00,800 --> 00:04:04,120
+اللحظات كان سرعته خمسين وفي لحظة من اللحظات كانت
+
+55
+00:04:04,120 --> 00:04:07,260
+اربعين وفي لحظة من اللحظات كانت ستين اذا ال
+
+56
+00:04:07,260 --> 00:04:10,180
+average خمسين في نقطة وصلة خمسين اذا ال average
+
+57
+00:04:10,180 --> 00:04:13,900
+ستين في نقطة وصلة ستين صح ولا لأ اذا برضه صحيحة
+
+58
+00:04:14,050 --> 00:04:18,990
+والتالتة ما هي واضحة إنها صحيحة إذا معناته في
+
+59
+00:04:18,990 --> 00:04:22,050
+الأولى ولا في التانية ولا في التالتة ولا في كلهم
+
+60
+00:04:22,050 --> 00:04:27,730
+في كلهم تمام الآن
+
+61
+00:04:27,730 --> 00:04:34,690
+بدي نحكي عن ال acceleration تسارعطبعا نرجع دايما
+
+62
+00:04:34,690 --> 00:04:39,110
+نقول لكل مسمى من اسمه نصيب سموه تسارع لأنه مش سرعة
+
+63
+00:04:39,110 --> 00:04:43,890
+تسارع لغويا يعني تسارعة جاعة بيه السرعة بتتغير ..
+
+64
+00:04:43,890 --> 00:04:51,130
+بتتغير هنا بشتق X بالنسبالتي يعني اللي بتغير X
+
+65
+00:04:51,130 --> 00:04:57,630
+طلعت سرعة جالي لو جمت X وحطيت V تطلع تسارعةتمام؟
+
+66
+00:04:57,630 --> 00:05:01,630
+لأن إيش اللي بدى يتغير؟ السرعة إذا لو تغيرت ..
+
+67
+00:05:01,630 --> 00:05:05,690
+بالنسبالي الزمن .. لو تغيرت السرعة بنقول الجسم له
+
+68
+00:05:05,690 --> 00:05:09,350
+تسارع اتفجنا هيك؟ إذا هيك عارف الـ acceleration
+
+69
+00:05:09,350 --> 00:05:14,150
+when the velocity of a particle velocity عارفناش
+
+70
+00:05:14,150 --> 00:05:18,650
+معناتها varies with time أو changes with time
+
+71
+00:05:18,650 --> 00:05:22,390
+بتتغير مع الزمنThe particle is said to be
+
+72
+00:05:22,390 --> 00:05:29,130
+accelerating بمعنى
+
+73
+00:05:29,130 --> 00:05:34,310
+آخر has an acceleration لما تكون السرعة ثابتة
+
+74
+00:05:34,310 --> 00:05:41,310
+تتغير جدش تسرعه سفرصح ولا لأ؟ إيش معناته؟ بيقوللي
+
+75
+00:05:41,310 --> 00:05:46,430
+معناته حيكون في عندك كميتين إجداد إيش هي؟ بيقوللي
+
+76
+00:05:46,430 --> 00:05:51,630
+A average بتسوي delta V على delta T شوف إيش اللي
+
+77
+00:05:51,630 --> 00:05:57,750
+اتغير؟ V اتغيرت الآن و A instantaneous بتسوي
+
+78
+00:05:57,750 --> 00:06:04,620
+مستقلة مين؟ DV على DTإذا بدل ما تتغير ال position
+
+79
+00:06:04,620 --> 00:06:09,100
+اتغير الآن السرعة اتغيرت السرعة صار في عندي
+
+80
+00:06:09,100 --> 00:06:12,960
+acceleration اتفقنا يا بنات؟ إذا ال acceleration
+
+81
+00:06:12,960 --> 00:06:16,940
+في عندك average وفي عندك instantaneous
+
+82
+00:06:19,500 --> 00:06:25,860
+اللي هو ده المشطقة طيب مشطقة ال V ماعرف اشطقها طب
+
+83
+00:06:25,860 --> 00:06:29,540
+هي ال V مش جاية من اشتقاق ال X إذا لو أشطقت ال X
+
+84
+00:06:29,540 --> 00:06:33,660
+مرتين بتطلع تسارع ولا لأ؟ إذا هذه التسارع ممكن
+
+85
+00:06:33,660 --> 00:06:37,200
+أقول هي المشطقة التانية ل X بالنسبة للزمن أه أول
+
+86
+00:06:37,200 --> 00:06:40,770
+مرة أشطق بتطلع سرعة أشطق مرة مرة بتطلع تسارعصحيح
+
+87
+00:06:40,770 --> 00:06:46,290
+ولا لا؟ تمام التسارعة كمية فيزيائية مشهورة، جديدة،
+
+88
+00:06:46,290 --> 00:06:50,650
+لا هي L ولا هي M ولا هي T لكن هي L على T تربيع ولا
+
+89
+00:06:50,650 --> 00:06:53,870
+لا؟ L على T تربيع معناته وحداتها متر per second
+
+90
+00:06:53,870 --> 00:06:57,290
+تربية أو centimeter per second تربية أو foot per
+
+91
+00:06:57,290 --> 00:07:01,770
+second تربية الوحدة الـ SI unit في النظام العالمي
+
+92
+00:07:01,770 --> 00:07:06,770
+متر per second تربية لاحظت أننا حكينا حاجة جديدة؟
+
+93
+00:07:06,770 --> 00:07:15,120
+سهلة، تمامجالي حلو جالي الاشتقاق ربطيلي يا ب ميل
+
+94
+00:07:15,120 --> 00:07:22,640
+ولا لأ مشهور اشتقاق ميل حلو طيب هدي ميل و هدي ميل
+
+95
+00:07:22,640 --> 00:07:26,600
+هدي ميل الخط الواصل ما بين النقطتي البداية
+
+96
+00:07:26,600 --> 00:07:33,640
+والنهاية ولا لأو هذه ميل الخط المماس للرسم عند
+
+97
+00:07:33,640 --> 00:07:39,080
+نقطة ما صح؟ اذا بقوللي in the velocity لما يكون
+
+98
+00:07:39,080 --> 00:07:44,840
+عندك رسمة بين ال V و ال T لان مش ال X و ال T ال V
+
+99
+00:07:44,840 --> 00:07:49,720
+و ال T in the velocity time graph اي رسمة هذه
+
+100
+00:07:49,720 --> 00:07:54,270
+بنسميها velocity time graph graph رسمةبقول لي the
+
+101
+00:07:54,270 --> 00:07:59,630
+average acceleration if the slope هو الميل of the
+
+102
+00:07:59,630 --> 00:08:05,840
+line connecting هاي بداية و هاي نهايةأعمل خط جيب
+
+103
+00:08:05,840 --> 00:08:09,400
+ميله هذه هي ال average acceleration ال average
+
+104
+00:08:09,400 --> 00:08:12,720
+acceleration اذا the average acceleration is the
+
+105
+00:08:12,720 --> 00:08:17,620
+slope ميل of the line connecting the initial and
+
+106
+00:08:17,620 --> 00:08:20,800
+the final points اللي بربط من نقطتي البداية
+
+107
+00:08:20,800 --> 00:08:26,910
+والنهاية while بينماThe instantaneous acceleration
+
+108
+00:08:26,910 --> 00:08:31,750
+at any time is the slope of the tangent at that
+
+109
+00:08:31,750 --> 00:08:36,450
+time هو ميلي المماس يعني أنا بدي عند النقطة هادي
+
+110
+00:08:36,450 --> 00:08:42,890
+عند هذه النقطة بقوله بسيطة بدي أعمل مماس صح؟ و بدي
+
+111
+00:08:42,890 --> 00:08:46,570
+بميله كان أفق السفر كانت عند النقطة هادي بعمل هيك
+
+112
+00:08:46,570 --> 00:08:50,790
+صح ولا لأ؟ و بدي بميله هذه مفهومة و معروفة بس
+
+113
+00:08:50,790 --> 00:08:54,270
+بنذكر بعض فينا هيا أحكي يا بنتي
+
+114
+00:09:01,430 --> 00:09:05,450
+مثل البرسكين التربيع ال acceleration ال velocity
+
+115
+00:09:05,450 --> 00:09:10,350
+المكتوب هنا velocity بخطأ هذه خطأ مطبعي و هنا شوف
+
+116
+00:09:10,350 --> 00:09:13,890
+اه هذه acceleration ماحنا نحكي عن ال acceleration
+
+117
+00:09:13,890 --> 00:09:17,470
+مفهومة بس هذه خطأ مطبعي هذه كلمة acceleration
+
+118
+00:09:17,470 --> 00:09:18,190
+كلامك صحية
+
+119
+00:09:23,530 --> 00:09:28,690
+إذن هذه نقطة بداية وهذه نقطة نهاية بت الخط جالي
+
+120
+00:09:28,690 --> 00:09:31,730
+هادى the slope of the line connecting A and B is
+
+121
+00:09:31,730 --> 00:09:36,530
+the average acceleration between A and B بد الصرعة
+
+122
+00:09:36,530 --> 00:09:42,930
+عند النقطة B لحظة باخد tangent و باخد ميلو معروفة
+
+123
+00:09:42,930 --> 00:09:48,410
+تكرار للكلام اللي حاكيناه تمام هلجيت ال velocity
+
+124
+00:09:48,410 --> 00:09:51,690
+قولنا بتختلف عن ال speed ولا لأ ال velocity اللي
+
+125
+00:09:51,690 --> 00:09:55,600
+لها directionو عشان احنا في chapter 2 لسه ماخلصناش
+
+126
+00:09:55,600 --> 00:09:59,760
+chapter 3 قلنا ال direction بدنا نستعيد عنه موجب و
+
+127
+00:09:59,760 --> 00:10:04,780
+سالب و قلنا الحركة العمودية لأعلى موجب و لأسفل
+
+128
+00:10:04,780 --> 00:10:10,100
+سالب و الحركة الأفقية يمين موجب و يسار سالب تمه و
+
+129
+00:10:10,100 --> 00:10:14,340
+قاللي هذه ممكن تغيرها حسب انت ايش بدك لكن هذا ال
+
+130
+00:10:14,340 --> 00:10:18,020
+default حلو قاللي ال acceleration جاية من ال
+
+131
+00:10:18,020 --> 00:10:21,980
+velocityفهمتوا عليا؟ يعني معناته إيها direction
+
+132
+00:10:21,980 --> 00:10:26,360
+لأن ال velocity إيها direction جالي حلو جالي
+
+133
+00:10:26,360 --> 00:10:28,640
+معناته ال acceleration ممكن تكون موجبة وممكن تكون
+
+134
+00:10:28,640 --> 00:10:32,920
+سالبة مش حسب ال direction حسب ال direction تمه
+
+135
+00:10:32,920 --> 00:10:39,040
+جالي the acceleration is positive اتجاهها positive
+
+136
+00:10:39,040 --> 00:10:43,980
+موجب يعني باتجاه يمين أو يسار حسب موجبك when the
+
+137
+00:10:43,980 --> 00:10:49,140
+velocity is increasing لما تكون السرعة متزايدةin
+
+138
+00:10:49,140 --> 00:10:54,620
+the positive x direction speeding up بزيادة السرعة
+
+139
+00:10:54,620 --> 00:10:58,540
+أديكم trick أخدتهوا في ال calculus أديكم سؤال في
+
+140
+00:10:58,540 --> 00:11:03,440
+توجيهي أديكم دالة وقالكم هادي الدالة دالة بتعرف ما
+
+141
+00:11:03,440 --> 00:11:07,800
+دالة function بتاخدوها متزايدة ولا متنقصة كيف
+
+142
+00:11:07,800 --> 00:11:09,580
+تعملوا كنتوا تشتقوها
+
+143
+00:11:12,570 --> 00:11:17,530
+إذا موجبة تقولوا عنها متزايدة، مظبوط ولا لا؟ حلو،
+
+144
+00:11:17,530 --> 00:11:21,990
+هاي نقعد نتطبق، أنا مش اللي تسارع اشتقاق ال
+
+145
+00:11:21,990 --> 00:11:26,710
+velocity، إذا ال velocity بتزيد، ده اللي ما هي،
+
+146
+00:11:26,710 --> 00:11:30,570
+تتوقع ال acceleration تكون موجبة ولا لا؟ صحيح؟ طب
+
+147
+00:11:30,570 --> 00:11:35,750
+وإذا بتتناقص، تطلع سالبة؟بهذه الحالة إيش بيقول
+
+148
+00:11:35,750 --> 00:11:38,410
+ليه؟ Velocity and acceleration are in the same
+
+149
+00:11:38,410 --> 00:11:43,110
+direction لما تكون السرعة بتزيد ها انتبهولي دخلوا
+
+150
+00:11:43,110 --> 00:11:47,330
+المعلومة في مخكم إذا السرعة بتزيد التصارع والسرعة
+
+151
+00:11:47,330 --> 00:11:54,210
+بنفس الاتجاه تمام مش هنتنقلهم اتجاه السرعة بتزيد
+
+152
+00:11:54,210 --> 00:12:00,390
+هجيت هديكم trick واحد رايح على انصرات كيف تجه
+
+153
+00:12:00,390 --> 00:12:07,070
+سرعته؟تجاه انصرات سرعته بتزيد كيف التسارع اتجاهه
+
+154
+00:12:07,070 --> 00:12:13,070
+انصرات انصرات انصرات اتفقنا هيك حلو طلعوا الواحدة
+
+155
+00:12:13,070 --> 00:12:17,950
+التانية بيقولني the acceleration is negativewhen
+
+156
+00:12:17,950 --> 00:12:22,770
+the velocity is decreasing بتتناقص in the positive
+
+157
+00:12:22,770 --> 00:12:25,070
+x direction أنا ماخد ال positive x direction ال
+
+158
+00:12:25,070 --> 00:12:29,830
+default تمام slowing down velocity and
+
+159
+00:12:29,830 --> 00:12:33,530
+acceleration are in opposite direction بيكونوا عكس
+
+160
+00:12:33,530 --> 00:12:39,330
+بعض يعني نرجع سيارة رايحة عنصرات و قاعدة بتتباطع
+
+161
+00:12:39,330 --> 00:12:43,970
+بدأت توقف في الآخرهيجيت هي وين رايحة؟ عن صراط،
+
+162
+00:12:43,970 --> 00:12:49,310
+صرعتها كيف اتجاهها؟ عن صراط، تساروحها؟ ع جباليا، ع
+
+163
+00:12:49,310 --> 00:12:55,250
+جباليا، العكس، فهمتوا عليا؟ إذا إذا الصرعة تتزايد،
+
+164
+00:12:55,250 --> 00:13:00,730
+الصرعة والتسارع مع بعض، إذا الصرعة بتتناقص، الصرعة
+
+165
+00:13:00,730 --> 00:13:04,430
+والتسارع عكس بعض، دخلة المعلومة، هجيت positive ولا
+
+166
+00:13:04,430 --> 00:13:08,770
+negative جثة تانية، حسب positive تبعيتمام؟ حسب انت
+
+167
+00:13:08,770 --> 00:13:12,210
+ايش ماخده الـ positive ماخده الشرق ولا الغرب أما
+
+168
+00:13:12,210 --> 00:13:15,350
+لازم يكونوا مع بعض إذا السرعة بتزيد و لازم يكونوا
+
+169
+00:13:15,350 --> 00:13:21,610
+ضد بعض إذا كانت تتناقص تمام يا بنات؟ أي استفسار؟
+
+170
+00:13:21,610 --> 00:13:29,110
+دخلنا المعلومة هذه quiz نشوف إيش كنا نحكي صيني ولا
+
+171
+00:13:29,110 --> 00:13:37,170
+عربي؟ تماميقولني if a car is travelling eastward
+
+172
+00:13:37,170 --> 00:13:42,290
+رايحة شرق، اتجاه السرعة كيف؟ شرق، هو هذي معطى،
+
+173
+00:13:42,290 --> 00:13:49,350
+مبينةواضحة وصريحة and slowing down تتباطى تباطى
+
+174
+00:13:49,350 --> 00:14:01,870
+تباطى
+
+175
+00:14:01,870 --> 00:14:09,010
+تباطى تباطى تباطى
+
+176
+00:14:09,010 --> 00:14:11,770
+تباطى تباطى تباطى تباطى تباطى تباطى تباطى تباطى
+
+177
+00:14:11,770 --> 00:14:11,910
+تباطى تباطى تباطى تباطى تباطى تباطى تباطى تباطى
+
+178
+00:14:11,910 --> 00:14:11,910
+تباطى تباطى تباطى تباطى تباطى تباطى تباطى تباطى
+
+179
+00:14:11,910 --> 00:14:11,910
+تباطى تباطى تباطى تباطى تباطى تباطى تباطى تباطى
+
+180
+00:14:11,910 --> 00:14:11,910
+تباطى تباطى تباطى تباطى تباطى تباطى تباطى تباطى
+
+181
+00:14:11,910 --> 00:14:14,730
+تباطى تباطى تباطى تباطى تباطى تباطى تباطEast نعب
+
+182
+00:14:14,730 --> 00:14:18,430
+عيد بس بيقول Slow down إذا عكس بعيد إيش عكس ال
+
+183
+00:14:18,430 --> 00:14:23,490
+East؟ West إذا ال West طلع هنا لا هيك ولا هيك وها
+
+184
+00:14:23,490 --> 00:14:27,370
+دي زيك زاك مرة رايح و مرة جاه مفهوم مظبوط ولا لأ
+
+185
+00:14:27,370 --> 00:14:33,010
+إذا الخيار الصح إذا استوعبته كلمتي معناته Westward
+
+186
+00:14:33,010 --> 00:14:38,820
+ولا لأ Westward حلو كان لك إيه ماني quiz نكملWhich
+
+187
+00:14:38,820 --> 00:14:43,240
+of the following statements is true؟ قال بيدي تديك
+
+188
+00:14:43,240 --> 00:14:50,960
+جمال و تقولي مين منها صح ومين منها غلط تمام If a
+
+189
+00:14:50,960 --> 00:14:57,760
+car is traveling eastward سيارة رايحة east its
+
+190
+00:14:57,760 --> 00:15:03,730
+acceleration must be eastحلو هيكم شطرين شايفوا ما
+
+191
+00:15:03,730 --> 00:15:07,250
+اشتركوا لأنه قلتلي انت ايش بعرفني ما حقه لو انت
+
+192
+00:15:07,250 --> 00:15:12,090
+كملتيلي معطيات لأ ممكن تكون عكسه ولا لأ اذا حسب
+
+193
+00:15:12,090 --> 00:15:18,010
+السرعة متزايدة او مش متزايدة تمام ازاي جت الكهربا
+
+194
+00:15:18,010 --> 00:15:25,690
+ارحمنا يا سان ماشيتش تمام if a car is slowing down
+
+195
+00:15:25,690 --> 00:15:32,110
+تمام هجيت غشتشني جالي بتتباطأX acceleration must
+
+196
+00:15:32,110 --> 00:15:37,230
+be negative يا الله أعلم كيف ال negative تبعي انت
+
+197
+00:15:37,230 --> 00:15:42,030
+ما جابتليش لسه مادتنيش معطيات كافية انا بقولك
+
+198
+00:15:42,030 --> 00:15:45,430
+slowing down لو قلتلي السرعة والتسارع ضد بعض بقولك
+
+199
+00:15:45,430 --> 00:15:49,550
+اه لكن انت بتقوللي negative و positive حسب اتجاهي
+
+200
+00:15:49,550 --> 00:15:56,630
+صحيح تمام حلو يعني مثلا هيك السرعة معناته التسارع
+
+201
+00:15:56,630 --> 00:16:00,060
+هيك ولا لأ طب يمكن انا هيك هو موجه بيهفهمتوا
+
+202
+00:16:00,060 --> 00:16:04,400
+عليها؟ اذا حسب ال direction وانت ماقلتليش .. انت
+
+203
+00:16:04,400 --> 00:16:09,760
+ماقلتليش حلو a particle with constant acceleration
+
+204
+00:16:09,760 --> 00:16:13,480
+هنا في خطوة مش عارف انا عند الشباب لجته صح او في
+
+205
+00:16:13,480 --> 00:16:17,560
+شعب هن هنا can never stop can never .. عندكم
+
+206
+00:16:17,560 --> 00:16:21,180
+never؟ bravo عليكم طبعا .. طبعا الشعب اللي جابلكم
+
+207
+00:16:21,180 --> 00:16:25,220
+كانت never موجودة can never stop بيقولي واحد
+
+208
+00:16:25,220 --> 00:16:29,400
+constant acceleration اديكم مثال لها السقوط الحر
+
+209
+00:16:30,480 --> 00:16:34,420
+constant acceleration ولا لأ الجسم لما تضربه بجفش
+
+210
+00:16:34,420 --> 00:16:40,860
+بالمرة بجف بس لحظيا إذا ممكن يجف ممكن يجف إذا هذه
+
+211
+00:16:40,860 --> 00:16:46,130
+برضه مش صحيحة نشوف الأخيرةa particle with constant
+
+212
+00:16:46,130 --> 00:16:51,090
+acceleration can never stop and stay stop مش ممكن
+
+213
+00:16:51,090 --> 00:16:55,270
+يجف يظل واقف لازم يعود يرجع ويتحرك اللي هو بيعمل
+
+214
+00:16:55,270 --> 00:17:00,250
+reversing بنعكس إذا الأخيرة هي الغلط ولا ممكن يجف
+
+215
+00:17:00,250 --> 00:17:05,650
+يظل واقف بيجف فاصل حظيا صح عشان يرجع هي الصح مانعش
+
+216
+00:17:05,650 --> 00:17:10,550
+قولت؟ تمام يعني هو الخيار اللي بدي أخده إذا الخيار
+
+217
+00:17:10,550 --> 00:17:16,620
+إيش هو؟أه يا بنات أي سفسار احنا متفجين جاريقين مما
+
+218
+00:17:16,620 --> 00:17:19,920
+فيه الكفاية أنه نسأل بدون تردد أنا إيه جاني الشاب
+
+219
+00:17:19,920 --> 00:17:22,740
+الصبحيات بعد ما خلصت من العهد و الله قليل تسأل بدي
+
+220
+00:17:22,740 --> 00:17:27,440
+أسألك رحت الحسنات منه لإنه ماثبتش غيره أنا صرت
+
+221
+00:17:27,440 --> 00:17:33,990
+أجاوبه إله لحاله احكيالـ C و D هال gate بيقولي
+
+222
+00:17:33,990 --> 00:17:36,970
+constant acceleration تمام؟ ال constant
+
+223
+00:17:36,970 --> 00:17:41,030
+acceleration بيقولي و لا ممكن يجف بقوله لأ انا
+
+224
+00:17:41,030 --> 00:17:45,370
+افترض ان ال acceleration ها دي بتباطع فيها ايش
+
+225
+00:17:45,370 --> 00:17:49,530
+بتباطع يعني؟ في الآخر ايش بيصير فيه؟ و دي جف صح؟
+
+226
+00:17:49,530 --> 00:17:53,430
+يظن ان دي غلط و اديتك مثال السقوط الحُرف هذا
+
+227
+00:17:53,430 --> 00:17:57,510
+الجلمةبدي اطلع الى فوق، ايش التصارع تبعه؟ تصارع
+
+228
+00:17:57,510 --> 00:18:01,150
+جاذبية ولا لا؟ ثابت ولا مش ثابت التصارع الجاذبية؟
+
+229
+00:18:01,150 --> 00:18:06,330
+بده يضلوا واصل السماء؟لأ عند ضغطة معينة بدي يجف صح
+
+230
+00:18:06,330 --> 00:18:10,190
+ولا .. اذا هذا غلط الكلمة انه هي تسارق ثابت لكن
+
+231
+00:18:10,190 --> 00:18:14,970
+واجف نجي للاخيرة بيقولي طيب ممنوع يجف يظل واقف
+
+232
+00:18:14,970 --> 00:18:17,670
+بيقوله اه هذا بيجف بيظل شويه ولا بيحرض و بيقول
+
+233
+00:18:17,670 --> 00:18:23,030
+بديش ها بديش هنزل صح اللو؟ لأ بعد برجع اذا هو بيجف
+
+234
+00:18:23,030 --> 00:18:28,610
+لكن مضلش واقف مزال في تسارع بدي رجعه فيمتى عليها؟
+
+235
+00:18:28,610 --> 00:18:29,330
+احكي يا بنتين
+
+236
+00:18:33,160 --> 00:18:37,040
+يعني واحدة مكملة للتانية انه لازم الجسم لما يوصل
+
+237
+00:18:37,040 --> 00:18:40,780
+لنقطة معينة يابي يعني بنزل بيكمل لإن التصارع ما
+
+238
+00:18:40,780 --> 00:18:45,360
+زال ثابت بيبقى موجود طبعا هو تصارع بيبقى يأكسه مش
+
+239
+00:18:45,360 --> 00:18:48,820
+مظبوط ولا .. فبيرجعه فلازم يرجعه لو أجينا
+
+240
+00:18:48,820 --> 00:18:52,080
+بالامتحان نفس السؤال الـC وD نفس ما هما هانت من
+
+241
+00:18:52,080 --> 00:18:58,200
+أصحتك؟ لأ مانالش عدلتها لأ هي الـDأه بس الصح
+
+242
+00:18:58,200 --> 00:19:01,360
+الأكتر حاجة دي تمام و أنا عدلتها يعني في الآخر
+
+243
+00:19:01,360 --> 00:19:03,780
+طلعت عملي مهام عدل عينكم حلو
+
+244
+00:19:06,320 --> 00:19:09,660
+نجيها المثال، هذا مثال سهل، فيه كتير أمثلة سهلة
+
+245
+00:19:09,660 --> 00:19:12,660
+The velocity of a particle يا بنات moving along
+
+246
+00:19:12,660 --> 00:19:17,400
+the X-axis varies with time بتتغير مع الزمن، ماذا
+
+247
+00:19:17,400 --> 00:19:19,940
+بتتغير مع الزمن؟ زي في acceleration ولا لا؟ في
+
+248
+00:19:19,940 --> 00:19:22,980
+acceleration قاللي كيف بتتغير؟ قولتله تبعلي
+
+249
+00:19:22,980 --> 00:19:27,220
+المعادلة اللي أنت شايفها أربعين ناقص خمسة تتربيع
+
+250
+00:19:27,220 --> 00:19:32,290
+شايفين المعادلة؟ شايفينهاwith z in meter per
+
+251
+00:19:32,290 --> 00:19:34,930
+second and t in second يعني أنا بستخدم الـ SI
+
+252
+00:19:34,930 --> 00:19:41,470
+system تمام؟ إيش بدك؟ حاجة بتحصل حالي Find the
+
+253
+00:19:41,470 --> 00:19:46,330
+average acceleration for the interval من 0 ل 2
+
+254
+00:19:46,330 --> 00:19:49,870
+second بدي ال average acceleration في فترة زمنية
+
+255
+00:19:49,870 --> 00:19:54,550
+معروفة من 0 ل 2 second تمام؟والمطلوب التاني ..
+
+256
+00:19:54,550 --> 00:19:57,470
+شكرا يا سامي determine the acceleration ال T
+
+257
+00:19:57,470 --> 00:20:01,030
+بتساوي 2 second ماذا ذاك اللحظة معينة مع اننا نتود
+
+258
+00:20:01,030 --> 00:20:09,310
+التسارع اللحظي تمه .. ها .. هنا هنا هذه القوانين
+
+259
+00:20:09,310 --> 00:20:16,570
+صحيك ولا لأ؟ Delta V معناته V لما T بتساوي 2 نقص V
+
+260
+00:20:16,570 --> 00:20:23,770
+لما T بتساوي 0 ولا لأ؟ على 2 نقص 0صحيحيك تمام هذه
+
+261
+00:20:23,770 --> 00:20:28,150
+بدنا نجيبها من اين نجيبها هذه و هذه من المعادلة
+
+262
+00:20:28,150 --> 00:20:35,850
+يلا ايه average بتساوي منى نجلني يلا اربعين ناقص
+
+263
+00:20:35,850 --> 00:20:41,910
+خمسة في اربعة خمسة في اربعة اربعين ناقص عشرين اذا
+
+264
+00:20:41,910 --> 00:20:44,930
+هذه عشرين ناقص
+
+265
+00:20:46,370 --> 00:20:50,910
+سفر يعني ناقص اربعين اه بالظبط ناقص اربعين لإنه
+
+266
+00:20:50,910 --> 00:20:57,030
+عوضت بحالك بسفر فناقص اربعين ع اتنين ناقص عشرين
+
+267
+00:20:57,030 --> 00:21:05,270
+على اتنين minus 10 ايه يا بنات واضح شو سويته سهلة
+
+268
+00:21:05,270 --> 00:21:11,170
+تمام سهلة جدا احكي يا بنتى كيف
+
+269
+00:21:16,980 --> 00:21:26,360
+علي صوتك اه لأ بتديكي الصراع اللحظية و هو بدوش
+
+270
+00:21:26,360 --> 00:21:32,700
+الصراع اللحظية مينفعش لما يقولي الصراع المتوسطة
+
+271
+00:21:32,700 --> 00:21:38,760
+مينفع أستقل لأ التعريف شفاه التعريف بيقولي A
+
+272
+00:21:38,760 --> 00:21:42,800
+average بيسوي DV على DT ولا Delta V على Delta T
+
+273
+00:21:42,800 --> 00:21:48,050
+Delta و Delta مش اشتقاقفهمتوا عليّ؟ دلوقت أنا بركز
+
+274
+00:21:48,050 --> 00:21:53,470
+بيش لإن هذا خطأ شائع بيجي، مينفعش، تشتاق، أنا مش
+
+275
+00:21:53,470 --> 00:21:56,890
+طالب الصراع للتسارع اللحظي، أنا بدي التسارع
+
+276
+00:21:56,890 --> 00:22:02,070
+المتوسط، التسارع المطلوب التاني هالجهة، إيش بده؟
+
+277
+00:22:02,070 --> 00:22:07,150
+التسارع عند لحظة تمام، هاي هاي يعني بدك هادي،
+
+278
+00:22:07,150 --> 00:22:11,230
+بقوله يلّا، هالجهة تبقى متشاطرة على الاستقاب،
+
+279
+00:22:11,230 --> 00:22:18,370
+اشتقىاربعين نقص خمسة T يعني نقص عشرة T هيجيك بدك و
+
+280
+00:22:18,370 --> 00:22:22,190
+عند أي زمان عندتي اتنين second بقوله اذا ايه عندتي
+
+281
+00:22:22,190 --> 00:22:27,890
+بتسوى اتنين second بتسوى نقص عشرين تمام
+
+282
+00:22:27,890 --> 00:22:33,310
+يا بنات تمام حلنا
+
+283
+00:22:33,310 --> 00:22:40,710
+السؤال وهينطلع لما يقولي بدي average اشتقلأ انتبه
+
+284
+00:22:40,710 --> 00:22:46,270
+بدي أوض في المعاجلة تمام أوضنا و جيبنا تمام و لما
+
+285
+00:22:46,270 --> 00:22:51,070
+جيبنا ال instantaneously روحت اشتقت و طلعتها تمام
+
+286
+00:22:56,070 --> 00:23:00,190
+في اكسليراشن في اكسليراشن ايش تعرفي الاكسليراشن
+
+287
+00:23:00,190 --> 00:23:03,670
+معدل تغير سرعة بالنسبة للزمن في منطقة متوسط وفي
+
+288
+00:23:03,670 --> 00:23:07,830
+منها لعبة نجي للتسارع جلي أحيانا التسارع يا بنات
+
+289
+00:23:07,830 --> 00:23:12,930
+بيكون ثابت زي مثلا نفترض عندي هذه الأرقام تشوفولي
+
+290
+00:23:12,930 --> 00:23:17,860
+كيف يزيد هذه الأرقام سرعاتتمام؟ اتنين، اربعة، ستة،
+
+291
+00:23:17,860 --> 00:23:21,180
+تمانية، عشرة، زادت ولا زاق؟ ايه كيب الزيادة ده؟
+
+292
+00:23:21,180 --> 00:23:24,320
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+293
+00:23:24,320 --> 00:23:24,580
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+294
+00:23:24,580 --> 00:23:25,200
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+295
+00:23:25,200 --> 00:23:27,340
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+296
+00:23:27,340 --> 00:23:34,600
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+297
+00:23:34,600 --> 00:23:39,920
+اتنفي عندك معادلات تستطيع اشتقاقها اذا بيقول
+
+298
+00:23:39,920 --> 00:23:44,200
+particle under constant acceleration اذا انت عندك
+
+299
+00:23:44,200 --> 00:23:50,840
+معطى ان ايه مالها constant a is constant طبعا
+
+300
+00:23:50,840 --> 00:23:57,120
+وياكم هيك نجرب الجلم و نكتب مع بعض و نجرب في حدا
+
+301
+00:23:57,120 --> 00:24:04,440
+منكم ماخلصش صف رابع و صف تامنووصلنا هنا اذا انا
+
+302
+00:24:04,440 --> 00:24:07,980
+ممكن تبهولي مازال خلصته رابع وتامن اثبتولي هال
+
+303
+00:24:07,980 --> 00:24:15,900
+gate تمام a is constant بيديكم
+
+304
+00:24:15,900 --> 00:24:20,600
+ألقام تجيبولي متوسطهم تعرف تجيب المتوسطات 5 5 5 5
+
+305
+00:24:20,600 --> 00:24:21,200
+5 5
+
+306
+00:24:25,340 --> 00:24:30,440
+خمسة مظبوط او لا لما يكون الشغل ثابت اه اروح اجمحه
+
+307
+00:24:30,440 --> 00:24:33,780
+و اجلس مع عددهم و ارخم حالت مايوم انت ماغيرتش اشي
+
+308
+00:24:33,780 --> 00:24:41,060
+طيب ايه ال constant بقدر اقول ان ايه average هي
+
+309
+00:24:41,060 --> 00:24:47,360
+نفسها ايه اه مازال constant اه نفسها نفسها والله
+
+310
+00:24:47,360 --> 00:24:52,100
+هاي ها ده ما قلتلكم هاي خمسة هاي خمسة هاي خمسة هاي
+
+311
+00:24:52,100 --> 00:24:58,710
+خمسةأي قيمة منهم جديش والمتوسط اذا اللحظة دي
+
+312
+00:24:58,710 --> 00:25:03,890
+والمتوسط زي بعض صح ولا لأ طب آمين جالي هادي لها
+
+313
+00:25:03,890 --> 00:25:08,110
+قانون ولا لأ اللي توسأت عنه مش اشتقاق جالي هادي
+
+314
+00:25:08,110 --> 00:25:12,810
+والله جالولي V final نقص V initial على T final نقص
+
+315
+00:25:12,810 --> 00:25:16,290
+T initial اعتبر T initial سفر يا سيدي مانت دايما
+
+316
+00:25:16,290 --> 00:25:21,130
+بتشغل الساعة من بداية فبتعتبر Tinitial السفر وما
+
+317
+00:25:21,130 --> 00:25:24,790
+زال بطل في عندك T initial فشلة T واحدة مضاجين
+
+318
+00:25:24,790 --> 00:25:31,090
+final تمام بتساوي ايه؟ وين اللي جال خلص رابع؟ نضرب
+
+319
+00:25:31,090 --> 00:25:37,130
+درب تبادلي نضرب درب تبادلي imply that او هذا يعني
+
+320
+00:25:37,130 --> 00:25:43,610
+The final ماقس V initial برضه
+
+321
+00:25:43,610 --> 00:25:47,210
+في صف رابع حد بيدحطها الشجرة التانية فصار V final
+
+322
+00:25:47,210 --> 00:25:48,750
+بتساوي V initial
+
+323
+00:25:53,650 --> 00:25:58,210
+شوفتهوا؟ بتعرفوه؟ وخفظينه زي سمنه صح ولا لأ؟ هاي
+
+324
+00:25:58,210 --> 00:26:01,770
+أول قانون أهل الشتقاق مش كتير مهم بس يعني احنا ما
+
+325
+00:26:01,770 --> 00:26:05,870
+زال رابعه و تامين مخلصينه مستقى يعني هاي أول ..
+
+326
+00:26:05,870 --> 00:26:11,950
+فيها إيه سفسار يا بنات؟ تمام حلو ال gate A is
+
+327
+00:26:11,950 --> 00:26:17,730
+constant هذا شرط لأنه علوان هذادائما شرط صح ولا لأ
+
+328
+00:26:17,730 --> 00:26:22,670
+حلو اطلعولي على هذه سرعات بتديكم يهم انتوا كتبتم
+
+329
+00:26:22,670 --> 00:26:27,950
+خمسات كانت تسارعات سرعة اتنين اربعة ستة تمانية
+
+330
+00:26:27,950 --> 00:26:35,050
+عشرة كيف الزيادة مش ثابت بتغير من يجيبلي ال
+
+331
+00:26:35,050 --> 00:26:41,150
+average المعدل ايش كيف نجيب المعدل احنا معاكي يلا
+
+332
+00:26:41,150 --> 00:26:48,550
+اجمعيلي اتنين واربعةاتنين واربعة ستة وستة و تمانية
+
+333
+00:26:48,550 --> 00:26:52,270
+و عشرة واحد ع اتنين تلقى اتة اربع خمسة تلاتين ع
+
+334
+00:26:52,270 --> 00:26:57,110
+خمسة ستة ال average جالي يطلع هدول لو مليون ده
+
+335
+00:26:57,110 --> 00:27:00,630
+تجمع المليون و تجسم ع مليون يطلع هال trick إذا
+
+336
+00:27:00,630 --> 00:27:07,390
+زيادة ثابت أخودي الأول و الأخر و جسم ع اتنين اتنين
+
+337
+00:27:07,390 --> 00:27:12,540
+و عشرةع تمين ايه؟ و لا طلعت ستة نفس الجواب بس بشرط
+
+338
+00:27:12,540 --> 00:27:14,960
+ان تكون الزيادة ثابتة و انا عندي ال acceleration
+
+339
+00:27:14,960 --> 00:27:20,320
+مالها ثابتة ده اللي في هذه الحالة هذه سرعات V
+
+340
+00:27:20,320 --> 00:27:25,860
+average قطعا الأولى زائد الأخيرة عتنين
+
+341
+00:27:28,600 --> 00:27:31,200
+فده القانون اللي خدناه في المدرسة ماعرفش اخدت هو
+
+342
+00:27:31,200 --> 00:27:36,040
+اي صفر بلاش اتبل عليكم اقول رابع لأ مش رابع تمام
+
+343
+00:27:36,040 --> 00:27:39,720
+اعلى شوية من رابع انتوا اكتشفتوا الاحصة دي المعدل
+
+344
+00:27:39,720 --> 00:27:43,780
+و مش المعدل تمام اه تمام يعني اذا انجليت رابع تمام
+
+345
+00:27:43,780 --> 00:27:50,660
+عشان كده تمام حلوجيلي طيب مين يذكرني في average
+
+346
+00:27:50,660 --> 00:27:58,340
+قانونها إيش X final نقص X initial إذا X final نقص
+
+347
+00:27:58,340 --> 00:28:02,320
+X initial على T final نقص T initial بتقولنا T
+
+348
+00:28:02,320 --> 00:28:10,960
+بتساوي V initial زي V final على 2 ضرب تبادي و تبقى
+
+349
+00:28:10,960 --> 00:28:19,430
+صفرابع من هنا خلينا نقولبقول X final مقص X initial
+
+350
+00:28:19,430 --> 00:28:29,150
+بتساوي نص V initial زي V final في T هاي كمان
+
+351
+00:28:29,150 --> 00:28:36,790
+معادلة تمام؟ حلو قال لي طيب رجعنا للهادي لسه قال
+
+352
+00:28:36,790 --> 00:28:45,620
+لي هادي مينفعش حتة منها مش هي نفسها اهشحتني يلّا
+
+353
+00:28:45,620 --> 00:28:51,200
+نشحت بقوله
+
+354
+00:28:51,200 --> 00:28:59,080
+X final مقص X initial على T بتساوي V initial زائد
+
+355
+00:28:59,080 --> 00:29:07,620
+V final زائد V initial زائد AT عطني متابعين
+
+356
+00:29:07,620 --> 00:29:15,900
+معايا؟ V initial زائد V initial إذن هذه صارتاتنين
+
+357
+00:29:15,900 --> 00:29:21,440
+V initial صح ولا لأ تمام جالي هيك بترتب ليها بقول
+
+358
+00:29:21,440 --> 00:29:28,080
+X final نقص X initial على T بتسوي V initial زي نص
+
+359
+00:29:28,080 --> 00:29:32,220
+A T صح
+
+360
+00:29:32,220 --> 00:29:40,620
+صحته متابعين حلو يلا درب تبادلي درب تبادلي بتصير
+
+361
+00:29:40,620 --> 00:29:47,530
+هاتي هيك هاتي و هاتي تربيةوهي القانون الحلو تبعنا
+
+362
+00:29:47,530 --> 00:29:51,930
+X final نقص X initial بيسوا V initial في T زي نص
+
+363
+00:29:51,930 --> 00:30:00,790
+AT تربية ام صح صحين هاي كمان قانون طيب نرجع
+
+364
+00:30:00,790 --> 00:30:11,490
+لصف رابع بدي T من هنا انت اه ما هو قوليلي نجليلي T
+
+365
+00:30:13,150 --> 00:30:20,630
+حلو إذا T بتساوي Vfinal نقص Vinitial على إيه؟ صحية
+
+366
+00:30:20,630 --> 00:30:27,330
+تمام؟ أه كنا بنعرف قال لي حلو بنفهدي T تعوض علينا؟
+
+367
+00:30:28,300 --> 00:30:31,720
+بدي أعوضها، هشوف إيش بتطلع معايا بصحلي ولا بصحلي
+
+368
+00:30:31,720 --> 00:30:38,960
+إيش؟ بصحلي بقول x final نقص x initial بتساوي v
+
+369
+00:30:38,960 --> 00:30:44,240
+initial بدل t بدي أحط v final نقص v initial على a
+
+370
+00:30:44,240 --> 00:30:52,040
+زاد نص a بدي أربح هذه v final نقص v initial تربيع
+
+371
+00:30:52,040 --> 00:30:56,420
+على a تربيع صح ولا لأ؟ لأنه بدي أربح هذه و بدي
+
+372
+00:30:56,420 --> 00:31:01,330
+أربح هذهطيب اما علمتكم انكم في صفرابيع تلت و خمس
+
+373
+00:31:01,330 --> 00:31:07,890
+كيف تجيبوه؟ تلت و خمس كيف كنتوا تجيبوه؟
+
+374
+00:31:07,890 --> 00:31:11,130
+جمع
+
+375
+00:31:11,130 --> 00:31:17,050
+الكثور اللي عتيادية انسيتوها مش من عامل مشتراك تلت
+
+376
+00:31:17,050 --> 00:31:24,870
+و خمس بنحط فيش في المقام؟ خلاص ايه بالدقيقة وصلت
+
+377
+00:31:26,590 --> 00:31:29,610
+أخدت الخمسة عشر لإنه لجيت انا المفروض أخد الكبير
+
+378
+00:31:29,610 --> 00:31:32,290
+بس الكبير بظلطش معايا اللي هو تلاتة أو خمسة روح
+
+379
+00:31:32,290 --> 00:31:36,270
+اتكبرت أكتر و أكتر دي بتال خمسة لكن خمس زائد عشر
+
+380
+00:31:36,270 --> 00:31:40,550
+إيش هيخدتها عاملهم الشراك؟ عشرة عشرة صح ولا لأ؟
+
+381
+00:31:40,550 --> 00:31:44,550
+اتطلع ايه إيش بدي أسوي؟ بيقوللي أنت إيش لعملته؟
+
+382
+00:31:44,550 --> 00:31:52,880
+وين أنا وصلت هنا؟ ه .. هذي .. هذي هي شفينهاصح؟
+
+383
+00:31:52,880 --> 00:31:56,220
+صارت اتنين ايه و هنا ايه؟ ايش اخد عالم المشارك؟
+
+384
+00:31:56,220 --> 00:31:58,240
+ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟
+
+385
+00:31:58,240 --> 00:32:00,280
+اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين
+
+386
+00:32:00,280 --> 00:32:04,320
+ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟
+
+387
+00:32:04,320 --> 00:32:08,360
+اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين
+
+388
+00:32:08,360 --> 00:32:12,780
+ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟ اتنين ايه؟
+
+389
+00:32:12,780 --> 00:32:18,240
+اتنين ايه؟ اتنين
+
+390
+00:32:20,710 --> 00:32:26,550
+وحدنا المقام ايش احطشيه في المقام هداشيه اضربوه في
+
+391
+00:32:26,550 --> 00:32:31,950
+اتنين اذا اضربولي هدي اتنين V initial V final نقص
+
+392
+00:32:31,950 --> 00:32:43,430
+اتنين V initial تربيع اه صح صح تمام زائد مين
+
+393
+00:32:43,430 --> 00:32:51,600
+يربعلي هدي ربع V final تربيعنقص اتنين V initial V
+
+394
+00:32:51,600 --> 00:32:58,460
+final زائد V initial تربيع تمام هيك؟ طلعولي الأول
+
+395
+00:32:58,460 --> 00:33:09,160
+و الأخير يا عيني عليكم اتطلعي ناقص V initial تربيع
+
+396
+00:33:09,160 --> 00:33:14,800
+زائد V initial تربيع ناقص V initial تربيع صحيح؟
+
+397
+00:33:14,800 --> 00:33:21,210
+اذا هذه متساويها بالأصمر المرة هذه هاي المقام
+
+398
+00:33:21,210 --> 00:33:26,970
+اتنين ايه ناقص
+
+399
+00:33:26,970 --> 00:33:33,250
+V initial تربيع تبعين
+
+400
+00:33:33,250 --> 00:33:37,150
+معاه؟ قال لي ها دي ايش مش ساوي كله X final ناقص X
+
+401
+00:33:37,150 --> 00:33:43,250
+initial هاي ها X final ناقص X initial اضرب ضرب
+
+402
+00:33:43,250 --> 00:33:55,050
+تبادلي ضربناصار X final نقص X initial في 2A بتساوي
+
+403
+00:33:55,050 --> 00:34:00,730
+V initial تربيع بالسالب زي V final تربيع رطب
+
+404
+00:34:00,730 --> 00:34:04,810
+المعادلة زي ما علمونا حطل ال V initial ع الشجة
+
+405
+00:34:04,810 --> 00:34:12,590
+التانيةهي كانت سلبش بتصير V final تربيع بتساوي V
+
+406
+00:34:12,590 --> 00:34:16,870
+initial تربيع زي اتنين A X final نقص X initial
+
+407
+00:34:16,870 --> 00:34:23,870
+المعادلة الأخيرة هاي الأربع معادلات والحمد لله
+
+408
+00:34:23,870 --> 00:34:28,970
+الاشتقاق بجيب هشي انا بأنها معلومة رابع تامة
+
+409
+00:34:31,190 --> 00:34:34,030
+ماصدقتوا انت بتقولوا ماصدقنا ننجح من الرابع اننا
+
+410
+00:34:34,030 --> 00:34:38,370
+ننجح على الرابع تمام اه يا بنات تمام اذا في عندي
+
+411
+00:34:38,370 --> 00:34:43,430
+اربع معادلات اهم معادلتين اللي بتمنى تحفظوهم الاول
+
+412
+00:34:43,430 --> 00:34:47,930
+والتاني الاول والتاني وين الاول اللي محيته والتاني
+
+413
+00:34:47,930 --> 00:34:52,930
+هذاالأول Vfinal بيسوي Vinitial زي a2 والتاني
+
+414
+00:34:52,930 --> 00:34:56,490
+Xfinal نقص Xinitial بيسوي Vinitial في T زي نص aT
+
+415
+00:34:56,490 --> 00:34:59,890
+تربيع والتانين التالت والرابع بشتقهم من التانين
+
+416
+00:34:59,890 --> 00:35:06,090
+الأولانين تفرجش معايا أول والتاني هو المهمإذن لما
+
+417
+00:35:06,090 --> 00:35:08,970
+تكون التسارع ثابت في عندى أربع معادلات ممكن
+
+418
+00:35:08,970 --> 00:35:13,830
+نستخدمهم ولا لأ إذا قيمي ثابت أصلا مينفعش أشتقهم
+
+419
+00:35:13,830 --> 00:35:21,290
+مفشله من البداية حلو إذا هذا كل الكلام عملته هي
+
+420
+00:35:21,290 --> 00:35:27,290
+أول واحدة طلعناها بعدين جبنا و عوضناه خليني نلعب
+
+421
+00:35:27,290 --> 00:35:32,350
+شوية بال power point يعني نسليكم شوية تمام تبعنا و
+
+422
+00:35:32,350 --> 00:35:36,960
+عملنا طلعنا التانيةتمام؟ و جالي برضه نفس العملية
+
+423
+00:35:36,960 --> 00:35:43,500
+طلعت التالتة جالي substituting for T عوض من T from
+
+424
+00:35:43,500 --> 00:35:47,420
+the first equation اللي ادتنينياها انت من المعادلة
+
+425
+00:35:47,420 --> 00:35:51,300
+الأولى في المعادلة التانية التانية اللي كانت هي
+
+426
+00:35:51,300 --> 00:35:56,120
+هذه جالي عملتها و اشتغلت اللي اشتغلتوا معايا فيها
+
+427
+00:35:56,120 --> 00:35:59,740
+فطلعت الرابعة تمام يا بنات؟ حلو
+
+428
+00:36:02,580 --> 00:36:06,120
+two samurais عشان .. راح أحطهم تحت بعض بس عشان
+
+429
+00:36:06,120 --> 00:36:16,840
+يرتبلي يوم حلوين هيك أسهللي تمام هيك؟ حلو example
+
+430
+00:36:16,840 --> 00:36:22,400
+a jet جت يعني طيارة حربية تمام اسمعتوا في حاجة اسم
+
+431
+00:36:22,400 --> 00:36:28,890
+حامل الطائرات؟ Shiaسفينة .. سفينة كبيرة بتحمل
+
+432
+00:36:28,890 --> 00:36:32,710
+طيارات والطيارات بتطير منها و بترجعلها و طبعا
+
+433
+00:36:32,710 --> 00:36:35,690
+انتوا بتعرفوا الطيارة لما بدها تنزل على الأرض على
+
+434
+00:36:35,690 --> 00:36:39,450
+السفينة ولا على الأرض العادية بدها مضرش لأنه أول
+
+435
+00:36:39,450 --> 00:36:43,190
+ما تلمس الأرض بتجافلأ بتاخد وجهة عبارة عن المتجاف
+
+436
+00:36:43,190 --> 00:36:46,790
+عشان كده فيه مدرجات طويلة في المطارات عشان كده
+
+437
+00:36:46,790 --> 00:36:51,170
+المطارات غالبا بيحطوها في اماكن اما صحراء او جنب
+
+438
+00:36:51,170 --> 00:36:55,790
+بحار عشان مايكونش فيه عمارات تمام؟ بيقوللي ها دي
+
+439
+00:36:56,550 --> 00:37:02,650
+طائرة حربية Jet Lance بديها تفبط on an aircraft
+
+440
+00:37:02,650 --> 00:37:07,550
+carrier حامل الطائرات carrier من carry بتعرفش
+
+441
+00:37:07,550 --> 00:37:11,550
+معاناة carry بيحمل اذا aircraft carrier حامل
+
+442
+00:37:11,550 --> 00:37:15,090
+الطائرات aircraft برضه طيارة بقى مائة الف نوع
+
+443
+00:37:15,090 --> 00:37:19,170
+طيارة ما أنتم بتعرفوا و planes برضه طائرات هذا هي
+
+444
+00:37:19,170 --> 00:37:25,240
+يلابقول لي أول ما لمست أرض السفينة اللي حاملة
+
+445
+00:37:25,240 --> 00:37:29,080
+الطائرات كانت سرعتها 140 ميل بال hour قال لي أنا
+
+446
+00:37:29,080 --> 00:37:32,480
+ال chapter واحد اللي قلتلك كيف اتحول بدي رايحك منه
+
+447
+00:37:32,480 --> 00:37:36,800
+انا بحولك و خالص 63 متر per second ايه رايحنا،
+
+448
+00:37:36,800 --> 00:37:42,120
+مظبط او لا؟ اذا ان اول ما لمس الأرض كانت سرعة 63
+
+449
+00:37:42,120 --> 00:37:46,780
+متر per second بيقول لي what is its acceleration؟
+
+450
+00:37:46,780 --> 00:37:52,870
+بده ايه؟assume constant عشان أستخدم الأربع حوارين
+
+451
+00:37:52,870 --> 00:37:57,430
+تمام هيك بيقوللي if it stops in two seconds
+
+452
+00:37:57,430 --> 00:38:02,110
+بيقوللي إذا الطيارة وكفت بعد ثانيتين من ساعت ما
+
+453
+00:38:02,110 --> 00:38:07,910
+لمست الأرض وكفت جديش التسارع النهائية بالسرعة
+
+454
+00:38:07,910 --> 00:38:13,090
+التدائية تلاتة وستين والزمن؟ تسارع تسارع بده
+
+455
+00:38:13,090 --> 00:38:15,790
+التسارع ذاكروني في القانون الأول
+
+456
+00:38:21,190 --> 00:38:26,530
+Vfinal بتساوي Vinitial زايد AT Vfinal مُعطَى ولا
+
+457
+00:38:26,530 --> 00:38:30,030
+مش مُعطَى؟ مُعطَى Vfinal مُعطَى ولا مش مُعطَى؟
+
+458
+00:38:30,030 --> 00:38:30,130
+Vfinal مُعطَى ولا مش مُعطَى؟ Vfinal مُعطَى ولا مش
+
+459
+00:38:30,130 --> 00:38:30,130
+مُعطَى؟ Vfinal مُعطَى ولا مش مُعطَى؟ Vfinal مُعطَى
+
+460
+00:38:30,130 --> 00:38:30,130
+ولا مش مُعطَى؟ Vfinal مُعطَى ولا مش مُعطَى؟ Vfinal
+
+461
+00:38:30,130 --> 00:38:30,850
+مُعطَى ولا مش مُعطَى؟ Vfinal مُعطَى ولا مش مُعطَى؟
+
+462
+00:38:30,850 --> 00:38:38,650
+Vfinal مُعطَى ولا مش مُعطَى؟ Vfinal مُعطَى ولا مش
+
+463
+00:38:38,650 --> 00:38:46,800
+مُعطَى؟ Vfinal مُبقول if the jets touches down at
+
+464
+00:38:46,800 --> 00:38:50,080
+a position x initial يعني قاللي ال position أول ما
+
+465
+00:38:50,080 --> 00:38:54,040
+لمست الأرض هي ما رجعتك بدي x final يعني قداش
+
+466
+00:38:54,040 --> 00:38:57,120
+المسافر اللي جتعتها لما وقفت بسيطة مثلا إنت جيبتي
+
+467
+00:38:57,120 --> 00:39:01,180
+الزمان و ال acceleration قاعد في أي معادلة تجيب x
+
+468
+00:39:01,180 --> 00:39:05,080
+المعادلة الأخيرة اللي هو x final نقص x initial
+
+469
+00:39:05,080 --> 00:39:09,580
+بيسوا v initial في t زي نص AT تربيع و إيه جبتها؟
+
+470
+00:39:09,580 --> 00:39:15,400
+خلصنا إذن بيقولليThe initial point is the point at
+
+471
+00:39:15,400 --> 00:39:18,900
+which the jet hits the ground X initial هي السفر
+
+472
+00:39:18,900 --> 00:39:23,060
+At this point, the initial بتسوى تلاتة و ستين متر
+
+473
+00:39:23,060 --> 00:39:26,580
+per second و انتوا قولتولي و the final قولتولي سفر
+
+474
+00:39:26,580 --> 00:39:31,080
+لأنها عبارة عن stop قاللي هذا القانون الحلو
+
+475
+00:39:31,080 --> 00:39:37,060
+بتطلعلي أول مطلوب طلعنا طلعت ناقص تلاتين متر per
+
+476
+00:39:37,060 --> 00:39:41,810
+second تربية slowing downمظبوط ولا لا؟ قطع لأنه في
+
+477
+00:39:41,810 --> 00:39:49,530
+الآخر بدي اجف تمام هلجيت لو الطيارة ماشي هيك اتجاه
+
+478
+00:39:49,530 --> 00:39:54,530
+التصالح؟ براو عليكم عكس لأنها بتتناقص هذه المعلومة
+
+479
+00:39:54,530 --> 00:39:59,790
+اللي عندي حلو بجلب ال DX قولتله هاي القانون ايه
+
+480
+00:39:59,790 --> 00:40:03,970
+هذا ممكن استخدمه؟ لإن انت بديك XYX V initial
+
+481
+00:40:03,970 --> 00:40:08,170
+مديتنيها ولا لا؟ و V final مديتنيها ولا لا؟ بعوض
+
+482
+00:40:09,850 --> 00:40:16,010
+هذا هى طالع الـ 63 ايش بيقولى اه هنا واحد بيقولى
+
+483
+00:40:16,010 --> 00:40:20,090
+طب لو استخدمت القانون التانى اللى هو X final نقص X
+
+484
+00:40:20,090 --> 00:40:24,250
+initial يه سفر V initial في T زائد نص AT تربيع
+
+485
+00:40:24,250 --> 00:40:30,010
+بتطلع جواب مختلف نفس الجوابطريقين بيأدوا إلى نفس
+
+486
+00:40:30,010 --> 00:40:34,010
+روما هدوا القانونين هدى أنا بحب هدى أكتر بس الكتاب
+
+487
+00:40:34,010 --> 00:40:37,830
+مستخدم هداك القانون و أنا دايما بربط الحمار زي ما
+
+488
+00:40:37,830 --> 00:40:42,850
+بده صاحبه فهو هيك بده المثال فخطط في ال slides لكن
+
+489
+00:40:42,850 --> 00:40:46,770
+انا لو بده حوالي بحلب هدى لإنه هدى القانون انا
+
+490
+00:40:46,770 --> 00:40:50,890
+حافظه أكتر لإنه هدى أساسي و هداك فرعية تمام مش
+
+491
+00:40:50,890 --> 00:40:54,630
+مشكلة لكن في الآخر انا ب .. أحكي بإنفع نجيب مثلا
+
+492
+00:40:54,630 --> 00:41:01,300
+من قانون ال DP و الأه اللي هي delta x و delta t
+
+493
+00:41:01,300 --> 00:41:06,920
+شهدك بيعطيك سرعة متوسطة تعرفيها سرعة متوسطة؟ لأ بس
+
+494
+00:41:06,920 --> 00:41:08,980
+هو ماعطيلي السرعة الابتدائية و السرعة اللي هي هي
+
+495
+00:41:08,980 --> 00:41:14,380
+كده لها سحر يعني معناته .. اه بيجيبيها؟ غالبا لكن
+
+496
+00:41:14,380 --> 00:41:18,820
+صح تفكيرك صح تمام بس دايما واحد بيخش على الطريق
+
+497
+00:41:18,820 --> 00:41:25,800
+السهل اه يا بنات صحصحولي بدنا ترجم اول
+
+498
+00:41:30,500 --> 00:41:35,380
+بتعرفوش مانعتها a traveling at a constant speed of
+
+499
+00:41:35,380 --> 00:41:40,460
+40 meter per second السيارة ماشية عدل وبسرعة ثابتة
+
+500
+00:41:40,460 --> 00:41:43,180
+والسيارة عشان تطلع بسرعة ثابتة لازم الطريق يكون
+
+501
+00:41:43,180 --> 00:41:48,140
+فاضي و لا مطبات ولا حاجة تمام هيك؟ في نص الليل
+
+502
+00:41:48,140 --> 00:41:52,580
+السيارة ماشية في شارع عمال مختار وعند مفترج
+
+503
+00:41:52,580 --> 00:41:57,410
+السراية في ..لوحة إعلانات كبيرة بتعرفوها اللي
+
+504
+00:41:57,410 --> 00:42:00,930
+بيعلقوا عليها شغلات كتيرة بيقوللي هناك متخبي شرطي
+
+505
+00:42:00,930 --> 00:42:07,750
+متخبي شرطيالسيارة و هي ماشية بأمان الله بسرعة 45
+
+506
+00:42:07,750 --> 00:42:12,330
+متر per second باسيز يعني مرت عن ال trooper ال
+
+507
+00:42:12,330 --> 00:42:17,010
+trooper معناته شرطي متنقل او جوال او على موتوسيكل
+
+508
+00:42:17,010 --> 00:42:22,150
+هذا بنسميه trooper شرطي ال trooper on a motorcycle
+
+509
+00:42:22,150 --> 00:42:26,810
+على مطير و هو قاعد طافه الموتور و قاعد و متخبي و
+
+510
+00:42:26,810 --> 00:42:30,730
+بده يتصيد للسيارات اللي بتخالفحلوة فهذه مرت بأمان
+
+511
+00:42:30,730 --> 00:42:33,730
+والدنيا ليه؟ وإيش في قاعد رفها إنه في شوفت قاعد
+
+512
+00:42:33,730 --> 00:42:40,440
+متخبي؟ ماشية بسرعة كبيرة 45 متر per secondجاللي
+
+513
+00:42:40,440 --> 00:42:44,620
+hidden behind a billboard هذا الشرطي hidden يعني
+
+514
+00:42:44,620 --> 00:42:49,280
+متخبي خلف billboard يعني لوحة إعلانات اللي قلت
+
+515
+00:42:49,280 --> 00:42:53,580
+عنها توي في الصلاية حلو بقوللي بعد ما اكتشف ان
+
+516
+00:42:53,580 --> 00:42:57,280
+هادي قاعدة ماشية بسرعة كبيرة أكبر من السرعة
+
+517
+00:42:57,280 --> 00:43:02,220
+المسموح تمشي فيها جاللي عبل ما فكر وشغل كانت مرة
+
+518
+00:43:02,220 --> 00:43:05,680
+ثانية ثانية مش كتير لكن الثانية كانت في السيارة
+
+519
+00:43:05,680 --> 00:43:11,010
+جنبه ولا مشيتماشيت ما هي ماشية بيقول لي one second
+
+520
+00:43:11,010 --> 00:43:15,790
+بعد ثانية after the speeding car passes the
+
+521
+00:43:15,790 --> 00:43:19,630
+billboard بعد ثانية ما مرت السيارة عن ال billboard
+
+522
+00:43:19,630 --> 00:43:23,250
+اللي هي اللوحة و هو الشرطي نفسه ما هناك كان واقف
+
+523
+00:43:23,250 --> 00:43:27,250
+قال لي the trooper sits out from the billboard
+
+524
+00:43:27,250 --> 00:43:32,070
+انطلق من ال billboard و راح يلحق السيارة اتفجنا يا
+
+525
+00:43:32,070 --> 00:43:38,610
+بنات؟ بعد ثانية من مرور السيارة تمout of from the
+
+526
+00:43:38,610 --> 00:43:41,550
+billboard to catch the car accelerating كان واقف
+
+527
+00:43:41,550 --> 00:43:45,430
+لتروبر ايه تصارع التروبر ابتدائية لأنه كان واقف
+
+528
+00:43:45,430 --> 00:43:51,650
+تصارع لتروبر أطانيا تلاتة متر per second حلو how
+
+529
+00:43:51,650 --> 00:43:55,830
+long does it take جديش لتروبر أخذ زمن عشان يمسك
+
+530
+00:43:55,830 --> 00:44:00,970
+السيارة يلحقها فاهم السؤال أول بالعربي بعدين
+
+531
+00:44:00,970 --> 00:44:05,750
+بنترجمه علميا الآنواحدة واحدة هالجيث بتطلعولي على
+
+532
+00:44:05,750 --> 00:44:10,750
+ال car كلمة constant speed إيش يعني؟ جدّيش
+
+533
+00:44:10,750 --> 00:44:16,190
+تصالحها؟ proud مظبوط ولا لأ؟ هو بيقوللي ال car
+
+534
+00:44:16,190 --> 00:44:22,370
+كانت تمشي بسرعة ثابتة يعني تصالحه ماله سفر بدي
+
+535
+00:44:22,370 --> 00:44:27,310
+أعمل هيك و أعمل هيك و أقول هذا ال car وهذا ال
+
+536
+00:44:27,310 --> 00:44:34,810
+trooper إيش trooper يعني؟ الشرطيأول حاجة ايه لل
+
+537
+00:44:34,810 --> 00:44:39,710
+car بتساوي سفر؟ من أين عرفت؟ من ال constant speed
+
+538
+00:44:39,710 --> 00:44:46,410
+اذا هو اللي قاللي ايه لل Etrober بتساوي تلاتة متر
+
+539
+00:44:46,410 --> 00:44:49,930
+per second تربيه؟ هيه أطانيها ولا ما أطانيشها؟
+
+540
+00:44:49,930 --> 00:44:56,190
+تمام؟ إيش بدك؟ قاللي بدي الزمن اللي أخده الشرطي
+
+541
+00:44:56,190 --> 00:45:00,570
+إذا أنا بدي أشغل ساعة الإيقاف أول ما اتحرك الشرطي
+
+542
+00:45:01,400 --> 00:45:06,460
+مظبوطك ولا لا؟ لأنه بدي زمان يستخرخ الشرطي حلو هجت
+
+543
+00:45:06,460 --> 00:45:10,800
+هم مروا على بعض عند وين؟ عند السراية و هو ماشي
+
+544
+00:45:10,800 --> 00:45:15,960
+هلجيك بدهم يمسكوا بعض في مجال انهم يمسكوا بعض يكون
+
+545
+00:45:15,960 --> 00:45:21,070
+الشرطي عند السامر و السيارة عند الساحة؟لازم يكونوا
+
+546
+00:45:21,070 --> 00:45:24,310
+في نفس الموضوع ولا لأ؟ إذا انت عشان بتقوللي بيبقوا
+
+547
+00:45:24,310 --> 00:45:28,190
+يمسكوا بعض لازم X final للشرطي تسوي X final
+
+548
+00:45:28,190 --> 00:45:31,990
+للسيارة ولا لأ؟ هاي ترك السؤال طب إيش بقى كنت
+
+549
+00:45:31,990 --> 00:45:35,410
+تسوي؟ قاللي جيب X final للسيارة و X final للتروبر
+
+550
+00:45:35,410 --> 00:45:39,910
+و سويهم بعض صح ولا لأ؟ بتطلع أيه اللي بدك إيه طيب
+
+551
+00:45:39,910 --> 00:45:46,190
+نرجع قاللي V لل car بتسوي 45 متر per second مش انت
+
+552
+00:45:46,190 --> 00:45:53,300
+قلتلي هيهاV initial لـ Retrober بتساوي سفر؟ فح؟
+
+553
+00:45:53,300 --> 00:46:00,580
+هذي معطة؟ تمى؟ بقوله يلّا نشتغل بقوله X initial
+
+554
+00:46:00,580 --> 00:46:04,920
+للسيارة إيش يعني initial أول ما اتحرك الشرطي؟ كانت
+
+555
+00:46:04,920 --> 00:46:09,480
+جنبه؟ كيف بدي أعرف جدي وين كانت؟ بقوله مش أنت دتني
+
+556
+00:46:09,480 --> 00:46:14,540
+صراعتها؟ 45 في جدي إيش؟ في واحد لإن واحد سكنت
+
+557
+00:46:16,660 --> 00:46:21,940
+initial للـ car بتساوي V initial للـ car في T اللي
+
+558
+00:46:21,940 --> 00:46:26,360
+هو واحد second ولا لأ هتتهادي initial للـ car هي
+
+559
+00:46:26,360 --> 00:46:30,920
+نفسها ما هو ما بتتغيرش بتساوي خمسة و أربعين متر
+
+560
+00:46:30,920 --> 00:46:39,200
+هذه X initial للـ car مظبوطك ولا لأ تم اتحرك
+
+561
+00:46:39,200 --> 00:46:44,240
+الشرطي هذه السيارة هناوصلت هنا هذه المسافة 45 متر
+
+562
+00:46:44,240 --> 00:46:52,180
+بدأ يبدأ يجري حلو بقول X final نقص X initial لل
+
+563
+00:46:52,180 --> 00:46:58,160
+car بتسوي V initial لل car في T زي اجمال اصفر A لل
+
+564
+00:46:58,160 --> 00:47:01,680
+car في T تربيع سمعتوا في القانون هذا طيب ال A لل
+
+565
+00:47:01,680 --> 00:47:05,120
+car قد ياش اذا هذه ماكنتش دعوة فيها يا ابني هذه
+
+566
+00:47:05,120 --> 00:47:13,080
+سفر ماهي مش سفرتم اكس final لل car نقص خمسة
+
+567
+00:47:13,080 --> 00:47:19,180
+واربعين مشانية بتساوي خمسة واربعين T ولا لأ؟ وقف
+
+568
+00:47:19,180 --> 00:47:25,760
+هنا خلاص اجيبت هذه تمام؟ حلو نيجي للشرطة حبيبنا
+
+569
+00:47:25,760 --> 00:47:33,090
+بقوله اكس final نقص اكس initial لل Etroberبتساوي V
+
+570
+00:47:33,090 --> 00:47:39,490
+initial للتروبر في T زي نص A للتروبر في T تربيع مش
+
+571
+00:47:39,490 --> 00:47:45,670
+هذا قانون جديش V initial للتروبر براو عليكم وها دي
+
+572
+00:47:45,670 --> 00:47:50,630
+كان لسفر ولا مالسفر اذا X final للتروبر بتساوي نص
+
+573
+00:47:50,630 --> 00:47:59,290
+في تلاتة في T تربيع تلاتة في نصواحد و نص .. تلاتة
+
+574
+00:47:59,290 --> 00:48:02,190
+اتنين .. مظبوط .. واحد و نص .. اجيب مهادي و احط
+
+575
+00:48:02,190 --> 00:48:06,870
+واحد و نص .. قعد واحد يقول ليش اللي عملته .. واحد
+
+576
+00:48:06,870 --> 00:48:09,250
+و نص .. مهو كان .. اذا هسرح .. مهو يقول كانت تلاتة
+
+577
+00:48:09,250 --> 00:48:12,850
+اتنين ايش اللي وديها .. صارت .. تمام .. حلو ..
+
+578
+00:48:12,850 --> 00:48:18,050
+هجيت مسكوا بعض .. اذا قطعا هادي بتسوي هادي .. صح
+
+579
+00:48:18,050 --> 00:48:21,290
+.. اذا مزال بتقولي واكتشف دمي مسكوا بعض .. اذا
+
+580
+00:48:21,290 --> 00:48:25,630
+قطعا مسكوا بعض عند السامر او عند الساحة .. احكي ..
+
+581
+00:48:35,740 --> 00:48:44,860
+خمس واربعين المسافة بيساوي الصلعة في الزمن الصلعة
+
+582
+00:48:44,860 --> 00:48:47,880
+خمس واربعين والزمن واحد اضربي
+
+583
+00:48:55,000 --> 00:49:00,140
+بس طبعا مهما خلوها تسأل انا بدي انا اتسأل طلعي one
+
+584
+00:49:00,140 --> 00:49:05,020
+second اذا ال one second انا اخترعت اختراع؟ تمام
+
+585
+00:49:05,800 --> 00:49:10,940
+حلو براه عليكي تمام يا بنات اتطلعوا يا بنات بقول
+
+586
+00:49:10,940 --> 00:49:16,420
+عشان الشرط يمسك السيارة لازم X للشرط تسوي X
+
+587
+00:49:16,420 --> 00:49:22,160
+للسيارة final اذا معناته لازم بالأصمر خمسة و
+
+588
+00:49:22,160 --> 00:49:27,120
+أربعين او اه بدي اجيب هدي هنا يا بنات خمسة و
+
+589
+00:49:27,120 --> 00:49:31,400
+أربعين زائد خمسة و أربعين T تسوي واحد و نص T تربية
+
+590
+00:49:31,400 --> 00:49:37,740
+سويت هدي بهديمظبوط هيك ولا لأ؟ بدي أرطب المعادلة
+
+591
+00:49:37,740 --> 00:49:42,280
+أرطبها أجيب هدول الاتنين الحلوين هنا صارت واحد و
+
+592
+00:49:42,280 --> 00:49:47,860
+نص T تربيع زائد خمسة و أربعين T زائد خمسة و أربعين
+
+593
+00:49:47,860 --> 00:49:55,180
+بتساوي سفر هذه معادلة من درجة التانية بتديك حل ..
+
+594
+00:49:55,180 --> 00:50:00,960
+أكم حل؟ حل ليه؟ حل .. حلوهذه معادلة رياضية جبرية
+
+595
+00:50:00,960 --> 00:50:04,440
+أخدتها زمان أنا بالنسبة للفيزيا يقص اللي عندنا أخد
+
+596
+00:50:04,440 --> 00:50:09,160
+عشرة من عشرة والباقي بديش إياه لإيش؟ لأن طب و
+
+597
+00:50:09,160 --> 00:50:12,980
+قلتلكم مين مش مخلص رابع و قلتكم و خلصنا رابع و
+
+598
+00:50:12,980 --> 00:50:16,800
+خلصتوا تامين إذا خلاص أنا متأكد بديش تحلولي رابع و
+
+599
+00:50:16,800 --> 00:50:21,440
+تامين هل جيت من هنا لما إجيت حلت يا بنات طلعت T
+
+600
+00:50:21,440 --> 00:50:26,170
+بتساوي واحد و تلاتين secondصدقنا الكتاب احنا بدنا
+
+601
+00:50:26,170 --> 00:50:29,750
+نرجع لرقم 48 صدقين الكتاب طبعا كده بتتأكد انه صح
+
+602
+00:50:29,750 --> 00:50:33,850
+ولا لأ بروح بعود تتحقق المعادل معناته أكيد صادق
+
+603
+00:50:33,850 --> 00:50:39,670
+طيب طلعت الزمن زي ما تبدك لو إيه ساقلني وين مسكه
+
+604
+00:50:39,670 --> 00:50:44,390
+بعض معناته مش بال Deposition ولا لأ طب أعود هل ولا
+
+605
+00:50:44,390 --> 00:50:44,770
+هل
+
+606
+00:50:48,110 --> 00:50:54,010
+ما هما زبايا عوّض هنا و لا عوّض هنا هتطلع عندك نفس
+
+607
+00:50:54,010 --> 00:50:58,930
+الإجابة و لا لأ طلعت حوالي one point اربعة اربعة
+
+608
+00:50:58,930 --> 00:51:02,950
+في عشرة أُس ثلاثة متر يعني حوالي واحد و نص كيلو
+
+609
+00:51:02,950 --> 00:51:06,730
+ألف و أربعمية و أربعين متر يعني حوالي واحد و نص
+
+610
+00:51:06,730 --> 00:51:11,750
+كيلو و احنا قلنا من عند الصراية للسامر يدوب كيلو
+
+611
+00:51:11,750 --> 00:51:16,200
+يدوب لساحة تكون هذه المسافةعشان نضلنا نجدر
+
+612
+00:51:16,200 --> 00:51:20,760
+المسافات مش الواحد يفكر حاله يمشي من الصرايا
+
+613
+00:51:20,760 --> 00:51:24,120
+للساحة يقول أمي والله مشيت اليوم كتير ويقول
+
+614
+00:51:24,120 --> 00:51:28,740
+مامشيشيشي مشيله كيلو نص وكيلو نص لما ييجوا يعملوا
+
+615
+00:51:28,740 --> 00:51:31,620
+برامج الرياضة بيقولك بيجي تمشي لك خمسة ستة كيلو
+
+616
+00:51:31,620 --> 00:51:36,360
+عقل شيء مش تمشي كيلو نص تتحملوا جميلة كل الناس لأ
+
+617
+00:51:36,360 --> 00:51:37,420
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a717289b2112c4c0bded44e28c3496d3c205aec1
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc.srt
@@ -0,0 +1,1031 @@
+1
+00:00:05,090 --> 00:00:09,660
+تمام، نسمي باسم الله ونستكمل دروسنا اليوم هنا
+
+2
+00:00:09,660 --> 00:00:15,960
+وبالتالي بدنا نعيد الـ vector product اللي حاولت
+
+3
+00:00:15,960 --> 00:00:20,640
+أُضطر أني أُخلصه وما آخذش حقه، وبالتالي بدنا نعيد الـ
+
+4
+00:00:20,640 --> 00:00:24,180
+vector product of two vectors. قلنا في عندي ثلاثة
+
+5
+00:00:24,180 --> 00:00:28,660
+أنواع من الضرب: ضرب scalar في vector، واتفقنا أنه
+
+6
+00:00:28,660 --> 00:00:32,000
+بيطلع vector، إما مع نفس الاتجاه إذا كان الـ scalar
+
+7
+00:00:32,000 --> 00:00:35,520
+positive، أو عكس الاتجاه إذا كان الـ scalar negative.
+
+8
+00:00:36,110 --> 00:00:41,150
+بعدين، في عندنا dot product، أو إيه، له اسم ثاني،
+
+9
+00:00:41,150 --> 00:00:48,310
+scalar product، إن لو كان في عندي a dot الـ b، هذا
+
+10
+00:00:48,310 --> 00:00:53,250
+بيساوي magnitude الـ a في magnitude الـ b في cosine
+
+11
+00:00:53,250 --> 00:00:57,550
+الزاوية اللي بينهم، صح ولا لأ؟ وهذه القاعدة خلتني
+
+12
+00:00:57,550 --> 00:01:02,350
+أقول إن هذا بيطلع ax bx
+
+13
+00:01:03,740 --> 00:01:11,660
+زائد Ay By زائد Az Bz، واتفقنا إن لا هنا في I ولا هنا
+
+14
+00:01:11,660 --> 00:01:16,700
+في J ولا هنا في K، لأن الناتج scalar، اتفقنا هيك.
+
+15
+00:01:16,700 --> 00:01:21,500
+تمام. جا لي، إيش النوع الثالث؟ قولت بيكون vector في
+
+16
+00:01:21,500 --> 00:01:27,040
+vector، لكن الناتج أيضاً vector. إذن معناته the
+
+17
+00:01:27,040 --> 00:01:31,620
+vector product. إذن اسمه vector product عشان الناتج
+
+18
+00:01:31,620 --> 00:01:37,670
+vector، is between two vectors A and B، وتُكتب على
+
+19
+00:01:37,670 --> 00:01:44,070
+إنها A cross الـ B is a third vector اللي دُلّيت عليه
+
+20
+00:01:44,070 --> 00:01:48,830
+الرمز C. هذا الـ vector الثالث. ماذا للـ vector من
+
+21
+00:01:48,830 --> 00:01:52,330
+magnitude و direction، صح ولا لأ؟ قلنا الـ magnitude
+
+22
+00:01:52,330 --> 00:01:59,250
+تبعه، magnitude الـ A cross الـ B بتساوي magnitude الـ A في
+
+23
+00:01:59,250 --> 00:02:03,890
+magnitude الـ B في sin الزاوية اللي بينهم. طب والـ
+
+24
+00:02:03,890 --> 00:02:07,850
+direction؟ قال لي: الـ direction الناتج بدّه يكون
+
+25
+00:02:07,850 --> 00:02:13,110
+عمودي على الاثنين، عمودي على الاثنين، بمعنى آخر عمودي
+
+26
+00:02:13,110 --> 00:02:18,550
+على مستواهما، لأن عندي نظرية بتقول: العمودي على مستوى
+
+27
+00:02:18,550 --> 00:02:24,350
+عمودي على كل الخطوط جوا المستوى، صح ولا لأ؟ تمام. إذن الـ
+
+28
+00:02:24,350 --> 00:02:32,890
+vector C هو عمودي على مستوى
+
+29
+00:02:32,890 --> 00:02:36,130
+A و B. لأن هناك درجتان لـ M
+
+30
+00:02:44,460 --> 00:02:49,780
+هذا الأولاني في العلوي والثاني في اللوح، صح ولا لأ؟
+
+31
+00:02:49,780 --> 00:02:53,840
+إذاً، الثالث اللي بدّه ييجي ناتج من الـ cross product
+
+32
+00:02:53,840 --> 00:02:57,640
+بدّه يكون مستوى عمودي عليهما. إيش يعني؟ بدّه يكون
+
+33
+00:02:57,640 --> 00:03:03,340
+عمودي على اللوح، لا out ولا into، صح؟
+
+34
+00:03:03,340 --> 00:03:07,840
+لا out ولا into اللي أنتم بتقولوها، dot و cross. تمام.
+
+35
+00:03:07,840 --> 00:03:11,540
+قال: مين بدّه يحدد؟ قال: إيدك اليمنى هي اللي هتحدد.
+
+36
+00:03:12,140 --> 00:03:16,560
+إيدك اليمنى، كيف؟ قال لي: أنت إيش بدك؟ قلت له: بدي A
+
+37
+00:03:16,560 --> 00:03:22,120
+cross الـ B. قال لي: في هذه الحالة، حط أصابعك الأربعة
+
+38
+00:03:22,120 --> 00:03:28,180
+مع A ولف باتجاه B، وشوف إبهامك، وإن بده يدلّك، قال لي: Out.
+
+39
+00:03:28,180 --> 00:03:37,940
+إذاً هذا K out، z direction. لكن لو بدك B cross الـ A،
+
+40
+00:03:37,940 --> 00:03:43,120
+بقول: أصابع الأربعة مع B، لفّ وين ما بده يروح، إذا دلّ
+
+41
+00:03:43,120 --> 00:03:47,240
+للدّاخل. إذن A cross الـ B لا تساوي B cross الـ A،
+
+42
+00:03:47,240 --> 00:03:52,270
+بتساوي العكس تبعها. مظبوط ولا لأ؟ حلو.  هذه النقاط اللي
+
+43
+00:03:52,270 --> 00:03:58,070
+بتخليني أقول التالي: I و J و K، سمعنا فيهم؟ و
+
+44
+00:03:58,070 --> 00:04:02,470
+مرتبطين جوا مخنا، إن الـ I مع السين، والـ J مع الصاد،
+
+45
+00:04:02,470 --> 00:04:06,830
+والـ K مع العين. مظبوط ولا لأ؟ جا لي: إذا لو قلت لك
+
+46
+00:04:06,830 --> 00:04:13,550
+I cross الـ J، تصوّرهم واعمل قاعدة يدك اليمنى. أنتم
+
+47
+00:04:13,550 --> 00:04:22,180
+شايفين؟ هي x، هي I، وهي J، مش هيك؟ إذاً هتطلع K، هتطلع
+
+48
+00:04:22,180 --> 00:04:24,880
+K، صحيح. إذن هذه هتطلع K.
+
+49
+00:04:27,910 --> 00:04:34,370
+جا لي: طيب لو قلت لك J X K؟ لأنّ هذه بالكم هي K
+
+50
+00:04:34,370 --> 00:04:41,770
+out، صح؟ لو إجيت أنت بدّك تعمل J X K بقاعدة اليد
+
+51
+00:04:41,770 --> 00:04:47,910
+اليمنى، هتطلع I موجبة. مظبوط ولا لأ؟ هتطلع I موجبة.
+
+52
+00:04:47,910 --> 00:04:57,730
+إذن J X K هتطلع I. طيب شوف لي K cross الـ I. جا لي:
+
+53
+00:04:57,730 --> 00:05:04,270
+هتطلع معك J. إذن K cross الـ I هتطلع J. اعكس أي
+
+54
+00:05:04,270 --> 00:05:09,790
+اثنين، بصير سالب. مظبوط ولا لأ؟ تمام. أنا طبعاً بدي أحفظهم
+
+55
+00:05:09,790 --> 00:05:15,210
+هدول. جا لي: بسهّل عليك حفظهم، كيف أسهّل عليك حفظهم؟ جا لي:
+
+56
+00:05:15,210 --> 00:05:22,370
+حط لي هذول الثلاثة I J K على رأس مثلّث. هذه طريقة عشان
+
+57
+00:05:22,370 --> 00:05:28,950
+تسهيل الحفظ. تمام، أو تسهيل التعامل معهم. جا لي: إذا
+
+58
+00:05:28,950 --> 00:05:33,750
+ضربت اثنين، هتطلع الثالثة، قطعيّاً، صح ولا لأ؟ لأنّ
+
+59
+00:05:33,750 --> 00:05:37,530
+النتيجة بتكون عمودية على الاثنين. إيش العمودي على
+
+60
+00:05:37,530 --> 00:05:41,970
+السين والصاد؟ عين. إيش العمودي على الصاد والعين؟ سين.
+
+61
+00:05:41,970 --> 00:05:46,710
+مظبوط ولا لأ؟ إذاً، حفظناهم، عرفناهم. جا لي: إذا لما تضرب
+
+62
+00:05:46,710 --> 00:05:50,530
+اثنين، بتطلع الثالثة، بضلّ عليك، موجب ولا سالب؟ جا لي:
+
+63
+00:05:50,530 --> 00:05:55,740
+بدّي أفهمك هالقاعدة، هي قاعدة عادية. إذا أنتَ بتضرب
+
+64
+00:05:55,740 --> 00:06:01,880
+I X J، مع عقارب الساعة، بتطلع الثالثة موجبة. I X J = K. طب
+
+65
+00:06:01,880 --> 00:06:08,000
+J X I، ثالثها K. J X K، مش هيك؟ مع عقارب الساعة
+
+66
+00:06:08,000 --> 00:06:15,100
+بتطلع الثالثة موجبة. K X I، طلعت الثالثة تمام، والـ
+
+67
+00:06:15,100 --> 00:06:21,080
+المعكوس، بتحطّ سالب. سهلة، هالشيء. قال لي: خمنتوني على أنه
+
+68
+00:06:21,080 --> 00:06:25,060
+احنا بنعرف إن مع عقارب الساعة موجب، هذيك تجربة لهيدي.
+
+69
+00:06:25,060 --> 00:06:29,380
+هيدي مجرّد قاعدة عشان نعرف كيف نطبّق قاعدة اليد
+
+70
+00:06:29,380 --> 00:06:38,760
+اليمنى، تمام؟ إيه الرمز؟ تمام. إذن the rule، هذه
+
+71
+00:06:38,760 --> 00:06:41,820
+قاعدة اليد اليمنى، اللي شرحناها: إنك تحطّ أصابعك
+
+72
+00:06:41,820 --> 00:06:46,100
+الأربعة مع الأول، لفّ بالاتجاه الثاني، إبهامك بده يدلّك
+
+73
+00:06:46,100 --> 00:06:49,340
+الثالث. إذن the rule states that... states that يا
+
+74
+00:06:49,340 --> 00:06:53,920
+نصّ على ما... ما هي هذه states that، تمام؟ the rule
+
+75
+00:06:53,920 --> 00:06:58,760
+وهذه الـ S عشان هذه الـ rule single، تعرفوها، أخذتوها
+
+76
+00:06:58,760 --> 00:07:03,400
+في الـ grammar، تمام. It states that the four fingers
+
+77
+00:07:03,400 --> 00:07:07,700
+of your right... of the right hand are pointed
+
+78
+00:07:07,700 --> 00:07:12,880
+يُشير، are pointed along A، مظبوط ولا لأ؟ إذن
+
+79
+00:07:12,880 --> 00:07:17,340
+بوجه أصابعك الأربعة نحو A، and then curved، يعني
+
+80
+00:07:17,340 --> 00:07:22,880
+لَفّها، curved toward B، باتجاه B.
+
+81
+00:07:22,880 --> 00:07:26,080
+through the smaller angle، باتجاه B، الزاوية
+
+82
+00:07:26,080 --> 00:07:31,180
+الأصغر. The thumb then gives the
+
+83
+00:07:31,180 --> 00:07:34,400
+direction of C. حقّ قاعدّة اليد اليمنى. لما أنا سألتهم أنا
+
+84
+00:07:34,400 --> 00:07:40,760
+وياكم. تمام. بس بنترجم للعربي. Using this rule, it is
+
+85
+00:07:40,760 --> 00:07:46,210
+clear that A X B بتساوي سالب B X A، صح ولا لأ؟
+
+86
+00:07:46,210 --> 00:07:51,410
+وعملناها وأثبتناها. هذا الكلام صحيح. طيب، جا لي: حلو.
+
+87
+00:07:51,410 --> 00:07:59,230
+جا لي: By the same rule, one can verify، يتأكّد أو يُثبت،
+
+88
+00:07:59,230 --> 00:08:07,790
+I X I بتساوي J X J بتساوي K X K بتساوي 0. ليه 0؟ لأنّ
+
+89
+00:08:07,790 --> 00:08:11,830
+magnitude صفر، صفر. لأنّ الـ cross بيقول: magnitude
+
+90
+00:08:11,830 --> 00:08:15,670
+الأول في magnitude الثاني في sin الزاوية اللي
+
+91
+00:08:15,670 --> 00:08:19,370
+بينهم. والـ vectors نفسهم. إذن الزاوية دي إيش؟
+
+92
+00:08:19,370 --> 00:08:26,070
+Zero. إذن خلصنا. قال لي: قاعدة اليد اليمنى، أو القاعدة
+
+93
+00:08:26,070 --> 00:08:34,020
+هذه بتقول التالي: هذه هي I cross الـ J، أعطت K. J
+
+94
+00:08:34,020 --> 00:08:44,720
+cross الـ K أعطت I. K cross الـ I أعطت J. صح، تمام. مش
+
+95
+00:08:44,720 --> 00:08:52,160
+عاجبك شيء؟ عندك سؤال؟ أنا أنا أنا أنا أنا أنا أنا
+
+96
+00:08:52,160 --> 00:08:53,260
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+97
+00:08:53,260 --> 00:08:53,340
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+98
+00:08:53,340 --> 00:08:53,920
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+99
+00:08:53,920 --> 00:08:58,940
+أنا أنا أنا أنا أنا أنا أنا
+
+100
+00:08:58,940 --> 00:09:01,640
+أنا. يعني هل له علاقة بالتعامد ولا ما له علاقة
+
+101
+00:09:01,640 --> 00:09:05,880
+بالتعامد؟ له علاقة بالتعامد، لأنه لما تضرب اثنين
+
+102
+00:09:05,880 --> 00:09:09,340
+من الـ vectors، بدّه يطلع الثالث متعامد على الاثنين.
+
+103
+00:09:09,340 --> 00:09:16,770
+لازم. وبما إنّ الـ Z عمودي على الـ X والـ Y، بصحّ له ياخذ أيّة
+
+104
+00:09:16,770 --> 00:09:19,790
+بس قاعدة اليد اليمنى ليه إيش جاية؟ قاعدة اليد
+
+105
+00:09:19,790 --> 00:09:23,350
+اليمنى بتقول لك: أنت بتقول لي عمودي، طب عمودي لفوق ولا
+
+106
+00:09:23,350 --> 00:09:27,450
+لتحت؟ يعني هي عمودية على الطاولة، هتكون عمودية على
+
+107
+00:09:27,450 --> 00:09:30,850
+الطاولة ولا لأ؟ طب لو كان لتحت، برضه عمودي على
+
+108
+00:09:30,850 --> 00:09:34,490
+الطاولة. إذن أنا بدّي أحدّد واحد منهم. جا لي: اليد اليمنى
+
+109
+00:09:34,490 --> 00:09:40,950
+اتفقنا هي اللي بتحدّد. فهمتوا عليّ كيف؟ بس، تمام. جا لي: حلو.
+
+110
+00:09:40,950 --> 00:09:45,290
+إذاً أنتم فهمتوا، يلا يا بنات، بدنا نضرب احنا وياكم
+
+111
+00:09:45,290 --> 00:09:51,470
+cross product الـ A، مكتوبة هيك: ثلاثة مركّبات، والـ B
+
+112
+00:09:51,470 --> 00:09:55,270
+ثلاثة مركّبات. هي الصيغة العامة، تحت أيّ vector تضربي
+
+113
+00:09:55,270 --> 00:09:59,830
+vector. جوا في جوا، في حد ما يعرفش يضرب جوا في جوا؟ مش
+
+114
+00:09:59,830 --> 00:10:04,030
+بنجيب هذا وبنضرب في هدول كلهم، وبنجيب هذا وبنضرب
+
+115
+00:10:04,030 --> 00:10:07,610
+في كل هدول، وهكذا. جا لي: اشتغل. قولت له: هاي، اشتغلت.
+
+116
+00:10:10,130 --> 00:10:13,270
+طلعوا عليهم ضرب جبري عادي اللي اخذته في المدرسة.
+
+117
+00:10:13,270 --> 00:10:21,370
+تمام. استنوا شوية. جا لي: وين في I X I، أو J X J، أو K
+
+118
+00:10:21,370 --> 00:10:28,410
+X K، إيش بتحط محله؟ قال لي: ها، مظبوط هيك ولا لأ؟
+
+119
+00:10:28,410 --> 00:10:32,770
+هدول زيرو، راحوا. قال لي: إيش هتضلّ؟ قال لي: أول term
+
+120
+00:10:32,770 --> 00:10:41,540
+هنا I X J. تعال، I X J إيش بيطلع؟ K. مش واحد، لأنه هذا
+
+121
+00:10:41,540 --> 00:10:46,720
+cross product، بده يطلع vector، مش رقم، بده يطلع
+
+122
+00:10:46,720 --> 00:10:51,280
+vector. إذن هذا، بقى، بتحطّ لي محله... أنا أنا أنا أنا
+
+123
+00:10:51,280 --> 00:10:51,660
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+124
+00:10:54,800 --> 00:11:02,160
+طيب، I cross الـ K = سالب J. ها، I cross الـ K مشيت ضدّ
+
+125
+00:11:02,160 --> 00:11:08,200
+عقارب الساعة، إذن سالب J، حطّينا سالب J. تمام يا بنات؟
+
+126
+00:11:08,200 --> 00:11:18,340
+تمام. نجي لهنا، J cross الـ I = سالب K. هناك، مهمّش إنّه J
+
+127
+00:11:18,340 --> 00:11:22,880
+سالب K، طلعوا هذا سالب K، وهذا K، ممكن آخذ الـ K
+
+128
+00:11:22,880 --> 00:11:25,360
+عامل مشترك ولا لأ؟ أنا دي بدّي آخذ الـ K عامل
+
+129
+00:11:25,360 --> 00:11:31,020
+مشترك. حلو. ده اللي، ها، دي J cross الـ K، J cross
+
+130
+00:11:31,020 --> 00:11:37,160
+الـ I موجب. إذن I بالموجب. حلو. نجي لهذا، ده اللي K
+
+131
+00:11:37,160 --> 00:11:41,900
+cross الـ I = J. هي صار عندي J وهنا سالب J. J مع
+
+132
+00:11:41,900 --> 00:11:45,810
+J بأخذ عامل مشترك. تمام. قال لي: دلوقت عندك أخير يا
+
+133
+00:11:45,810 --> 00:11:50,450
+قلت له: هذا سالب I. طيب، نجمع: حطّ الـ I مع الـ I لحال، والـ J مع
+
+134
+00:11:50,450 --> 00:11:55,910
+الـ J لحال، والـ K مع الـ K لحال. جمعنا، طلعت هذا الرقم.
+
+135
+00:11:55,910 --> 00:12:03,260
+ده مطوّل، طويل، صح؟ إحنا هذا حلو وقدرنا عليه، نحفظه.
+
+136
+00:12:03,260 --> 00:12:05,820
+وقلنا: السيني مع السيني، الصادي مع الصادي، والعيني
+
+137
+00:12:05,820 --> 00:12:09,280
+مع العيني. سهل نتعامل معه، وده إيش اللي خلّاني
+
+138
+00:12:09,280 --> 00:12:13,980
+أحفظه؟ قعدت أنا بدّي أعمل له logarithm عشان أعرف
+
+139
+00:12:13,980 --> 00:12:17,220
+أحفظه؟ ولا أعمل له برنامج حاسوب عشان أحفظه؟ صعب
+
+140
+00:12:17,220 --> 00:12:21,960
+الأمور، وهُمّ بيطلعوا هيك. قالوا: إيه؟ هدف، مش بحاجة
+
+141
+00:12:21,960 --> 00:12:27,660
+أخذناها في المدرسة، الشيء اللي قالته لي. لو كتبت لك هيك
+
+142
+00:12:31,800 --> 00:12:37,840
+محدد. قالوا: والله آه، يلا نجرّب. برافو عليكم أنتم
+
+143
+00:12:37,840 --> 00:12:41,940
+طمّنتوني كلّكم، قلتوا: إيه؟ أخذناها، واللي فهمت، أخذناها
+
+144
+00:12:41,940 --> 00:12:46,900
+في توجيهي، يعني طازة، لسه، إيه، معناها ما رح ننسىها.
+
+145
+00:12:46,900 --> 00:12:53,140
+كيف كنا نعمل يا بنات؟ معناه، مع الأسف، هذه طويلة شاشة
+
+146
+00:12:53,140 --> 00:12:56,820
+ومش قادرين نكتب في الشاشة، فبناخذ ورقة ونكتب هنا.
+
+147
+00:12:56,820 --> 00:13:06,200
+نقول هاي إيش؟ عشان نذكّر بعض. أوّل صفّ، بحطّ I J K، اللي
+
+148
+00:13:06,200 --> 00:13:13,940
+بتعرفوه. ثاني صفّ، مركّبات الـ A: مركّبة تحت I، سينيّة، وتحت
+
+149
+00:13:13,940 --> 00:13:21,700
+J، صادِيّة، وهذه Z، عينيّة. نيجي لثاني B، بقول: Bx By Bz، مش هيك؟
+
+150
+00:13:21,700 --> 00:13:27,460
+مظبوط؟ وكنا بنقول: plus negative plus... بنذكّر بعض.
+
+151
+00:13:27,460 --> 00:13:34,140
+جا لي: بالساوي: جوا I زائد جوا J ناقص أو ناقص
+
+152
+00:13:34,140 --> 00:13:39,800
+ملاحظة، ناقص مهمّش برضه، J زائد جوا K. مش هيك؟ إحنا بنعمل
+
+153
+00:13:39,800 --> 00:13:49,170
+عشان أجيب هذه، إيش بسوي؟ بِسكر صفّ عمود. يلاّ نِسكر، سكرنا
+
+154
+00:13:49,170 --> 00:13:58,510
+هذه وسكرنا هذه، Ay Bz ناقص Az By.  اطلعولي الـ I اللي
+
+155
+00:13:58,510 --> 00:14:04,290
+جبتها أنا نفسها ولا لأ؟ والله نفسها. نيجي للـ J.
+
+156
+00:14:04,290 --> 00:14:10,530
+بسكر هذه وبسكر هذه، Ax Bz
+
+157
+00:14:15,190 --> 00:14:19,430
+AxBz - AzBx. شوفوا إيش اللي فرّجت، أنا حاطط هنا زائد و
+
+158
+00:14:19,430 --> 00:14:28,090
+جايبة نفسها. صح ولا لأ؟ زائد، بِسكر هذه وبِسكر هذه، AxBy
+
+159
+00:14:28,090 --> 00:14:37,870
+AxBy - AyBx. هو هذه سهلة، بتتحفظ. هذه، احفظ هذه و
+
+160
+00:14:37,870 --> 00:14:39,950
+خلصنا. مظبوطة.
+
+161
+00:14:46,010 --> 00:14:53,730
+حلو. نشوف في شيء مش مفهوم. تمام. الـ cross product، اسمه
+
+162
+00:14:53,730 --> 00:14:57,070
+vector product،
+
+223
+00:20:25,780 --> 00:20:30,480
+مستطيل ولا متوازي أضلاع ولا  شبه منحرف
+
+224
+00:20:30,480 --> 00:20:35,920
+القاعدة في الارتفاع بس قاعدة في الارتفاع كل
+
+225
+00:20:35,920 --> 00:20:40,550
+الأشكال المربعة قاعدة في الارتفاع  مثلث  مش
+
+226
+00:20:40,550 --> 00:20:45,070
+رباعي نص رباعي عشان تيجي يجي من النص المثلث نص
+
+227
+00:20:45,070 --> 00:20:48,310
+قاعدة في الارتفاع لكن متوازي الأضلاع قاعدة في
+
+228
+00:20:48,310 --> 00:20:52,090
+الارتفاع المستطيل قاعدة في الارتفاع المربع قاعدة
+
+229
+00:20:52,090 --> 00:20:56,510
+في الارتفاع شبه المنحرف قاعدة في الارتفاع وتيجي
+
+230
+00:20:56,510 --> 00:20:59,270
+الارتفاع طول في عرض ما هو العرض في المستطيل هو
+
+231
+00:20:59,270 --> 00:21:04,950
+الارتفاع، هو الارتفاع المربع  أضلاعه متساوية  ما
+
+232
+00:21:04,950 --> 00:21:08,210
+هو ليش أضلاعه متساوية لأن ضلع هو القاعدة ضلع
+
+233
+00:21:08,210 --> 00:21:12,350
+ارتفاع، مصطلح اللي إذا ما فيش عندي قانون للمساحة
+
+234
+00:21:12,350 --> 00:21:17,930
+للأشكال الرباعية لواحد قاعدة في ارتفاع بس طب وين
+
+235
+00:21:17,930 --> 00:21:21,630
+الارتفاع بيه ارتفاع كيف كنتوا تجيبوا الارتفاع أيه
+
+236
+00:21:21,630 --> 00:21:28,250
+براو علينا هذا ارتفاع صح مش هيك كنا نعمله جيلي حلو
+
+237
+00:21:28,250 --> 00:21:30,030
+جيلي هب هذه زاوية
+
+238
+00:21:33,480 --> 00:21:37,120
+تمام؟  الزاوية اللي أنتم شايفينها بتساوي مقابل
+
+239
+00:21:37,120 --> 00:21:42,980
+على وتر، حلو مقابل على وتر، ماشي تعرفها بقوله جا
+
+240
+00:21:42,980 --> 00:21:51,380
+الثيتا بتساوي H على B كـ magnitude إذا H بتساوي B
+
+241
+00:21:51,380 --> 00:21:58,000
+في جا الثيتا، هنجي نرجع لل area، area قاعدة في
+
+242
+00:21:58,000 --> 00:22:04,930
+ارتفاع، صح؟ القاعدة إيش؟ A إذا الـ magnitude الـ E في
+
+243
+00:22:04,930 --> 00:22:11,370
+H هي H في B sin θ، بنسميه هذا A × B
+
+244
+00:22:11,370 --> 00:22:15,770
+صح؟
+
+245
+00:22:15,770 --> 00:22:19,950
+طب هذا A × B النتيجة إيش لازم يكون؟ is a
+
+246
+00:22:19,950 --> 00:22:25,390
+area vector، الـ Area vector اتجاهها؟ قال عمودي
+
+247
+00:22:25,390 --> 00:22:30,370
+على السطح لأن A وB بتشكل الـ plane يعني هي الطاولة
+
+248
+00:22:30,370 --> 00:22:37,090
+هي A و هي B مساحتها vector اتجاهها؟ بقول عمودي
+
+249
+00:22:37,090 --> 00:22:40,470
+على الطاولة لازم تكون عمودي على الطاولة عشان تكون
+
+250
+00:22:40,470 --> 00:22:44,530
+عمودي على مستوى الـ two vectors تمام؟ هذا أظن أحد
+
+251
+00:22:44,530 --> 00:22:49,490
+أساليب الكتاب أنك تثبت أن الـ Area بتساوي A × الـ
+
+252
+00:22:49,490 --> 00:22:57,890
+B، هنا أثبتنا تمام؟ أيه الصفر؟ عيد و إيش عيد فيه؟
+
+253
+00:22:57,890 --> 00:23:03,650
+ما هو مش أنت هتجد عيد عيد مفهوم مساحة متوازي أضلاع
+
+254
+00:23:03,650 --> 00:23:08,510
+بالقاعدة في الارتفاع، بتحرفها؟ أه؟ واو
+
+255
+00:23:08,510 --> 00:23:12,610
+تخجليش، بتعرف أن مساحة متوازي الأضلاع  قاعدة في
+
+256
+00:23:12,610 --> 00:23:17,290
+ارتفاع؟ حلو هذا متوازي الأضلاع ولا لا يا بنتي؟ هذا
+
+257
+00:23:17,290 --> 00:23:21,070
+ارتفاع ولا مش ارتفاع؟ بقدر أجيب بدلالة هذه على
+
+258
+00:23:21,070 --> 00:23:24,630
+اعتبار أن جا الزاوية بتساوي H على B ولا لا؟ إذا
+
+259
+00:23:24,630 --> 00:23:29,230
+قلت H اللي أنت بتدور عليه الارتفاع بتساوي B في جا
+
+260
+00:23:29,230 --> 00:23:33,950
+الزاوية ضرب تبادلي، قلت يلا تروح لصف سادس ولا
+
+261
+00:23:33,950 --> 00:23:39,670
+خامس أن مساحة متوازي الأضلاع بتساوي قاعدة A في
+
+262
+00:23:39,670 --> 00:23:45,710
+الارتفاع H، وH هنا عوضت عنه قلت له أول ما قلت لي A في
+
+263
+00:23:45,710 --> 00:23:49,170
+B في جا الزاوية θ، ولسه عرفتها ده cross
+
+264
+00:23:49,170 --> 00:23:53,850
+product، cross product يعني إنه vector product إذا
+
+265
+00:23:53,850 --> 00:23:58,850
+الناتج قطعًا vector إذا الـ area is a vector اتجاه
+
+266
+00:23:58,850 --> 00:24:03,450
+عمودي على الاتنين إذا عمودي على المساحة عمودي على
+
+267
+00:24:03,450 --> 00:24:06,670
+السطح تمام يا بنتي؟ غيرها
+
+268
+00:24:09,970 --> 00:24:15,970
+هذا خلصنا منه، شوفوا
+
+269
+00:24:15,970 --> 00:24:22,850
+هالشغلات، طلعوا هدول أربع علاقات بيقول لي مين منهم
+
+270
+00:24:22,850 --> 00:24:28,470
+دائمًا صفر، بدا نبدأ بالأخيرة يا بنات الأخيرة
+
+271
+00:24:28,470 --> 00:24:34,110
+طلعوا لي اللي بين الجثتين إيش بينهم، dot إيش بيطلع
+
+272
+00:24:34,110 --> 00:24:39,100
+هل الـ cross مسموح يكون بين scalar و vector؟ إذا
+
+273
+00:24:39,100 --> 00:24:41,220
+مايقول لي هذا اللي كاتب ومايعرفش إيش معناه vectors
+
+274
+00:24:41,220 --> 00:24:46,520
+إذا هذه فالت منها هذه ولا كأنها خيار عندي لأنه
+
+275
+00:24:46,520 --> 00:24:53,060
+كتابة غلط أصلًا، إذا الخيار الآخر مرفوض لأن أنت عامل
+
+276
+00:24:53,060 --> 00:24:57,960
+حاجة مبدئية خطأ هتطلق cross product بين scalar و
+
+277
+00:24:57,960 --> 00:25:00,960
+vector وهذا ممنوع لأن قلت لي الـ vector و product
+
+278
+00:25:00,960 --> 00:25:04,220
+between two vectors زي الـ scalar product between
+
+279
+00:25:04,220 --> 00:25:09,090
+two vectors، تمى قال طيب نشوف هذه، قال لي أنت إيش
+
+280
+00:25:09,090 --> 00:25:12,610
+بتقولي هذا العمود عمودي على الـA ولا مش عمودي على
+
+281
+00:25:12,610 --> 00:25:18,390
+الـA؟ عمودي على الـA يعني هذا الأصل A يكون .. بدي
+
+282
+00:25:18,390 --> 00:25:22,830
+أفترض العمود C يا بنات، افترضوا الـC تمى .. هذه
+
+283
+00:25:22,830 --> 00:25:27,170
+المفروض يكون magnitude الـC في magnitude الـA في
+
+284
+00:25:27,170 --> 00:25:33,920
+sin 90 صح؟ وهذه واحد، إذًا magnitude of C في
+
+285
+00:25:33,920 --> 00:25:37,360
+magnitude of A، طب أنت بتقولي magnitude of C صفر
+
+286
+00:25:37,360 --> 00:25:41,420
+وديتني معلومة أو magnitude of A صفر، إذًا هذه مش
+
+287
+00:25:41,420 --> 00:25:48,780
+بالضرورة تكون صفر ولا صفر، لأ، نشوف C .. C جالي
+
+288
+00:25:48,780 --> 00:25:53,940
+برضه C عمودي على الـ B لأنه عمودي على الاتنين، إذًا
+
+289
+00:25:53,940 --> 00:26:01,120
+هذه C في B في sin 90 اللي هي 1، إذًا برضه صفر
+
+290
+00:26:01,120 --> 00:26:10,720
+دائمًا؟ لأ، قال لي نشوف بي، قال لي C في B في cos
+
+291
+00:26:10,720 --> 00:26:16,980
+التسعين مش جا الآن، ليش cos؟ قلت له إنه في dot
+
+292
+00:26:16,980 --> 00:26:20,440
+product و الـ dot بتعطي cos ولا مش cos؟
+
+293
+00:26:20,440 --> 00:26:24,140
+cos، قال لي قداش cos التسعين in C الـ
+
+294
+00:26:24,140 --> 00:26:28,140
+calculator موجودة، cos التسعين بتطلع صفر، إذًا هذه
+
+295
+00:26:28,140 --> 00:26:33,060
+دائمًا صفر بغض النظر قداش هدول صح ولا لأ إن شاء الله
+
+296
+00:26:33,060 --> 00:26:37,680
+هدول يكونوا مليون هنا فيه صفر، إذًا الشيء اللي دائمًا
+
+297
+00:26:37,680 --> 00:26:45,580
+صفر هذه أول
+
+298
+00:26:45,580 --> 00:26:50,480
+واحدة، افترض أن هي sin 90 مش أي زاوية ثانية، آه ليش
+
+299
+00:26:50,480 --> 00:26:58,210
+صح، صح معايا، وصلت، حلو، ليش تخيلني شوية، اللي ناتج
+
+300
+00:26:58,210 --> 00:27:00,950
+اللي سميته الـC مش لازم يكون عمودي على الـA و عمودي
+
+301
+00:27:00,950 --> 00:27:04,510
+على الـB؟ آه لازم، لازم حلو، إذا عمودي على الـA و
+
+302
+00:27:04,510 --> 00:27:06,630
+أنا مش عمودي على الـA عشان كده خدت التسعين عشان
+
+303
+00:27:06,630 --> 00:27:11,330
+كده خدت التسعين، طب و الـB؟ برضه عمودي على الـB إذا
+
+304
+00:27:11,330 --> 00:27:16,030
+برضه اللي تحته زيه عرفتي ليش؟ غيرها، احكي، لأ vector
+
+305
+00:27:16,030 --> 00:27:21,210
+لا dot ولا
+
+306
+00:27:21,210 --> 00:27:27,590
+cross، طلع vector يعني A × B vector، dot vector
+
+307
+00:27:27,590 --> 00:27:33,730
+أنت بتقول عن B مش A × B vector اللي سميته C
+
+308
+00:27:33,730 --> 00:27:37,610
+بينفع أحط dot product بين vector و vector، dot
+
+309
+00:27:37,610 --> 00:27:42,650
+product بين vector و vector، آه مش scalar من جاك
+
+310
+00:27:42,650 --> 00:27:47,490
+تطلع scalar، إيه اللي بين جثتين في B اللي بين جثتين
+
+311
+00:27:47,490 --> 00:27:53,190
+scalar، vector و dot product between two vectors
+
+312
+00:27:53,190 --> 00:27:57,630
+مسموح لي، بس الأخير اللي مش مسموح لي لأنه بين جثتين
+
+313
+00:27:57,630 --> 00:28:02,350
+طلع scalar ومنفعش يتحط بين scalar و vector cross
+
+314
+00:28:02,350 --> 00:28:05,630
+أو dot تمام، غيرها
+
+315
+00:28:09,960 --> 00:28:13,300
+أف بيتساوي M إيه؟ هيديك scalar في الـ vector، scalar
+
+316
+00:28:13,300 --> 00:28:16,740
+في الـ vector، حطيت منهم dot يعني أنتم عمكم سمعتوا
+
+317
+00:28:16,740 --> 00:28:23,560
+أن قانون نيوتن هيك بيساوي M ⋅ A أو M × A
+
+318
+00:28:23,560 --> 00:28:30,820
+لأ، حط M A على طول صحيح، لأ تمام خلاص الشرطة
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc_postprocess.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..66656d2d77f7c912169ab60e876e8be001e9cfa5
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc_postprocess.srt
@@ -0,0 +1,1272 @@
+1
+00:00:05,090 --> 00:00:09,660
+تمام انسمى باسم الله و نستكملدومنا اليوم هنا
+
+2
+00:00:09,660 --> 00:00:15,960
+وبالتالي بدنا نعيد ال vector product اللي حاولت
+
+3
+00:00:15,960 --> 00:00:20,640
+اضغط اني اخلصه ومااخدش حقه وبالتالي بدنا نعيد ال
+
+4
+00:00:20,640 --> 00:00:24,180
+vector product of two vectors قولنا في عندي تلت
+
+5
+00:00:24,180 --> 00:00:28,660
+أنواع من الضرب ضرب scalar في vector واتفقنا انه
+
+6
+00:00:28,660 --> 00:00:32,000
+بطلع vector اما مع نفس الاتجاه اذا كان ال scalar
+
+7
+00:00:32,000 --> 00:00:35,520
+positive او عكس الاتجاه اذا كان ال scalar negative
+
+8
+00:00:36,110 --> 00:00:41,150
+بعدين جن في عنا dot product او إيه له اسم تاني
+
+9
+00:00:41,150 --> 00:00:48,310
+scalar product ان لو كان في عندي a dot ال b هذا
+
+10
+00:00:48,310 --> 00:00:53,250
+بيساوي magnitude ال a في magnitude ال b في cosine
+
+11
+00:00:53,250 --> 00:00:57,550
+الزاوية اللي بينهم صح ولا لأ؟ وهذه القاعدة خلتني
+
+12
+00:00:57,550 --> 00:01:02,350
+أقول ان هذا بيطلع ax bx
+
+13
+00:01:03,740 --> 00:01:11,660
+زاد Ay By زاد Az Bz واتفقنا ان لا هنا في I ولا هنا
+
+14
+00:01:11,660 --> 00:01:16,700
+في J ولا هنا في K لأن الناتج Scalar متفاجنا هيك
+
+15
+00:01:16,700 --> 00:01:21,500
+تمام جالي ايش النوع التالت قولت بيكون vector في
+
+16
+00:01:21,500 --> 00:01:27,040
+vector لكن الناتج ايضا vector اذا معناته the
+
+17
+00:01:27,040 --> 00:01:31,620
+vector product اذا اسمه vector product عشان الناتج
+
+18
+00:01:31,620 --> 00:01:37,670
+vectoris between two vectors A and B وتُكتب على
+
+19
+00:01:37,670 --> 00:01:44,070
+إنها A cross الـB is a third vector اللي ديته
+
+20
+00:01:44,070 --> 00:01:48,830
+الرمز C هذا ال vector التالت ماذا ال vector إله
+
+21
+00:01:48,830 --> 00:01:52,330
+magnitude و direction صح ولا لأ قلنا ال magnitude
+
+22
+00:01:52,330 --> 00:01:59,250
+تبعهمجنتيود ال a cross ال b بتسوي مجنتيود ال a في
+
+23
+00:01:59,250 --> 00:02:03,890
+مجنتيود ال b في ال sign الزاوية اللي بينهم طب و ال
+
+24
+00:02:03,890 --> 00:02:07,850
+direction قال لي ال direction الناتج بدي يكون
+
+25
+00:02:07,850 --> 00:02:13,110
+عمودي على التنين عمودي على التنين بمعنى آخر عمودي
+
+26
+00:02:13,110 --> 00:02:18,550
+على مستواهم لأن عندي نظرية بتقول العمودي على مستوى
+
+27
+00:02:18,550 --> 00:02:24,350
+عمودي على كل خطوط جوا المستوى ولا لأ تمامإذن الـ
+
+28
+00:02:24,350 --> 00:02:32,890
+vector C هو عمودي للمستوى
+
+29
+00:02:32,890 --> 00:02:36,130
+A وB لأن هناك 2 درجة لـ M
+
+30
+00:02:44,460 --> 00:02:49,780
+هذا الأولاني في العلوح والتاني في اللوح صح ولا لأ؟
+
+31
+00:02:49,780 --> 00:02:53,840
+إذا التالت اللي بده ييجي ناتج من الـ cross product
+
+32
+00:02:53,840 --> 00:02:57,640
+بديه يكون مستوى عمودي عليهم إيش يعني؟ بديه يكون
+
+33
+00:02:57,640 --> 00:03:03,340
+عمودي على اللوح عمودي على اللوح لا out لا into صح؟
+
+34
+00:03:03,340 --> 00:03:07,840
+لا out لا into اللي انتوا بتقولوها dot و cross تمى
+
+35
+00:03:07,840 --> 00:03:11,540
+قال مين بديه يحدد؟ قال إيه دا كل يمنا اللي هتحدد
+
+36
+00:03:12,140 --> 00:03:16,560
+إيدك اليمنى كيف؟ قال لي إنت إيش بدك؟ قلتلي بدي E
+
+37
+00:03:16,560 --> 00:03:22,120
+cross ال B قاللي في هذه الحالة حط أصابعك الأربعة
+
+38
+00:03:22,120 --> 00:03:28,180
+مع A ولف باتجاه B وشوف إبهامك وإن بوديك قاللي Out
+
+39
+00:03:28,180 --> 00:03:37,940
+إذاً هذا Kout z direction لكن لو بدك بي cross ال a
+
+40
+00:03:37,940 --> 00:03:43,120
+بقول أصابع الأربعة مع بي لف وين بها مكان إذا هدل
+
+41
+00:03:43,120 --> 00:03:47,240
+الداخل إذا a cross ال b لاتساوي بي cross ال a
+
+42
+00:03:47,240 --> 00:03:52,270
+بيساوي العكس تبعها مظبوط ولا لأ؟ حلوده النهاد اللي
+
+43
+00:03:52,270 --> 00:03:58,070
+بتخليني اقول التالي I و J و K سمعنا فيهم؟ و
+
+44
+00:03:58,070 --> 00:04:02,470
+مربوطين جوا مخنا ان ال I مع السين و ال J مع الصعد
+
+45
+00:04:02,470 --> 00:04:06,830
+و ال K مع العين؟ مظبوط ولا لأ؟ جالي إذا لو قولتلك
+
+46
+00:04:06,830 --> 00:04:13,550
+I كرس الجي تصورهم و اعمل قاعدة يدي اليمنى؟ انتوا
+
+47
+00:04:13,550 --> 00:04:22,180
+شايفين؟ هي X هي I و هي J مش هيك؟ إذا هتطلع Kهتطلع
+
+48
+00:04:22,180 --> 00:04:24,880
+K صحيح اذا هذه هتطلع K
+
+49
+00:04:27,910 --> 00:04:34,370
+جالي طيب لو قلتلك J X K لأن دي بالكم هذه هي كال K
+
+50
+00:04:34,370 --> 00:04:41,770
+Out صح؟ لو إجيت انت بدك تعمل J X K بقاعدة اليدي
+
+51
+00:04:41,770 --> 00:04:47,910
+اليمنى هتطلع I موجبة، مظبوط او لأ؟ هتطلع I موجبة،
+
+52
+00:04:47,910 --> 00:04:57,730
+اذا J X K هتطلع I، طيب شوفليكي كروس الـ I جلي
+
+53
+00:04:57,730 --> 00:05:04,270
+هتطلع معاك J إذا كي كروس ال I هتطلع J اعكس أي
+
+54
+00:05:04,270 --> 00:05:09,790
+تنتين بصي سالب مظبوط ولا لأ تم انا طبعا بدي أحفظهم
+
+55
+00:05:09,790 --> 00:05:15,210
+هدول جلي بسهل عليك حفظهم كيف تسهل علي حفظهم جلي
+
+56
+00:05:15,210 --> 00:05:22,370
+حطلي هدول التلاتة I J K على رأس مثلثهذه طريقة عشان
+
+57
+00:05:22,370 --> 00:05:28,950
+تسهيل الحفظ تمام او تسهيل التعامل معاهمجالي إذا
+
+58
+00:05:28,950 --> 00:05:33,750
+ضربت تنتين هتطلع التالتة قطعا صح ولا لأ؟ لأن
+
+59
+00:05:33,750 --> 00:05:37,530
+الناتج بيكون عمودي على التنتين إيش العمودي على
+
+60
+00:05:37,530 --> 00:05:41,970
+الصين والصاد؟ عين إيش العمودي على الصد والعين؟ صين
+
+61
+00:05:41,970 --> 00:05:46,710
+مظبط ولا لأ؟ إذا محفظين، معرفين جالي إذا لما تضرب
+
+62
+00:05:46,710 --> 00:05:50,530
+تنتين تطلع التالتة، بضل عليك، موجب ولا سالب؟ جالي
+
+63
+00:05:50,530 --> 00:05:55,740
+بدي أفهمك هالقاعدةها قاعدة عادية اذا انت بتضن قاعد
+
+64
+00:05:55,740 --> 00:06:01,880
+I X G مع قرب الساعة بتطلع التالتة موجبة I X G K طب
+
+65
+00:06:01,880 --> 00:06:08,000
+J X I ثالث K J X K J X K مش هيد مع قرب الساعة
+
+66
+00:06:08,000 --> 00:06:15,100
+بتطلع التالتة موجبة K X I طلعت التالتة تمام و
+
+67
+00:06:15,100 --> 00:06:21,080
+المعكوس بتحط ثالث سهلة هلجتاللي خمتوني على انه
+
+68
+00:06:21,080 --> 00:06:25,060
+احنا بنعرف انه اقرب الساعة موجب هديك تجربش لهدي
+
+69
+00:06:25,060 --> 00:06:29,380
+هدي مجلة قاعد عشان نعرف كيف نطبق قاعدة اليدي
+
+70
+00:06:29,380 --> 00:06:38,760
+اليمنى تمام؟ ايه الصفصار؟ تمإذاً the rule هذه
+
+71
+00:06:38,760 --> 00:06:41,820
+قاعدة يد اليمن اللي توشرحناها إنه حط أصابعك
+
+72
+00:06:41,820 --> 00:06:46,100
+الأربعة مع الأول لف بالاتجاه التاني إبهامك بالدي
+
+73
+00:06:46,100 --> 00:06:49,340
+التالت إذاً the rule states that .. states that يا
+
+74
+00:06:49,340 --> 00:06:53,920
+نص على ما .. ما هي هذه states that تمام؟ the rule
+
+75
+00:06:53,920 --> 00:06:58,760
+و هذه ال S عشان هذه ال rule singleتعرفوها خدتوها
+
+76
+00:06:58,760 --> 00:07:03,400
+في ال grammar تمام it states that the four fingers
+
+77
+00:07:03,400 --> 00:07:07,700
+of your right .. of the right hand are pointed
+
+78
+00:07:07,700 --> 00:07:12,880
+يشير point are pointed along a مظبوط ولا لأ؟ إذا
+
+79
+00:07:12,880 --> 00:07:17,340
+بوجه صبيع الأربع ما الأول a and then curved يعني
+
+80
+00:07:17,340 --> 00:07:22,880
+لفها curved and then curved toward بيه باتجاه بيه
+
+81
+00:07:22,880 --> 00:07:26,080
+through the smaller angle باتجاه بيه الزاوية
+
+82
+00:07:26,080 --> 00:07:31,180
+الأصغرthe thumb of الابهام then gives the
+
+83
+00:07:31,180 --> 00:07:34,400
+direction of C حق قادة الهجوم لما أنا سألحت أنا
+
+84
+00:07:34,400 --> 00:07:40,760
+وياكم تمام بس بنترجم العربي using this rule it is
+
+85
+00:07:40,760 --> 00:07:46,210
+clear thatA X B بيتساوي سالب B X A ولا لأ؟
+
+86
+00:07:46,210 --> 00:07:51,410
+وعملناها و أثبتناها دي الكلام صحيح طيب جالي حلو
+
+87
+00:07:51,410 --> 00:07:59,230
+جالي by the same rule one can verify يتأكد أو يثبت
+
+88
+00:07:59,230 --> 00:08:07,790
+I X I بتساوي J X J بتساوي K X K بتساوي 0 ليه 0؟لأن
+
+89
+00:08:07,790 --> 00:08:11,830
+صين الصفر صفر لأن الـ cross بيقول لـ magnitude
+
+90
+00:08:11,830 --> 00:08:15,670
+الأول في magnitude التاني في الصين الزاوية اللي
+
+91
+00:08:15,670 --> 00:08:19,370
+بينهم وما زال ال vectors نفسهم إذا زاوية دي إيش؟
+
+92
+00:08:19,370 --> 00:08:26,070
+Zero إذا خلصنا قاللي قاعدة اليد اليمنى أو القاعدة
+
+93
+00:08:26,070 --> 00:08:34,020
+هذه بتقول التاليهذه هي I cross الـ J اعطت K J
+
+94
+00:08:34,020 --> 00:08:44,720
+cross الـ K اعطت I K cross الـ I اعطت J صح تمام مش
+
+95
+00:08:44,720 --> 00:08:52,160
+عاجبك اشي عندك سؤال انا انا انا انا انا انا انا
+
+96
+00:08:52,160 --> 00:08:53,260
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+97
+00:08:53,260 --> 00:08:53,340
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+98
+00:08:53,340 --> 00:08:53,920
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+99
+00:08:53,920 --> 00:08:58,940
+انا انا انا انا انا انا انا
+
+100
+00:08:58,940 --> 00:09:01,640
+انايعني هل إله علاقة بالتعامد ولا ما إله علاقة
+
+101
+00:09:01,640 --> 00:09:05,880
+بالتعامد؟ إله علاقة بالتعامد لأنه لما تضرب تنتين
+
+102
+00:09:05,880 --> 00:09:09,340
+كل الصبودات، بده يطلع التالت متعمد على التنتين،
+
+103
+00:09:09,340 --> 00:09:16,770
+لازم، وبما إن ال Z عمودي على ال X وY بصحله ياخدأيه
+
+104
+00:09:16,770 --> 00:09:19,790
+بس قاعدة اليد اليمنى ليه إيش جاية؟ قاعدة اليد
+
+105
+00:09:19,790 --> 00:09:23,350
+اليمنى بتقولك انت بتقوللي عمودي طب عمودي لفوق ولا
+
+106
+00:09:23,350 --> 00:09:27,450
+لتحت؟ يعني هي عمودي على الطاولة هجتهد عمودي على
+
+107
+00:09:27,450 --> 00:09:30,850
+الطاولة ولا لأ؟ طب لو كان لتحت برضه عمودي على
+
+108
+00:09:30,850 --> 00:09:34,490
+الطاولة إذا أنا بدي أحدد واحد منهم جلي اليد اليمنى
+
+109
+00:09:34,490 --> 00:09:40,950
+اتفقنا هي اللي اتحدد فمت عليا كيف؟ بس تمامجاله حلو
+
+110
+00:09:40,950 --> 00:09:45,290
+اذا انت امنت يلّا يا بنات بدنا نضرب احنا وياكم
+
+111
+00:09:45,290 --> 00:09:51,470
+cross product ال A مش مكتبه يلو تلت مركبات و ال B
+
+112
+00:09:51,470 --> 00:09:55,270
+تلت مركبات هي الصيغة العامة تحت اي vector اضرب
+
+113
+00:09:55,270 --> 00:09:59,830
+vector جوس في جوس في حد ماعرفش اضرب جوس في جوس مش
+
+114
+00:09:59,830 --> 00:10:04,030
+بنجيب هدا و بنضرب في هدول كلهم و بنجيب هدا و بنضرب
+
+115
+00:10:04,030 --> 00:10:07,610
+في كل هدول و هكذا جالي اشتغل قولتله هاي اشتغلت
+
+116
+00:10:10,130 --> 00:10:13,270
+طلعوا عليهم ضرب الجثر العادي اللي أخدته في المدرسة
+
+117
+00:10:13,270 --> 00:10:21,370
+تمام استنوا شويه هلجيت وين في I X I أو J X J أو K
+
+118
+00:10:21,370 --> 00:10:28,410
+X K إيش بتحط محله؟ قال لي ها مظبوط هيك ولا لأ؟
+
+119
+00:10:28,410 --> 00:10:32,770
+هدول زيروا راحوا قال لي إيش هتضل؟ قال لي اول term
+
+120
+00:10:32,770 --> 00:10:41,540
+هنا I X J تعال I X J إيش بطلع؟ KK مش واحد لأنه هذا
+
+121
+00:10:41,540 --> 00:10:46,720
+cross product بديه يطلع vector واحد رقم بديه يطلع
+
+122
+00:10:46,720 --> 00:10:51,280
+vector اذا هذا بقى هتحطلي محله انا اه انا انا انا
+
+123
+00:10:51,280 --> 00:10:51,660
+انا انا انا انا انا انا انا انا انا انا انا
+
+124
+00:10:54,800 --> 00:11:02,160
+طيب I cross ال K سالب J ها I cross ال K مشيت ضد
+
+125
+00:11:02,160 --> 00:11:08,200
+عقارب الساعة اذا سالب J حطينا سالب J تمام يا بنات
+
+126
+00:11:08,200 --> 00:11:18,340
+تمام نجهان J cross ال I سالب Kهناك مهمش انه جي
+
+127
+00:11:18,340 --> 00:11:22,880
+سالب كي طلعوا هذا سالب كي وهذا كي ممكن اخد الكي
+
+128
+00:11:22,880 --> 00:11:25,360
+عالم المشترك ولا لأ انا دي بدي اخد الكي عالم
+
+129
+00:11:25,360 --> 00:11:31,020
+المشترك حلو ده اللي ها دي جي cross ال كي جي cross
+
+130
+00:11:31,020 --> 00:11:37,160
+ال اي موجب اذا اي بالموجب حلو نجي لهذا ده اللي كي
+
+131
+00:11:37,160 --> 00:11:41,900
+cross ال اي جي هى صار عندى جي و هنا سالب جي جي مع
+
+132
+00:11:41,900 --> 00:11:45,810
+جي باخد عالم المشتركتمام قال لي دل عندك أخي يا
+
+133
+00:11:45,810 --> 00:11:50,450
+قلتله هذا سلب I طيب جمع حط ال I ل I لحال و ال J مع
+
+134
+00:11:50,450 --> 00:11:55,910
+ال J لحال و ال K مع ال K لحال جمعنا طلعت هذا الرقم
+
+135
+00:11:55,910 --> 00:12:03,260
+ده مطول طويل صحوإحنا هذا حلو وقدرنا عليه نحفظه
+
+136
+00:12:03,260 --> 00:12:05,820
+وقلنا الصيني مع الصيني الصاضي مع الصاضي و العيني
+
+137
+00:12:05,820 --> 00:12:09,280
+مع العيني سهل نتعامل معاه وده إيش اللي خليني
+
+138
+00:12:09,280 --> 00:12:13,980
+أحفظه؟ قعدت أنا بدي أعمل ليه logarithm عشان أعرف
+
+139
+00:12:13,980 --> 00:12:17,220
+أحفظه؟ ولا أعمللي برنامج حسوب عشان أحفظنيه؟ صعب
+
+140
+00:12:17,220 --> 00:12:21,960
+الأمور وهم بتطلعوا هيك قالوا إيه؟ هدف مش بحاجة
+
+141
+00:12:21,960 --> 00:12:27,660
+أخدناها في المدرسة الشيية قالها دي لو كتبتلك هيك
+
+142
+00:12:31,800 --> 00:12:37,840
+محدد قالوا والله اه يالا نجرب براو عليكم انتو
+
+143
+00:12:37,840 --> 00:12:41,940
+طمنتوني كلكم قلتوا ايه؟ أخدناها واللي فهمت أخدناها
+
+144
+00:12:41,940 --> 00:12:46,900
+في توجيهي يعني طازة لسه ايه معناها مالحجناش ننساها
+
+145
+00:12:46,900 --> 00:12:53,140
+كيف كنا نعمل يا بنات معناه مع الأسف هذه هطيل شاشة
+
+146
+00:12:53,140 --> 00:12:56,820
+ومش جادرين نكتب في الشاشة فبنانا الطر نكتب هنا
+
+147
+00:12:56,820 --> 00:13:06,200
+نقول هاي ايه؟عشان نذكر بعض اول صف بحط IJK اللي
+
+148
+00:13:06,200 --> 00:13:13,940
+بتعرفوه تاني صف مركبات الـA مركبات تحت I ثيني وتحت
+
+149
+00:13:13,940 --> 00:13:21,700
+J صادم وهذه Z نيجد تاني بيه بقول BX BY BZ مش هيك
+
+150
+00:13:21,700 --> 00:13:27,460
+مظلومات وكنت بتقوله plus negative plusبنذكر بعض
+
+151
+00:13:27,460 --> 00:13:34,140
+جادين بقول بالساوي جوس I زائد جوس ناقص او ناقص
+
+152
+00:13:34,140 --> 00:13:39,800
+ملاحظة ناقص مهمش برضه J زائد جوس K مش هيكلنا نعمل
+
+153
+00:13:39,800 --> 00:13:49,170
+عشان اجيب هادي ايش هسويسكر صف عمود يلّا نسكر سكرنا
+
+154
+00:13:49,170 --> 00:13:58,510
+هذه و سكرنا هذه Ay Bz ناقص Az By اطلعولي ال I اللي
+
+155
+00:13:58,510 --> 00:14:04,290
+جلبتها أنا نفسها ولا لأ؟ والله نفسها نجي للـ J
+
+156
+00:14:04,290 --> 00:14:10,530
+أسكر هذه و أسكر هذه Ax Bz
+
+157
+00:14:15,190 --> 00:14:19,430
+axbz-azbx شوفوا ايش اللي افرجت انا حاطط هنا زائد و
+
+158
+00:14:19,430 --> 00:14:28,090
+جالب نفسها صح ولا لأ زائد سكر هذه و سكر هذه axbz
+
+159
+00:14:28,090 --> 00:14:37,870
+axby axby-aybx هو هذه سهلة اتحفظش هذه احفظ هذه و
+
+160
+00:14:37,870 --> 00:14:39,950
+خلصنا مظبوطة للا
+
+161
+00:14:46,010 --> 00:14:53,730
+حلو نشوف في شي مش مفهوم تمام ال cross product اسمه
+
+162
+00:14:53,730 --> 00:14:57,070
+vector product صح عرفنا ليه يسمو cross عشان ال
+
+163
+00:14:57,070 --> 00:15:00,730
+cross و لسه منها vector product عشان النتيج vector
+
+164
+00:15:00,730 --> 00:15:04,550
+ايش بجربل التنين عمودي عليهم التنين عمودي عليهم
+
+165
+00:15:04,550 --> 00:15:09,670
+التنين عمودي ع مستواهم صح ولا لأ تمام نيجي نحل
+
+166
+00:15:09,670 --> 00:15:17,320
+هالسؤال قلي شوفهيتوا vectors هدول الأول مراكبة
+
+167
+00:15:17,320 --> 00:15:21,340
+ثينية و إله مراكبة صادية صح والتاني إله مراكبة
+
+168
+00:15:21,340 --> 00:15:25,560
+ثينية و صادية مالوش ولا واحدة منهم إله مراكبة زدية
+
+169
+00:15:25,560 --> 00:15:32,020
+يعني التنين وجعين في اللوح ثين و صاد طيب نعمل
+
+170
+00:15:32,020 --> 00:15:35,570
+cross product لازم يكون عمودي على اللوحاذا لازم
+
+171
+00:15:35,570 --> 00:15:42,590
+يكون رقمه K تجاهه صح ولا لأ؟ يلّا نجرب قال لي كيف؟
+
+172
+00:15:42,590 --> 00:15:50,170
+قال لي هي ايه cross ال B؟ اعطتني
+
+173
+00:15:50,170 --> 00:15:57,150
+ايه ولا ماعطتنيش؟ يلّا ننقل Zero اتنين تلاتة Zero
+
+174
+00:15:57,150 --> 00:16:07,310
+ناقص واحد اتنين Zeroتمام؟ معطية السؤال جلبت ساوي I
+
+175
+00:16:07,310 --> 00:16:14,170
+Gos I ذات Gos J ذات Gos K مش هيك بنعمل؟ او ناقص
+
+176
+00:16:14,170 --> 00:16:16,850
+انتوا هنا بتعملوا بهمش قدما يشوفوا قبل ما عرفت
+
+177
+00:16:16,850 --> 00:16:20,350
+الناس ماعرفت أن ال I كتر من جاي سفر اتسنى شوية
+
+178
+00:16:20,350 --> 00:16:26,870
+هجيتي يلا ساكرولي ال I تلاتة في سفر ناقص سفر في
+
+179
+00:16:26,870 --> 00:16:33,630
+اتنى اذا اول واحدة روحتي الله يعطيها العافيةشوف
+
+180
+00:16:33,630 --> 00:16:43,290
+الـ J فاكره اتنين في سفر ناقص سفر في ناقص واحد روح
+
+181
+00:16:43,290 --> 00:16:48,690
+ايش ده اللي مركبة مدلسي ال K كنت متوقعها انا قالي
+
+182
+00:16:48,690 --> 00:16:55,350
+سكر ال K اتنين في اتنين ناقص ناقص اذا سبعة K اذا
+
+183
+00:16:55,350 --> 00:16:56,850
+الجواب سبعة K
+
+184
+00:17:01,440 --> 00:17:05,220
+هجيت هذا السبعة K عمودي على هذا و لا مش عمودي و
+
+185
+00:17:05,220 --> 00:17:09,320
+الله عمودي و عمودي على هذا و لا لأ عمودي لو جبت
+
+186
+00:17:09,320 --> 00:17:15,120
+اعملت dot product بين هذا C و A لازم يطلع Zero
+
+187
+00:17:15,120 --> 00:17:22,560
+افترضوا هذا C مش C هذا هجيت C هذا عمودي على A و لا
+
+188
+00:17:22,560 --> 00:17:28,880
+مش عمودي اذا بيعني ان C dot ال A ايه يجب ان يكون
+
+189
+00:17:30,520 --> 00:17:33,840
+يالا اعملوا dot product ايش في ال dot product
+
+190
+00:17:33,840 --> 00:17:37,440
+بيسوي؟ الصيني مع الصيني والصاضي مع الصاضي والعيني
+
+191
+00:17:37,440 --> 00:17:42,200
+مع العيني الصيني هناك اتنين والصيني ليه ال C؟ سفر
+
+192
+00:17:42,200 --> 00:17:47,960
+فيه اللي صيني هذا؟ اللي صاضي؟ اذا التلاتة فيه سفر،
+
+193
+00:17:47,960 --> 00:17:51,620
+هذا الكلش عنده K و الله سفر، اذا هذا بيضمن ان هو
+
+194
+00:17:51,620 --> 00:17:55,780
+عمودي، طب ادربولي C dot ال B
+
+195
+00:17:58,680 --> 00:18:02,880
+لأنه عمودي على التنين ولا لأ؟ سفر في المطلوب
+
+196
+00:18:02,880 --> 00:18:08,260
+التاني بيقول طب اثبتلي ان a cross ال b بتسوي سالب
+
+197
+00:18:08,260 --> 00:18:15,540
+b cross ال a قلتله لو بدك انت الآن بي cross ال a
+
+198
+00:18:15,540 --> 00:18:20,050
+ايش يسوي؟ قلتله جلبابدأ في الـB، ايش الـB؟ قال
+
+199
+00:18:20,050 --> 00:18:25,210
+يناقص واحد، اتنين، سفر، اتنين، تلاتة، سفر، مش
+
+200
+00:18:25,210 --> 00:18:28,350
+هيكبني اعمال؟ نيجي يشوف المراكبة الصينية، قلتله
+
+201
+00:18:28,350 --> 00:18:37,370
+كملي السفرصح؟ الصديّة الـ Z ماقس تلاتة ماقس أربعة
+
+202
+00:18:37,370 --> 00:18:42,890
+ماقس سبعة اذا انطلعت صحيحة ان A cross الـB بتسوي
+
+203
+00:18:42,890 --> 00:18:45,550
+سالب B cross الـA اذا بيقولي find the cross
+
+204
+00:18:45,550 --> 00:18:48,730
+product between two vectors طلعناها سبعة كده
+
+205
+00:18:48,730 --> 00:18:54,130
+وبجلوا بعدين بيقولي verify that اثبت او تحقق من ان
+
+206
+00:18:54,130 --> 00:18:58,930
+A cross الـB قطعا بتسوي سالب B cross الـA تمام يا
+
+207
+00:18:58,930 --> 00:18:59,490
+بنات؟
+
+208
+00:19:02,000 --> 00:19:06,400
+في حد بسأل؟ بدي أرجع لشغل معين قبل ما أخش على ال
+
+209
+00:19:06,400 --> 00:19:10,860
+quiz لخير لما جبنا ال vector و أعرفنا ال vector في
+
+210
+00:19:10,860 --> 00:19:15,400
+أول الشبطة قلنا فيه أنثي على ال vectors قلنا
+
+211
+00:19:15,400 --> 00:19:19,900
+displacement و ال velocity و ال acceleration و ال
+
+212
+00:19:19,900 --> 00:19:24,340
+force و المساحة تمام؟ و في منكم ماعجبهمش أن
+
+213
+00:19:24,340 --> 00:19:29,160
+المساحة تكون vector مظبوط ولا لأ؟ ماعجبناش قلنا
+
+214
+00:19:29,160 --> 00:19:35,070
+تعالى نشوفبتعرفوا لو أرسم متوازي الأضلاع؟ شوفتهوا
+
+215
+00:19:35,070 --> 00:19:40,110
+قبل كده، بدنا نرسم متوازي الأضلاع، هاي متوازي
+
+216
+00:19:40,110 --> 00:19:46,130
+أضلاع تمام، هذا الضلع بدي أسميه vector A و هذا
+
+217
+00:19:46,130 --> 00:19:51,530
+الضلع بدي أسميه vector B تمام هيك يا بنات؟ حلو،
+
+218
+00:19:51,530 --> 00:19:56,310
+يلا ذكروني عاد، مساحة متوازي الأضلاع
+
+219
+00:20:03,340 --> 00:20:08,800
+أه يعني بقى واحد وان نصشوف يا بنات بنحن نحفظ حاجة
+
+220
+00:20:08,800 --> 00:20:15,040
+معينة شوفوا بننأسس لحاجة شوفوا قدرتنا احنا على
+
+221
+00:20:15,040 --> 00:20:20,580
+الحفظ محدودة وبالتالي اتغلبناش عشان نحفظ كيف يعني
+
+222
+00:20:20,580 --> 00:20:25,780
+ما تعملوناش متقانون كل الأشكال المربعة مربع ولا
+
+223
+00:20:25,780 --> 00:20:30,480
+مستطيل ولا متوازي أطلع ولا لبنديكية ولا شبه منحرف
+
+224
+00:20:30,480 --> 00:20:35,920
+القاعدة في الارتفاع بس قاعدة في الارتفاع كل
+
+225
+00:20:35,920 --> 00:20:40,550
+الأشكال المربعةقاعدة في الارتفاع هجت المثلث مش
+
+226
+00:20:40,550 --> 00:20:45,070
+رباعي نص رباعي عشان تيجي يجي من النص المثلث نص
+
+227
+00:20:45,070 --> 00:20:48,310
+قاعدة في الارتفاع لكن متوازن الأضلاع قاعدة في
+
+228
+00:20:48,310 --> 00:20:52,090
+الارتفاع المستطيل قاعدة في الارتفاع المربع قاعدة
+
+229
+00:20:52,090 --> 00:20:56,510
+في الارتفاع شبه الملحرف قاعدة في الارتفاع وتيجي
+
+230
+00:20:56,510 --> 00:20:59,270
+الارتفاع طول في عرض ما هو العرض في المستطيل هو
+
+231
+00:20:59,270 --> 00:21:04,950
+الارتفاعهو الارتفاع المربع بصموني اتضلع تربية ما
+
+232
+00:21:04,950 --> 00:21:08,210
+هو ليش اتضلع تربية لأن اتضلع هو القاعدة اتضلع
+
+233
+00:21:08,210 --> 00:21:12,350
+ارتفاع مصطلح اللي اذا مافيش عندي قانون للمساحة
+
+234
+00:21:12,350 --> 00:21:17,930
+للاشكال الربعية لواحد قاعدة في ارتفاع بس طب وين
+
+235
+00:21:17,930 --> 00:21:21,630
+ارتفاع بيه ارتفاع كيف كنتوا تجيبوا الارتفاع ايه
+
+236
+00:21:21,630 --> 00:21:28,250
+براو علينا هذا ارتفاع صح مش هيكنا نعمله جيلي حلو
+
+237
+00:21:28,250 --> 00:21:30,030
+جيلي هب هذي زاوية
+
+238
+00:21:33,480 --> 00:21:37,120
+تمام؟ صين الزاوية اللى انتوا شايفينها بتساوي مقابل
+
+239
+00:21:37,120 --> 00:21:42,980
+على وطر حلو مقابل على وطر ماشيك تعرفها بقوله صين
+
+240
+00:21:42,980 --> 00:21:51,380
+الثيتا بتساوي H على بي ك magnitude اذا H بتساوي بي
+
+241
+00:21:51,380 --> 00:21:58,000
+في صين الثيتا هجيجي نرجع لل area area قاعدة في
+
+242
+00:21:58,000 --> 00:22:04,930
+ارتفاعصح؟ القاعدة ايش؟ A إذا ال magnitude ال E في
+
+243
+00:22:04,930 --> 00:22:11,370
+H هي H في B Sine of Theta بنيمله هذه A cross ال B
+
+244
+00:22:11,370 --> 00:22:15,770
+صح؟
+
+245
+00:22:15,770 --> 00:22:19,950
+طب هذه A cross ال B النتيجة إيش لازم يكون؟ is an
+
+246
+00:22:19,950 --> 00:22:25,390
+area vectorالـ Area vector كيف اتجاهها؟ قال عمودي
+
+247
+00:22:25,390 --> 00:22:30,370
+على السطح لأن A وB بتشكل ال plane يعني هي الطاولة
+
+248
+00:22:30,370 --> 00:22:37,090
+هي A و هي B مساحتها vector كيف اتجاهها؟ بقول عمودي
+
+249
+00:22:37,090 --> 00:22:40,470
+على الطاولة لازم تكون عمودي على الطاولة عشان تكون
+
+250
+00:22:40,470 --> 00:22:44,530
+عمودي على مستوى ال two vectors تمام؟ هذا أظن أحد
+
+251
+00:22:44,530 --> 00:22:49,490
+أسلوب الكتاب أنك تثبت أن الـ Area بتسوي A cross ال
+
+252
+00:22:49,490 --> 00:22:57,890
+Bهنا أثبتنا تمام؟ أيه الصفصار؟ عيد و إيش عيد فيه؟
+
+253
+00:22:57,890 --> 00:23:03,650
+ما هو مش أنت هجد عيد عيد مفهوم مساحة متوازن أطلعة
+
+254
+00:23:03,650 --> 00:23:08,510
+بالساعة القاعدة في الارتفاع، بتحرفيها؟ أه؟ واو
+
+255
+00:23:08,510 --> 00:23:12,610
+تخجليشبتعرف ان مساحة متوازي الأضلاع بسوء قاعدة في
+
+256
+00:23:12,610 --> 00:23:17,290
+ارتفاع؟ حلو هذا متوازي الأضلاع ولا لا يا بنتي؟ هذا
+
+257
+00:23:17,290 --> 00:23:21,070
+ارتفاع ولا مش ارتفاع؟ بقدر اجيبه بدلالة هذه على
+
+258
+00:23:21,070 --> 00:23:24,630
+اعتبار ان صين الزاوية بتسوي H على B ولا لا؟ اذا
+
+259
+00:23:24,630 --> 00:23:29,230
+قولت H اللي انت بتدور عليه الارتفاع بتسوي B في صين
+
+260
+00:23:29,230 --> 00:23:33,950
+الزاوية ضرب ضرب تبادلي قولت يلا تروح لصف سادس ولا
+
+261
+00:23:33,950 --> 00:23:39,670
+خامس ان مساحة متوازي الأضلاع بتسوء قاعدة Aفي
+
+262
+00:23:39,670 --> 00:23:45,710
+الارتفاع H وH هنا عوضت عنه قلتله أول ما قلتلي A في
+
+263
+00:23:45,710 --> 00:23:49,170
+B في صيني الزاوية تا و لسه أعرفتها ده cross
+
+264
+00:23:49,170 --> 00:23:53,850
+product cross product يعني انها vector product اذا
+
+265
+00:23:53,850 --> 00:23:58,850
+الناتج قطعا vector اذا ال area is a vector كف تجاه
+
+266
+00:23:58,850 --> 00:24:03,450
+عمودي على التنتين اذا عمودي على المساحة عمودي على
+
+267
+00:24:03,450 --> 00:24:06,670
+السطح تمام يا بنتي؟ غيرها
+
+268
+00:24:09,970 --> 00:24:15,970
+هذا خلّصنا منه شوفوا
+
+269
+00:24:15,970 --> 00:24:22,850
+هالشغلات طلّعوا هدول أربع علاقات بيقولّي مين منهم
+
+270
+00:24:22,850 --> 00:24:28,470
+دائما Zero بدا نبدأ بالأخيرة يا بنات الأخيرة
+
+271
+00:24:28,470 --> 00:24:34,110
+طلّعولي اللي بين الجثين إيش بينهم Dot إيش بيطلّع
+
+272
+00:24:34,110 --> 00:24:39,100
+هل ال cross مسموح يكون بين scalar و vectorأذا
+
+273
+00:24:39,100 --> 00:24:41,220
+مايقوللي هذا اللي كاتب ومايعرفش إيش معناه vectors
+
+274
+00:24:41,220 --> 00:24:46,520
+إذا هذه فالتك منها هذه ولا كأنها خيار عندي لأنه
+
+275
+00:24:46,520 --> 00:24:53,060
+كتابة غلط أصلا إذا الخيار الأخر مرفوض لإن انت عامل
+
+276
+00:24:53,060 --> 00:24:57,960
+حاجة مبدئية قطأ هتطلق cross product بين scalar و
+
+277
+00:24:57,960 --> 00:25:00,960
+vector وهذا ممنوع لأن قلتلي ال vector و product
+
+278
+00:25:00,960 --> 00:25:04,220
+between two vectors زي ال scalar product between
+
+279
+00:25:04,220 --> 00:25:09,090
+two vectorsتمى قال لطيب يشوف هذه قال لي أنت إيش
+
+280
+00:25:09,090 --> 00:25:12,610
+بتقولي هذا الجوس أمودي على الـA ولا مش عمودي على
+
+281
+00:25:12,610 --> 00:25:18,390
+الـA؟ عمودي على الـA يعني هذا الأصل A يكون .. بدي
+
+282
+00:25:18,390 --> 00:25:22,830
+أفترض الجوس C يا بنات افترضوا الـC تمى .. هذه
+
+283
+00:25:22,830 --> 00:25:27,170
+المفروض يكون magnitude الـC في magnitude الـA في
+
+284
+00:25:27,170 --> 00:25:33,920
+sign التسعين صح؟ وهذه واحدإذاً magnitude of C في
+
+285
+00:25:33,920 --> 00:25:37,360
+magnitude of A طب أنت بتقولي magnitude of C سفر
+
+286
+00:25:37,360 --> 00:25:41,420
+وديتني معلومة أو magnitude of A سفر إذاً هذه مش
+
+287
+00:25:41,420 --> 00:25:48,780
+بالضرورة تكون سفر ولا سفر لأ انشوف C .. C جالي
+
+288
+00:25:48,780 --> 00:25:53,940
+برضه C عمودي على ال B لأنه عمودي على التنتين إذاً
+
+289
+00:25:53,940 --> 00:26:01,120
+هذه C في B في sign ال 90 اللي هي 1إذاً برضه سفر
+
+290
+00:26:01,120 --> 00:26:10,720
+دايما؟ لأ قال لي نشوف بي قال لي C في بي في cosine
+
+291
+00:26:10,720 --> 00:26:16,980
+التسعين مش صين الآن ليش cosine؟ قلت له إنه في dot
+
+292
+00:26:16,980 --> 00:26:20,440
+product و ال dot بتعطي cosine ولا مش cosine؟
+
+293
+00:26:20,440 --> 00:26:24,140
+cosine قال لي قداش cosine التسعين in C ال
+
+294
+00:26:24,140 --> 00:26:28,140
+calculator موجودة cosine التسعين بتطلع سفرإذن هذه
+
+295
+00:26:28,140 --> 00:26:33,060
+دايما سفر بغض النظر كدش هدول صح ولا لأ ان شاء الله
+
+296
+00:26:33,060 --> 00:26:37,680
+هدوا يكونوا مليون هنا فيه سفر إذن الشي اللي دايما
+
+297
+00:26:37,680 --> 00:26:45,580
+سفر هذي أول
+
+298
+00:26:45,580 --> 00:26:50,480
+واحدة افترض ان هي صين 90 مش اي زاوية تانية اه ليش
+
+299
+00:26:50,480 --> 00:26:58,210
+صح صحي معايا و صالك حلو ليشتخيلني شوية اللي ناتج
+
+300
+00:26:58,210 --> 00:27:00,950
+اللي سمته الـC مش لازم يكون عمودي على الـA و عمودي
+
+301
+00:27:00,950 --> 00:27:04,510
+على الـB؟ آه لازم لازم حلو إذا عمودي على الـA و
+
+302
+00:27:04,510 --> 00:27:06,630
+أنا مش عمودي على الـA عشان كده خدت التسعين عشان
+
+303
+00:27:06,630 --> 00:27:11,330
+كده خدت التسعين طب و الـB؟ برضه عمودي على الـB إذا
+
+304
+00:27:11,330 --> 00:27:16,030
+برضه اللي تحته زيه عرفتي ليش؟ غيرها احكي لا vector
+
+305
+00:27:16,030 --> 00:27:21,210
+لا dot ولا
+
+306
+00:27:21,210 --> 00:27:27,590
+crossطلعت vector يعني a cross b vector dot vector
+
+307
+00:27:27,590 --> 00:27:33,730
+انت بتقول عن b مش a cross b vector اللي سميته c
+
+308
+00:27:33,730 --> 00:27:37,610
+بنفع حط dot product بين vector و vector dot
+
+309
+00:27:37,610 --> 00:27:42,650
+product بين vector و vector اه مش scalar من جالك
+
+310
+00:27:42,650 --> 00:27:47,490
+تطلع scalar ايه اللي بين جثين في b اللي بين جثين
+
+311
+00:27:47,490 --> 00:27:53,190
+scalarvector و dot product between two vectors
+
+312
+00:27:53,190 --> 00:27:57,630
+مسموحلي بس الأخير اللي مش مسموحلي لأنه بين جثين
+
+313
+00:27:57,630 --> 00:28:02,350
+طلع scalar ومنفعش اتحط بين scalar و vector cross
+
+314
+00:28:02,350 --> 00:28:05,630
+او dot تمام غيرها
+
+315
+00:28:09,960 --> 00:28:13,300
+أف بيتساوي M إيه؟ هيديك Scalar في ال vector Scalar
+
+316
+00:28:13,300 --> 00:28:16,740
+في ال vector حطيت منهم Dot يعني أنتوا عمكم سمعتوا
+
+317
+00:28:16,740 --> 00:28:23,560
+أن قانون الميوتين هيك بيساوي M Dot A أو M Cross A
+
+318
+00:28:23,560 --> 00:28:30,820
+لأ حط M A على طول صحيح لأ تمام خلاص الشرطة
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc_raw.json b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1d282b218a90664026df70499b202073df54ecfd
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 769, "start": 5.09, "end": 7.69, "text": "تمام انسمى باسم الله و نستكمل", "tokens": [39237, 10943, 16472, 38251, 7578, 4724, 32277, 2304, 21984, 4032, 8717, 14851, 24793, 1211], "avg_logprob": -0.346093757947286, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 5.09, "end": 5.55, "word": "تمام", "probability": 0.4906005859375}, {"start": 5.55, "end": 6.45, "word": " انسمى", "probability": 0.4273274739583333}, {"start": 6.45, "end": 6.73, "word": " باسم", "probability": 0.92138671875}, {"start": 6.73, "end": 6.95, "word": " الله", "probability": 0.97021484375}, {"start": 6.95, "end": 7.09, "word": " و", "probability": 0.9462890625}, {"start": 7.09, "end": 7.69, "word": " نستكمل", "probability": 0.9180908203125}], "temperature": 1.0}, {"id": 2, "seek": 3552, "start": 8.4, "end": 35.52, "text": "دومنا اليوم هنا وبالتالي بدنا نعيد ال vector product اللي حاولت اضغط اني اخلصه ومااخدش حقه وبالتالي بدنا نعيد ال vector product of two vectors قولنا في عندي تلت أنواع من الضرب ضرب scalar في vector واتفقنا انه بطلع vector اما مع نفس الاتجاه اذا كان ال scalar positive او عكس الاتجاه اذا كان ال scalar negative", "tokens": [3215, 20498, 8315, 45595, 20498, 34105, 46599, 6027, 2655, 6027, 1829, 47525, 8315, 8717, 3615, 25708, 2423, 8062, 1674, 13672, 1829, 11331, 995, 12610, 2655, 1975, 11242, 17082, 9566, 16472, 1829, 1975, 9778, 1211, 9381, 3224, 4032, 15042, 47283, 3215, 8592, 11331, 4587, 3224, 46599, 6027, 2655, 6027, 1829, 47525, 8315, 8717, 3615, 25708, 2423, 8062, 1674, 295, 732, 18875, 12174, 12610, 8315, 8978, 18871, 16254, 6055, 1211, 2655, 14739, 14407, 3615, 9154, 6024, 114, 25513, 48812, 25513, 39684, 8978, 8062, 4032, 9307, 5172, 4587, 8315, 16472, 3224, 4724, 9566, 1211, 3615, 8062, 1975, 15042, 20449, 8717, 36178, 2423, 9307, 7435, 40294, 1975, 15730, 25961, 2423, 39684, 3353, 1975, 2407, 6225, 4117, 3794, 2423, 9307, 7435, 40294, 1975, 15730, 25961, 2423, 39684, 3671], "avg_logprob": -0.12405494684653898, 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and then curved toward بيه باتجاه بيه through the smaller angle باتجاه بيه الزاوية الأصغر", "tokens": [2655, 3615, 28480, 2407, 11296, 16490, 3215, 2655, 2407, 11296, 8978, 2423, 22317, 46811, 10943, 309, 4368, 300, 264, 1451, 7350, 295, 428, 558, 4386, 295, 264, 558, 1011, 366, 10932, 7251, 8592, 13546, 935, 366, 10932, 2051, 257, 3714, 19913, 3555, 2407, 9566, 49429, 5296, 10721, 22807, 11933, 15730, 4724, 29245, 3224, 20328, 21292, 3615, 16247, 25513, 3615, 19446, 16247, 12610, 257, 293, 550, 24991, 37495, 22653, 5296, 5172, 11296, 24991, 293, 550, 24991, 7361, 4724, 1829, 3224, 4724, 9307, 7435, 40294, 4724, 1829, 3224, 807, 264, 4356, 5802, 4724, 9307, 7435, 40294, 4724, 1829, 3224, 6024, 110, 995, 2407, 10632, 16247, 9381, 17082, 2288], "avg_logprob": -0.2302862141176919, "compression_ratio": 1.6171875, "no_speech_prob": 3.635883331298828e-06, "words": [{"start": 417.32, "end": 417.98, "word": "تعرفوها", "probability": 0.9056640625}, {"start": 417.98, "end": 418.76, "word": " خدتوها", "probability": 0.86689453125}, {"start": 418.76, "end": 418.9, "word": " في", "probability": 0.92919921875}, {"start": 418.9, "end": 419.0, "word": " ال", "probability": 0.83349609375}, {"start": 419.0, "end": 419.26, "word": " grammar", "probability": 0.69580078125}, {"start": 419.26, "end": 419.82, "word": " تمام", "probability": 0.776611328125}, {"start": 419.82, "end": 420.5, "word": " it", "probability": 0.27880859375}, {"start": 420.5, "end": 420.94, "word": " states", "probability": 0.90625}, {"start": 420.94, "end": 421.38, "word": " that", "probability": 0.9453125}, {"start": 421.38, "end": 422.04, "word": " the", "probability": 0.77294921875}, {"start": 422.04, "end": 422.6, "word": " four", "probability": 0.84423828125}, {"start": 422.6, "end": 423.4, "word": " fingers", "probability": 0.923828125}, {"start": 423.4, "end": 424.42, "word": " of", "probability": 0.94580078125}, {"start": 424.42, "end": 424.78, "word": " your", "probability": 0.495361328125}, {"start": 424.78, "end": 425.34, "word": " right", "probability": 0.87744140625}, {"start": 425.34, "end": 425.52, "word": " ..", "probability": 0.364013671875}, {"start": 425.52, "end": 425.7, "word": " of", "probability": 0.86572265625}, {"start": 425.7, "end": 425.88, "word": " the", "probability": 0.91259765625}, {"start": 425.88, "end": 426.16, "word": " right", "probability": 0.9189453125}, {"start": 426.16, "end": 426.54, "word": " hand", "probability": 0.91162109375}, {"start": 426.54, "end": 426.98, "word": " are", "probability": 0.943359375}, {"start": 426.98, "end": 427.7, "word": " pointed", "probability": 0.9033203125}, {"start": 427.7, "end": 428.52, "word": " يشير", "probability": 0.89404296875}, {"start": 428.52, "end": 429.04, "word": " point", "probability": 0.72509765625}, {"start": 429.04, "end": 429.82, "word": " are", "probability": 0.763671875}, {"start": 429.82, "end": 430.48, "word": " pointed", "probability": 0.92822265625}, {"start": 430.48, "end": 430.98, "word": " 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{"start": 435.72, "end": 436.18, "word": " then", "probability": 0.91455078125}, {"start": 436.18, "end": 436.82, "word": " curved", "probability": 0.4599609375}, {"start": 436.82, "end": 437.34, "word": " يعني", "probability": 0.966064453125}, {"start": 437.34, "end": 438.14, "word": " لفها", "probability": 0.96533203125}, {"start": 438.14, "end": 439.06, "word": " curved", "probability": 0.9169921875}, {"start": 439.06, "end": 439.78, "word": " and", "probability": 0.8994140625}, {"start": 439.78, "end": 440.1, "word": " then", "probability": 0.89697265625}, {"start": 440.1, "end": 440.68, "word": " curved", "probability": 0.9189453125}, {"start": 440.68, "end": 441.22, "word": " toward", "probability": 0.29638671875}, {"start": 441.22, "end": 441.66, "word": " بيه", "probability": 0.61279296875}, {"start": 441.66, "end": 442.14, "word": " باتجاه", "probability": 0.89697265625}, {"start": 442.14, "end": 442.88, "word": " بيه", "probability": 0.9811197916666666}, {"start": 442.88, "end": 443.2, "word": " through", "probability": 0.83740234375}, {"start": 443.2, "end": 443.46, "word": " the", "probability": 0.89892578125}, {"start": 443.46, "end": 443.78, "word": " smaller", "probability": 0.50634765625}, {"start": 443.78, "end": 444.34, "word": " angle", "probability": 0.87109375}, {"start": 444.34, "end": 444.94, "word": " باتجاه", "probability": 0.8404541015625}, {"start": 444.94, "end": 445.22, "word": " بيه", "probability": 0.9088541666666666}, {"start": 445.22, "end": 446.08, "word": " الزاوية", "probability": 0.81064453125}, {"start": 446.08, "end": 446.52, "word": " الأصغر", "probability": 0.994140625}], "temperature": 1.0}, {"id": 21, "seek": 46194, "start": 447.12, "end": 461.94, "text": "the thumb of الابهام then gives the direction of C حق قادة الهجوم لما أنا سألحت أنا وياكم تمام بس بنترجم العربي using this rule it is clear that", "tokens": [3322, 9298, 295, 2423, 16758, 3224, 10943, 550, 2709, 264, 3513, 295, 383, 11331, 4587, 12174, 18513, 3660, 2423, 3224, 7435, 20498, 5296, 15042, 41850, 8608, 10721, 1211, 33753, 41850, 4032, 25528, 24793, 46811, 10943, 4724, 3794, 4724, 29399, 47341, 2304, 18863, 2288, 21292, 1228, 341, 4978, 309, 307, 1850, 300], "avg_logprob": -0.48407452782759297, "compression_ratio": 1.2987012987012987, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 447.12, "end": 447.36, "word": "the", "probability": 0.12103271484375}, {"start": 447.36, "end": 447.82, "word": " thumb", "probability": 0.332763671875}, {"start": 447.82, "end": 448.18, "word": " of", "probability": 0.263671875}, {"start": 448.18, "end": 449.16, "word": " الابهام", "probability": 0.63446044921875}, {"start": 449.16, "end": 450.6, "word": " then", "probability": 0.352783203125}, {"start": 450.6, "end": 450.98, "word": " gives", "probability": 0.765625}, {"start": 450.98, "end": 451.18, "word": " the", "probability": 0.82958984375}, {"start": 451.18, "end": 451.7, "word": " direction", "probability": 0.96533203125}, {"start": 451.7, "end": 451.98, "word": " of", "probability": 0.97607421875}, {"start": 451.98, "end": 452.28, "word": " C", "probability": 0.619140625}, {"start": 452.28, "end": 453.14, "word": " حق", "probability": 0.50018310546875}, {"start": 453.14, "end": 453.4, "word": " قادة", "probability": 0.635009765625}, {"start": 453.4, "end": 453.68, "word": " الهجوم", "probability": 0.56787109375}, {"start": 453.68, "end": 453.86, "word": " لما", "probability": 0.4637451171875}, {"start": 453.86, "end": 453.98, "word": " أنا", "probability": 0.59814453125}, {"start": 453.98, "end": 454.24, "word": " سألحت", "probability": 0.629302978515625}, {"start": 454.24, "end": 454.4, "word": " أنا", "probability": 0.283447265625}, {"start": 454.4, "end": 454.88, "word": " وياكم", "probability": 0.9039713541666666}, {"start": 454.88, "end": 455.64, "word": " تمام", "probability": 0.814453125}, {"start": 455.64, "end": 455.84, "word": " بس", "probability": 0.85400390625}, {"start": 455.84, "end": 457.0, "word": " بنترجم", "probability": 0.83905029296875}, {"start": 457.0, "end": 457.46, "word": " العربي", "probability": 0.9124348958333334}, {"start": 457.46, "end": 458.78, "word": " using", "probability": 0.89892578125}, {"start": 458.78, "end": 459.24, "word": " this", "probability": 0.9658203125}, {"start": 459.24, "end": 459.76, "word": " rule", "probability": 0.92724609375}, {"start": 459.76, "end": 460.58, "word": " it", "probability": 0.94140625}, {"start": 460.58, "end": 460.76, "word": " is", "probability": 0.96826171875}, {"start": 460.76, "end": 461.3, "word": " clear", "probability": 0.8212890625}, {"start": 461.3, "end": 461.94, "word": " that", "probability": 0.95166015625}], "temperature": 1.0}, {"id": 22, "seek": 48629, "start": 462.71, "end": 486.29, "text": "A X B بيتساوي سالب B X A ولا لأ؟ وعملناها و أثبتناها دي الكلام صحيح طيب جالي حلو جالي by the same rule one can verify يتأكد أو يثبت I X I بتساوي J X J بتساوي K X K بتساوي 0 ليه 0؟", "tokens": [32, 1783, 363, 4724, 1829, 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vector", "probability": 0.98486328125}, {"start": 1652.35, "end": 1653.07, "word": " اللي", "probability": 0.91162109375}, {"start": 1653.07, "end": 1653.47, "word": " سميته", "probability": 0.85693359375}, {"start": 1653.47, "end": 1653.73, "word": " c", "probability": 0.5615234375}, {"start": 1653.73, "end": 1654.57, "word": " بنفع", "probability": 0.7630208333333334}, {"start": 1654.57, "end": 1654.77, "word": " حط", "probability": 0.3896484375}, {"start": 1654.77, "end": 1654.91, "word": " dot", "probability": 0.86279296875}, {"start": 1654.91, "end": 1655.31, "word": " product", "probability": 0.962890625}, {"start": 1655.31, "end": 1655.57, "word": " بين", "probability": 0.8466796875}, {"start": 1655.57, "end": 1655.85, "word": " vector", "probability": 0.9794921875}, {"start": 1655.85, "end": 1655.93, "word": " و", "probability": 0.9951171875}, {"start": 1655.93, "end": 1656.29, "word": " vector", "probability": 0.9755859375}, {"start": 1656.29, "end": 1657.61, "word": " dot", "probability": 0.126953125}, {"start": 1657.61, "end": 1658.07, "word": " product", "probability": 0.970703125}, {"start": 1658.07, "end": 1658.21, "word": " بين", "probability": 0.8857421875}, {"start": 1658.21, "end": 1658.47, "word": " vector", "probability": 0.984375}, {"start": 1658.47, "end": 1658.57, "word": " و", "probability": 0.9931640625}, {"start": 1658.57, "end": 1658.85, "word": " vector", "probability": 0.9794921875}, {"start": 1658.85, "end": 1659.53, "word": " اه", "probability": 0.6397705078125}, {"start": 1659.53, "end": 1660.15, "word": " مش", "probability": 0.71875}, {"start": 1660.15, "end": 1662.23, "word": " scalar", "probability": 0.94287109375}, {"start": 1662.23, "end": 1662.39, "word": " من", "probability": 0.8447265625}, {"start": 1662.39, "end": 1662.65, "word": " جالك", "probability": 0.6859537760416666}, {"start": 1662.65, "end": 1662.85, "word": " تطلع", "probability": 0.843017578125}, {"start": 1662.85, "end": 1663.29, "word": " scalar", "probability": 0.75634765625}, {"start": 1663.29, "end": 1664.83, "word": " ايه", "probability": 0.70166015625}, {"start": 1664.83, "end": 1665.19, "word": " اللي", "probability": 0.851318359375}, {"start": 1665.19, "end": 1665.35, "word": " بين", "probability": 0.97705078125}, {"start": 1665.35, "end": 1665.69, "word": " جثين", "probability": 0.7477213541666666}, {"start": 1665.69, "end": 1665.87, "word": " في", "probability": 0.96533203125}, {"start": 1665.87, "end": 1666.21, "word": " b", "probability": 0.7333984375}, {"start": 1666.21, "end": 1666.83, "word": " اللي", "probability": 0.92138671875}, {"start": 1666.83, "end": 1666.99, "word": " بين", "probability": 0.982421875}, {"start": 1666.99, "end": 1667.49, "word": " جثين", "probability": 0.9874674479166666}, {"start": 1667.49, "end": 1667.95, "word": " scalar", "probability": 0.89013671875}], "temperature": 1.0}, {"id": 69, "seek": 168563, "start": 1669.19, "end": 1685.63, "text": "vector و dot product between two vectors مسموحلي بس الأخير اللي مش مسموحلي لأنه بين جثين طلع scalar ومنفعش اتحط بين scalar و vector cross او dot تمام غيرها", "tokens": [303, 1672, 4032, 5893, 1674, 1296, 732, 18875, 3714, 38251, 2407, 5016, 20292, 4724, 3794, 16247, 9778, 13546, 13672, 1829, 37893, 3714, 38251, 2407, 5016, 20292, 5296, 33456, 3224, 49374, 10874, 12984, 9957, 23032, 1211, 3615, 39684, 4032, 2304, 1863, 5172, 3615, 8592, 1975, 2655, 5016, 9566, 49374, 39684, 4032, 8062, 3278, 1975, 2407, 5893, 46811, 10943, 32771, 13546, 11296], "avg_logprob": -0.3114754059275643, "compression_ratio": 1.4387096774193548, "no_speech_prob": 2.3245811462402344e-06, "words": [{"start": 1669.19, "end": 1669.79, "word": "vector", "probability": 0.439361572265625}, {"start": 1669.79, "end": 1670.69, "word": " و", "probability": 0.5517578125}, {"start": 1670.69, "end": 1670.97, "word": " dot", "probability": 0.2086181640625}, {"start": 1670.97, "end": 1671.63, "word": " product", "probability": 0.64599609375}, {"start": 1671.63, "end": 1672.31, "word": " between", "probability": 0.55712890625}, {"start": 1672.31, "end": 1672.63, "word": " two", "probability": 0.90185546875}, {"start": 1672.63, "end": 1673.19, "word": " vectors", "probability": 0.96435546875}, {"start": 1673.19, "end": 1673.95, "word": " مسموحلي", "probability": 0.686181640625}, {"start": 1673.95, "end": 1674.69, "word": " بس", "probability": 0.846923828125}, {"start": 1674.69, "end": 1675.27, "word": " الأخير", "probability": 0.8499348958333334}, {"start": 1675.27, "end": 1675.39, "word": " اللي", "probability": 0.710693359375}, {"start": 1675.39, "end": 1675.55, "word": " مش", "probability": 0.982421875}, {"start": 1675.55, "end": 1676.21, "word": " مسموحلي", "probability": 0.94169921875}, {"start": 1676.21, "end": 1676.89, "word": " لأنه", "probability": 0.7789713541666666}, {"start": 1676.89, "end": 1677.07, "word": " بين", "probability": 0.87060546875}, {"start": 1677.07, "end": 1677.63, "word": " جثين", "probability": 0.7379557291666666}, {"start": 1677.63, "end": 1678.03, "word": " طلع", "probability": 0.95654296875}, {"start": 1678.03, "end": 1678.61, "word": " scalar", "probability": 0.8720703125}, {"start": 1678.61, "end": 1680.39, "word": " ومنفعش", "probability": 0.8083089192708334}, {"start": 1680.39, "end": 1680.75, "word": " اتحط", "probability": 0.759521484375}, {"start": 1680.75, "end": 1680.91, "word": " بين", "probability": 0.96240234375}, {"start": 1680.91, "end": 1681.37, "word": " scalar", "probability": 0.9130859375}, {"start": 1681.37, "end": 1681.53, "word": " و", "probability": 0.99365234375}, {"start": 1681.53, "end": 1681.85, "word": " vector", "probability": 0.8251953125}, {"start": 1681.85, "end": 1682.35, "word": " cross", "probability": 0.5869140625}, {"start": 1682.35, "end": 1682.63, "word": " او", "probability": 0.726806640625}, {"start": 1682.63, "end": 1683.01, "word": " dot", "probability": 0.9638671875}, {"start": 1683.01, "end": 1685.03, "word": " تمام", "probability": 0.751708984375}, {"start": 1685.03, "end": 1685.63, "word": " غيرها", "probability": 0.857421875}], "temperature": 1.0}, {"id": 70, "seek": 171082, "start": 1689.96, "end": 1710.82, "text": "أف بيتساوي M إيه؟ هيديك Scalar في ال vector Scalar في ال vector حطيت منهم Dot يعني أنتوا عمكم سمعتوا أن قانون الميوتين هيك بيساوي M Dot A أو M Cross A لأ حط M A على طول صحيح لأ تمام خلاص الشرطة", "tokens": [10721, 5172, 4724, 1829, 2655, 3794, 995, 45865, 376, 11933, 1829, 3224, 22807, 39896, 16254, 4117, 2747, 12031, 8978, 2423, 8062, 2747, 12031, 8978, 2423, 8062, 11331, 9566, 36081, 9154, 16095, 38753, 37495, 22653, 14739, 2655, 14407, 6225, 2304, 24793, 8608, 2304, 34268, 14407, 14739, 12174, 7649, 11536, 9673, 1829, 35473, 9957, 39896, 4117, 4724, 1829, 3794, 995, 45865, 376, 38753, 316, 34051, 376, 11623, 316, 5296, 10721, 11331, 9566, 376, 316, 15844, 23032, 12610, 20328, 5016, 1829, 5016, 5296, 10721, 46811, 10943, 16490, 1211, 33546, 25124, 2288, 9566, 3660], "avg_logprob": -0.3588598770099682, "compression_ratio": 1.556701030927835, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 1689.96, "end": 1690.32, "word": "أف", "probability": 0.5609130859375}, {"start": 1690.32, "end": 1690.68, "word": " بيتساوي", "probability": 0.5843912760416666}, {"start": 1690.68, "end": 1690.84, "word": " M", "probability": 0.1824951171875}, {"start": 1690.84, "end": 1691.02, "word": " إيه؟", "probability": 0.678802490234375}, {"start": 1691.02, "end": 1691.2, "word": " هيديك", "probability": 0.4794514973958333}, {"start": 1691.2, "end": 1691.62, "word": " Scalar", "probability": 0.6019287109375}, {"start": 1691.62, "end": 1691.82, "word": " في", "probability": 0.796875}, {"start": 1691.82, "end": 1691.86, "word": " ال", "probability": 0.79736328125}, {"start": 1691.86, "end": 1692.2, "word": " vector", "probability": 0.41552734375}, {"start": 1692.2, "end": 1693.3, "word": " Scalar", "probability": 0.668212890625}, {"start": 1693.3, "end": 1693.48, "word": " في", "probability": 0.93701171875}, {"start": 1693.48, "end": 1693.52, "word": " ال", "probability": 0.958984375}, {"start": 1693.52, "end": 1693.8, "word": " vector", "probability": 0.98583984375}, {"start": 1693.8, "end": 1694.26, "word": " حطيت", "probability": 0.6124674479166666}, {"start": 1694.26, "end": 1694.56, "word": " منهم", "probability": 0.979736328125}, {"start": 1694.56, "end": 1694.88, "word": " Dot", "probability": 0.57568359375}, {"start": 1694.88, "end": 1695.6, "word": " يعني", "probability": 0.81787109375}, {"start": 1695.6, "end": 1695.78, "word": " أنتوا", "probability": 0.6339518229166666}, {"start": 1695.78, "end": 1696.04, "word": " عمكم", "probability": 0.7511393229166666}, {"start": 1696.04, "end": 1696.74, "word": " سمعتوا", "probability": 0.9415283203125}, {"start": 1696.74, "end": 1697.1, "word": " أن", "probability": 0.51513671875}, {"start": 1697.1, "end": 1697.44, "word": " قانون", "probability": 0.95166015625}, {"start": 1697.44, "end": 1697.9, "word": " الميوتين", "probability": 0.7021484375}, {"start": 1697.9, "end": 1698.2, "word": " هيك", "probability": 0.93603515625}, {"start": 1698.2, "end": 1698.6, "word": " بيساوي", "probability": 0.776318359375}, {"start": 1698.6, "end": 1699.2, "word": " M", "probability": 0.8876953125}, {"start": 1699.2, "end": 1699.84, "word": " Dot", "probability": 0.82958984375}, {"start": 1699.84, "end": 1700.3, "word": " A", "probability": 0.56689453125}, {"start": 1700.3, "end": 1701.82, "word": " أو", "probability": 0.7919921875}, {"start": 1701.82, "end": 1702.38, "word": " M", "probability": 0.97119140625}, {"start": 1702.38, "end": 1702.98, "word": " Cross", "probability": 0.40087890625}, {"start": 1702.98, "end": 1703.56, "word": " A", "probability": 0.96533203125}, {"start": 1703.56, "end": 1704.62, "word": " لأ", "probability": 0.6419677734375}, {"start": 1704.62, "end": 1704.98, "word": " حط", "probability": 0.913818359375}, {"start": 1704.98, "end": 1705.18, "word": " M", "probability": 0.85546875}, {"start": 1705.18, "end": 1705.36, "word": " A", "probability": 0.70751953125}, {"start": 1705.36, "end": 1705.5, "word": " على", "probability": 0.92138671875}, {"start": 1705.5, "end": 1706.06, "word": " طول", "probability": 0.892578125}, {"start": 1706.06, "end": 1707.02, "word": " صحيح", "probability": 0.81317138671875}, {"start": 1707.02, "end": 1707.78, "word": " لأ", "probability": 0.90673828125}, {"start": 1707.78, "end": 1709.24, "word": " تمام", "probability": 0.4520263671875}, {"start": 1709.24, "end": 1710.26, "word": " خلاص", "probability": 0.8391927083333334}, {"start": 1710.26, "end": 1710.82, "word": " الشرطة", "probability": 0.9603271484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1711.47325, "duration_after_vad": 1637.0393749999973}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc_raw.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a8d774bff029dbb4d4ed335229772caa41bf528f
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/Np8yvGshxDc_raw.srt
@@ -0,0 +1,1284 @@
+1
+00:00:05,090 --> 00:00:09,660
+تمام انسمى باسم الله و نستكملدومنا اليوم هنا
+
+2
+00:00:09,660 --> 00:00:15,960
+وبالتالي بدنا نعيد ال vector product اللي حاولت
+
+3
+00:00:15,960 --> 00:00:20,640
+اضغط اني اخلصه ومااخدش حقه وبالتالي بدنا نعيد ال
+
+4
+00:00:20,640 --> 00:00:24,180
+vector product of two vectors قولنا في عندي تلت
+
+5
+00:00:24,180 --> 00:00:28,660
+أنواع من الضرب ضرب scalar في vector واتفقنا انه
+
+6
+00:00:28,660 --> 00:00:32,000
+بطلع vector اما مع نفس الاتجاه اذا كان ال scalar
+
+7
+00:00:32,000 --> 00:00:35,520
+positive او عكس الاتجاه اذا كان ال scalar negative
+
+8
+00:00:36,110 --> 00:00:41,150
+بعدين جن في عنا dot product او إيه له اسم تاني
+
+9
+00:00:41,150 --> 00:00:48,310
+scalar product ان لو كان في عندي a dot ال b هذا
+
+10
+00:00:48,310 --> 00:00:53,250
+بيساوي magnitude ال a في magnitude ال b في cosine
+
+11
+00:00:53,250 --> 00:00:57,550
+الزاوية اللي بينهم صح ولا لأ؟ وهذه القاعدة خلتني
+
+12
+00:00:57,550 --> 00:01:02,350
+أقول ان هذا بيطلع ax bx
+
+13
+00:01:03,740 --> 00:01:11,660
+زاد Ay By زاد Az Bz واتفقنا ان لا هنا في I ولا هنا
+
+14
+00:01:11,660 --> 00:01:16,700
+في J ولا هنا في K لأن الناتج Scalar متفاجنا هيك
+
+15
+00:01:16,700 --> 00:01:21,500
+تمام جالي ايش النوع التالت قولت بيكون vector في
+
+16
+00:01:21,500 --> 00:01:27,040
+vector لكن الناتج ايضا vector اذا معناته the
+
+17
+00:01:27,040 --> 00:01:31,620
+vector product اذا اسمه vector product عشان الناتج
+
+18
+00:01:31,620 --> 00:01:37,670
+vectoris between two vectors A and B وتُكتب على
+
+19
+00:01:37,670 --> 00:01:44,070
+إنها A cross الـB is a third vector اللي ديته
+
+20
+00:01:44,070 --> 00:01:48,830
+الرمز C هذا ال vector التالت ماذا ال vector إله
+
+21
+00:01:48,830 --> 00:01:52,330
+magnitude و direction صح ولا لأ قلنا ال magnitude
+
+22
+00:01:52,330 --> 00:01:59,250
+تبعهمجنتيود ال a cross ال b بتسوي مجنتيود ال a في
+
+23
+00:01:59,250 --> 00:02:03,890
+مجنتيود ال b في ال sign الزاوية اللي بينهم طب و ال
+
+24
+00:02:03,890 --> 00:02:07,850
+direction قال لي ال direction الناتج بدي يكون
+
+25
+00:02:07,850 --> 00:02:13,110
+عمودي على التنين عمودي على التنين بمعنى آخر عمودي
+
+26
+00:02:13,110 --> 00:02:18,550
+على مستواهم لأن عندي نظرية بتقول العمودي على مستوى
+
+27
+00:02:18,550 --> 00:02:24,350
+عمودي على كل خطوط جوا المستوى ولا لأ تمامإذن الـ
+
+28
+00:02:24,350 --> 00:02:32,890
+vector C هو عمودي للمستوى
+
+29
+00:02:32,890 --> 00:02:36,130
+A وB لأن هناك 2 درجة لـ M
+
+30
+00:02:44,460 --> 00:02:49,780
+هذا الأولاني في العلوح والتاني في اللوح صح ولا لأ؟
+
+31
+00:02:49,780 --> 00:02:53,840
+إذا التالت اللي بده ييجي ناتج من الـ cross product
+
+32
+00:02:53,840 --> 00:02:57,640
+بديه يكون مستوى عمودي عليهم إيش يعني؟ بديه يكون
+
+33
+00:02:57,640 --> 00:03:03,340
+عمودي على اللوح عمودي على اللوح لا out لا into صح؟
+
+34
+00:03:03,340 --> 00:03:07,840
+لا out لا into اللي انتوا بتقولوها dot و cross تمى
+
+35
+00:03:07,840 --> 00:03:11,540
+قال مين بديه يحدد؟ قال إيه دا كل يمنا اللي هتحدد
+
+36
+00:03:12,140 --> 00:03:16,560
+إيدك اليمنى كيف؟ قال لي إنت إيش بدك؟ قلتلي بدي E
+
+37
+00:03:16,560 --> 00:03:22,120
+cross ال B قاللي في هذه الحالة حط أصابعك الأربعة
+
+38
+00:03:22,120 --> 00:03:28,180
+مع A ولف باتجاه B وشوف إبهامك وإن بوديك قاللي Out
+
+39
+00:03:28,180 --> 00:03:37,940
+إذاً هذا Kout z direction لكن لو بدك بي cross ال a
+
+40
+00:03:37,940 --> 00:03:43,120
+بقول أصابع الأربعة مع بي لف وين بها مكان إذا هدل
+
+41
+00:03:43,120 --> 00:03:47,240
+الداخل إذا a cross ال b لاتساوي بي cross ال a
+
+42
+00:03:47,240 --> 00:03:52,270
+بيساوي العكس تبعها مظبوط ولا لأ؟ حلوده النهاد اللي
+
+43
+00:03:52,270 --> 00:03:58,070
+بتخليني اقول التالي I و J و K سمعنا فيهم؟ و
+
+44
+00:03:58,070 --> 00:04:02,470
+مربوطين جوا مخنا ان ال I مع السين و ال J مع الصعد
+
+45
+00:04:02,470 --> 00:04:06,830
+و ال K مع العين؟ مظبوط ولا لأ؟ جالي إذا لو قولتلك
+
+46
+00:04:06,830 --> 00:04:13,550
+I كرس الجي تصورهم و اعمل قاعدة يدي اليمنى؟ انتوا
+
+47
+00:04:13,550 --> 00:04:22,180
+شايفين؟ هي X هي I و هي J مش هيك؟ إذا هتطلع Kهتطلع
+
+48
+00:04:22,180 --> 00:04:24,880
+K صحيح اذا هذه هتطلع K
+
+49
+00:04:27,910 --> 00:04:34,370
+جالي طيب لو قلتلك J X K لأن دي بالكم هذه هي كال K
+
+50
+00:04:34,370 --> 00:04:41,770
+Out صح؟ لو إجيت انت بدك تعمل J X K بقاعدة اليدي
+
+51
+00:04:41,770 --> 00:04:47,910
+اليمنى هتطلع I موجبة، مظبوط او لأ؟ هتطلع I موجبة،
+
+52
+00:04:47,910 --> 00:04:57,730
+اذا J X K هتطلع I، طيب شوفليكي كروس الـ I جلي
+
+53
+00:04:57,730 --> 00:05:04,270
+هتطلع معاك J إذا كي كروس ال I هتطلع J اعكس أي
+
+54
+00:05:04,270 --> 00:05:09,790
+تنتين بصي سالب مظبوط ولا لأ تم انا طبعا بدي أحفظهم
+
+55
+00:05:09,790 --> 00:05:15,210
+هدول جلي بسهل عليك حفظهم كيف تسهل علي حفظهم جلي
+
+56
+00:05:15,210 --> 00:05:22,370
+حطلي هدول التلاتة I J K على رأس مثلثهذه طريقة عشان
+
+57
+00:05:22,370 --> 00:05:28,950
+تسهيل الحفظ تمام او تسهيل التعامل معاهمجالي إذا
+
+58
+00:05:28,950 --> 00:05:33,750
+ضربت تنتين هتطلع التالتة قطعا صح ولا لأ؟ لأن
+
+59
+00:05:33,750 --> 00:05:37,530
+الناتج بيكون عمودي على التنتين إيش العمودي على
+
+60
+00:05:37,530 --> 00:05:41,970
+الصين والصاد؟ عين إيش العمودي على الصد والعين؟ صين
+
+61
+00:05:41,970 --> 00:05:46,710
+مظبط ولا لأ؟ إذا محفظين، معرفين جالي إذا لما تضرب
+
+62
+00:05:46,710 --> 00:05:50,530
+تنتين تطلع التالتة، بضل عليك، موجب ولا سالب؟ جالي
+
+63
+00:05:50,530 --> 00:05:55,740
+بدي أفهمك هالقاعدةها قاعدة عادية اذا انت بتضن قاعد
+
+64
+00:05:55,740 --> 00:06:01,880
+I X G مع قرب الساعة بتطلع التالتة موجبة I X G K طب
+
+65
+00:06:01,880 --> 00:06:08,000
+J X I ثالث K J X K J X K مش هيد مع قرب الساعة
+
+66
+00:06:08,000 --> 00:06:15,100
+بتطلع التالتة موجبة K X I طلعت التالتة تمام و
+
+67
+00:06:15,100 --> 00:06:21,080
+المعكوس بتحط ثالث سهلة هلجتاللي خمتوني على انه
+
+68
+00:06:21,080 --> 00:06:25,060
+احنا بنعرف انه اقرب الساعة موجب هديك تجربش لهدي
+
+69
+00:06:25,060 --> 00:06:29,380
+هدي مجلة قاعد عشان نعرف كيف نطبق قاعدة اليدي
+
+70
+00:06:29,380 --> 00:06:38,760
+اليمنى تمام؟ ايه الصفصار؟ تمإذاً the rule هذه
+
+71
+00:06:38,760 --> 00:06:41,820
+قاعدة يد اليمن اللي توشرحناها إنه حط أصابعك
+
+72
+00:06:41,820 --> 00:06:46,100
+الأربعة مع الأول لف بالاتجاه التاني إبهامك بالدي
+
+73
+00:06:46,100 --> 00:06:49,340
+التالت إذاً the rule states that .. states that يا
+
+74
+00:06:49,340 --> 00:06:53,920
+نص على ما .. ما هي هذه states that تمام؟ the rule
+
+75
+00:06:53,920 --> 00:06:58,760
+و هذه ال S عشان هذه ال rule singleتعرفوها خدتوها
+
+76
+00:06:58,760 --> 00:07:03,400
+في ال grammar تمام it states that the four fingers
+
+77
+00:07:03,400 --> 00:07:07,700
+of your right .. of the right hand are pointed
+
+78
+00:07:07,700 --> 00:07:12,880
+يشير point are pointed along a مظبوط ولا لأ؟ إذا
+
+79
+00:07:12,880 --> 00:07:17,340
+بوجه صبيع الأربع ما الأول a and then curved يعني
+
+80
+00:07:17,340 --> 00:07:22,880
+لفها curved and then curved toward بيه باتجاه بيه
+
+81
+00:07:22,880 --> 00:07:26,080
+through the smaller angle باتجاه بيه الزاوية
+
+82
+00:07:26,080 --> 00:07:31,180
+الأصغرthe thumb of الابهام then gives the
+
+83
+00:07:31,180 --> 00:07:34,400
+direction of C حق قادة الهجوم لما أنا سألحت أنا
+
+84
+00:07:34,400 --> 00:07:40,760
+وياكم تمام بس بنترجم العربي using this rule it is
+
+85
+00:07:40,760 --> 00:07:46,210
+clear thatA X B بيتساوي سالب B X A ولا لأ؟
+
+86
+00:07:46,210 --> 00:07:51,410
+وعملناها و أثبتناها دي الكلام صحيح طيب جالي حلو
+
+87
+00:07:51,410 --> 00:07:59,230
+جالي by the same rule one can verify يتأكد أو يثبت
+
+88
+00:07:59,230 --> 00:08:07,790
+I X I بتساوي J X J بتساوي K X K بتساوي 0 ليه 0؟لأن
+
+89
+00:08:07,790 --> 00:08:11,830
+صين الصفر صفر لأن الـ cross بيقول لـ magnitude
+
+90
+00:08:11,830 --> 00:08:15,670
+الأول في magnitude التاني في الصين الزاوية اللي
+
+91
+00:08:15,670 --> 00:08:19,370
+بينهم وما زال ال vectors نفسهم إذا زاوية دي إيش؟
+
+92
+00:08:19,370 --> 00:08:26,070
+Zero إذا خلصنا قاللي قاعدة اليد اليمنى أو القاعدة
+
+93
+00:08:26,070 --> 00:08:34,020
+هذه بتقول التاليهذه هي I cross الـ J اعطت K J
+
+94
+00:08:34,020 --> 00:08:44,720
+cross الـ K اعطت I K cross الـ I اعطت J صح تمام مش
+
+95
+00:08:44,720 --> 00:08:52,160
+عاجبك اشي عندك سؤال انا انا انا انا انا انا انا
+
+96
+00:08:52,160 --> 00:08:53,260
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+97
+00:08:53,260 --> 00:08:53,260
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+98
+00:08:53,260 --> 00:08:53,260
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+99
+00:08:53,260 --> 00:08:53,340
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+100
+00:08:53,340 --> 00:08:53,920
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+101
+00:08:53,920 --> 00:08:53,920
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+102
+00:08:53,920 --> 00:08:58,940
+انا انا انا انا انا انا انا
+
+103
+00:08:58,940 --> 00:09:01,640
+انايعني هل إله علاقة بالتعامد ولا ما إله علاقة
+
+104
+00:09:01,640 --> 00:09:05,880
+بالتعامد؟ إله علاقة بالتعامد لأنه لما تضرب تنتين
+
+105
+00:09:05,880 --> 00:09:09,340
+كل الصبودات، بده يطلع التالت متعمد على التنتين،
+
+106
+00:09:09,340 --> 00:09:16,770
+لازم، وبما إن ال Z عمودي على ال X وY بصحله ياخدأيه
+
+107
+00:09:16,770 --> 00:09:19,790
+بس قاعدة اليد اليمنى ليه إيش جاية؟ قاعدة اليد
+
+108
+00:09:19,790 --> 00:09:23,350
+اليمنى بتقولك انت بتقوللي عمودي طب عمودي لفوق ولا
+
+109
+00:09:23,350 --> 00:09:27,450
+لتحت؟ يعني هي عمودي على الطاولة هجتهد عمودي على
+
+110
+00:09:27,450 --> 00:09:30,850
+الطاولة ولا لأ؟ طب لو كان لتحت برضه عمودي على
+
+111
+00:09:30,850 --> 00:09:34,490
+الطاولة إذا أنا بدي أحدد واحد منهم جلي اليد اليمنى
+
+112
+00:09:34,490 --> 00:09:40,950
+اتفقنا هي اللي اتحدد فمت عليا كيف؟ بس تمامجاله حلو
+
+113
+00:09:40,950 --> 00:09:45,290
+اذا انت امنت يلّا يا بنات بدنا نضرب احنا وياكم
+
+114
+00:09:45,290 --> 00:09:51,470
+cross product ال A مش مكتبه يلو تلت مركبات و ال B
+
+115
+00:09:51,470 --> 00:09:55,270
+تلت مركبات هي الصيغة العامة تحت اي vector اضرب
+
+116
+00:09:55,270 --> 00:09:59,830
+vector جوس في جوس في حد ماعرفش اضرب جوس في جوس مش
+
+117
+00:09:59,830 --> 00:10:04,030
+بنجيب هدا و بنضرب في هدول كلهم و بنجيب هدا و بنضرب
+
+118
+00:10:04,030 --> 00:10:07,610
+في كل هدول و هكذا جالي اشتغل قولتله هاي اشتغلت
+
+119
+00:10:10,130 --> 00:10:13,270
+طلعوا عليهم ضرب الجثر العادي اللي أخدته في المدرسة
+
+120
+00:10:13,270 --> 00:10:21,370
+تمام استنوا شويه هلجيت وين في I X I أو J X J أو K
+
+121
+00:10:21,370 --> 00:10:28,410
+X K إيش بتحط محله؟ قال لي ها مظبوط هيك ولا لأ؟
+
+122
+00:10:28,410 --> 00:10:32,770
+هدول زيروا راحوا قال لي إيش هتضل؟ قال لي اول term
+
+123
+00:10:32,770 --> 00:10:41,540
+هنا I X J تعال I X J إيش بطلع؟ KK مش واحد لأنه هذا
+
+124
+00:10:41,540 --> 00:10:46,720
+cross product بديه يطلع vector واحد رقم بديه يطلع
+
+125
+00:10:46,720 --> 00:10:51,280
+vector اذا هذا بقى هتحطلي محله انا اه انا انا انا
+
+126
+00:10:51,280 --> 00:10:51,660
+انا انا انا انا انا انا انا انا انا انا انا
+
+127
+00:10:54,800 --> 00:11:02,160
+طيب I cross ال K سالب J ها I cross ال K مشيت ضد
+
+128
+00:11:02,160 --> 00:11:08,200
+عقارب الساعة اذا سالب J حطينا سالب J تمام يا بنات
+
+129
+00:11:08,200 --> 00:11:18,340
+تمام نجهان J cross ال I سالب Kهناك مهمش انه جي
+
+130
+00:11:18,340 --> 00:11:22,880
+سالب كي طلعوا هذا سالب كي وهذا كي ممكن اخد الكي
+
+131
+00:11:22,880 --> 00:11:25,360
+عالم المشترك ولا لأ انا دي بدي اخد الكي عالم
+
+132
+00:11:25,360 --> 00:11:31,020
+المشترك حلو ده اللي ها دي جي cross ال كي جي cross
+
+133
+00:11:31,020 --> 00:11:37,160
+ال اي موجب اذا اي بالموجب حلو نجي لهذا ده اللي كي
+
+134
+00:11:37,160 --> 00:11:41,900
+cross ال اي جي هى صار عندى جي و هنا سالب جي جي مع
+
+135
+00:11:41,900 --> 00:11:45,810
+جي باخد عالم المشتركتمام قال لي دل عندك أخي يا
+
+136
+00:11:45,810 --> 00:11:50,450
+قلتله هذا سلب I طيب جمع حط ال I ل I لحال و ال J مع
+
+137
+00:11:50,450 --> 00:11:55,910
+ال J لحال و ال K مع ال K لحال جمعنا طلعت هذا الرقم
+
+138
+00:11:55,910 --> 00:12:03,260
+ده مطول طويل صحوإحنا هذا حلو وقدرنا عليه نحفظه
+
+139
+00:12:03,260 --> 00:12:05,820
+وقلنا الصيني مع الصيني الصاضي مع الصاضي و العيني
+
+140
+00:12:05,820 --> 00:12:09,280
+مع العيني سهل نتعامل معاه وده إيش اللي خليني
+
+141
+00:12:09,280 --> 00:12:13,980
+أحفظه؟ قعدت أنا بدي أعمل ليه logarithm عشان أعرف
+
+142
+00:12:13,980 --> 00:12:17,220
+أحفظه؟ ولا أعمللي برنامج حسوب عشان أحفظنيه؟ صعب
+
+143
+00:12:17,220 --> 00:12:21,960
+الأمور وهم بتطلعوا هيك قالوا إيه؟ هدف مش بحاجة
+
+144
+00:12:21,960 --> 00:12:27,660
+أخدناها في المدرسة الشيية قالها دي لو كتبتلك هيك
+
+145
+00:12:31,800 --> 00:12:37,840
+محدد قالوا والله اه يالا نجرب براو عليكم انتو
+
+146
+00:12:37,840 --> 00:12:41,940
+طمنتوني كلكم قلتوا ايه؟ أخدناها واللي فهمت أخدناها
+
+147
+00:12:41,940 --> 00:12:46,900
+في توجيهي يعني طازة لسه ايه معناها مالحجناش ننساها
+
+148
+00:12:46,900 --> 00:12:53,140
+كيف كنا نعمل يا بنات معناه مع الأسف هذه هطيل شاشة
+
+149
+00:12:53,140 --> 00:12:56,820
+ومش جادرين نكتب في الشاشة فبنانا الطر نكتب هنا
+
+150
+00:12:56,820 --> 00:13:06,200
+نقول هاي ايه؟عشان نذكر بعض اول صف بحط IJK اللي
+
+151
+00:13:06,200 --> 00:13:13,940
+بتعرفوه تاني صف مركبات الـA مركبات تحت I ثيني وتحت
+
+152
+00:13:13,940 --> 00:13:21,700
+J صادم وهذه Z نيجد تاني بيه بقول BX BY BZ مش هيك
+
+153
+00:13:21,700 --> 00:13:27,460
+مظلومات وكنت بتقوله plus negative plusبنذكر بعض
+
+154
+00:13:27,460 --> 00:13:34,140
+جادين بقول بالساوي جوس I زائد جوس ناقص او ناقص
+
+155
+00:13:34,140 --> 00:13:39,800
+ملاحظة ناقص مهمش برضه J زائد جوس K مش هيكلنا نعمل
+
+156
+00:13:39,800 --> 00:13:49,170
+عشان اجيب هادي ايش هسويسكر صف عمود يلّا نسكر سكرنا
+
+157
+00:13:49,170 --> 00:13:58,510
+هذه و سكرنا هذه Ay Bz ناقص Az By اطلعولي ال I اللي
+
+158
+00:13:58,510 --> 00:14:04,290
+جلبتها أنا نفسها ولا لأ؟ والله نفسها نجي للـ J
+
+159
+00:14:04,290 --> 00:14:10,530
+أسكر هذه و أسكر هذه Ax Bz
+
+160
+00:14:15,190 --> 00:14:19,430
+axbz-azbx شوفوا ايش اللي افرجت انا حاطط هنا زائد و
+
+161
+00:14:19,430 --> 00:14:28,090
+جالب نفسها صح ولا لأ زائد سكر هذه و سكر هذه axbz
+
+162
+00:14:28,090 --> 00:14:37,870
+axby axby-aybx هو هذه سهلة اتحفظش هذه احفظ هذه و
+
+163
+00:14:37,870 --> 00:14:39,950
+خلصنا مظبوطة للا
+
+164
+00:14:46,010 --> 00:14:53,730
+حلو نشوف في شي مش مفهوم تمام ال cross product اسمه
+
+165
+00:14:53,730 --> 00:14:57,070
+vector product صح عرفنا ليه يسمو cross عشان ال
+
+166
+00:14:57,070 --> 00:15:00,730
+cross و لسه منها vector product عشان النتيج vector
+
+167
+00:15:00,730 --> 00:15:04,550
+ايش بجربل التنين عمودي عليهم التنين عمودي عليهم
+
+168
+00:15:04,550 --> 00:15:09,670
+التنين عمودي ع مستواهم صح ولا لأ تمام نيجي نحل
+
+169
+00:15:09,670 --> 00:15:17,320
+هالسؤال قلي شوفهيتوا vectors هدول الأول مراكبة
+
+170
+00:15:17,320 --> 00:15:21,340
+ثينية و إله مراكبة صادية صح والتاني إله مراكبة
+
+171
+00:15:21,340 --> 00:15:25,560
+ثينية و صادية مالوش ولا واحدة منهم إله مراكبة زدية
+
+172
+00:15:25,560 --> 00:15:32,020
+يعني التنين وجعين في اللوح ثين و صاد طيب نعمل
+
+173
+00:15:32,020 --> 00:15:35,570
+cross product لازم يكون عمودي على اللوحاذا لازم
+
+174
+00:15:35,570 --> 00:15:42,590
+يكون رقمه K تجاهه صح ولا لأ؟ يلّا نجرب قال لي كيف؟
+
+175
+00:15:42,590 --> 00:15:50,170
+قال لي هي ايه cross ال B؟ اعطتني
+
+176
+00:15:50,170 --> 00:15:57,150
+ايه ولا ماعطتنيش؟ يلّا ننقل Zero اتنين تلاتة Zero
+
+177
+00:15:57,150 --> 00:16:07,310
+ناقص واحد اتنين Zeroتمام؟ معطية السؤال جلبت ساوي I
+
+178
+00:16:07,310 --> 00:16:14,170
+Gos I ذات Gos J ذات Gos K مش هيك بنعمل؟ او ناقص
+
+179
+00:16:14,170 --> 00:16:16,850
+انتوا هنا بتعملوا بهمش قدما يشوفوا قبل ما عرفت
+
+180
+00:16:16,850 --> 00:16:20,350
+الناس ماعرفت أن ال I كتر من جاي سفر اتسنى شوية
+
+181
+00:16:20,350 --> 00:16:26,870
+هجيتي يلا ساكرولي ال I تلاتة في سفر ناقص سفر في
+
+182
+00:16:26,870 --> 00:16:33,630
+اتنى اذا اول واحدة روحتي الله يعطيها العافيةشوف
+
+183
+00:16:33,630 --> 00:16:43,290
+الـ J فاكره اتنين في سفر ناقص سفر في ناقص واحد روح
+
+184
+00:16:43,290 --> 00:16:48,690
+ايش ده اللي مركبة مدلسي ال K كنت متوقعها انا قالي
+
+185
+00:16:48,690 --> 00:16:55,350
+سكر ال K اتنين في اتنين ناقص ناقص اذا سبعة K اذا
+
+186
+00:16:55,350 --> 00:16:56,850
+الجواب سبعة K
+
+187
+00:17:01,440 --> 00:17:05,220
+هجيت هذا السبعة K عمودي على هذا و لا مش عمودي و
+
+188
+00:17:05,220 --> 00:17:09,320
+الله عمودي و عمودي على هذا و لا لأ عمودي لو جبت
+
+189
+00:17:09,320 --> 00:17:15,120
+اعملت dot product بين هذا C و A لازم يطلع Zero
+
+190
+00:17:15,120 --> 00:17:22,560
+افترضوا هذا C مش C هذا هجيت C هذا عمودي على A و لا
+
+191
+00:17:22,560 --> 00:17:28,880
+مش عمودي اذا بيعني ان C dot ال A ايه يجب ان يكون
+
+192
+00:17:30,520 --> 00:17:33,840
+يالا اعملوا dot product ايش في ال dot product
+
+193
+00:17:33,840 --> 00:17:37,440
+بيسوي؟ الصيني مع الصيني والصاضي مع الصاضي والعيني
+
+194
+00:17:37,440 --> 00:17:42,200
+مع العيني الصيني هناك اتنين والصيني ليه ال C؟ سفر
+
+195
+00:17:42,200 --> 00:17:47,960
+فيه اللي صيني هذا؟ اللي صاضي؟ اذا التلاتة فيه سفر،
+
+196
+00:17:47,960 --> 00:17:51,620
+هذا الكلش عنده K و الله سفر، اذا هذا بيضمن ان هو
+
+197
+00:17:51,620 --> 00:17:55,780
+عمودي، طب ادربولي C dot ال B
+
+198
+00:17:58,680 --> 00:18:02,880
+لأنه عمودي على التنين ولا لأ؟ سفر في المطلوب
+
+199
+00:18:02,880 --> 00:18:08,260
+التاني بيقول طب اثبتلي ان a cross ال b بتسوي سالب
+
+200
+00:18:08,260 --> 00:18:15,540
+b cross ال a قلتله لو بدك انت الآن بي cross ال a
+
+201
+00:18:15,540 --> 00:18:20,050
+ايش يسوي؟ قلتله جلبابدأ في الـB، ايش الـB؟ قال
+
+202
+00:18:20,050 --> 00:18:25,210
+يناقص واحد، اتنين، سفر، اتنين، تلاتة، سفر، مش
+
+203
+00:18:25,210 --> 00:18:28,350
+هيكبني اعمال؟ نيجي يشوف المراكبة الصينية، قلتله
+
+204
+00:18:28,350 --> 00:18:37,370
+كملي السفرصح؟ الصديّة الـ Z ماقس تلاتة ماقس أربعة
+
+205
+00:18:37,370 --> 00:18:42,890
+ماقس سبعة اذا انطلعت صحيحة ان A cross الـB بتسوي
+
+206
+00:18:42,890 --> 00:18:45,550
+سالب B cross الـA اذا بيقولي find the cross
+
+207
+00:18:45,550 --> 00:18:48,730
+product between two vectors طلعناها سبعة كده
+
+208
+00:18:48,730 --> 00:18:54,130
+وبجلوا بعدين بيقولي verify that اثبت او تحقق من ان
+
+209
+00:18:54,130 --> 00:18:58,930
+A cross الـB قطعا بتسوي سالب B cross الـA تمام يا
+
+210
+00:18:58,930 --> 00:18:59,490
+بنات؟
+
+211
+00:19:02,000 --> 00:19:06,400
+في حد بسأل؟ بدي أرجع لشغل معين قبل ما أخش على ال
+
+212
+00:19:06,400 --> 00:19:10,860
+quiz لخير لما جبنا ال vector و أعرفنا ال vector في
+
+213
+00:19:10,860 --> 00:19:15,400
+أول الشبطة قلنا فيه أنثي على ال vectors قلنا
+
+214
+00:19:15,400 --> 00:19:19,900
+displacement و ال velocity و ال acceleration و ال
+
+215
+00:19:19,900 --> 00:19:24,340
+force و المساحة تمام؟ و في منكم ماعجبهمش أن
+
+216
+00:19:24,340 --> 00:19:29,160
+المساحة تكون vector مظبوط ولا لأ؟ ماعجبناش قلنا
+
+217
+00:19:29,160 --> 00:19:35,070
+تعالى نشوفبتعرفوا لو أرسم متوازي الأضلاع؟ شوفتهوا
+
+218
+00:19:35,070 --> 00:19:40,110
+قبل كده، بدنا نرسم متوازي الأضلاع، هاي متوازي
+
+219
+00:19:40,110 --> 00:19:46,130
+أضلاع تمام، هذا الضلع بدي أسميه vector A و هذا
+
+220
+00:19:46,130 --> 00:19:51,530
+الضلع بدي أسميه vector B تمام هيك يا بنات؟ حلو،
+
+221
+00:19:51,530 --> 00:19:56,310
+يلا ذكروني عاد، مساحة متوازي الأضلاع
+
+222
+00:20:03,340 --> 00:20:08,800
+أه يعني بقى واحد وان نصشوف يا بنات بنحن نحفظ حاجة
+
+223
+00:20:08,800 --> 00:20:15,040
+معينة شوفوا بننأسس لحاجة شوفوا قدرتنا احنا على
+
+224
+00:20:15,040 --> 00:20:20,580
+الحفظ محدودة وبالتالي اتغلبناش عشان نحفظ كيف يعني
+
+225
+00:20:20,580 --> 00:20:25,780
+ما تعملوناش متقانون كل الأشكال المربعة مربع ولا
+
+226
+00:20:25,780 --> 00:20:30,480
+مستطيل ولا متوازي أطلع ولا لبنديكية ولا شبه منحرف
+
+227
+00:20:30,480 --> 00:20:35,920
+القاعدة في الارتفاع بس قاعدة في الارتفاع كل
+
+228
+00:20:35,920 --> 00:20:40,550
+الأشكال المربعةقاعدة في الارتفاع هجت المثلث مش
+
+229
+00:20:40,550 --> 00:20:45,070
+رباعي نص رباعي عشان تيجي يجي من النص المثلث نص
+
+230
+00:20:45,070 --> 00:20:48,310
+قاعدة في الارتفاع لكن متوازن الأضلاع قاعدة في
+
+231
+00:20:48,310 --> 00:20:52,090
+الارتفاع المستطيل قاعدة في الارتفاع المربع قاعدة
+
+232
+00:20:52,090 --> 00:20:56,510
+في الارتفاع شبه الملحرف قاعدة في الارتفاع وتيجي
+
+233
+00:20:56,510 --> 00:20:59,270
+الارتفاع طول في عرض ما هو العرض في المستطيل هو
+
+234
+00:20:59,270 --> 00:21:04,950
+الارتفاعهو الارتفاع المربع بصموني اتضلع تربية ما
+
+235
+00:21:04,950 --> 00:21:08,210
+هو ليش اتضلع تربية لأن اتضلع هو القاعدة اتضلع
+
+236
+00:21:08,210 --> 00:21:12,350
+ارتفاع مصطلح اللي اذا مافيش عندي قانون للمساحة
+
+237
+00:21:12,350 --> 00:21:17,930
+للاشكال الربعية لواحد قاعدة في ارتفاع بس طب وين
+
+238
+00:21:17,930 --> 00:21:21,630
+ارتفاع بيه ارتفاع كيف كنتوا تجيبوا الارتفاع ايه
+
+239
+00:21:21,630 --> 00:21:28,250
+براو علينا هذا ارتفاع صح مش هيكنا نعمله جيلي حلو
+
+240
+00:21:28,250 --> 00:21:30,030
+جيلي هب هذي زاوية
+
+241
+00:21:33,480 --> 00:21:37,120
+تمام؟ صين الزاوية اللى انتوا شايفينها بتساوي مقابل
+
+242
+00:21:37,120 --> 00:21:42,980
+على وطر حلو مقابل على وطر ماشيك تعرفها بقوله صين
+
+243
+00:21:42,980 --> 00:21:51,380
+الثيتا بتساوي H على بي ك magnitude اذا H بتساوي بي
+
+244
+00:21:51,380 --> 00:21:58,000
+في صين الثيتا هجيجي نرجع لل area area قاعدة في
+
+245
+00:21:58,000 --> 00:22:04,930
+ارتفاعصح؟ القاعدة ايش؟ A إذا ال magnitude ال E في
+
+246
+00:22:04,930 --> 00:22:11,370
+H هي H في B Sine of Theta بنيمله هذه A cross ال B
+
+247
+00:22:11,370 --> 00:22:15,770
+صح؟
+
+248
+00:22:15,770 --> 00:22:19,950
+طب هذه A cross ال B النتيجة إيش لازم يكون؟ is an
+
+249
+00:22:19,950 --> 00:22:25,390
+area vectorالـ Area vector كيف اتجاهها؟ قال عمودي
+
+250
+00:22:25,390 --> 00:22:30,370
+على السطح لأن A وB بتشكل ال plane يعني هي الطاولة
+
+251
+00:22:30,370 --> 00:22:37,090
+هي A و هي B مساحتها vector كيف اتجاهها؟ بقول عمودي
+
+252
+00:22:37,090 --> 00:22:40,470
+على الطاولة لازم تكون عمودي على الطاولة عشان تكون
+
+253
+00:22:40,470 --> 00:22:44,530
+عمودي على مستوى ال two vectors تمام؟ هذا أظن أحد
+
+254
+00:22:44,530 --> 00:22:49,490
+أسلوب الكتاب أنك تثبت أن الـ Area بتسوي A cross ال
+
+255
+00:22:49,490 --> 00:22:57,890
+Bهنا أثبتنا تمام؟ أيه الصفصار؟ عيد و إيش عيد فيه؟
+
+256
+00:22:57,890 --> 00:23:03,650
+ما هو مش أنت هجد عيد عيد مفهوم مساحة متوازن أطلعة
+
+257
+00:23:03,650 --> 00:23:08,510
+بالساعة القاعدة في الارتفاع، بتحرفيها؟ أه؟ واو
+
+258
+00:23:08,510 --> 00:23:12,610
+تخجليشبتعرف ان مساحة متوازي الأضلاع بسوء قاعدة في
+
+259
+00:23:12,610 --> 00:23:17,290
+ارتفاع؟ حلو هذا متوازي الأضلاع ولا لا يا بنتي؟ هذا
+
+260
+00:23:17,290 --> 00:23:21,070
+ارتفاع ولا مش ارتفاع؟ بقدر اجيبه بدلالة هذه على
+
+261
+00:23:21,070 --> 00:23:24,630
+اعتبار ان صين الزاوية بتسوي H على B ولا لا؟ اذا
+
+262
+00:23:24,630 --> 00:23:29,230
+قولت H اللي انت بتدور عليه الارتفاع بتسوي B في صين
+
+263
+00:23:29,230 --> 00:23:33,950
+الزاوية ضرب ضرب تبادلي قولت يلا تروح لصف سادس ولا
+
+264
+00:23:33,950 --> 00:23:39,670
+خامس ان مساحة متوازي الأضلاع بتسوء قاعدة Aفي
+
+265
+00:23:39,670 --> 00:23:45,710
+الارتفاع H وH هنا عوضت عنه قلتله أول ما قلتلي A في
+
+266
+00:23:45,710 --> 00:23:49,170
+B في صيني الزاوية تا و لسه أعرفتها ده cross
+
+267
+00:23:49,170 --> 00:23:53,850
+product cross product يعني انها vector product اذا
+
+268
+00:23:53,850 --> 00:23:58,850
+الناتج قطعا vector اذا ال area is a vector كف تجاه
+
+269
+00:23:58,850 --> 00:24:03,450
+عمودي على التنتين اذا عمودي على المساحة عمودي على
+
+270
+00:24:03,450 --> 00:24:06,670
+السطح تمام يا بنتي؟ غيرها
+
+271
+00:24:09,970 --> 00:24:15,970
+هذا خلّصنا منه شوفوا
+
+272
+00:24:15,970 --> 00:24:22,850
+هالشغلات طلّعوا هدول أربع علاقات بيقولّي مين منهم
+
+273
+00:24:22,850 --> 00:24:28,470
+دائما Zero بدا نبدأ بالأخيرة يا بنات الأخيرة
+
+274
+00:24:28,470 --> 00:24:34,110
+طلّعولي اللي بين الجثين إيش بينهم Dot إيش بيطلّع
+
+275
+00:24:34,110 --> 00:24:39,100
+هل ال cross مسموح يكون بين scalar و vectorأذا
+
+276
+00:24:39,100 --> 00:24:41,220
+مايقوللي هذا اللي كاتب ومايعرفش إيش معناه vectors
+
+277
+00:24:41,220 --> 00:24:46,520
+إذا هذه فالتك منها هذه ولا كأنها خيار عندي لأنه
+
+278
+00:24:46,520 --> 00:24:53,060
+كتابة غلط أصلا إذا الخيار الأخر مرفوض لإن انت عامل
+
+279
+00:24:53,060 --> 00:24:57,960
+حاجة مبدئية قطأ هتطلق cross product بين scalar و
+
+280
+00:24:57,960 --> 00:25:00,960
+vector وهذا ممنوع لأن قلتلي ال vector و product
+
+281
+00:25:00,960 --> 00:25:04,220
+between two vectors زي ال scalar product between
+
+282
+00:25:04,220 --> 00:25:09,090
+two vectorsتمى قال لطيب يشوف هذه قال لي أنت إيش
+
+283
+00:25:09,090 --> 00:25:12,610
+بتقولي هذا الجوس أمودي على الـA ولا مش عمودي على
+
+284
+00:25:12,610 --> 00:25:18,390
+الـA؟ عمودي على الـA يعني هذا الأصل A يكون .. بدي
+
+285
+00:25:18,390 --> 00:25:22,830
+أفترض الجوس C يا بنات افترضوا الـC تمى .. هذه
+
+286
+00:25:22,830 --> 00:25:27,170
+المفروض يكون magnitude الـC في magnitude الـA في
+
+287
+00:25:27,170 --> 00:25:33,920
+sign التسعين صح؟ وهذه واحدإذاً magnitude of C في
+
+288
+00:25:33,920 --> 00:25:37,360
+magnitude of A طب أنت بتقولي magnitude of C سفر
+
+289
+00:25:37,360 --> 00:25:41,420
+وديتني معلومة أو magnitude of A سفر إذاً هذه مش
+
+290
+00:25:41,420 --> 00:25:48,780
+بالضرورة تكون سفر ولا سفر لأ انشوف C .. C جالي
+
+291
+00:25:48,780 --> 00:25:53,940
+برضه C عمودي على ال B لأنه عمودي على التنتين إذاً
+
+292
+00:25:53,940 --> 00:26:01,120
+هذه C في B في sign ال 90 اللي هي 1إذاً برضه سفر
+
+293
+00:26:01,120 --> 00:26:10,720
+دايما؟ لأ قال لي نشوف بي قال لي C في بي في cosine
+
+294
+00:26:10,720 --> 00:26:16,980
+التسعين مش صين الآن ليش cosine؟ قلت له إنه في dot
+
+295
+00:26:16,980 --> 00:26:20,440
+product و ال dot بتعطي cosine ولا مش cosine؟
+
+296
+00:26:20,440 --> 00:26:24,140
+cosine قال لي قداش cosine التسعين in C ال
+
+297
+00:26:24,140 --> 00:26:28,140
+calculator موجودة cosine التسعين بتطلع سفرإذن هذه
+
+298
+00:26:28,140 --> 00:26:33,060
+دايما سفر بغض النظر كدش هدول صح ولا لأ ان شاء الله
+
+299
+00:26:33,060 --> 00:26:37,680
+هدوا يكونوا مليون هنا فيه سفر إذن الشي اللي دايما
+
+300
+00:26:37,680 --> 00:26:45,580
+سفر هذي أول
+
+301
+00:26:45,580 --> 00:26:50,480
+واحدة افترض ان هي صين 90 مش اي زاوية تانية اه ليش
+
+302
+00:26:50,480 --> 00:26:58,210
+صح صحي معايا و صالك حلو ليشتخيلني شوية اللي ناتج
+
+303
+00:26:58,210 --> 00:27:00,950
+اللي سمته الـC مش لازم يكون عمودي على الـA و عمودي
+
+304
+00:27:00,950 --> 00:27:04,510
+على الـB؟ آه لازم لازم حلو إذا عمودي على الـA و
+
+305
+00:27:04,510 --> 00:27:06,630
+أنا مش عمودي على الـA عشان كده خدت التسعين عشان
+
+306
+00:27:06,630 --> 00:27:11,330
+كده خدت التسعين طب و الـB؟ برضه عمودي على الـB إذا
+
+307
+00:27:11,330 --> 00:27:16,030
+برضه اللي تحته زيه عرفتي ليش؟ غيرها احكي لا vector
+
+308
+00:27:16,030 --> 00:27:21,210
+لا dot ولا
+
+309
+00:27:21,210 --> 00:27:27,590
+crossطلعت vector يعني a cross b vector dot vector
+
+310
+00:27:27,590 --> 00:27:33,730
+انت بتقول عن b مش a cross b vector اللي سميته c
+
+311
+00:27:33,730 --> 00:27:37,610
+بنفع حط dot product بين vector و vector dot
+
+312
+00:27:37,610 --> 00:27:42,650
+product بين vector و vector اه مش scalar من جالك
+
+313
+00:27:42,650 --> 00:27:47,490
+تطلع scalar ايه اللي بين جثين في b اللي بين جثين
+
+314
+00:27:47,490 --> 00:27:53,190
+scalarvector و dot product between two vectors
+
+315
+00:27:53,190 --> 00:27:57,630
+مسموحلي بس الأخير اللي مش مسموحلي لأنه بين جثين
+
+316
+00:27:57,630 --> 00:28:02,350
+طلع scalar ومنفعش اتحط بين scalar و vector cross
+
+317
+00:28:02,350 --> 00:28:05,630
+او dot تمام غيرها
+
+318
+00:28:09,960 --> 00:28:13,300
+أف بيتساوي M إيه؟ هيديك Scalar في ال vector Scalar
+
+319
+00:28:13,300 --> 00:28:16,740
+في ال vector حطيت منهم Dot يعني أنتوا عمكم سمعتوا
+
+320
+00:28:16,740 --> 00:28:23,560
+أن قانون الميوتين هيك بيساوي M Dot A أو M Cross A
+
+321
+00:28:23,560 --> 00:28:30,820
+لأ حط M A على طول صحيح لأ تمام خلاص الشرطة
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/ZAyehpbNc4A.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/ZAyehpbNc4A.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a7c290f1b1f31cad414ce893ae6d44ff33e7416b
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/ZAyehpbNc4A.srt
@@ -0,0 +1,1936 @@
+
+1
+00:00:05,210 --> 00:00:09,830
+تمام يا بنات، نكمل اليوم إن شاء الله ونحاول ننجز
+
+2
+00:00:09,830 --> 00:00:13,350
+هذا الـ chapter على الأقل اللي بتعلق بالـ quiz عشان
+
+3
+00:00:13,350 --> 00:00:17,550
+نكون جاهزين للـ quiz يوم الخميس بإذن الله، في كل
+
+4
+00:00:17,550 --> 00:00:23,150
+الأحوال. بعد ما أخذنا الـ vectors وعرفنا أنه بنرسمه
+
+5
+00:00:23,150 --> 00:00:29,590
+بخط مستقيم، على رأس السهم، وكيف نجمعه، وكيف نتعامل
+
+6
+00:00:29,590 --> 00:00:34,350
+ونطرحه. تعاملنا معه بطريقتين: طريقة المثلث وطريقة
+
+7
+00:00:34,350 --> 00:00:37,890
+متوازي الأضلاع، مظبوط ولا لأ؟ وقلنا هذه الطريقة مش
+
+8
+00:00:37,890 --> 00:00:43,050
+عملية، بدنا طريقة أحلى، بدنا طريقة تكون بدون رسم.
+
+9
+00:00:43,790 --> 00:00:48,470
+اتفق العلماء على أنهم يكتبوا الـ vector بصيغة، أول
+
+10
+00:00:48,470 --> 00:00:52,710
+ما تشوفها على طول، يرسم في مخك شكل الـ vector
+
+11
+00:00:52,710 --> 00:00:58,010
+اتجاهه ومقداره. كيف جاؤوا؟ بدنا نستعين بشغلة
+
+12
+00:00:58,010 --> 00:01:05,420
+بنسميها متجه الوحدة، تمام؟ واتفقوا على ثلاثة unit
+
+13
+00:01:05,420 --> 00:01:12,580
+vectors، متجهات معروفة، رموزها محفوظة: I، موجب في أي
+
+14
+00:01:12,580 --> 00:01:20,200
+محور السيني الموجب، J، صادي موجب، وK، زدي موجب. جاي I
+
+15
+00:01:20,200 --> 00:01:27,430
+معروف، سالب I، العكس. J لأعلى، سالب J لأسفل، وهكذا K
+
+16
+00:01:27,430 --> 00:01:33,910
+out، minus K، into the page.  تمّت هذه الـ unit vectors
+
+17
+00:01:33,910 --> 00:01:39,090
+اللي اتفقنا عليها. صار من صيغة الـ vector ممكن أنا
+
+18
+00:01:39,090 --> 00:01:43,310
+أعرف اتجاهه. قال لي: تمّ، بس مش دائماً الـ vectors
+
+19
+00:01:43,310 --> 00:01:48,690
+بيكون باتجاه سيني فقط، أو صادي فقط، ولا لأ؟ قال لي: زي
+
+20
+00:01:48,690 --> 00:01:53,470
+أيش قلت له؟ زي هذا الـ vector، مظبوط ولا لأ؟ قال لي: هذا
+
+21
+00:01:53,470 --> 00:01:58,690
+لا هو سيني ولا هو صادي. رجع شوية الذاكرة بالنسبة له.
+
+22
+00:01:58,690 --> 00:02:03,930
+قال لي: طيب، هذا بقدر أقول هو مجموع two vectors حسب
+
+23
+00:02:03,930 --> 00:02:07,470
+قاعدة متوازي الأضلاع، هذان two vectors. قال لي: هذول
+
+24
+00:02:08,840 --> 00:02:12,660
+صح ولا لأ؟ صار الـ vector اللي أنت رسمتيه، قطر
+
+25
+00:02:12,660 --> 00:02:18,200
+في متوازي أضلاع، أحد أضلاعه أفقي، والثاني عمودي.
+
+26
+00:02:18,200 --> 00:02:21,580
+بمعنى آخر، واحد سيني، واحد صادي، ولا لأ؟ قولوا: تمام،
+
+27
+00:02:21,580 --> 00:02:25,900
+قلت له: يعني أنت تقدر تكتب لي هيك؟
+
+28
+00:02:25,900 --> 00:02:32,760
+ولا لأ؟ هذا سيني، ولا مش سيني؟ قلت له: حط جنبه I، مش
+
+29
+00:02:32,760 --> 00:02:37,700
+الـ I بفهم منه أنه باتجاه السين، والثاني حط جنبه J.
+
+30
+00:02:38,640 --> 00:02:45,920
+خلاص. إذًا، لو كتبت لكم هيك يا بنات: A = 2I
+
+31
+00:02:45,920 --> 00:02:52,280
++ 3J، اتخيلوا، اتخيلتوا ولا لأ؟ يعني لو جئت رسمت
+
+32
+00:02:52,280 --> 00:02:58,820
+أنا محاور زي هيك، معناته هنا بقول 2، وهنا 3، وبعمل
+
+33
+00:02:58,820 --> 00:03:04,880
+هيك، بقول: هي الـ vector، ولا لأ؟ خلاص، إذًا أنا بيلزمني أ-
+
+34
+00:03:04,880 --> 00:03:10,260
+رسمه، بيلزمني تكتبوا لي هذين الاثنين اللي جنب الـ I والـ
+
+35
+00:03:10,260 --> 00:03:14,240
+اللي جنب الـ J. قال لي: طب، بدنا اسم اللي هم هذول؟
+
+36
+00:03:14,240 --> 00:03:19,800
+قال لي: هذا كله، أو جزء منه؟ جزء، يعني مركبة، ولا
+
+37
+00:03:19,800 --> 00:03:23,840
+مش مركبة؟ سميها مركبة. طب، هذه المركبة، أيها؟ قال لي:
+
+38
+00:03:23,840 --> 00:03:31,140
+مش هذه السينية، وهذه صادية، تمام؟ إذًا، معناته، قال لك:
+
+39
+00:03:31,140 --> 00:03:35,560
+كتبته هيك: Ax and Ay، هذول اللي أنا كتبتهم، 2 وثلاثة هنا. in general، Ax يعني A السينية، المركبة
+
+40
+00:03:35,560 --> 00:03:41,420
+السينية، وAy، إيش ممكن نسميهم؟ قال لي: ها تبقى تسميها
+
+41
+00:03:41,420 --> 00:03:44,420
+الـ X component والـ Y component، المركبة السينية والـ
+
+42
+00:03:44,420 --> 00:03:48,300
+المركبة الصادية. إذًا Ax and Ay are called يسموا
+
+43
+00:03:48,300 --> 00:03:52,540
+respectively، بالترتيب. يعني الـ X component لهذا، والـ
+
+44
+00:03:52,540 --> 00:03:56,960
+Y component لهذا. واضحة، تمام؟ of the vector A. إذًا كل
+
+45
+00:03:56,960 --> 00:04:02,060
+vector A له مركبات، بقدر أجيبها، وأتعامل معها على
+
+46
+00:04:02,060 --> 00:04:06,580
+هذه الأساس. قل لي: حلو. هاي زاوية معينة، بقول لي: تطلع
+
+47
+00:04:13,260 --> 00:04:17,260
+الهندسة اللي أخذناها في المحاضرة، بتقدر تقول لي أن
+
+48
+00:04:17,260 --> 00:04:21,960
+cos الزاوية = مجاور/وتر، ولا لا؟ مش المجاور
+
+49
+00:04:21,960 --> 00:04:24,840
+بالنسبة لي للزاوية المرسومة، هي المركبة السينية، ولا
+
+50
+00:04:24,840 --> 00:04:32,480
+لا؟ والوتر هي الـ A كلها؟ cos الزاوية = مقابل
+
+51
+00:04:32,480 --> 00:04:35,820
+/وتر، ولا لا؟ لما ضربت ضرب تبادلي، ليه؟ ما يحتاج
+
+52
+00:04:35,820 --> 00:04:42,000
+كذا نعمل، نقول: cos θ = مجاور/وتر، صح؟
+
+53
+00:04:42,000 --> 00:04:45,680
+أضرب ضرب تبادلي، إيش صارت؟ Ax = A cos
+
+54
+00:04:45,680 --> 00:04:49,720
+الزاوية. sin الزاوية = Ay / A.  ضربنا ضرب
+
+55
+00:04:49,720 --> 00:04:55,500
+تبادلي، إيش؟ إذًا، أنت من الرسمة، بقدر أجيب المركبات
+
+56
+00:04:55,500 --> 00:05:03,220
+ولا لا؟ ومن المركبات بقدر أرسم، تمام؟ حلو. طيب، جاء لي
+
+57
+00:05:03,220 --> 00:05:08,400
+إيش؟ الـ vector لما تكتبيه زي هيك، فهمت؟ وبقدر
+
+58
+00:05:08,400 --> 00:05:12,520
+أرسمه، بتقدر تجيب لي مقداره، وتقول لي: آه، في the page.
+
+59
+00:05:12,520 --> 00:05:20,820
+صح؟ هذا، مش هو مقدار الـ vector؟ مش هذا معروف؟ وهذا
+
+60
+00:05:20,820 --> 00:05:26,240
+هو نفسه هذا. إذًا، معناته المقدار = √(السيني² + الصادي²) واجمعهم، وخذ الجذر التربيعي. إذًا بيقول لي: the
+
+61
+00:05:29,720 --> 00:05:35,420
+magnitude of the vector is given by هذه من الفيزياء
+
+62
+00:05:35,420 --> 00:05:38,600
+course. في صعوبة يا بنات؟ يلا، هاي اللي بيكثروا
+
+63
+00:05:38,600 --> 00:05:44,800
+حبيبنا، إيش؟ إيش بدي؟ يعني، الإتجاه، المقدار، إيش
+
+64
+00:05:44,800 --> 00:05:48,040
+بيساوي؟
+
+65
+00:05:48,040 --> 00:05:56,160
+فحص جذر الثلاثة، باستخدام الكالكيليتور، بدي بالرقم، صحيحة؟
+
+66
+00:05:56,160 --> 00:05:59,380
+ما بنعرف، احنا حافظين كل الجذور؟ احنا دلوقت عارفين
+
+67
+00:05:59,380 --> 00:06:04,800
+جذر الـ 25، 5، أو الباقية، أو احنا بنحسبها مع بعض، صح ولا
+
+68
+00:06:04,800 --> 00:06:10,100
+لأ؟ جذر الـ 13، تمام يا بنات؟ حلو. جاي لي: طيب، مرات الـ
+
+69
+00:06:10,100 --> 00:06:13,520
+vector بيعطيك مركباته، بيقول لك: آه، ده مقداره، ده
+
+70
+00:06:13,520 --> 00:06:16,980
+مقداره. طب، لو بدي الـ direction تبعه بالضبط، كيف
+
+71
+00:06:16,980 --> 00:06:20,380
+اتجاهه؟ بقول له: أنت لما تقول لي: بدي الـ direction
+
+72
+00:06:20,380 --> 00:06:25,400
+بيكفي تجيب لي زاوية. نقول: والله، بعمل زاوية مقدارها كذا
+
+73
+00:06:25,400 --> 00:06:29,900
+مع المحور السيني، مش بيكفيني؟ طب، كيف أجيب الزاوية؟
+
+74
+00:06:29,900 --> 00:06:35,240
+الـ tan، لأن tan الزاوية = مقابل/مجاور، مش
+
+75
+00:06:35,240 --> 00:06:38,820
+المقابل، المركبة الصادية، والمجاور، هي المركبة
+
+76
+00:06:38,820 --> 00:06:43,940
+السينية. إذًا، معناته؟ بقول: to find the direction of a
+
+77
+00:06:43,940 --> 00:06:48,660
+vector، it is enough to determine بيكفي إنك تحدد
+
+78
+00:06:48,660 --> 00:06:53,080
+the angle θ the vector makes with a specific axis،
+
+79
+00:06:53,080 --> 00:06:56,340
+احنا بنعتبره المحور السيني، لكن ممكن أي محور يعني
+
+80
+00:06:57,220 --> 00:07:01,100
+تمام؟ the angle... the angle a vector makes with
+
+81
+00:07:01,100 --> 00:07:04,940
+the x-axis، زي ما حكيت، الـ tan، وبالتالي الزاوية
+
+82
+00:07:04,940 --> 00:07:09,400
+= shift tan، اللي في العلم بيقولوا عنها tan inverse
+
+83
+00:07:09,400 --> 00:07:14,260
+أو arc tan، ما تفرقش، خليكوا على shift tan تحت الـ
+
+84
+00:07:14,260 --> 00:07:17,340
+calculator، لغة الـ calculator، تمام؟ أما Adam يسميها
+
+85
+00:07:17,340 --> 00:07:24,380
+tan inverse، Ay/Ax، تمام؟ جاي لي: طب، لو كان في عندي
+
+86
+00:07:24,380 --> 00:07:29,530
+فراغ، بيصير ثلاث مركبات، ولا لأ؟ لما يكون الـ vector في
+
+87
+00:07:29,530 --> 00:07:33,150
+فراغ، مش في plane، مش مستوى، بيصير في عندك ثلاث
+
+88
+00:07:33,150 --> 00:07:37,930
+مُركّبات. قلت له: بسيطة، حط الثالثة. حطينا الثالثة، لما
+
+89
+00:07:37,930 --> 00:07:42,810
+يكونوا ثلاثة، بيصير الـ vector إيش؟ كـ magnitude، مش
+
+90
+00:07:42,810 --> 00:07:45,750
+أنت قلت لي: لما يكونوا اثنين، حسب في الـ course، هيك
+
+91
+00:07:45,750 --> 00:07:49,990
+بتعمله. لما يكون ثلاثة، حط الثالثة يا سيدي، ما ننزعلهاش.
+
+92
+00:07:50,660 --> 00:07:53,880
+بنحط زائد Az². لما يكون ثلاثة، الـ direction
+
+93
+00:07:53,880 --> 00:07:56,880
+بيقول لي: صعب الـ direction عليك، لأنه لما يكون في عندك
+
+94
+00:07:56,880 --> 00:08:01,100
+فراغ، بدو يكون في عندك ثلاث زوايا. بتصير زاوية مع
+
+95
+00:08:01,100 --> 00:08:03,820
+السين، وزاوية مع الصاد، وزاوية مع العين. مش مطلوب
+
+96
+00:08:03,820 --> 00:08:07,960
+مننا، مش مطلوب منكم، الحمد لله. احنا ده، ده، ده، بناخد
+
+97
+00:08:07,960 --> 00:08:13,120
+اللي... اللي بنقدر عليه، بنطلبه منكم، واللي شوية، بنأجله
+
+98
+00:08:13,120 --> 00:08:16,320
+مش في عما... بنأج... بنأجله، مش عندنا... السنة
+
+99
+00:08:16,320 --> 00:08:19,060
+التاسعة. احنا بقى بيقول: بسم الله، في الجامعة، في سنة
+
+100
+00:08:19,060 --> 00:08:22,460
+ثانية، في سنة ثالثة، في سنة رابعة، ولسه العلم كتير
+
+101
+00:08:22,460 --> 00:08:29,000
+بيجي، وفي سنة خامسة، ماذا هي الملاحق... الناس لسه
+
+102
+00:08:29,000 --> 00:08:38,440
+عاجلة. احكي، ارفعي صوتك! بالفرق، وموجه. هذا متجه، وهذه
+
+103
+00:08:38,440 --> 00:08:44,600
+اتجاهه هيك، وإن هتعلق ولا في الفرق، هي في الفراغ، بدي
+
+104
+00:08:44,600 --> 00:08:52,320
+تكون عندك محور ثالث، اللي هو Z. كيف؟ XYZ، هذا لا هو
+
+105
+00:08:52,320 --> 00:08:56,900
+لا سيني، ولا صادي، ولا زدي. في الفراغ، بتحلل لثلاث
+
+106
+00:08:56,900 --> 00:09:03,880
+مُركّباته. آه، مش العالم يقول: ده، ده، ده، علينا. ده، ده، ده، ده
+
+107
+00:09:03,880 --> 00:09:10,120
+واحدة واحدة. ليش منأجل لثلاث؟ هو... هو له ثلاث عُرف
+
+108
+00:09:10,120 --> 00:09:16,400
+عشان يسويله إنحلال، تمام؟ هيك إنحلال هو... هو في
+
+109
+00:09:16,400 --> 00:09:20,580
+الفراغ، هو في الفراغ. إيش يعني في الفراغ؟ إله ثلاث
+
+110
+00:09:20,580 --> 00:09:26,720
+أبعاد، إذًا إله ثلاث مُركّبات، تمام؟ هو دي طبيعة
+
+111
+00:09:26,720 --> 00:09:31,560
+الأشياء. كل vector إله ثلاث مُركّبات، حتى لو كان في
+
+112
+00:09:31,560 --> 00:09:36,700
+مستوى، بيقولوا: ثُلث سفر، ثُلث سفر، لكن in general،
+
+113
+00:09:36,700 --> 00:09:41,610
+بيقول: كل vector إله ثلاث مُركّبات، لأن طبيعة الأشياء
+
+114
+00:09:41,610 --> 00:09:46,230
+يا ربنا خلقها فراغ، three dimensions، وإن يكون موجود
+
+115
+00:09:46,230 --> 00:09:51,050
+في plane أو في line، حالة خاصة، حالات خاصة. فهمتوا
+
+116
+00:09:51,050 --> 00:09:57,450
+عليها؟ هي أصل الأشياء أنها تكون ثلاث أبعاد.  قال
+
+117
+00:09:57,450 --> 00:10:01,850
+لي: الـ vector إله مُركّبات؟ أمين. لا اثنين، لا ثلاثة. طب
+
+118
+00:10:01,850 --> 00:10:05,450
+لو في vector عندك صفر، قال لك: تتوقع فيه مركبة من
+
+119
+00:10:05,450 --> 00:10:13,720
+المُركّبات ما تكونش صفر في مجال؟ كيف؟ vector مقداره
+
+120
+00:10:13,720 --> 00:10:21,520
+صفر، تمام؟ هل في مجال أحد مركباته ما يكونش صفر؟
+
+121
+00:10:21,520 --> 00:10:26,840
+من اللي بيقول آه، يفسر لي، احنا راضين نسمع، كيف؟ بدك
+
+122
+00:10:26,840 --> 00:10:34,020
+حاجة تلغيها؟ مفهوش، مفهوش. ولا ممكن؟ اللي بيقول ممكن
+
+123
+00:10:34,020 --> 00:10:39,740
+يرفع صوته، ويقنعني، كيف ممكن vector مقداره صفر، مركباته مش
+
+124
+00:10:39,740 --> 00:10:44,940
+صفر، ومقداره صفر، ولازم يكون مقداره صفر. في مجال؟
+
+125
+00:10:44,940 --> 00:10:50,320
+انتوا هادية، تشوفوا، لو واحدة من هدول مش صفر، و-
+
+126
+00:10:50,320 --> 00:10:53,080
+بتجمعوهم، بتاخدوا الجذر التربيعي، بتطلع هنا صفر؟
+
+127
+00:10:53,080 --> 00:10:58,360
+ولا ممكن؟ إذًا إيش بيقول لي؟ Note that if the vector
+
+128
+00:10:58,360 --> 00:11:03,820
+A is zero، إذًا من بعرف على طول كل مركبته مالها؟ صفر
+
+129
+00:11:03,820 --> 00:11:09,420
+قطعاً، كل مركبته صفر، تمام يا بنات؟ واللي محتاجة
+
+130
+00:11:09,420 --> 00:11:14,400
+تقول، بس تكون شجاعة، وتقول، وتقنعنا. بس بدنا شجاعة.
+
+131
+00:11:14,400 --> 00:11:21,740
+احكوا، أعيد؟ في مجال vector يكون مقداره صفر، ها-
+
+132
+00:11:21,740 --> 00:11:28,860
+مقداره صفر، واحد مركبته مش صفر؟ فش مجال، ولا ممكن؟
+
+133
+00:11:31,100 --> 00:11:35,820
+ما بنفعش يكونوا عكس بعض، لأن هذا سيني وهذا صادي، فيه
+
+134
+00:11:35,820 --> 00:11:41,600
+مُركّبات نفس المقدار، كل نفس الشيء، بس واحد موجب و-
+
+135
+00:11:41,600 --> 00:11:45,900
+واحد سالب. لأ، ما نجمعهم، هدول موجب وهذا سالب
+
+136
+00:11:45,900 --> 00:11:48,740
+خمسة وسالب خمسة، ما نجمعهم، لأن واحد سيني وواحد
+
+137
+00:11:48,740 --> 00:11:54,220
+صادي. هدول ما يجربوش لبعض، ما بنفعش يلغوا بعض، زي ما أنت
+
+138
+00:11:54,220 --> 00:12:03,330
+متوقعة. ما بنفعش يلغوا بعض. بالضبط. إذًا، فما فيه مجال بالمرة.
+
+139
+00:12:03,330 --> 00:12:07,750
+حلو، صحيح.
+
+140
+00:12:07,750 --> 00:12:13,850
+جاي لي: خلاص، الـ vector عرفت كيف أكتبه. هاي vector و-
+
+141
+00:12:13,850 --> 00:12:17,150
+هاي vector.
+
+142
+00:12:17,150 --> 00:12:23,470
+بتتخيلوه.
+
+143
+00:12:23,470 --> 00:12:27,970
+بتتخيلوه، صح؟ بتتخيلوا إيش؟ الأول، أنه في الربع، مرة وين
+
+144
+00:12:30,540 --> 00:12:36,000
+في الربع الرابع، صح؟ ممتازين. بدي أجمعهم. جاي لي: ترسمهم
+
+145
+00:12:36,000 --> 00:12:41,860
+إيش؟ الآن، بدي أجمع بدون رسم، بدي أجمع وأستفيد من
+
+146
+00:12:41,860 --> 00:12:44,660
+الروضة، روحنا... و... و... وحطينا فلوس على الفاضل، من
+
+147
+00:12:44,660 --> 00:12:47,180
+هنا، نستفيد من الروضة، اللي جمعنا؟ بدي نجمع، زي ما
+
+148
+00:12:47,180 --> 00:12:50,700
+كنا نجمع في الروضة، بس إيش أسوي؟ جاي لي: بدك تجمع
+
+149
+00:12:50,700 --> 00:12:54,500
+السيني مع السيني، والصادي مع الصادي. ممنوع تجمع
+
+150
+00:12:54,500 --> 00:12:59,100
+السيني مع الصادي. اجمع السيني مع السيني. هي A، أنها
+
+151
+00:12:59,100 --> 00:13:03,760
+سينية، ولا مالهاش؟ وB، اجمع السيني، تبقى A مع السيني
+
+152
+00:13:03,760 --> 00:13:09,980
+تبقى B، ويطلع 4I، واجمع الصادي مع الصادي، نقصت
+
+153
+00:13:09,980 --> 00:13:15,500
+2J. هاي مجموعهم، هاي مجموعهم، يوريني مثل المجموع
+
+154
+00:13:15,500 --> 00:13:20,040
+طب، وذا الـ vectors مش مكتوبين هيك؟ جاي لي: بتخليهم هم
+
+155
+00:13:20,040 --> 00:13:26,440
+يقولوا هيك. إذًا، لو كان عندي Vector، ورسم لي إياه، جاي لي:
+
+156
+00:13:26,440 --> 00:13:31,560
+أول حاجة تعملها قبل ما تجمع، حلله، يا جيب مركباته.
+
+157
+00:13:31,560 --> 00:13:37,160
+إذًا بقول لي: Now to add two vectors analytically، يعني
+
+158
+00:13:37,160 --> 00:13:41,780
+بدون رسم، تحليليًا، يعني جبريًا، يعني جمع الروضة اللي
+
+159
+00:13:41,780 --> 00:13:46,600
+اتعلمناها، كيف أسوي؟ جاي لي: proceed as follow، اتبع
+
+160
+00:13:46,600 --> 00:13:52,610
+الخطوات التالية: resolve، حلل أي vector إلى مركباته.
+
+161
+00:13:52,610 --> 00:13:57,130
+resolve each vector into its components according
+
+162
+00:13:57,130 --> 00:1
+
+223
+00:19:12,040 --> 00:19:16,040
+إتعلمت تجمع of two displacement vectors؟  دالي ال
+
+224
+00:19:16,040 --> 00:19:19,620
+two vectors. بس بدي أنا أديك مثال حي فيزيائي، هي
+
+225
+00:19:19,620 --> 00:19:23,080
+displacement أحد أمثلة الvectors ولا لأ؟ is itصح الكلام؟
+
+226
+00:19:23,080 --> 00:19:26,940
+ليش حطيت displacement؟ عشان أحط متر؟ عشان
+
+227
+00:19:26,940 --> 00:19:31,460
+أصير في فيزياء؟ وهيبي؟  بدا نيجي معايا يا بناتي، ودي
+
+228
+00:19:31,460 --> 00:19:37,080
+مصعب السؤال. الصيني مع الصيني، أربعة واثنين نقصت
+
+229
+00:19:37,080 --> 00:19:42,260
+نيجي سلبت، نيجي خلص المثال هذا، هو
+
+230
+00:19:45,380 --> 00:19:49,580
+مظبوط ولا لأ؟ بدي مقدار الresult، بقدر اجيبه؟ اه
+
+231
+00:19:49,580 --> 00:19:54,100
+طبعا. بدي الزاوية، بقدر اجيبها؟ ten صح؟ إذا لو بدو
+
+232
+00:19:54,100 --> 00:19:58,600
+الmagnitude بجيبها، ولو بدو الزاوية بجيبها، تمام.
+
+233
+00:19:58,600 --> 00:20:03,180
+هيك يا بنات؟ مواضع هنا سهلة، جامعة عادي، جامعة
+
+234
+00:20:03,180 --> 00:20:05,520
+الصينية مع الصينية، والصادية مع الصادية. مظبوط ولا
+
+235
+00:20:05,520 --> 00:20:10,000
+لأ؟ نشوف، بقول
+
+236
+00:20:10,000 --> 00:20:13,000
+الآن، في عندي particle، يجي على باله يعمل مش
+
+237
+00:20:13,000 --> 00:20:18,670
+إزاحتين، تلاتة تلات إزاحات. a particle undergoes ثلاث
+
+238
+00:20:18,670 --> 00:20:23,350
+three consecutive displacements. عملت ثلاث إزاحات
+
+239
+00:20:23,350 --> 00:20:28,810
+متتالية، consecutive، متتالية. الشماعة قالي هاي هوا
+
+240
+00:20:28,810 --> 00:20:32,130
+اتفرجوا أنتم حتى الآن بالدنيا، هم جاهزين، محللين
+
+241
+00:20:32,130 --> 00:20:35,930
+وخالصين. قالي بدي الresultant، إن شاء الله يكونوا
+
+242
+00:20:35,930 --> 00:20:40,730
+عشرة. إيش هسوي؟ الصيني لحال، والصاضي لحال، والأغاني
+
+243
+00:20:40,730 --> 00:20:46,320
+لحال.  إختلف إشي، اثنتين ولا تلاتة ولا عشرة، مجرد أنه
+
+244
+00:20:46,320 --> 00:20:49,940
+طويل ولا قصير. السؤال مظبوط ولا لأ؟ قالي يالا، إيش بدك
+
+245
+00:20:49,940 --> 00:20:54,640
+قال، find the resultant displacement، المحصلة، and
+
+246
+00:20:54,640 --> 00:21:02,700
+its magnitude، وmagnitude، مقدارها، تمام. ها كيف
+
+247
+00:21:02,700 --> 00:21:10,350
+بنعمل؟ بنقوله، سهل، بنقوله R اللي هي بتساوي A زائد B
+
+248
+00:21:10,350 --> 00:21:16,230
+زائد C. بتساوي، يالا نجمع، البلد. بنقول Calculator، خمسة
+
+249
+00:21:16,230 --> 00:21:19,710
+وعشرين، تلاتة وعشرين، ونقص تلاتة عشر، اثنين، خمسة، و
+
+250
+00:21:19,710 --> 00:21:26,590
+عشرين. إذا خمسة وعشرين I، واحد وثلاتين J. هدي سهل
+
+251
+00:21:26,590 --> 00:21:35,490
+لأ، لأن الأخيرة صفر. إذا أنا اتناش، نقص خمسة، احكي
+
+252
+00:21:36,690 --> 00:21:43,390
+عليه، صوتكم، اللي بيحكي اه
+
+253
+00:21:43,390 --> 00:21:48,250
+مالها هذيك؟
+
+254
+00:21:48,250 --> 00:21:52,250
+ثلاثين، نقص أربعة، طايز زاد خمسة، وكان الجامعة واحدة
+
+255
+00:21:52,250 --> 00:22:00,850
+تمام. طيب يلا يا بنات، خمسة وعشرين تربيع، زائد واحد و
+
+256
+00:22:00,850 --> 00:22:03,990
+ثلاثين تربيع، زائد تسعة وأربعين، اللي هي سبعة تربيع
+
+257
+00:22:04,850 --> 00:22:07,110
+وأربعين point أربعة. ما بديش الأربعة، بيكفيني
+
+258
+00:22:07,110 --> 00:22:11,670
+الأربعين، وهي أربعين طبعا، هه، عشان ما تزعجش، وهي
+
+259
+00:22:11,670 --> 00:22:21,310
+point أربعة. خلاص هو إيش كتب؟ فأنت تقوليه، مش مشكلة
+
+260
+00:22:21,310 --> 00:22:25,170
+ممكن تحوليها، ما هو الgaussian system، مش system
+
+261
+00:22:25,170 --> 00:22:29,870
+system، مقبول منك، يعني اللي بدي يحول يحول، أي
+
+262
+00:22:29,870 --> 00:22:32,430
+استفسار يا بنات، تمام؟
+
+263
+00:22:35,450 --> 00:22:39,970
+شوف السؤال، هجيتني رجال يقولوا ليه، بديش أديكي، هم
+
+264
+00:22:39,970 --> 00:22:48,050
+جاهزين، بديكي تجيبي أنت المواكبات، مظبوط، بقولي a
+
+265
+00:22:48,050 --> 00:22:55,530
+hiker، إيش بنسميه الـhiker؟ احنا صياد
+
+266
+00:22:55,530 --> 00:23:02,130
+ولا تبع…لها كلمة ثانية، مش شائعة في مخي، من هايك
+
+267
+00:23:02,130 --> 00:23:07,770
+…بتصلقوا هدول…بتصلقوا البيت كومية، مش مشكلة. a
+
+268
+00:23:07,770 --> 00:23:12,610
+hiker begins a trip، trip يعني رحلة، رحلة، by first
+
+269
+00:23:12,610 --> 00:23:18,910
+walking، كيف بدت؟ قالت، مشيت، كان معها سيارة، قررت
+
+270
+00:23:18,910 --> 00:23:24,230
+السيارة هنا، وبدت تمشي رحلتها، مشيت خمسة وعشرين
+
+271
+00:23:24,230 --> 00:23:31,210
+كيلومتر south east، South East، جنوب شرق. محط ليش
+
+272
+00:23:31,210 --> 00:23:34,030
+زاوية؟ معناته في النص بالظبط ولا لأ؟ الزاوية 45
+
+273
+00:23:34,030 --> 00:23:39,330
+South East from her car، من سيارتها، سيارتها جونه
+
+274
+00:23:39,330 --> 00:23:46,830
+هناك، نقطة الأصل، حلو. she stops، تعبت، قعدت، طلعت على
+
+275
+00:23:46,830 --> 00:23:53,460
+الساعة، غابت الشمس،وقفت، وقفت هناك، وقفت هناك، وقفت
+
+276
+00:23:53,460 --> 00:24:00,100
+هناك، وقفت
+
+277
+00:24:00,100 --> 00:24:02,540
+هناك وقفت، هناك وقفت، هناك وقفت، هناك وقفت، هناك وقفت
+
+278
+00:24:02,540 --> 00:24:02,620
+هناك وقفت، هناك وقفت، هناك وقفت، هناك وقفت، هناك وقفت
+
+279
+00:24:02,620 --> 00:24:02,640
+هناك وقفت، هناك وقفت، هناك وقفت، هناك وقفت، هناك وقفت
+
+280
+00:24:02,640 --> 00:24:03,320
+هناك وقفت، هناك وقفت، هناك وقفت، هناك وقفت، هناك وقفت
+
+281
+00:24:03,320 --> 00:24:18,080
+هناك وقفت، هناك وقفت، هناك وقفت
+
+282
+00:24:18,080 --> 00:24:24,000
+هنا، 60 degree north of east، 60 درجة شمال الشرق
+
+283
+00:24:24,000 --> 00:24:30,480
+شايفين؟ شمال الشرق، 60 درجة، حلو. جالي، وهي ماشية بدل
+
+284
+00:24:30,480 --> 00:24:35,920
+اتجاهها، طلعت لجات البرج تبع، حالس الغابة، جلست ونسنا
+
+285
+00:24:35,920 --> 00:24:42,520
+تمام. وقفت هنا، خلاص وصلت الونس زي ما بنسميه، تمام؟ in
+
+286
+00:24:42,520 --> 00:24:46,560
+a direction 60 degree north of east، at which point
+
+287
+00:24:46,560 --> 00:24:50,420
+في تلك النقطة، she discovers a forest rangers tower،
+
+288
+00:24:50,420 --> 00:24:54,500
+forest rangers، هو حارس الغابة، تمام؟ forest…
+
+289
+00:24:54,500 --> 00:24:57,780
+أنتوا عارفين أنا غابة؟ تمام، هذه قصة، مانا اتعرفيها
+
+290
+00:24:57,780 --> 00:25:01,460
+إحنا بس عايزكي، بنحكي عشان نتعرفي إننا بنكمل مصطلح
+
+291
+00:25:01,460 --> 00:25:04,560
+إنجليزي، وإحنا مش جايوركن في امتحان، دي بنكون زي
+
+292
+00:25:04,560 --> 00:25:08,450
+هيك. إحنا بدنا نقعد نخش على جوجل و نترجم؟ لأ، بنجيب
+
+293
+00:25:08,450 --> 00:25:11,350
+لكم أبسط من هنا، بس هاد موجودة في الكتاب فبنقراها
+
+294
+00:25:11,350 --> 00:25:16,670
+إيش بدها؟ قالت، determine the components of each
+
+295
+00:25:16,670 --> 00:25:21,370
+displacement، هي عملت إزاحتين، إزاحة southeast، و
+
+296
+00:25:21,370 --> 00:25:27,850
+إزاحة northeast، ب 60 درجة، بدي مركباتها، طيب وبعدين؟
+
+297
+00:25:27,850 --> 00:25:31,350
+قالت، بعد كده بدك تجمعلي الإزاحتين، طب أنا إذا جبت
+
+298
+00:25:31,350 --> 00:25:34,230
+المركبة، تخلصت المسألة، صحيح ولا لأ؟
+
+299
+00:25:37,970 --> 00:25:40,610
+اتطلعوا…اتطلعولي على اللوحة، هلجيت؟ شوفوا
+
+300
+00:25:40,610 --> 00:25:45,830
+المركبة إيه اللي نازلها دي؟ بقدر أقول هذه عبارة
+
+301
+00:25:45,830 --> 00:25:51,870
+عن هاي مركبتينها ولا لأ؟ مظبوط هيك ولا لأ؟ تمام،
+
+302
+00:25:51,870 --> 00:25:55,910
+بدي أطلع على المركبة الصادية، كيف اتجاهها؟ إذا
+
+303
+00:25:55,910 --> 00:26:02,270
+لازم تكون سالبة، صح؟ لازم تكون سالبة قطعا، هلجيت؟
+
+304
+00:26:03,010 --> 00:26:08,690
+أنا بعرف الزاوية، إليها، مجاور، إليها مقابل، المجاورة
+
+305
+00:26:08,690 --> 00:26:13,390
+بدي آخذ cosine، والمقابل بدي آخذ sine، نجي نتطلع على
+
+306
+00:26:13,390 --> 00:26:16,950
+هذه الحلوة، وهذه الزاوية اللي جدتني إياها، هذه
+
+307
+00:26:16,950 --> 00:26:21,240
+المركبة جارت هذه ولا لا؟ جارتها، إذا إيش بيتاخد؟ cos
+
+308
+00:26:21,240 --> 00:26:28,040
+،إذا على طول بدي أقوله الآن المركبة الصينية، و
+
+309
+00:26:28,040 --> 00:26:35,980
+اللي هي الموجبة بحسب الرسمة، بقوله ax بتساوي a cos
+
+310
+00:26:35,980 --> 00:26:44,020
+45، صح ولا لأ؟ مقداره إيه؟ جالي 25 كيلومتر، إذا 25 في
+
+311
+00:26:44,020 --> 00:26:47,320
+cos 45، طلع 17.7 كيلومتر
+
+312
+00:26:53,230 --> 00:26:58,470
+الcosine، والsine، تمام. دائما، تقول، جان، بعيد ال
+
+313
+00:26:58,470 --> 00:27:01,890
+cosine، بيساوي مجاور على وتر، تمام، وال…والsine
+
+314
+00:27:01,890 --> 00:27:06,790
+المقابل على…حلو، شفافة الزاوية، اه، 45، حلو، شفافة
+
+315
+00:27:06,790 --> 00:27:11,210
+الحمرة، فوق هذه، مقابل ولا مجاور؟ لها بالنصف للزاوية
+
+316
+00:27:11,210 --> 00:27:16,330
+اه اه، بالنصف للزاوية، مجاور، عشان كده أخذنا ال
+
+317
+00:27:16,330 --> 00:27:21,890
+cosine، اه، تمام. طيب، نجي لهذه، هذه هي نفسها هادي
+
+318
+00:27:21,890 --> 00:27:27,120
+دلبالكلأ، الموازية بتصير مقابل هادي، إذا بياخد صيني
+
+319
+00:27:27,120 --> 00:27:32,480
+ولا لأ؟ إذا بقى أقول، اي، وراي، تلبقى كل عصفر حتى
+
+320
+00:27:32,480 --> 00:27:32,960
+السالب
+
+321
+00:27:36,330 --> 00:27:40,970
+عرفت ليش حطيت السالب؟ سألتكم عنه، قلت له الأسفل، إذا
+
+322
+00:27:40,970 --> 00:27:45,390
+معناته المركبة الصادية لازم تكون الأسفل، قلت له هذه
+
+323
+00:27:45,390 --> 00:27:50,870
+بيساوي سالب 17.7 كيلومتر، لأن صينية 45، وصادية 45
+
+324
+00:27:50,870 --> 00:27:59,910
+إخوة، صح؟ تمام. إذا بقوله من هنا، بقدر أقول، a بيساوي
+
+325
+00:27:59,910 --> 00:28:08,940
+17.7 I، ناقص 17.7 J كيلومتر، ولا لأ؟ هذه المركبات
+
+326
+00:28:08,940 --> 00:28:13,720
+البدائية، هلأ إيه؟ بالنبي خلصت من a، صح؟ أيسر، صار
+
+327
+00:28:13,720 --> 00:28:18,600
+على إيه؟ نجي ل b الحلوة الثانية، بقوله b، هادي
+
+328
+00:28:18,600 --> 00:28:31,360
+خلصنا من هادي، قلت له b، هادي؟
+
+329
+00:28:33,570 --> 00:28:38,230
+بصيها دي، cosine، ودي sine، بصيها دي cosine لها حسب
+
+330
+00:28:38,230 --> 00:28:43,330
+الtheta تبعتك، يعني أنت بتكتب الtheta دي، صح؟ بس تصير
+
+331
+00:28:43,330 --> 00:28:49,170
+إيش المجاور لها، الصادية، صحيح ولا لأ؟ بس ما حصل الحظ
+
+332
+00:28:49,170 --> 00:28:56,550
+الآن، 45، neutral، تفرجش، تمام. لكن لو كان الزاوية غير
+
+333
+00:28:56,550 --> 00:28:59,790
+45، تفرج، بصي، بكتن، تبقي غيرت الزاوية، بكتن تتغير ال
+
+334
+00:28:59,790 --> 00:29:02,770
+sine، والcosine، تمام يا بنت، تمام.
+
+335
+00:29:04,990 --> 00:29:09,530
+طلعوا حاجات b، طلعوا بـb، بدي مركباتها، هل هي مجموع
+
+336
+00:29:09,530 --> 00:29:20,770
+هدول مركبتين ولا لأ؟ ليش؟ اه هي متوازية أضلاع، كيف؟
+
+337
+00:29:20,770 --> 00:29:26,650
+عند أخره، مش إحنا بنقول متوازية أضلاع، مانا سينا تانا
+
+338
+00:29:26,650 --> 00:29:32,010
+جالي، حلو، بدي المركبات، حاجات الصينية موجبة، و
+
+339
+00:29:32,010 --> 00:29:37,970
+الصادية برضه موجبة، هل جيت…من اللي توسألت على
+
+340
+00:29:37,970 --> 00:29:44,590
+الزاوية؟ اه، انتبهيلي، هل جيت الزاوية مش 45؟ 60؟ طيب
+
+341
+00:29:44,590 --> 00:29:50,950
+أنا ال60، فضربوها، ولا مرسومة؟ مشوفة للجميع، المركبة
+
+342
+00:29:50,950 --> 00:29:55,830
+الصينية، جارتها ولا مقابلها؟ جارتها، لو غيرت الزاوية
+
+343
+00:29:55,830 --> 00:30:04,800
+بصير 30، هديك، تمام. فبقدر أقول، bx بتساوي b cos
+
+344
+00:30:04,800 --> 00:30:09,400
+الستين، بتساوي أربعين في cos الستين، عشرين كيلومتر
+
+345
+00:30:09,400 --> 00:30:13,920
+b
+
+346
+00:30:13,920 --> 00:30:20,960
+واي، بتساوي، برضه زائد، وهادي زائد، b sin الستين، و
+
+347
+00:30:20,960 --> 00:30:25,080
+بتساوي أربعة
+
+348
+00:30:25,080 --> 00:30:27,340
+وثلاثين وستة كيلومتر
+
+349
+00:30:30,380 --> 00:30:35,080
+كيف حللت ال60؟ كيف يعني ال60؟ هو إيه، حلتها جدا، و
+
+350
+00:30:35,080 --> 00:30:39,540
+صعيب، حلو، هجيه، شفافة ال60، الصينية، شفافة المركبة
+
+351
+00:30:39,540 --> 00:30:43,280
+الصينية الحمراء، جارتها ولا مقابل لها؟ عارف، فعلا أنا
+
+352
+00:30:43,280 --> 00:30:49,120
+بس لإنه جيت الenvy هيك رايحة، اه، طلع عليها إنك
+
+353
+00:30:49,120 --> 00:30:58,520
+عشانها بعيدة عليكي، هاي فيكتور هو، هاي بدي أحللها
+
+354
+00:31:00,470 --> 00:31:05,490
+فبتكون تحليلها كيف؟ بقوله هيك وهيك، عشان تطلع وتر
+
+355
+00:31:05,490 --> 00:31:13,970
+في متوازي أضلاع، غيرها، تقدر الآن من هدول الاثنتين
+
+356
+00:31:13,970 --> 00:31:21,650
+أقول إن b بتساوي عشرين I، زائد أربعة وثلاثين point
+
+357
+00:31:21,650 --> 00:31:29,740
+ستة J، صح ولا لا يا بنات؟ أجهز المطلوب الثاني، المطلوب
+
+358
+00:31:29,740 --> 00:31:33,000
+الثاني، إيش بده؟ قالي بدي أجمع، قلت له أجمع الصيني
+
+359
+00:31:33,000 --> 00:31:39,220
+مع الصيني، والصادي مع الصادي، فالآن R اللي هي A زائد
+
+360
+00:31:39,220 --> 00:31:46,920
+B، بتساوي سبعة وثلاثين point سبعة I، زائد سبعتاشر J
+
+361
+00:31:46,920 --> 00:31:53,900
+كيلومتر تقريبا، هذه فيها أقل، أسألك، فأنت من
+
+362
+00:31:53,900 --> 00:32:00,980
+الكلام، ولا إيش إيه؟ نسجك من دون خطأ، الله تمام، نسجك
+
+363
+00:32:00,980 --> 00:32:12,000
+احكوا يا بنات، أي صفصار؟ جمع سهل، سهل جدا، اه، هذا هو
+
+364
+00:32:12,000 --> 00:32:18,640
+بدك زاوية، بنجيبلك اللي بدك إياه، بنعملك إياه، هنجيب
+
+365
+00:32:18,640 --> 00:32:22,740
+شغلة شوية متقدمة، إحنا الجماعة أخذناها في الروضة، صح
+
+366
+00:32:22,740 --> 00:32:29,300
+ولا لأ؟ ضرب الvectors، product، معناته ضرب، product
+
+367
+00:32:29,300 --> 00:32:35,120
+of vectors، قالي، هتواجه تلات أنواع من الضرب، تلات
+
+368
+00:32:35,120 --> 00:32:40,920
+أنواع، أول نوع، multiply، يعني اضرب، multiplying، ضرب
+
+369
+00:32:40,920 --> 00:32:45,840
+برضه، يعني product ضرب، وmultiplying ضرب، اتفقنا؟
+
+370
+00:32:45,840 --> 00:32:49,260
+multiplying a vector by a scalar، دي دكتور يكتره
+
+371
+00:32:49,260 --> 00:32:55,720
+بالـ vector في scalar، نمحي هذا كله، هجيت، ونشوف هي
+
+372
+00:32:55,720 --> 00:33:00,200
+ممكن نضرب vector في scalar في العلم؟ نقول اه، قالي
+
+373
+00:33:00,200 --> 00:33:01,620
+ياخد هذا القانون
+
+374
+00:33:05,850 --> 00:33:13,090
+في حد ما أخدهوش؟ الـM scalar، والـA ضربها tiny
+
+375
+00:33:13,090 --> 00:33:18,790
+vector في scalar، صح ولا لأ؟ تمام، هذا ممكن يكون له
+
+376
+00:33:18,790 --> 00:33:25,970
+ثلاث مركبات، ماهو vector صحيح، طب بتدربوا في M، الـM
+
+377
+00:33:25,970 --> 00:33:30,710
+هذه بتفوت على التلات مركبات كلها، هي قاعدة الضرب
+
+378
+00:33:30,710 --> 00:33:33,550
+بتاعة الـscalar في الـvector، بيقولي if Lambda
+
+379
+00:33:33,550 --> 00:33:40,650
+الـLambda، أي scalar، M، T زمن، Volume، Temperature،
+
+380
+00:33:40,650 --> 00:33:45,010
+ذاكرينهم، Energy، إذا هذه Lambda بتمثل أي كمية
+
+381
+00:33:45,010 --> 00:33:48,330
+scalar، قالي بدي أضربها في الـvector A، إيش الـ
+
+382
+00:33:48,330 --> 00:33:52,980
+vector A؟ Force، velocity، displacement، acceleration،
+
+383
+00:33:52,980 --> 00:33:58,040
+صح ولا لأ؟ إذا وجهتها كذا أمور، طلع يسوّنها في ال
+
+384
+00:33:58,040 --> 00:34:04,660
+lambda، وزّعناها على كل المركبات، تمام؟ إيش يعني
+
+385
+00:34:04,660 --> 00:
+
+445
+00:39:22,900 --> 00:39:37,540
+ما نخلطش لإنه كان جدا بجانبنا، احكي اه
+
+446
+00:39:37,540 --> 00:39:46,860
+حلو، أما كيش سمعتي في طاقة سلبية، هاه؟ بلاش بلاش بلاش
+
+447
+00:39:46,860 --> 00:39:50,170
+إيش إنّا في الطاقة ونغلب حياتنا لما تكون الدنيا
+
+448
+00:39:50,170 --> 00:39:52,030
+باردة و مرتاحة والناس والصلاة تقريبا... جدّيش
+
+449
+00:39:52,030 --> 00:39:56,670
+درجة الحرارة بتكون؟ تحت الصفر... كيف أقول؟ ماهي
+
+450
+00:39:56,670 --> 00:40:09,730
+Scalar... إذا الـScalar... أحكيه... كيف؟ ليش
+
+451
+00:40:09,730 --> 00:40:16,090
+بنعمل هيك؟ هيك تعريفها يا بنتي... هيك التعريف... إيش
+
+452
+00:40:16,090 --> 00:40:21,330
+اسمك إنتي؟ علي صوتك... أسيل، ليه سموك يا أسيل؟ نفس
+
+453
+00:40:21,330 --> 00:40:26,970
+السؤال، ليه سموك يا أسيل؟ في شغلات، هذا التعريف قعدت
+
+454
+00:40:26,970 --> 00:40:31,630
+هيك، هذا تعريفه عشان تظبط كل العلم، قالوا دوتو
+
+455
+00:40:31,630 --> 00:40:36,550
+برودكت يعرف defined as، إذا كانت تعريف، ليش المتر
+
+456
+00:40:36,550 --> 00:40:41,950
+عامة يعتبروها جدّي؟ ما أخليهوش منها لحيفة، إذا في شغلات
+
+457
+00:40:41,950 --> 00:40:48,580
+بتقعد، قعدت هي هيك، بصي، متعرف عليها تمام؟ بيقول لي sons
+
+458
+00:40:48,580 --> 00:40:54,360
+I, J and K are unit vectors perpendicular to each
+
+459
+00:40:54,360 --> 00:40:59,160
+other، متعامدين على بعض، and using the last equation
+
+460
+00:40:59,160 --> 00:41:03,100
+اللي كتبته أنا وكتبته وأنا وياكم صحيح هيك؟ قال لي
+
+461
+00:41:03,100 --> 00:41:08,520
+هيا نضرب الـA ضرب الـB، قال لي هي الـA وهي الـB، بدي
+
+462
+00:41:08,520 --> 00:41:12,120
+أضرب جوس بجوس ولا لأ؟ وفي حد ما عشان يضرب جوس
+
+463
+00:41:12,120 --> 00:41:17,650
+بجوس، وضربت جوس بجوس، طلعوا اللي انش طلع معايا I ضرب
+
+464
+00:41:17,650 --> 00:41:22,270
+الـI جالي، والله هادي صفر وهادي صفر وهادي صفر
+
+465
+00:41:22,270 --> 00:41:25,030
+وهادي صفر وهادي صفر وهادي صفر وهادي صفر و
+
+466
+00:41:25,030 --> 00:41:29,250
+وهادي صفر وهادي صفر وهادي صفر وهادي صفر و ها
+
+467
+00:41:29,250 --> 00:41:34,770
+دي صفر وهادي صفر وهادي صفر وهادي صفر وهادي
+
+468
+00:41:34,770 --> 00:41:34,970
+صفر وهادي صفر وهادي صفر وهادي صفر وهادي
+
+469
+00:41:34,970 --> 00:41:36,530
+صفر وهادي صفر وهادي صفر وهادي صفر وهادي
+
+470
+00:41:36,530 --> 00:41:44,630
+صفر وهادي صفر
+
+471
+00:41:44,630 --> 00:41:51,420
+وواحد وجي ضرب جي وكي ضرب كي، دوري أوردي، محلل الدرّب
+
+472
+00:41:51,420 --> 00:41:55,600
+بدرب الصيني مع الصيني، والصاضي مع الصاضي، والعيني
+
+473
+00:41:55,600 --> 00:42:03,360
+مع العيني، وبس، وبجمع وبجمع، حلو، هاي إيه، وهاي
+
+474
+00:42:03,360 --> 00:42:13,460
+بيه، بتساوي هذه، إيه، ثلاثة إيه ناقص خمسة جي زائد كيه
+
+475
+00:42:13,460 --> 00:42:21,350
+هذا، بتوفيكتور عشوائي، بدي إيه ضرب الـB، بقوله بالثاوي
+
+476
+00:42:21,350 --> 00:42:28,790
+اتنين في ثلاثة، اتاوي
+
+477
+00:42:28,790 --> 00:42:34,890
+أنا قُلت، هتطلع Scalar، بالاحمر عشان الـI والـJ والـ
+
+478
+00:42:34,890 --> 00:42:39,830
+K مسمحهمش، إذا اتنين في ثلاثة، ستة
+
+479
+00:42:43,750 --> 00:42:48,650
+شوفوا، ٦I-١٥G زيادة ٤K، بتكون أحد الخيارات الأربعة
+
+480
+00:42:48,650 --> 00:42:56,510
+بحطها عشان أن أوقع بالفخ، لو حطيت I وG وK
+
+481
+00:42:56,510 --> 00:43:01,870
+بتاخدوها؟ هي هي هيك، ساعتها لجيت بقوله هنا نقص
+
+482
+00:43:01,870 --> 00:43:07,070
+خمسة عشر، وهذه أظن عشرة، إذا معناته نقص خمسة، طلعشي
+
+483
+00:43:07,070 --> 00:43:11,130
+جواب طالع رقم Scalar صحيح؟ Scalar
+
+484
+00:43:14,480 --> 00:43:20,660
+قال لي، ها هي two vectors، أسهل، إيه بتساوي اتنين I
+
+485
+00:43:20,660 --> 00:43:25,480
+زائد ثلاثة G، وبيساوي سالب I زائد اتنين G، إيش بدك؟ قال
+
+486
+00:43:25,480 --> 00:43:30,100
+لي، بدي تضرب ليهم، find the dot product، وبعدين
+
+487
+00:43:30,100 --> 00:43:33,020
+بيجيب لي الزاوية اللي بينهم، مين ده في الضرب؟ مين اللي
+
+488
+00:43:33,020 --> 00:43:38,760
+طو جلط I؟ بتتنجلني؟ وين هذه جلطة I؟ عشان... لما
+
+489
+00:43:38,760 --> 00:43:44,780
+ضربت جلط I مش طو، هنا جلط ٦I، أنت بكتب دربي لي هالجيت
+
+490
+00:43:44,780 --> 00:43:52,280
+عشان ما تخبطيش، ادربي اتنين، أيوة، إذا إيه ضرب الـB
+
+491
+00:43:52,280 --> 00:44:00,700
+بيساوي سالب اتنين، إيش الجواب؟ تمام، هيك اسحقت خارب
+
+492
+00:44:00,700 --> 00:44:07,120
+بيضيعش I وG وK، لأن أنا بتعامل مع dot product، طلع
+
+493
+00:44:07,120 --> 00:44:10,380
+المطلوب التاني، إيش بقول؟ ليه بدي الزاوية؟ قُلت له
+
+494
+00:44:10,380 --> 00:44:16,160
+توعي، أنت قُلت لي A dot الـB، بيساوي ماجنتيود الـA في
+
+495
+00:44:16,160 --> 00:44:21,360
+ماجنتيود الـB في كوساين الـθ بينهم، صح؟ هجيت A
+
+496
+00:44:21,360 --> 00:44:24,900
+dot الـB، جبتها ولا لأ؟ ما جبتيها، أنت بقوله، ها دي
+
+497
+00:44:24,900 --> 00:44:30,720
+أربعة، ماجنتيود الـA، مين يجيب لي إياها؟ يرجو يلا، تسعة
+
+498
+00:44:31,770 --> 00:44:42,270
+زائد تلاتة عشر، إذا جذر تلاتة عشر، مجموع الـB، هذه
+
+499
+00:44:42,270 --> 00:44:45,490
+خطأ، قد يبقى في بالك شائع، لأن أنت بتقول لي نقص واحد
+
+500
+00:44:45,490 --> 00:44:49,770
+تربيع أربعة
+
+501
+00:44:49,770 --> 00:44:58,840
+زائد واحد، فبالتالي في جذر الخمسة، cos θ، خلصنا، إذا
+
+502
+00:44:58,840 --> 00:45:03,720
+أربعة على جذر تلاتة وستين، في جذر طبعا، هيك بيصير cos θ
+
+503
+00:45:03,720 --> 00:45:11,000
+بتساوي أربعة على جذر خمسة وستين، بتطلعوها
+
+504
+00:45:11,000 --> 00:45:18,300
+بتطلع ستين، طلعنا كويس
+
+505
+00:45:20,870 --> 00:45:23,410
+أنا قاعد بأسرع، عامل حسابي إنه ممكن يكون الأربع
+
+506
+00:45:23,410 --> 00:45:27,570
+الإجازة، أنا بحاجة، عشان كده اتحملوني، أنت حاجات
+
+507
+00:45:27,570 --> 00:45:30,110
+مكيفين، بيقولوا يا رب متحملينك، بس أطلّع الأربع
+
+508
+00:45:30,110 --> 00:45:37,190
+الإجازة، تمام، ناخد راحتنا يوم الأربع، تمام، طلع يا
+
+509
+00:45:37,190 --> 00:45:42,130
+بنات، هجيت cosine، الزاوية عندكم معلومة أكيدة إنه
+
+510
+00:45:42,130 --> 00:45:46,190
+مستحيل تكون أكبر من واحد، معلومة معروفة، هي من صفر
+
+511
+00:45:46,190 --> 00:45:53,860
+لواحد، قال لي، هذه الحلوة، بقدر أقول إن A ضرب B مستحيل
+
+512
+00:45:53,860 --> 00:45:58,500
+تكون أكبر من A في B، مش مستحيل، ليش مستحيل تكون
+
+513
+00:45:58,500 --> 00:46:02,460
+أكبر؟ عشان تكون أكبر لازم تكون هذه أكبر من واحد، لكن
+
+514
+00:46:02,460 --> 00:46:08,220
+بقدر أقول، ممكن تساوي، إذا كوساين السفر واحد، وممكن تكون
+
+515
+00:46:08,220 --> 00:46:13,420
+أصغر، إذا الزاوية من صفر للزاوية اللي بتحدد تطلع
+
+516
+00:46:13,420 --> 00:46:16,500
+ليك ويز، إيش بيقول؟ بيقول which of the following
+
+517
+00:46:16,500 --> 00:46:19,320
+statements is true، عظّم إن هذه الجملة معروفة
+
+518
+00:46:19,320 --> 00:46:23,460
+بالانجليزي، إيش من هذه الجملة التالية صحيحة؟ بيقول
+
+519
+00:46:23,460 --> 00:46:28,260
+لي، A ضرب B is larger than magnitude الـA في الـB
+
+520
+00:46:28,260 --> 00:46:32,720
+بيقول له، ولا ممكن، ولا ممكن، لأنه عمري ما سمعت
+
+521
+00:46:32,720 --> 00:46:38,690
+كوساين زاوية أكبر من واحد، ولا في حد سمعه يدلنا، A
+
+522
+00:46:38,690 --> 00:46:43,310
+ضرب طول B is smaller than FB، بقوله مش بالضرورة، ممكن
+
+523
+00:46:43,310 --> 00:46:50,370
+يتساوي، إذا برضه هذه مش دقيقة، صحيحة ولا لأ؟ هذه مثل
+
+524
+00:46:50,370 --> 00:46:55,070
+اللي عارفين، أحيانا أكبر، وأحيانا أصغر، مستحيل
+
+525
+00:46:55,070 --> 00:47:02,070
+بيشوف الأخيرة، A ضرب طول B could be equal، يعني ممكن
+
+526
+00:47:02,070 --> 00:47:06,670
+تكون مساوية، بقوله اه، إذا كانت الزاوية zero، إذا هذا
+
+527
+00:47:06,670 --> 00:47:12,470
+صحيح طبعا، أنتم تعلمتم، لأن لما شفتم الكوساينز إنه
+
+528
+00:47:12,470 --> 00:47:15,530
+في من الكوساينز اللي أمه ده عيالها، بيطلع واحد من هدول
+
+529
+00:47:15,530 --> 00:47:22,110
+صح، اه، أنتم ما طلعتكيش، ما طلعتكيش لأ، هدول موجودين
+
+530
+00:47:22,110 --> 00:47:26,750
+مختفين جوا، فمرات بيطلع هو نفسه، ومرات بيطلع تغيير
+
+531
+00:47:26,750 --> 00:47:31,370
+بسيط، أما فيه يطلع علم نفسه اللي بيعمل مرضه شكله
+
+532
+00:47:31,370 --> 00:47:37,740
+مش طالع عليك، ارجعي لحالك، وعلاقتك مع أمك قبل ما
+
+533
+00:47:37,740 --> 00:47:47,420
+تموتي، على الـquiz، روح قولي لأمك ادعي لي، تمام، هل
+
+534
+00:47:47,420 --> 00:47:50,240
+جيت عشان الـquiz، فيه ملو كان، لأن الخميس الـquiz في
+
+535
+00:47:50,240 --> 00:47:53,760
+كل الأحوال، بغض النظر عن الإجازة، عشان ما تقولوش هذا
+
+536
+00:47:53,760 --> 00:47:57,980
+ما أخذناش cross product أو vector product، الـvector
+
+537
+00:47:57,980 --> 00:48:00,840
+product، يا بنات، سمّيته vector product، عشان الناتج
+
+538
+00:48:00,840 --> 00:48:05,820
+vector، الناتج ماله vector، إذا بيقول لي طبعا أنا
+
+539
+00:48:05,820 --> 00:48:10,860
+هأعيده يوم السبت أو يوم الأربع، لكن بدي أسجلّه شوية
+
+540
+00:48:10,860 --> 00:48:16,340
+عشان الـquiz، تمام، فاتحملونّي، بيقول إذا vector product
+
+541
+00:48:16,340 --> 00:48:19,520
+of two vectors a and b، هذا لازم يكون between two
+
+542
+00:48:19,520 --> 00:48:25,160
+vectors أيضا، written as، كيف بنكتب؟ A cross الـB is
+
+543
+00:48:25,160 --> 00:48:30,140
+a third vector، إذا لنا نتيج ماله vector، with ما
+
+544
+00:48:30,140 --> 00:48:32,680
+زال vector، بدك تديني إليه، تنتين magnitude و
+
+545
+00:48:32,680 --> 00:48:37,490
+direction، صح؟ الـmagnitude تبقى هذا هو مجنتيودي
+
+546
+00:48:37,490 --> 00:48:41,590
+الـC، اللي هو مجنتيود الـA في الـB، بيساوي A في B في
+
+547
+00:48:41,590 --> 00:48:46,870
+ساين الزاوية، تمام؟ بدي الـdirection، قال لي، الـ
+
+548
+00:48:46,870 --> 00:48:52,630
+vector C له direction، لازم يكون عمودي على مستوى
+
+549
+00:48:52,630 --> 00:48:56,690
+الـA وB، ولما يكون عمودي على المستوى معناته
+
+550
+00:48:56,690 --> 00:48:59,850
+عمودي على كل الخطوط جوا المستوى، مش هي كانت في
+
+551
+00:48:59,850 --> 00:49:05,660
+نظرية؟ تمام، إذا C عمودي على A ولا لأ؟ وC عمودي على
+
+552
+00:49:05,660 --> 00:49:12,780
+B ولا لأ؟ قاطع، العمودي على الاثنين، قال لي طيب، بنات، هي
+
+553
+00:49:12,780 --> 00:49:20,020
+A وهي B، الاثنين عاللوح، بدي أضربهم أطلع C، cross
+
+554
+00:49:20,020 --> 00:49:23,740
+product، بدي أطلع، عندي لازم عمودي على الاثنين، في
+
+555
+00:49:23,740 --> 00:49:28,860
+عندي احتمالين، لأ عليكم، لأ علوح، بنتعلم كيف نعرف إنه
+
+556
+00:49:28,860 --> 00:49:31,920
+عليكم ولا علي اللوح؟ قال لي، في قاعدة اليد اليمنى
+
+557
+00:49:31,920 --> 00:49:36,280
+بتعرفوها، حلو، كلكم بتعرفوها، هيها أصابعك الأربع
+
+558
+00:49:36,280 --> 00:49:41,620
+افردهم وحطهم باتجاه الـA، أصابعنا الأربع حطّوناهم في
+
+559
+00:49:41,620 --> 00:49:47,480
+اتجاه الـA، ولف باتجاه الـB، لفّهم أصابعك الأربع بعد
+
+560
+00:49:47,480 --> 00:49:54,080
+كذا، هيهم شايفينها، هي A وهي B، اتفقنا، أصابع الأربعة
+
+561
+00:49:54,080 --> 00:50:00,630
+هيهم، بلف هيك هيك، بلفّه للخارج
+
+562
+00:50:00,630 --> 00:50:05,670
+طيب بدي B cross الـA، بي، إذا أنا أصابعي الأربعة مع
+
+563
+00:50:05,670 --> 00:50:10,650
+مين؟ مع B، مع B، بدي ألفّه، معناته لازم يكون بيبقى من
+
+564
+00:50:10,650 --> 00:50:14,230
+دوا، إيش بيدلّ؟ بيقول لي A cross الـB بيساوي سالب B
+
+565
+00:50:14,230 --> 00:50:22,370
+cross الـA، إذا لو عكسته، هتحطّي اشاره سالب، أمين؟ حلو، ساين
+
+566
+00:50:22,370 --> 00:50:28,110
+السفر قداش؟ صفر، وصفر، وصفر، وصفر، وصفر، وصفر
+
+567
+00:50:28,110 --> 00:50:35,210
+تسعين، حلو، معناته I X I، I X I، I X I، I X I، I X I، I
+
+568
+00:50:35,210 --> 00:50:35,450
+X I، I I X I، I I X I، I I X I، I I X I، I I X
+
+569
+00:50:35,450 --> 00:50:37,690
+I، I I X I، I I X I، I I X I، I I X I، I I X I
+
+570
+00:50:37,690 --> 00:50:40,950
+I، I X I، I I X I، I I X I، I I X I، I I X I I
+
+571
+00:50:40,950 --> 00:50:41,590
+I X I، I I X I، I I X I، I I X I، I I X I I I
+
+572
+00:50:41,590 --> 00:50:44,530
+X I، I I X I، I I X I، I I X I، I I X I I I X
+
+573
+00:50:44,530 --> 00:50:45,970
+I، I I X I، I I X I، I I X I، I I X I I I X I
+
+574
+00:50:45,970 --> 00:50:52,080
+I I X I، I I X I، I I X I، I I X I I K، يعني K
+
+575
+00:50:52,080 --> 00:50:58,660
+إذاً I cross الـJ بيعطي K، J cross الـI سالب K، صح
+
+576
+00:50:58,660 --> 00:51:06,780
+ولا... طب تتوقعوا J cross الـK، I، J cross الـK، I
+
+577
+00:51:06,780 --> 00:51:11,800
+تمام، هذه القاعدة من جيبها بعد كده، أطلع واحد هذه
+
+578
+00:51:11,800 --> 00:51:18,160
+القاعدة التي درّبنا، قال لي في عندك، كيف تجيب I x J x
+
+579
+00:51:18,160 --> 00:51:22,220
+K؟ قال لي، هاي I وJ وK، شايفينهم؟ بدي أضرب كل
+
+580
+00:51:22,220 --> 00:51:25,780
+الاثنين مع بعض، يطلع الثالث، قاطعا ولا لأ؟ بدي يطلع
+
+581
+00:51:25,780 --> 00:51:30,020
+الثالث، I x J، بدي يطلع K أو سالب K، مظبوط؟ J x K بدي
+
+582
+00:51:30,020 --> 00:51:34,800
+يطلع معاك I أو سالب I، K x I، بدي يطلع لك J أو سالب
+
+583
+00:51:34,800 --> 00:51:37,660
+J، كيف تبقى أعرف موجب ولا سالب؟ قال لي، طلع القاعدة
+
+584
+00:51:37,660 --> 00:51:42,220
+الحلوة، وحطّهم على رأس مثلث، حطّناهم، وقولي... و
+
+585
+00:51:42,220 --> 00:51:47,490
+اعملي يوم هيك، ها جيت أنت ماشي بدك تضرب، sorry، I
+
+586
+00:51:47,490 --> 00:51:51,490
+cross الـJ، بقول، I cross الـJ، أنا ماشي، وكاين مع عقارب
+
+587
+00:51:51,490 --> 00:51:56,190
+الساعة، بيطلع الثالث موجب، لو بدي أقول J cross الـI
+
+588
+00:51:56,190 --> 00:52:02,390
+بيصير عكس عقارب، بيطلع سالب K، طيب J cross... هي طلعت J
+
+589
+00:52:02,390 --> 00:52:04,630
+cross الـK، I
+
+590
+00:52:07,780 --> 00:52:14,000
+كي... لو... كي كروس الجي، سالب اي، تمام، كي كروس الاي
+
+591
+00:52:14,000 --> 00:52:21,040
+جي، اي كروس الكي، سالب امولة، تمام، هذه حلوين، بعدين
+
+592
+00:52:21,040 --> 00:52:26,580
+بنكملها عشان نغلب الكورس، هذا حال، نرجع له تفصيل، وهذا
+
+593
+00:52:26,580 --> 00:52:33,530
+بدنا نرجع له تفصيل، بدي الـquiz، بيسأل لي which of the
+
+594
+00:52:33,530 --> 00:52:37,230
+following is always zero؟ واطلعوا الخيارات تبعاتي
+
+595
+00:52:37,230 --> 00:52:41,330
+يا بنات، وانتبهوا عشان لو إيجي زيه في الـquiz، A
+
+596
+00:52:41,330 --> 00:52:46,010
+cross الـB cross الـA، كيف صفر؟ ما بعرفش، نيجي لهذا
+
+597
+00:52:46,010 --> 00:52:50,490
+انتبهوا لي، A cross الـB طلع فيكتور جديد، صح، عمودي
+
+598
+00:52:50,490 --> 00:52:55,840
+على هذا، مش عمودي على الثانية، أنا وعمودي على هذا، طب
+
+599
+00:52:55,840 --> 00:52:59,720
+ما زال هذا عمودي عليه، معناته هذا وهذا عموديات، و
+
+600
+00:52:59,720 --> 00:53:03,980
+ضدّ product، كوساين، وكوساين التسعين صفر، إذا هذا صفر
+
+601
+00:53:03,980 --> 00:53:11,580
+طب لو A cross الـB ضدّ الـB برضه صفر، برضه صفر
+
+602
+00:53:11,580 --> 00:53:15,800
+هذا وهذا ما لي دعوة فيهم، طلع هذا الحلو، قال لي
+
+603
+00:53:15,800 --> 00:53:20,360
+هذا أصلا الأعمى اللي بيصدقك، لأن هذا A ضرب الـB
+
+604
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/ZAyehpbNc4A_raw.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/ZAyehpbNc4A_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3b4154408f2146aabd1b09eab6bb78581485abc8
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/ZAyehpbNc4A_raw.srt
@@ -0,0 +1,2472 @@
+1
+00:00:05,210 --> 00:00:09,830
+تمام يا بنات نكمل اليوم ان شاء الله ونحاول ننجز
+
+2
+00:00:09,830 --> 00:00:13,350
+هذا ال chapter على الأقل اللي بتعلق بال quiz عشان
+
+3
+00:00:13,350 --> 00:00:17,550
+نكون جاهزين ل quiz يوم الخميس بإذن الله في كل
+
+4
+00:00:17,550 --> 00:00:23,150
+الأحوالبعد ما أخدنا ال vectors وعرفنا انه بنرسمه
+
+5
+00:00:23,150 --> 00:00:29,590
+بخط مستقيمه على رأس السهم وكيف نجمعه وكيف نتعامل
+
+6
+00:00:29,590 --> 00:00:34,350
+نطرحه اتعاملنا معه بطريقتين طريقة المثلث وطريقة
+
+7
+00:00:34,350 --> 00:00:37,890
+متوازي الأضلاع مظبوط ولا لأ؟ وقلنا هذه الطريقة مش
+
+8
+00:00:37,890 --> 00:00:43,050
+عملية بدنا طريقة أحلى بدنا طريقة تكون بدون رسم
+
+9
+00:00:43,790 --> 00:00:48,470
+اتفقوا العلماء على انهم يكتبوا ال vector بصيغة اول
+
+10
+00:00:48,470 --> 00:00:52,710
+ما تشوفها على طول يرسم في مخك الشوة ال vector
+
+11
+00:00:52,710 --> 00:00:58,010
+اتجاها و مقدارا كيف جالوا بدنا نستعين بشغلة
+
+12
+00:00:58,010 --> 00:01:05,420
+بنسميها متجه الوحدة تمام؟ واتفقوا على تلتunit
+
+13
+00:01:05,420 --> 00:01:12,580
+vectors متجهات معروفة رموزها محفوظة I ملزج بأي
+
+14
+00:01:12,580 --> 00:01:20,200
+محور الصيني الموجب J صاضي موجب و K زده موجب جالي I
+
+15
+00:01:20,200 --> 00:01:27,430
+معروف سالب I العكسJ لأعلى سالب J لأسفل و هكذا K
+
+16
+00:01:27,430 --> 00:01:33,910
+out minus K into the big تمى هذه ال unit vectors
+
+17
+00:01:33,910 --> 00:01:39,090
+اللي اتفقنا عليها صار من صيغة ال vector ممكن انا
+
+18
+00:01:39,090 --> 00:01:43,310
+اعرفون اتجاهه قاللي تمى بس مش دايما ال vectors
+
+19
+00:01:43,310 --> 00:01:48,690
+بيكون باتجاه سيني بس او صابي بس ولا لأ قاللي زي
+
+20
+00:01:48,690 --> 00:01:53,470
+ايش قلتله زي هذا ال vectorمظبط ولا لأ؟ قاللي هذا
+
+21
+00:01:53,470 --> 00:01:58,690
+لا هو سيني ولا هو صابي رجع شوية الذاكرة بالنسبة له
+
+22
+00:01:58,690 --> 00:02:03,930
+قاللي طيب هذا بقدر اقول هو مجموع two vectors حسب
+
+23
+00:02:03,930 --> 00:02:07,470
+قاعدة متوازي الأضلاع الشمال two vectors قاللي هدول
+
+24
+00:02:08,840 --> 00:02:12,660
+صح ولا لأ؟ صار الـ vector اللي انت رسمتي ليه قطر
+
+25
+00:02:12,660 --> 00:02:18,200
+في متوازي أضلاع أحد أضلاعه أفقي والتاني عمودي
+
+26
+00:02:18,200 --> 00:02:21,580
+بمعنى آخر واحد سيني واحد صاضي ولا لأ؟ قولوا تمام،
+
+27
+00:02:21,580 --> 00:02:25,900
+قولتلي يعني انت تقدر تكتبلي هيك؟
+
+28
+00:02:25,900 --> 00:02:32,760
+ولا لأ؟ هذا سيني ولا مش سيني؟ قلتلي حط جنبه I مش
+
+29
+00:02:32,760 --> 00:02:37,700
+ال I بفهم منه أنه باتجاه السين والتاني حط جنبه G
+
+30
+00:02:38,640 --> 00:02:45,920
+خلاص إذا رجيت لو كتبتلكم هيك يا بنات A بيساوي 2I
+
+31
+00:02:45,920 --> 00:02:52,280
+زائد 3G اتخيلوا اتخيلتوا ولا لأ يعني لو جيت رسمت
+
+32
+00:02:52,280 --> 00:02:58,820
+انا محاور زي هيك معناته هن بقول 2 و هن 3 و بعمل
+
+33
+00:02:58,820 --> 00:03:04,880
+هيك بقول هي ال vector ولا لأخلاص اذا انا بلزمني اش
+
+34
+00:03:04,880 --> 00:03:10,260
+رسمه بلزمني تكتبلي هدولش تنتين اللي جانبي ال I و
+
+35
+00:03:10,260 --> 00:03:14,240
+الجانبي ال J قاللي طب بدنا اسم اللي هم هادوا؟
+
+36
+00:03:14,240 --> 00:03:19,800
+قاللي هذا كل ايه ولا جزء منه؟ جزء يعني مركبة ولا
+
+37
+00:03:19,800 --> 00:03:23,840
+مش مركبة؟ سميها مركبة طب هذه المركبة انهي؟ قاللي
+
+38
+00:03:23,840 --> 00:03:31,140
+مش هذه الصينية و هذه صاليةتمام؟ إذا معناته قال لك
+
+39
+00:03:31,140 --> 00:03:35,560
+كتبته هيك AX and AY هدول اللي أنا كتبتهم اتنين و
+
+40
+00:03:35,560 --> 00:03:41,420
+تلاتة هنا in general AX يعني A الصينية المعوار
+
+41
+00:03:41,420 --> 00:03:44,420
+الصيني و AY إيش ممكن تسميهم قال ليها تبقى تسميها
+
+42
+00:03:44,420 --> 00:03:48,300
+ال X component و ال Y component المراكبة الصينية و
+
+43
+00:03:48,300 --> 00:03:52,540
+المراكبة الصادية إذا AX and AY are called يسموا
+
+44
+00:03:52,540 --> 00:03:56,960
+respectively بالترتيب يعني ال X component لهذهو ال
+
+45
+00:03:56,960 --> 00:04:02,060
+y component لهذه ماضحة تمام of the vector a إذا كل
+
+46
+00:04:02,060 --> 00:04:06,580
+vector a له مركبات بقدر أجيب ها و أتعمل معها على
+
+47
+00:04:06,580 --> 00:04:12,580
+هذه الأساس قللي حلو هاي زاوية معينة بقوللي تطلع
+
+48
+00:04:13,260 --> 00:04:17,260
+الهندسة اللي أخدناها في المجلسة بتقدر تقوللي ان
+
+49
+00:04:17,260 --> 00:04:21,960
+cos الزاوية بيسوي مجاور على وطر ولا لا؟ مش المجاور
+
+50
+00:04:21,960 --> 00:04:24,840
+بالنسبالي للزاوية المرسومة هي المراكبة الصينية ولا
+
+51
+00:04:24,840 --> 00:04:32,480
+لا؟ و الوطر هي الايه كلها؟ cos الزاوية بيسوي مقابل
+
+52
+00:04:32,480 --> 00:04:35,820
+على وطر ولا لا؟ لما ضربت ضربت تبادل ليه؟ ماحتاج
+
+53
+00:04:35,820 --> 00:04:42,000
+كده نعمل نقول cos الثيتا بيسوي مجاور على وطرصح
+
+54
+00:04:42,000 --> 00:04:45,680
+اضرب ضرب تبادل ايه صارت ax بتسوي ايه في cos
+
+55
+00:04:45,680 --> 00:04:49,720
+الزاوية sin الزاوية بتسوي ay أو ايه ضربنا ضرب
+
+56
+00:04:49,720 --> 00:04:55,500
+تبادل ايه اذا انت من الرسمة بقدر اجيب المراكبات
+
+57
+00:04:55,500 --> 00:05:03,220
+ولا لا و من المراكبات بقدر ارسل تمام حلو طيب جالي
+
+58
+00:05:03,220 --> 00:05:08,400
+ايهالـ vector لما تكتبلي يا زي هيك فهمت و بقدر
+
+59
+00:05:08,400 --> 00:05:12,520
+أرسمه بتقدر تجيبلي مقداره و تقولي اه في the horse
+
+60
+00:05:12,520 --> 00:05:20,820
+صح؟ هذا مش هي مقدار ال vector مش هذا معروف و هذا
+
+61
+00:05:20,820 --> 00:05:26,240
+هو نفسه هذا إذا معناته المقدار بيساوي ربع الصيني و
+
+62
+00:05:26,240 --> 00:05:29,720
+ربع الصاضي و جمعهم و خد جزء تربيعي إذا بيقولي the
+
+63
+00:05:29,720 --> 00:05:35,420
+magnitude of the vector is given byهذه من FIFA
+
+64
+00:05:35,420 --> 00:05:38,600
+course في صعوبة يا بنات يلّا هاي اللي بيكتروا
+
+65
+00:05:38,600 --> 00:05:44,800
+حبيبنا ايه؟ ايش بدي يعني الاجهة المجنقضر ايش
+
+66
+00:05:44,800 --> 00:05:48,040
+بيساوي؟
+
+67
+00:05:48,040 --> 00:05:56,160
+فح جزر التلتاش كفيالكالكولاتر بدي بالرقم صحيحة؟
+
+68
+00:05:56,160 --> 00:05:59,380
+مابنعش نعرف احنا حافظين كل جزر احنا دلوقت عارفين
+
+69
+00:05:59,380 --> 00:06:04,800
+جزر 25 خمسة او الباقية او احنا بتفوت معانا صح ولا
+
+70
+00:06:04,800 --> 00:06:10,100
+لأ جزر 13 تمام يا بنات؟ حلو جالي طيب مرات ال
+
+71
+00:06:10,100 --> 00:06:13,520
+vector بيعطيك مركباته بيقولك اه دي مقداره دي
+
+72
+00:06:13,520 --> 00:06:16,980
+مقداره طب لو بدي ال direction تبعه بالظبط كيف
+
+73
+00:06:16,980 --> 00:06:20,380
+اتجاهه بقوله انت لما تقول ليه بدي ال direction
+
+74
+00:06:20,380 --> 00:06:25,400
+بكفي جيبني زاويةانقول والله بعمل زاوية مقدارها كذا
+
+75
+00:06:25,400 --> 00:06:29,900
+مع المحور الصيني مش بيكفيني طب كيف اجيب الزاوية؟
+
+76
+00:06:29,900 --> 00:06:35,240
+التان لأن تان الزاوية بتثوي مقابل على مجاور مش
+
+77
+00:06:35,240 --> 00:06:38,820
+المقابل المراكبة الصادية والمجاور هي المراكبة
+
+78
+00:06:38,820 --> 00:06:43,940
+الصينية اذا معناته؟بقول to find the direction of a
+
+79
+00:06:43,940 --> 00:06:48,660
+vector it is enough to determine بكفي إنك اتحدد
+
+80
+00:06:48,660 --> 00:06:53,080
+the angle θ the vector makes with a specific axis
+
+81
+00:06:53,080 --> 00:06:56,340
+احنا بنعتبره المحور الصيني لكن ممكن أي محور يعني
+
+82
+00:06:57,220 --> 00:07:01,100
+تمام؟ the angle .. the angle a vector makes with
+
+83
+00:07:01,100 --> 00:07:04,940
+the x-axis زي ما حكيته التان وبالتالي الزاوية
+
+84
+00:07:04,940 --> 00:07:09,400
+بتسوي shift tan اللي بالعلم يقول عنها tan inverse
+
+85
+00:07:09,400 --> 00:07:14,260
+او arc tan ماتفرجش خليكم على shift tan تحت ال
+
+86
+00:07:14,260 --> 00:07:17,340
+calculator لغة ال calculator تمام؟ اما ادم يسميها
+
+87
+00:07:17,340 --> 00:07:24,380
+tan inverse ay على ax تمام؟ جالي طب لو كان في عندي
+
+88
+00:07:24,380 --> 00:07:29,530
+فراخبصير تلات مراكبات ولا لأ لما يكون ال vector في
+
+89
+00:07:29,530 --> 00:07:33,150
+فراغ مش في plane مش مستوى بيصير في عندك تلات
+
+90
+00:07:33,150 --> 00:07:37,930
+مراكبات قلت له بسيطة حط التالتة حطينا التالتة لما
+
+91
+00:07:37,930 --> 00:07:42,810
+يكونوا تلاتة بيصير ال vector ايه ك magnitude مش
+
+92
+00:07:42,810 --> 00:07:45,750
+انت قلتلي لما يكونوا تنتين حسب في ال course هيك
+
+93
+00:07:45,750 --> 00:07:49,990
+بتعمله لما يكون التالتة حط التالتة يا سيدي نزعلهاش
+
+94
+00:07:50,660 --> 00:07:53,880
+بنحط زائد is التربية لما يكون التالتة ال direction
+
+95
+00:07:53,880 --> 00:07:56,880
+يقولي صعب ال direction عليك لإنه لما يكون في عندك
+
+96
+00:07:56,880 --> 00:08:01,100
+فراغ بد يكون في عندك تلت زوايا بتصير زاوية مع
+
+97
+00:08:01,100 --> 00:08:03,820
+السين وزاوية مع الصعد وزاوية مع العين مش مطلوب
+
+98
+00:08:03,820 --> 00:08:07,960
+مننا مش مطلوب من الحمد لله احنا ده ده ده بناخد
+
+99
+00:08:07,960 --> 00:08:13,120
+اللي اللي بنقدر عليه بنطلبه منكم و اللي شويةبنأجله
+
+100
+00:08:13,120 --> 00:08:16,320
+مش في عماجمه .. بنأجه .. بنأجله مش عنا .. السنة
+
+101
+00:08:16,320 --> 00:08:19,060
+التاسعة احنا بقى بيقول بسم الله في الجامعة في سنة
+
+102
+00:08:19,060 --> 00:08:22,460
+تانية في سنة تالتة في سنة رابعة و لسه العلم كتير
+
+103
+00:08:22,460 --> 00:08:29,000
+بيجي و في سنة خامسة ماذا هي الملاحقين الناس لسه
+
+104
+00:08:29,000 --> 00:08:38,440
+عاجلة احكي اعلي صوتك بالفرق وموجهه هذا متجه وهذه
+
+105
+00:08:38,440 --> 00:08:44,600
+اتجاهه هيك وإن هتعلق ولا في الفرقهي في الفراخ بدي
+
+106
+00:08:44,600 --> 00:08:52,320
+تكون عندك محور تالت اللي هو تلع كيف XYYZ هذا لا هو
+
+107
+00:08:52,320 --> 00:08:56,900
+لا سيني ولا صادي ولا زدي في الفراخ بتحلل لتلت
+
+108
+00:08:56,900 --> 00:09:03,880
+مراكبها اه مش عالم يقول ده ده ده علينا ده ده ده ده
+
+109
+00:09:03,880 --> 00:09:10,120
+واحدة واحدة ليش من حاجله لتلت هو هو له تلت عفره
+
+110
+00:09:10,120 --> 00:09:16,400
+عشان يسويلههك انخلج، تمام؟ هك انخلج هو .. هو في
+
+111
+00:09:16,400 --> 00:09:20,580
+الفراغ هو في الفراغ، أيش يعني في الفراغ؟ إله تلت
+
+112
+00:09:20,580 --> 00:09:26,720
+أبعاد، إذا إله تلت مُركّبات، تمام؟ هو دي طبيعة
+
+113
+00:09:26,720 --> 00:09:31,560
+الأشياء، كل vector إله تلت مُركّبات، حتى لو كان في
+
+114
+00:09:31,560 --> 00:09:36,700
+لبلين، بيقولوا تلت سفر تلت سفر، لكن in general،
+
+115
+00:09:36,700 --> 00:09:41,610
+بيقول كل vector إله تلت مُركّباتلأن طبيعة الأشياء
+
+116
+00:09:41,610 --> 00:09:46,230
+يا ربنا خلقها فراغ three dimensions وإن يكون موجود
+
+117
+00:09:46,230 --> 00:09:51,050
+في plane أو في line حالة خاصة حالات خاصة فاهمت
+
+118
+00:09:51,050 --> 00:09:57,450
+عليها هى أصل الأشياء أنها تكون تلت أبعاد dial قال
+
+119
+00:09:57,450 --> 00:10:01,850
+لي ال vector إله مركبات أمين لا تنتين لا تلاتة طب
+
+120
+00:10:01,850 --> 00:10:05,450
+لو في vector عندك zero قال لك تتوقع فيه مركبة من
+
+121
+00:10:05,450 --> 00:10:13,720
+المركبات ما تكونش zeroفي مجال؟ كيف؟ vector مقداره
+
+122
+00:10:13,720 --> 00:10:21,520
+zero تمام؟ هل في مجال أحد مركباته مايكونيش zero؟
+
+123
+00:10:21,520 --> 00:10:26,840
+من اللي بيقول آه يفسلي احنا راضين نسمع كيف؟ بدك
+
+124
+00:10:26,840 --> 00:10:34,020
+حاجة تلغيها؟ مفهوش مفهوش ولا ممكناللي بيقول ممكن
+
+125
+00:10:34,020 --> 00:10:39,740
+يعلي صوتي ويقنعني كيف ممكن vector مؤحد مركباته مش
+
+126
+00:10:39,740 --> 00:10:44,940
+سفر ومقداره سفر ولازم يكون مقداره سفر، في مجال؟
+
+127
+00:10:44,940 --> 00:10:50,320
+انتوا هاديها، تشوفوا، لو واحدة من هدول مش سفر و
+
+128
+00:10:50,320 --> 00:10:53,080
+بتجمعوهم، بتاخدوا الجهاز الترابيعي بتطلع هنا، سفر؟
+
+129
+00:10:53,080 --> 00:10:58,360
+ولا ممكن؟ إذا إيش بيقوللي Note that if the vector
+
+130
+00:10:58,360 --> 00:11:03,820
+A is zeroإذن من بعرف على طول كل مركبته مالها Zero
+
+131
+00:11:03,820 --> 00:11:09,420
+قطعا كل مركبته Zero تمام يا ابنها؟ و اللي محتاجة
+
+132
+00:11:09,420 --> 00:11:14,400
+تقول بس تكون شجعة و تقول و تخنعنا بس بدنا شجعة
+
+133
+00:11:14,400 --> 00:11:21,740
+احكوا اعيد؟ في مجال vector يكون مقداره سفر ها
+
+134
+00:11:21,740 --> 00:11:28,860
+مقداره سفر واحد مركبته مش سفر فش مجال ولا ممكن
+
+135
+00:11:31,100 --> 00:11:35,820
+بنفعش يكونوا عكس بعض لإن هدا سيني و هدا صاضي هفيه
+
+136
+00:11:35,820 --> 00:11:41,600
+مراكبات نفس المقدار كل نفس الاشي بس واحد رمج و
+
+137
+00:11:41,600 --> 00:11:45,900
+واحد سالب لأ مانيش تعرفيهم هدول موجب و هدا سالب
+
+138
+00:11:45,900 --> 00:11:48,740
+خمسة و سالب خمسة مينجمعوش لإن واحد سيني و واحد
+
+139
+00:11:48,740 --> 00:11:54,220
+صاضي هدول ماجربوش لبعض بنفعش يلغوا بعض زي ما انت
+
+140
+00:11:54,220 --> 00:12:03,330
+متوقع بنفعش يلغوا بعضبالظبط اذا فمافيش مجال بالمرة
+
+141
+00:12:03,330 --> 00:12:07,750
+حلو الصحيح
+
+142
+00:12:07,750 --> 00:12:13,850
+جالي خلاص ال vector عرفت كيف اكتبه هاي vector و
+
+143
+00:12:13,850 --> 00:12:17,150
+هاي vector
+
+144
+00:12:17,150 --> 00:12:23,470
+بتتخيلوه
+
+145
+00:12:23,470 --> 00:12:27,970
+بتتخيلوه صح بتتخيل ايه الأول انه فجلس مرة وين
+
+146
+00:12:30,540 --> 00:12:36,000
+بالربع الرابع، صح؟ ممتازين، بدي أجمعهم جالي ترسمهم
+
+147
+00:12:36,000 --> 00:12:41,860
+إيش؟ الآن بدي أجمع بدون رسم بدي أجمع و أستفيد من
+
+148
+00:12:41,860 --> 00:12:44,660
+الراوضة روحنا و .. و .. و حطينا فلوس على الفاضل من
+
+149
+00:12:44,660 --> 00:12:47,180
+هنا نستفيد من الراوضة اللي جمعنا؟ بدي نجمع زي ما
+
+150
+00:12:47,180 --> 00:12:50,700
+كنا نجمع في الراوضة بس إيش هسوي؟ جالي بديك تجمع
+
+151
+00:12:50,700 --> 00:12:54,500
+السيني مع السيني والصاضي مع الصاضيممنوع تجمع
+
+152
+00:12:54,500 --> 00:12:59,100
+الصيني مع الصاضي اجمع الصيني مع الصاضي هي A أنها
+
+153
+00:12:59,100 --> 00:13:03,760
+صيني ولا مالهاش و B اجمع الصيني تبقى A مع الصيني
+
+154
+00:13:03,760 --> 00:13:09,980
+تبقى B و يطلع أربعة I و اجمع الصاضي مع الصاضي نقصت
+
+155
+00:13:09,980 --> 00:13:15,500
+نين جين هاي مجموحهم هاي مجموحهم يورني مثل المجموع
+
+156
+00:13:15,500 --> 00:13:20,040
+طب وذا ال vectors مش مكتوبين هيك جالي بتخليهم هم
+
+157
+00:13:20,040 --> 00:13:26,440
+يقولوا هيكإذا لو كان عندي Vector ورسمليه يا جالي
+
+158
+00:13:26,440 --> 00:13:31,560
+أول حاجة تعملها قبل ما تجمع حلليه يا جيب مركباته
+
+159
+00:13:31,560 --> 00:13:37,160
+إذا بقولي Now to add to vectors analytically يعني
+
+160
+00:13:37,160 --> 00:13:41,780
+بدون رسم تحليليا يعني جبريا يعني جمع الروضة اللي
+
+161
+00:13:41,780 --> 00:13:46,600
+اتعلمناها كيف أسوي جالي proceed as follow اتبع
+
+162
+00:13:46,600 --> 00:13:52,610
+الخطوات التاليةresolve حلل أي vector إلى مركبته
+
+163
+00:13:52,610 --> 00:13:57,130
+resolve each vector into its component according
+
+164
+00:13:57,130 --> 00:14:00,430
+to a suitable coordinate axis حسب محاول معينين
+
+165
+00:14:00,430 --> 00:14:05,230
+قالت طب لو كتبليهم هيك بدون تحليل هدول؟هي جاهز اذا
+
+166
+00:14:05,230 --> 00:14:08,790
+هذه الخطوة تلزمني لو كان ال vector ماتدانيش يا
+
+167
+00:14:08,790 --> 00:14:11,650
+بهذه الصيغة لكن لما يكون اتدانيها بهذه الصيغة
+
+168
+00:14:11,650 --> 00:14:15,650
+محلله جاهز ايش يعني حلله؟ جيبلي مراكبة الصينية و
+
+169
+00:14:15,650 --> 00:14:20,630
+مراكبة الصاضية هجيتي ال بي اللي فوقاني قداش مراكبة
+
+170
+00:14:20,630 --> 00:14:26,770
+الصينية الصاضية ناقص خمسة براو عليكم ناقص خمسة
+
+171
+00:14:26,770 --> 00:14:32,420
+تمام ايه مراكبة الصينيةفضية جاهزين ولا مش جاهزين؟
+
+172
+00:14:32,420 --> 00:14:37,020
+جاهزين قال لي بعد كده قال لي add algebraically
+
+173
+00:14:37,020 --> 00:14:42,240
+يعني جمع روضة جبريا يعني the x component of the
+
+174
+00:14:42,240 --> 00:14:46,800
+individual vectors to obtain the x component of
+
+175
+00:14:46,800 --> 00:14:51,120
+the resultant vector إذا المركبة الصينية للمحصلة
+
+176
+00:14:51,120 --> 00:14:54,920
+هي مجموع المركبات الصينية لل vectors اللي بتجمعهم
+
+177
+00:14:55,860 --> 00:14:59,560
+تمام do the same thing for the other components
+
+178
+00:14:59,560 --> 00:15:03,440
+نفس العملية ل Y و نفس العملية ل Z تمام يا بنات
+
+179
+00:15:03,440 --> 00:15:08,440
+يعني قال لي هاي two vectors هاي بقى تلاتة
+
+180
+00:15:08,440 --> 00:15:12,860
+dimensions اتلتة كتبته في الفراغ تمام قال لي بدي
+
+181
+00:15:12,860 --> 00:15:20,950
+اجمع قولتله هاي جميعطلع اش سويك ax بي x ay بي y az
+
+182
+00:15:20,950 --> 00:15:26,110
+بي z تمام؟ وحطت عند ال xi وعند ال yj وعند ال zk
+
+183
+00:15:26,110 --> 00:15:31,790
+يلا يا بناة ها بالأحمق خلينا نعمل أر يعني
+
+184
+00:15:31,790 --> 00:15:39,620
+resultant اللي هي بتسوي a بي بي يلا اجمعوليأربعة
+
+185
+00:15:39,620 --> 00:15:45,840
+اي ناقص اتنين جي شوفوا مايكترفنا اصلا الجامع رسمت
+
+186
+00:15:45,840 --> 00:15:51,460
+بدي طريقة المثلث ولا طريقة متوازن اضلاع اذا خلاص
+
+187
+00:15:51,460 --> 00:15:56,780
+تعاملت مع ال vector بطريقة حلوة و بدون اي اشكالية
+
+188
+00:15:56,780 --> 00:16:04,860
+لا بدي مصطرة ولا منجلة ولا بيكار اي استفسار فيرجار
+
+189
+00:16:05,870 --> 00:16:08,910
+انتوا خدتوا فرجار؟ احنا على أيامنا كنا بيقول عنه
+
+190
+00:16:08,910 --> 00:16:15,150
+بيكار فيه اختلاف في ال .. في الأجيال تمام احنا جيل
+
+191
+00:16:15,150 --> 00:16:22,090
+يد 2000 بتعرفيش اي شي ورد 2000؟ H2O H2O بتعرفوه؟
+
+192
+00:16:22,090 --> 00:16:26,690
+تبع كيميا، مية نعم احنا زمان كانت الرموز عندنا
+
+193
+00:16:26,690 --> 00:16:32,150
+بالعربي احنا .. احنا جيل يد 2000 يد يعني هيدروجين
+
+194
+00:16:32,150 --> 00:16:39,460
+و ألف اكسجين اه هي كان زمانجيلة يعني تمام اذا من
+
+195
+00:16:39,460 --> 00:16:48,380
+الجامعة عرفت كيف ادمع حلو quiz يعني انريح انريح
+
+196
+00:16:48,380 --> 00:16:53,580
+جالي بيدديك قدت vectors و تشوف ليه من هال vectors
+
+197
+00:16:53,580 --> 00:16:58,640
+مين منهم مقداره تعرفوا جيبوا مقدار لأي vector
+
+198
+00:16:58,640 --> 00:17:04,960
+بيساوي أحد مركباتهfor which of the following
+
+199
+00:17:04,960 --> 00:17:09,440
+vectors is the magnitude مقداره of the vector
+
+200
+00:17:09,440 --> 00:17:13,300
+equal to one of the components of the vector أحد
+
+201
+00:17:13,300 --> 00:17:18,940
+المركبات نيجي هذا المركبة الصينية كده؟ المركبة
+
+202
+00:17:18,940 --> 00:17:22,180
+الصادرية؟ المركبة الزدية؟ أبقى الله عليكم، بدي
+
+203
+00:17:22,180 --> 00:17:27,960
+أجيب المقدار، مين يجيبليها؟ أه انت اللي بتحكيه؟
+
+204
+00:17:27,960 --> 00:17:32,980
+نجليه، نبسط عليه أربعة؟
+
+205
+00:17:37,170 --> 00:17:40,890
+صحيك السؤال بيقوللي هل جزء التلاتين بيساوي اتنين؟
+
+206
+00:17:40,890 --> 00:17:46,110
+بيساوي خمسة؟ بيساوي واحد؟ اذا هذا لأ لأنه بيقوللي
+
+207
+00:17:46,110 --> 00:17:51,010
+هل المقدار اللي نجلتنيه بيساوي احد المواكبات؟ و هم
+
+208
+00:17:51,010 --> 00:18:01,790
+تلات مواكبات يلا هذا ايه اجديد؟ اربعة هل
+
+209
+00:18:01,790 --> 00:18:05,470
+جزء التسعة عشرين بيساوي اتنين؟ بيساوي خمسة؟ برضه
+
+210
+00:18:05,470 --> 00:18:12,870
+هذا لأمظبوط؟ و تابعين؟ جدش ال magnitude ال
+
+211
+00:18:12,870 --> 00:18:18,370
+magnitude لسه ع المرة قديكي يوم السبت مطول مش مطول
+
+212
+00:18:18,370 --> 00:18:22,310
+قولنا ممنوع ال magnitude يكون سالب ذاكرين؟ كنا
+
+213
+00:18:22,310 --> 00:18:27,250
+نحكي صيني زمان حكيناها دي جملة عشان كده لما جيبنى
+
+214
+00:18:27,250 --> 00:18:30,210
+ال absolute value لما حكيناه ليش أخدوا ال absolute
+
+215
+00:18:30,210 --> 00:18:33,770
+value و قولت لإنه بتجربة لأ إذا جدش ال magnitude
+
+216
+00:18:33,770 --> 00:18:40,520
+جدش ال componentماناس ثلاثة بيساوي بعض؟ لأ هذي
+
+217
+00:18:40,520 --> 00:18:45,860
+بتغوش دي في بالكم بتطمع الإنسان يقول هذي صح شوفها
+
+218
+00:18:45,860 --> 00:18:51,260
+الأخيرة هذي يا إذا بدي أصنع للآخر و أشوف من الصح
+
+219
+00:18:51,260 --> 00:18:55,800
+عشان ماجعش في المطب هذي جديش مقبرها و جديش ال
+
+220
+00:18:55,800 --> 00:18:59,640
+component تبعها الخمسة ال z component تبعها صحيح؟
+
+221
+00:18:59,640 --> 00:19:05,680
+حلو؟أيه السر سار؟ تمام يا بنادى؟ أمورنا سهلة
+
+222
+00:19:05,680 --> 00:19:12,040
+example find the sum إيش يعني sum؟ بدك تجمع متى و
+
+223
+00:19:12,040 --> 00:19:16,040
+إتعلمت تجمع؟ of two displacement vectors دالي ال
+
+224
+00:19:16,040 --> 00:19:19,620
+two vectors بس بدي أنا أديك مثال حي فيزيائي هي
+
+225
+00:19:19,620 --> 00:19:23,080
+displacement أحد أمثلة ال vectors ولا لأ؟ is it صح
+
+226
+00:19:23,080 --> 00:19:26,940
+الكلام؟ ليش حطت displacement عشان أحط متر؟ عشان
+
+227
+00:19:26,940 --> 00:19:31,460
+أصير فيزياء؟ وهيبي؟بدا نيجي معايا يا بناتي و دي
+
+228
+00:19:31,460 --> 00:19:37,080
+مصعب السؤال الصيني مع الصيني اربع و اتنين نقصت
+
+229
+00:19:37,080 --> 00:19:42,260
+نيجي سلبت نيجي خلص المثال هذا هو
+
+230
+00:19:45,380 --> 00:19:49,580
+مظبوطك ولا لأ؟ بدي مقدار ال result بقدر اجيبه؟ اه
+
+231
+00:19:49,580 --> 00:19:54,100
+طبعا بدي الزاوية بقدر اجيبها؟ ten صح؟ اذا لو بدو
+
+232
+00:19:54,100 --> 00:19:58,600
+ال magnitude بجيبها و لو بدو الزاوية بجيبها تمام
+
+233
+00:19:58,600 --> 00:20:03,180
+هيك يا بنات؟ مواضع هنا سهلة جامعة عادي جامعة
+
+234
+00:20:03,180 --> 00:20:05,520
+الصينية مع الصينية والصادية مع الصادية مظبوطك ولا
+
+235
+00:20:05,520 --> 00:20:10,000
+لأ؟ نشوف بقول
+
+236
+00:20:10,000 --> 00:20:13,000
+الان في عندي particle ايجي على باله يعمل مش
+
+237
+00:20:13,000 --> 00:20:18,670
+ازاحتين تلاتةتلات إذاحات a particle undergoes أجرة
+
+238
+00:20:18,670 --> 00:20:23,350
+three consecutive displacements عملت تلات إذاحات
+
+239
+00:20:23,350 --> 00:20:28,810
+متتالية consecutive متتالية الشمّة قال لي هايهوا
+
+240
+00:20:28,810 --> 00:20:32,130
+اتفرجوا انتوا حتى الآن بالدنيا هم جاهزين محللين
+
+241
+00:20:32,130 --> 00:20:35,930
+وخالصين قاللي بدي ال resultant ان شاء الله يكونوا
+
+242
+00:20:35,930 --> 00:20:40,730
+عشرة ايش هسوي الصيني لحال و الصاضي لحال و الأغاني
+
+243
+00:20:40,730 --> 00:20:46,320
+لحالاختلف اشي تنتين ولا تلاتة ولا عشرة مجرد انه
+
+244
+00:20:46,320 --> 00:20:49,940
+طويل ولا قصير السؤال مظبوط ولا لأ قال يالا ايش بدك
+
+245
+00:20:49,940 --> 00:20:54,640
+قال find the resultant displacement المحصلة and
+
+246
+00:20:54,640 --> 00:21:02,700
+its magnitude و magnitude مقدارها تمام ها كيف
+
+247
+00:21:02,700 --> 00:21:10,350
+بنعمل بنقوله سهل بنقوله Rاللي هي بتساوي A زائد B
+
+248
+00:21:10,350 --> 00:21:16,230
+زائد C بتساوي يالا نجمع البلد بنقول Calculator خمس
+
+249
+00:21:16,230 --> 00:21:19,710
+اتعش تلاتة و عشرين و نقص تلات عشر اتنين خمسة و
+
+250
+00:21:19,710 --> 00:21:26,590
+عشرين اذا خمسة و عشرين I واحد و تلاتين J هدي سهل
+
+251
+00:21:26,590 --> 00:21:35,490
+لأ لأن الأخيرة سفر اذا انا اتناش نقص خمسة احكي
+
+252
+00:21:36,690 --> 00:21:43,390
+عليه صوتكم اللي بيحكي اه
+
+253
+00:21:43,390 --> 00:21:48,250
+مالها هذيك
+
+254
+00:21:48,250 --> 00:21:52,250
+تلاتين نقص اربع طايز زاد خمسة وكان الجامعة واحدة
+
+255
+00:21:52,250 --> 00:22:00,850
+تمام طيب يلا يا بنات خمس و عشرين تربيع زاد واحد و
+
+256
+00:22:00,850 --> 00:22:03,990
+تلاتين تربيع زاد تسعة واربعين اللي هي سبعة تربيع
+
+257
+00:22:04,850 --> 00:22:07,110
+أربعين point أربعة ما بديش الأربعة بيكفيني
+
+258
+00:22:07,110 --> 00:22:11,670
+الأربعين وهي اربعين طبعا هه عشان ما تزعجش وهي
+
+259
+00:22:11,670 --> 00:22:21,310
+point أربعة خلاص هو ايش كتب فانت تقليها مش مشكلة
+
+260
+00:22:21,310 --> 00:22:25,170
+ممكن تحوليها ما هو ال gaussian system مش system
+
+261
+00:22:25,170 --> 00:22:29,870
+system مقبول منك يعني اللي بدي يحول يحول أي
+
+262
+00:22:29,870 --> 00:22:32,430
+استفسار يا بنات تمام؟
+
+263
+00:22:35,450 --> 00:22:39,970
+شوف السؤال هجيتني رجال يقولوا ليه بديش ادّيكي هم
+
+264
+00:22:39,970 --> 00:22:48,050
+جاهزين بديكي تجيبي انت المواكبات مظبوط بقولي a
+
+265
+00:22:48,050 --> 00:22:55,530
+hiker ايش بنسميه الهايكر احنا صياد
+
+266
+00:22:55,530 --> 00:23:02,130
+ولا تبع .. لها كلمة تانية مش شايعة في مخي من هايك
+
+267
+00:23:02,130 --> 00:23:07,770
+.. بتصلقوا هدول .. بتصلقواالبيت كومية مش مشكلة a
+
+268
+00:23:07,770 --> 00:23:12,610
+hacker begins a trip trip يعني رحلة رحلة by first
+
+269
+00:23:12,610 --> 00:23:18,910
+walking كيف بدت قالش مشيت كان معاها سيارة قررت
+
+270
+00:23:18,910 --> 00:23:24,230
+السيارة هنا و بدت تمشي رحلتها مشيت خمسة و عشرين
+
+271
+00:23:24,230 --> 00:23:31,210
+كيلومتر south eastSouth East جنوب شرق محط ليش
+
+272
+00:23:31,210 --> 00:23:34,030
+زاوية معناته في النص بالظبط ولا لأ الزاوية 45
+
+273
+00:23:34,030 --> 00:23:39,330
+South East from her car من سيارتها سيارتها جونه
+
+274
+00:23:39,330 --> 00:23:46,830
+هناك نقطة الاصل حلو she stops تعبت قعدت طلعت على
+
+275
+00:23:46,830 --> 00:23:53,460
+الساعة غابت الشمسوقفت وقفت هناك وقفت هناك وقفت
+
+276
+00:23:53,460 --> 00:24:00,100
+هناك وقفت
+
+277
+00:24:00,100 --> 00:24:02,540
+هناك وقفت هناك وقفت هناك وقفت هناك وقفت هناك وقفت
+
+278
+00:24:02,540 --> 00:24:02,620
+هناك وقفت هناك وقفت هناك وقفت هناك وقفت هناك وقفت
+
+279
+00:24:02,620 --> 00:24:02,620
+هناك وقفت هناك وقفت هناك وقفت هناك وقفت هناك وقفت
+
+280
+00:24:02,620 --> 00:24:02,620
+هناك وقفت هناك وقفت هناك وقفت هناك وقفت هناك وقفت
+
+281
+00:24:02,620 --> 00:24:02,640
+هناك وقفت هناك وقفت هناك وقفت هناك وقفت هناك وقفت
+
+282
+00:24:02,640 --> 00:24:03,320
+هناك وقفت هناك وقفت هناك وقفت هناك وقفت هناك وقفت
+
+283
+00:24:03,320 --> 00:24:18,080
+هناك وقفت هناك وقفت هناك وقفت
+
+284
+00:24:18,080 --> 00:24:24,000
+هنا60 degree north of east 60 درجة شمال الشرق
+
+285
+00:24:24,000 --> 00:24:30,480
+شايفين شمال الشرق 60 درجة حلو جالي و هي ماشية بدل
+
+286
+00:24:30,480 --> 00:24:35,920
+اتجاهها طلعت لجت البرج تبع حالس الغابة جلست ونسنا
+
+287
+00:24:35,920 --> 00:24:42,520
+تمام وقفت هنا خلاص وصلت الونس زي ما بنسميهتمام؟ in
+
+288
+00:24:42,520 --> 00:24:46,560
+a direction 60 degree north of east at which point
+
+289
+00:24:46,560 --> 00:24:50,420
+في تلك النقطة she discovers a forest rangers tower
+
+290
+00:24:50,420 --> 00:24:54,500
+forest rangers هو حارس الغادا تمام؟ forest ..
+
+291
+00:24:54,500 --> 00:24:57,780
+انتوا عارفين انا غادا؟ تمام هذه قصة مانا اتعرفيها
+
+292
+00:24:57,780 --> 00:25:01,460
+احنا بس عايزكي بنحكي عشان نتعرفي اننا بنكمل مصطلح
+
+293
+00:25:01,460 --> 00:25:04,560
+انجليزي و احنا مش جايوركن في امتحان دي بنكون زي
+
+294
+00:25:04,560 --> 00:25:08,450
+هيكاحنا بدنا نقعد نخش ع جوجل و نترجم؟ لأ، بنجيب
+
+295
+00:25:08,450 --> 00:25:11,350
+لكم أبسط من هنا بس هاد موجودة في الكتاب فبنقراها
+
+296
+00:25:11,350 --> 00:25:16,670
+إيش بدها؟ قالت determine the components of each
+
+297
+00:25:16,670 --> 00:25:21,370
+displacement هي عملت إذاحتين إذاحة southeast و
+
+298
+00:25:21,370 --> 00:25:27,850
+إذاحة northeast ب60 درجة بدي مركباتها طيب و بعدين؟
+
+299
+00:25:27,850 --> 00:25:31,350
+قالت بعد كده بدك تجمعلي الإذاحتين طب أنا إذا جبت
+
+300
+00:25:31,350 --> 00:25:34,230
+المركبة تخلصت المسألة صحيح ولا لأ؟
+
+301
+00:25:37,970 --> 00:25:40,610
+اتطلعوا .. اتطلعولي على اللوحة، هلجيت؟ شوفوا
+
+302
+00:25:40,610 --> 00:25:45,830
+المُركّبة إيه اللي نازلها دي بقدر أقول هذه عبارة
+
+303
+00:25:45,830 --> 00:25:51,870
+عن هاي مُركّبتينها ولا لأ؟ مظبوط هيك ولا لأ؟ تمام،
+
+304
+00:25:51,870 --> 00:25:55,910
+بدي اتطلع على المُركّبة الصادية، كيف اتجاهها؟ إذا
+
+305
+00:25:55,910 --> 00:26:02,270
+لازم تكون سالبة، صح؟ لازم تكون سالبة قطعا، هلجيت؟
+
+306
+00:26:03,010 --> 00:26:08,690
+أنا بعرف الزاوية إليها مجاور إليها مقابل المجاورة
+
+307
+00:26:08,690 --> 00:26:13,390
+بدي أخد cosine والمقابل بدي أخد sine نجي نتطلع على
+
+308
+00:26:13,390 --> 00:26:16,950
+هذه الحلوة وهذه الزاوية اللي جدتني إياها هذه
+
+309
+00:26:16,950 --> 00:26:21,240
+المركبة جارت هذه ولا لا؟ جارتها إذا إيش بيتاخد؟cos
+
+310
+00:26:21,240 --> 00:26:28,040
+, اذا على طول بدي اقوله الان المركبة الصينية و
+
+311
+00:26:28,040 --> 00:26:35,980
+اللي هي الموجبة بحسب الرسمة بقوله ax بتساوي a cos
+
+312
+00:26:35,980 --> 00:26:44,020
+45 صح ولا لأ؟ مقدش ايه؟ جالي 25 كيلومتر اذا 25 في
+
+313
+00:26:44,020 --> 00:26:47,320
+cos 45 طلع 17.7 كيلومتر
+
+314
+00:26:53,230 --> 00:26:58,470
+ال cosine و ال sine تمام دايما توقم جان بعيد ال
+
+315
+00:26:58,470 --> 00:27:01,890
+cosine بيسوي مجاور عواطر تمام و ال .. و ال sign
+
+316
+00:27:01,890 --> 00:27:06,790
+المقابل على .. حلو شفاح الزاوية اه 45 حلو شفاح
+
+317
+00:27:06,790 --> 00:27:11,210
+الحمرة فوق هذه مقابل ولا مجاور لها بالنصف للزاوية
+
+318
+00:27:11,210 --> 00:27:16,330
+اه اه بالنصف للزاوية مجاور عشان كده أخدنا ال
+
+319
+00:27:16,330 --> 00:27:21,890
+cosine اه تمام طيب ندي لهذه هذه هي نفسها هادي
+
+320
+00:27:21,890 --> 00:27:27,120
+دلبالكلأ الموازية بتصير مقابل هادي إذا بياخد صيني
+
+321
+00:27:27,120 --> 00:27:32,480
+ولا لأ؟ إذا بقى أقول اي وراي تلبقى كل عصفر حتى
+
+322
+00:27:32,480 --> 00:27:32,960
+السالب
+
+323
+00:27:36,330 --> 00:27:40,970
+عرفت ليش حطت السلب؟ سألتكم عنه قلت له الأسفل إذا
+
+324
+00:27:40,970 --> 00:27:45,390
+المعناته موكبة الصدرية لازم تكون الأسفل قلتله هذه
+
+325
+00:27:45,390 --> 00:27:50,870
+بيساوي سالب 17.7 كيلومتر لإن صينيا 45 وكسانيا 45
+
+326
+00:27:50,870 --> 00:27:59,910
+إخوة صح تمام إذا بقوله من هنا بقدر أقول ايه بيساوي
+
+327
+00:27:59,910 --> 00:28:08,940
+17.7 I نقل 17.7جا كيلومتر ولا لأ؟ هذه المراكبات
+
+328
+00:28:08,940 --> 00:28:13,720
+البدكية هلأ إيه؟ بالنبي خلصت من إيه صح؟ أيسر صار
+
+329
+00:28:13,720 --> 00:28:18,600
+على إيه؟ نجي ل بي الحلوة التانية بقوله بي هادي
+
+330
+00:28:18,600 --> 00:28:31,360
+خلصنا من هادي قلتله بي هادي؟
+
+331
+00:28:33,570 --> 00:28:38,230
+بصيها دي cosine و دي sine بصيها دي cosine لها حسب
+
+332
+00:28:38,230 --> 00:28:43,330
+ال zeta تبعتك يعني انت بتكتب ال zeta دي صح بس تصير
+
+333
+00:28:43,330 --> 00:28:49,170
+ايش المجول لها الصادية صحيح ولا لأ بس ما حصل الحظ
+
+334
+00:28:49,170 --> 00:28:56,550
+الآن 45 neutral تفرجش تمام لكن لو كان الزاوية غير
+
+335
+00:28:56,550 --> 00:28:59,790
+45 تفرج بصي بكتن تبقي غيرت الزاوية بكتن تتغير ال
+
+336
+00:28:59,790 --> 00:29:02,770
+sine و ال cosine تمام يا بنت تمام
+
+337
+00:29:04,990 --> 00:29:09,530
+طلعوا حاجات B طلعوا بيه بدي مراكباتها هل هي مجموح
+
+338
+00:29:09,530 --> 00:29:20,770
+هدول مراكبتين ولا لأ؟ ليش؟ اه هي متوازن أضلال كيف؟
+
+339
+00:29:20,770 --> 00:29:26,650
+عند أخره مش احنا بنقول متوازن أضلال مانا سينا تانا
+
+340
+00:29:26,650 --> 00:29:32,010
+جالي حلو بدي المراكبة حاجات الصينية موجبة و
+
+341
+00:29:32,010 --> 00:29:37,970
+الصادية برضه موجبةهل جيت .. من اللي توسألت على
+
+342
+00:29:37,970 --> 00:29:44,590
+الزاوية؟ اه انتبهيلي هل جيت الزاوية مش 45؟ 60؟ طيب
+
+343
+00:29:44,590 --> 00:29:50,950
+انا ال 60 فضربويا ولا مرسومة؟ مشوفة للجميع المركبة
+
+344
+00:29:50,950 --> 00:29:55,830
+الصينية جرتها ولا مقابلها؟ جرتها لو غيرت الزاوية
+
+345
+00:29:55,830 --> 00:30:04,800
+بصير 30 هديكتمام فبقدر اقول بي اكس بتساوي بي كسين
+
+346
+00:30:04,800 --> 00:30:09,400
+الستين بتساوي اربعين في كسين الستين عشرين كيلو متر
+
+347
+00:30:09,400 --> 00:30:13,920
+بي
+
+348
+00:30:13,920 --> 00:30:20,960
+واي بتساوي برضه زائد و هادي زائد بي سين الستين و
+
+349
+00:30:20,960 --> 00:30:25,080
+بتساوي اربعة
+
+350
+00:30:25,080 --> 00:30:27,340
+و تلاتين و ستة كيلو متر
+
+351
+00:30:30,380 --> 00:30:35,080
+كيف حللت ال 60 كيف يعني ال 60 هو ايه حلتها جدا و
+
+352
+00:30:35,080 --> 00:30:39,540
+صعيب حلو هجيه شفاها ال 60 الصينية شفاها المراكبة
+
+353
+00:30:39,540 --> 00:30:43,280
+الصينية الحمراء جالتها ولا مقابل لها عارف فعلا انا
+
+354
+00:30:43,280 --> 00:30:49,120
+بس لإنه جيت ال envy هيك رايحة اه طلع عليها انك
+
+355
+00:30:49,120 --> 00:30:58,520
+عشانها بعيدة عليكي هاي فيكتور هو هايه بدي أحللها
+
+356
+00:31:00,470 --> 00:31:05,490
+فبتكون تحليلها كيف؟ بقوله هيك و هيك عشان تطلع وطر
+
+357
+00:31:05,490 --> 00:31:13,970
+في متوازي عضلات غيرها تقدر الآن من هدول التنتين
+
+358
+00:31:13,970 --> 00:31:21,650
+اقول ان بي بتسوى عشرين I زائد اربعة وتلاتين point
+
+359
+00:31:21,650 --> 00:31:29,740
+ستة J صح ولا لا يا بنات؟ اجهز المطبب التانيالمطلوب
+
+360
+00:31:29,740 --> 00:31:33,000
+التاني ايش بده؟ قال لي بدي اجمع قلت له اجمع الصيني
+
+361
+00:31:33,000 --> 00:31:39,220
+مع الصيني والصاضي مع الصاضي فالان R اللي هي A زائد
+
+362
+00:31:39,220 --> 00:31:46,920
+B بتساوي سبعة وتلاتين point سبعة I زائد سبعتاشر J
+
+363
+00:31:46,920 --> 00:31:53,900
+كيلومتر تقريبا، هذه فيها أقل، اسألك، فانت من
+
+364
+00:31:53,900 --> 00:32:00,980
+الكلامولا إيش إيه؟ نسجك من دون خط الله تمام نسجك
+
+365
+00:32:00,980 --> 00:32:12,000
+احكوا يا بنات أي صفصار؟ جمع سهل سهل جدا اه هذا هو
+
+366
+00:32:12,000 --> 00:32:18,640
+بدك تزاوي بنجيبلك اللي بدك إياه بنعملك إياههنجيب
+
+367
+00:32:18,640 --> 00:32:22,740
+شغلة شوية متقدمة احنا الجماعة أخدناها في الروضة صح
+
+368
+00:32:22,740 --> 00:32:29,300
+ولا لأ ضرب ال vectors product معناتها ضرب product
+
+369
+00:32:29,300 --> 00:32:35,120
+of vectors قاللي هتواجه تلت أنواع من الضربتلت
+
+370
+00:32:35,120 --> 00:32:40,920
+أنواع اول نوع multiply يعني اضرب multiplying ضرب
+
+371
+00:32:40,920 --> 00:32:45,840
+برضه يعني product ضرب و multiplying ضرب اتفقنا؟
+
+372
+00:32:45,840 --> 00:32:49,260
+multiplying a vector by a scalar دي دكتور يكتره
+
+373
+00:32:49,260 --> 00:32:55,720
+بالان vector في scalar نمحي هذا كله هجيت و نشوف هى
+
+374
+00:32:55,720 --> 00:33:00,200
+ممكن نضرب vector في scalar في العلم؟ نقول اه قال
+
+375
+00:33:00,200 --> 00:33:01,620
+ياخدت هذا القانون
+
+376
+00:33:05,850 --> 00:33:13,090
+فى حد مااخدهوش الـ M scalar و الـ A ضرابة tiny
+
+377
+00:33:13,090 --> 00:33:18,790
+vector فى scalar صح ولا لأ تمام هذا ممكن يكون له
+
+378
+00:33:18,790 --> 00:33:25,970
+تلت مراكبات ماهو vector صحيح طب بتدربوا فى M الـ M
+
+379
+00:33:25,970 --> 00:33:30,710
+هذه بتفوت على التلت مراكبات كلهاهي قاعدة الضغط
+
+380
+00:33:30,710 --> 00:33:33,550
+بتاعة الـ Scalar في الـ Vector بيقولي if Lambda
+
+381
+00:33:33,550 --> 00:33:40,650
+الـ Lambda أي Scalar M T زمن Volume Temperature
+
+382
+00:33:40,650 --> 00:33:45,010
+ذاكرينهم Energy اذا هذه Lambda بتمثل اي كمية
+
+383
+00:33:45,010 --> 00:33:48,330
+Scalar قاللي بدي اضربها في الـ Vector A ايش الـ
+
+384
+00:33:48,330 --> 00:33:52,980
+Vector A؟ Forcevelocity displacement acceleration
+
+385
+00:33:52,980 --> 00:33:58,040
+صح ولا لأ؟ إذا وجهتها كذا أمور طلع يسوّنها في ال
+
+386
+00:33:58,040 --> 00:34:04,660
+lambda وزّعناها على كل المركبات تمام؟ إيش يعني
+
+387
+00:34:04,660 --> 00:34:10,680
+بالمرة؟ انطبخ هاي إيه؟ بيساوي اتنين I زي تلاتة J
+
+388
+00:34:10,680 --> 00:34:20,210
+زي أربعة K بدي أضربها في اتنين إيش هسوي؟بيصير 4I
+
+389
+00:34:20,210 --> 00:34:25,290
+زي 6J صعب؟
+
+390
+00:34:25,290 --> 00:34:31,830
+سهل طيب إيش معناته؟ قال لي يعني ال scalar هذا خش
+
+391
+00:34:31,830 --> 00:34:37,770
+على ال vector ماغيرش اتجاهه بس في احتمال يكون يعكس
+
+392
+00:34:37,770 --> 00:34:42,550
+الاتجاه و اكتش بعكس الاتجاه إذا كان سالمإذا كانت
+
+393
+00:34:42,550 --> 00:34:47,250
+سالب صح ولا لأ نجي لهذا القانون هدى ام بنعرفها لا
+
+394
+00:34:47,250 --> 00:34:52,090
+بنعرفهاش ممكن تكون سالبة لأ لأ ايش معناته معناته
+
+395
+00:34:52,090 --> 00:34:55,570
+هدى و هدى في نفس الاتجاه ولا لأ ولا ممكن يكونوا
+
+396
+00:34:55,570 --> 00:35:00,190
+عكس بعض ولا غير عن بعض بكرا في شبتر خمسة نجي بنقول
+
+397
+00:35:00,190 --> 00:35:04,350
+ال four شمالا الاكس لا ليش يكف اتجاهها بقعد الطريق
+
+398
+00:35:04,350 --> 00:35:11,250
+يفكر هدى بادى قطعا شمالا على طولبغض النظر ..
+
+399
+00:35:11,250 --> 00:35:15,850
+بتباطأ .. بتباطأش مالك الجعوة .. خلاص حسب ال force
+
+400
+00:35:15,850 --> 00:35:21,400
+.. ال accelerationبتكون تابعة إيه لها؟ بقول لي
+
+401
+00:35:21,400 --> 00:35:26,380
+note that the direction of lambda في a يعني درست
+
+402
+00:35:26,380 --> 00:35:30,100
+كيلوف ال vector is the same as the direction of a
+
+403
+00:35:30,100 --> 00:35:35,040
+إذا كانت lambda موجبة وعكسه إذا كانت سالبة عشان
+
+404
+00:35:35,040 --> 00:35:38,260
+علمونا إن شرط السالب تخش ع ال vector إيش بتسوي
+
+405
+00:35:38,260 --> 00:35:45,750
+فيه؟ تعكسه تمام؟ حلوخلصنا أول نوع النوع التاني
+
+406
+00:35:45,750 --> 00:35:52,410
+بيسموه اسمين من كتر العز والاسمين لكل مسمى من اسمه
+
+407
+00:35:52,410 --> 00:35:58,830
+نصيب لهم معنى scalar product او dot product dot
+
+408
+00:35:58,830 --> 00:36:03,290
+بالانجليزي معناته نقطة تمام ليش سميتها scalar عشان
+
+409
+00:36:03,290 --> 00:36:09,460
+الطالب مايخربطش لأن الناتج لازم يكون scalarبدك
+
+410
+00:36:09,460 --> 00:36:12,640
+تضربه في vector يطلع scalar هذا اللي أسميه scalar
+
+411
+00:36:12,640 --> 00:36:15,880
+product زي أيش في الفيزيا؟ قاللي الشغل
+
+412
+00:36:21,600 --> 00:36:26,520
+.D الـ F vector و الـ D displacement vector ضربتهم
+
+413
+00:36:26,520 --> 00:36:30,600
+طالع عندك work، energy، a scalar قال لي هذا بنسميه
+
+414
+00:36:30,600 --> 00:36:35,620
+scalar product تمى؟ قال لي the scalar product of
+
+415
+00:36:35,620 --> 00:36:39,780
+two vectors إذا الـ.product أو ال scalar product
+
+416
+00:36:39,780 --> 00:36:43,440
+بينفعش إلا يكون between two vectors بينفع يكون بين
+
+417
+00:36:43,440 --> 00:36:49,770
+vector و scalar؟ لأبنفعش Denoted by كيف بنكتبها؟
+
+418
+00:36:49,770 --> 00:36:57,710
+جالي بنقول A ونكتب B وكذا بنقراها A Dot ال B تمام؟
+
+419
+00:36:57,710 --> 00:37:02,690
+is a scalar ليش حاطينها بالأحمر؟ عشان شيّبونا
+
+420
+00:37:02,690 --> 00:37:05,870
+الطلاب بنقولهم scalar product سموه عشان النتيجة
+
+421
+00:37:05,870 --> 00:37:10,550
+scalar بنقولهم dot product و بنحط أربع خيارات من
+
+422
+00:37:10,550 --> 00:37:15,500
+ضمنهم vector بلو بختروابنفع؟ و هو اسمه scalar
+
+423
+00:37:15,500 --> 00:37:20,320
+product و حينا حاطنا بالأحمر عشان ممنوع الناتج
+
+424
+00:37:20,320 --> 00:37:23,860
+يكون vector صح ولا لأ؟ تمام، إيش هو ال vector كيف
+
+425
+00:37:23,860 --> 00:37:26,440
+باعرف إنه vector ولا scalar؟ إذا لجيت في I و J و
+
+426
+00:37:26,440 --> 00:37:30,120
+K، vector ولا مش vector هذا؟ لأن هذا I و J و K
+
+427
+00:37:30,120 --> 00:37:35,930
+بيديل على اتجاهات، حلووهي التعريف تبعي a بطل بي
+
+428
+00:37:35,930 --> 00:37:40,850
+بتسوي magnitude ال a في magnitude ال b في cosine
+
+429
+00:37:40,850 --> 00:37:44,710
+الزاوية اللي بينهم الزاوية إذا هذه هي الزاوية اللي
+
+430
+00:37:44,710 --> 00:37:47,410
+بينهم is the smallest angle between the two
+
+431
+00:37:47,410 --> 00:37:54,750
+vectors جالي حلو عرفت التعريف cosine الزاوية مية
+
+432
+00:37:54,750 --> 00:37:58,410
+مرة جبت cosine جبت cosine الخمسة و أربعين و cosine
+
+433
+00:37:58,410 --> 00:38:04,520
+التلاتين و cosine الستين كداش cosine السفر1 كسيمة
+
+434
+00:38:04,520 --> 00:38:10,060
+تسعين حلو جالي في I و G و K توي علمتني اياهم
+
+435
+00:38:10,060 --> 00:38:16,760
+ذاكرينهم I و G و K جديش ازاوة بين I و G اذا معناته
+
+436
+00:38:16,760 --> 00:38:24,350
+I.J سفر جديش ازاوة بين I و Kيسعين اذا بقدر استنتج
+
+437
+00:38:24,350 --> 00:38:30,710
+انه I Dot الجيه بتساوي سفر و I Dot الكيه بتساوي
+
+438
+00:38:30,710 --> 00:38:35,890
+سفر و جيه Dot الكيه بتساوي سفر طب اعكس هون برضه
+
+439
+00:38:35,890 --> 00:38:41,770
+سفر يعني ا Dot بيه و بيه Dot ايه زي بعض حلو جالي
+
+440
+00:38:41,770 --> 00:38:46,830
+الفكتور و أخوه نفسه كدهش الزوايا بينهم بتتوقع سفر
+
+441
+00:38:46,830 --> 00:38:52,770
+معناته بتتوقع I Dot I كدهشمقدار الأول جديش مقدار
+
+442
+00:38:52,770 --> 00:38:57,350
+الأول؟ ليش؟ لأنه unit vector برار عليكي لأنه متجه
+
+443
+00:38:57,350 --> 00:39:01,570
+واحدة و سويته متجه واحدة عشان مقداره واحد مقدار
+
+444
+00:39:01,570 --> 00:39:05,770
+الأول واحد في مقدار التاني واحد في قصان الصفر واحد
+
+445
+00:39:05,770 --> 00:39:17,470
+في واحد في واحد J dot J K dot K صحيكوا ولا لأ؟ اه
+
+446
+00:39:17,470 --> 00:39:22,900
+و قصان الصفرواحد دير بالك هه واحد ميح الحمد لله
+
+447
+00:39:22,900 --> 00:39:37,540
+مانخلطش لإنه كان جدا بجانبنا احكي اه
+
+448
+00:39:37,540 --> 00:39:46,860
+حلو اما كيش سمعتي في طاقة سلب هاه بلاش بلاش بلاش
+
+449
+00:39:46,860 --> 00:39:50,170
+إيش اننا في الطاقة ونغلب حياتنالما تكون الدنيا
+
+450
+00:39:50,170 --> 00:39:52,030
+باردة و مرتاحة و الناس و الصلاة تقريبا .. جديش
+
+451
+00:39:52,030 --> 00:39:56,670
+درجة حرارة بتكون؟ تحت السفر .. كيف أقول؟ ماهي
+
+452
+00:39:56,670 --> 00:40:09,730
+Scalar .. إذا ال Scalar .. أحكيه .. كيف؟ ليش
+
+453
+00:40:09,730 --> 00:40:16,090
+بنعمل هيك؟ هيك تعريفها يا بنتي .. هيك تعريف .. إيش
+
+454
+00:40:16,090 --> 00:40:21,330
+اسمك أنتي؟ علي صوتك ..أسيل ليه سموك يا أسيل؟ نفس
+
+455
+00:40:21,330 --> 00:40:26,970
+السؤال ليه سموك يا أسيل؟ في شغلات هذه التعريف قعدت
+
+456
+00:40:26,970 --> 00:40:31,630
+هيك هذه تعريفة عشان تظبط كل العلم قالوا دوتو
+
+457
+00:40:31,630 --> 00:40:36,550
+برودكت يعرف defined as إذا كانت تعريف ليش المتر
+
+458
+00:40:36,550 --> 00:40:41,950
+عامة يعتبروها جدي؟ ماخلهوش منها لحيفة إذا في شغلات
+
+459
+00:40:41,950 --> 00:40:48,580
+بتقعد قعدت هي هيك بصي متعرف عليها تمام؟بيقولي sons
+
+460
+00:40:48,580 --> 00:40:54,360
+I, J and K are unit vectors perpendicular to each
+
+461
+00:40:54,360 --> 00:40:59,160
+other متعمدين على بعض and using the last equation
+
+462
+00:40:59,160 --> 00:41:03,100
+اللي كتبته أنا وكتبته و أنا وياكم صحيح هيك؟ قال لي
+
+463
+00:41:03,100 --> 00:41:08,520
+هيا نضرب A ضط ال B قاللي هي ال A و هي ال B بدي
+
+464
+00:41:08,520 --> 00:41:12,120
+اضرب جوس بجوس ولا لأ؟ و في حد ما عشان يضرب جوس
+
+465
+00:41:12,120 --> 00:41:17,650
+بجوس و ضربت جوس بجوسطلعوا اللي انش طلع معايا I ضد
+
+466
+00:41:17,650 --> 00:41:22,270
+ال I جالي والله ها دي سفر و ها دي سفر و ها دي سفر
+
+467
+00:41:22,270 --> 00:41:25,030
+و ها دي سفر و ها دي سفر و ها دي سفر و ها دي سفر و
+
+468
+00:41:25,030 --> 00:41:29,250
+ها دي سفر و ها دي سفر و ها دي سفر و ها دي سفر و ها
+
+469
+00:41:29,250 --> 00:41:34,770
+دي سفر و ها دي سفر و ها دي سفر و ها دي سفر و ها دي
+
+470
+00:41:34,770 --> 00:41:34,970
+سفر و ها دي سفر و ها دي سفر و ها دي سفر و ها دي
+
+471
+00:41:34,970 --> 00:41:36,530
+سفر و ها دي سفر و ها دي سفر و ها دي سفر و ها دي
+
+472
+00:41:36,530 --> 00:41:44,630
+سفر و ها دي سفر
+
+473
+00:41:44,630 --> 00:41:51,420
+وواحد و جي ضط جي و كي ضط كي دوري أوردي محل الدرب
+
+474
+00:41:51,420 --> 00:41:55,600
+بدرب الصيني مع الصيني و الصاضي مع الصاضي و العيني
+
+475
+00:41:55,600 --> 00:42:03,360
+مع العيني و بس و بجمع و بجمع حلو ه هاي ايه و هاي
+
+476
+00:42:03,360 --> 00:42:13,460
+بيه بتساوي هذه ايه تلاتة ايه ناقص خمسة جي زائد كيه
+
+477
+00:42:13,460 --> 00:42:21,350
+هادا بتوفيكتر عشوائيبدي ايه ضد ال b بقوله بالثاوي
+
+478
+00:42:21,350 --> 00:42:28,790
+اتنين في تلاتة اتاوي
+
+479
+00:42:28,790 --> 00:42:34,890
+انا قولت هتطس scalar بالاحمر عشان ال I و ال J و ال
+
+480
+00:42:34,890 --> 00:42:39,830
+K مسمحهمش اذا اتنين في تلاتة ستة
+
+481
+00:42:43,750 --> 00:42:48,650
+شوفوا 6I-15G زيادة 4K بتكون أحد الخيارات الأربعة
+
+482
+00:42:48,650 --> 00:42:56,510
+بحطها عشان أن أوجع بالفخ لو حطيت I و G و K
+
+483
+00:42:56,510 --> 00:43:01,870
+بتاخدوها؟ هي هي هيك ساعتها لجيت بقوله هنا نقص
+
+484
+00:43:01,870 --> 00:43:07,070
+خمستاشر وهذه أظن عشرة إذا معناته نقص خمسة طلعشي
+
+485
+00:43:07,070 --> 00:43:11,130
+جواب طالع رقم scalar صحيح؟ scalar
+
+486
+00:43:14,480 --> 00:43:20,660
+قال لي ها هاي two vectors أسهل ايه بتساوي اتنين I
+
+487
+00:43:20,660 --> 00:43:25,480
+زي اتلاتة G وبيبتساوي سلب I زي اتنين G ايش بدك قال
+
+488
+00:43:25,480 --> 00:43:30,100
+لي بدي تضربليهم find the dot product و بعدين
+
+489
+00:43:30,100 --> 00:43:33,020
+بيجيبلي زاوية اللي بينهم مين ده في الضرب؟ مين اللي
+
+490
+00:43:33,020 --> 00:43:38,760
+طو جلط I؟ بتتنجلني؟ وين هذه جلطة I؟ عشان .. لما
+
+491
+00:43:38,760 --> 00:43:44,780
+ضربت جلط I مش طو هنا جلط 6Iانت بيكتب دربيلي هالجيت
+
+492
+00:43:44,780 --> 00:43:52,280
+عشان ما تخبطيش ادربي اتنين ايوة اذا ايه ضد ال b
+
+493
+00:43:52,280 --> 00:44:00,700
+بيسوي سالب اتنين ايش الجواب تمام هيك اسحقت خارب
+
+494
+00:44:00,700 --> 00:44:07,120
+بيضيهافش I وG وK لأن أنا بتعامل مع dot product طلع
+
+495
+00:44:07,120 --> 00:44:10,380
+المطلوب التاني ايش بقول ليه بدي الزاوية قولتله
+
+496
+00:44:10,380 --> 00:44:16,160
+توعي انت قولتلي A dot ال B سواء ماجنتيوت ال A في
+
+497
+00:44:16,160 --> 00:44:21,360
+ماجنتيوت ال B في كوسين ال theta بينهم صح هجيت A
+
+498
+00:44:21,360 --> 00:44:24,900
+dot ال B جبتها ولا لأ ماجبتيها انت بقوله ها دي
+
+499
+00:44:24,900 --> 00:44:30,720
+اربعة ماجنتيوت ال A مين يجيبليها يورجو يلا تسعة
+
+500
+00:44:31,770 --> 00:44:42,270
+تلات عشر إذا جزر تلات عشر مجموعه الـ B هذه
+
+501
+00:44:42,270 --> 00:44:45,490
+خطأ قد يبقى في بالك شائع لأن انت بتقولي نقص واحد
+
+502
+00:44:45,490 --> 00:44:49,770
+تربية أربعة
+
+503
+00:44:49,770 --> 00:44:58,840
+زائد واحد فبالتالي في جزر الخمسة cos θخلصنا اذا
+
+504
+00:44:58,840 --> 00:45:03,720
+اربعة على جزر تبتعش في جزر طبعا هيك بيصير cos θ
+
+505
+00:45:03,720 --> 00:45:11,000
+بتسوى اربعة على خدور خمسة و ستين بتطلعواها
+
+506
+00:45:11,000 --> 00:45:18,300
+بتطلع ستين طلعنا كويس
+
+507
+00:45:20,870 --> 00:45:23,410
+أنا قاعد بأسرع عامل حسابي انه ممكن يكون الأربع
+
+508
+00:45:23,410 --> 00:45:27,570
+الإجازة انا بحاجة عشان كده اتحملون انت حاجات
+
+509
+00:45:27,570 --> 00:45:30,110
+مكيفين بيقولوا يا رب متحملينك بس اطلع الأربع
+
+510
+00:45:30,110 --> 00:45:37,190
+الإجازة تمام ناخد راحتنا يوم الأربع تمام طلع يا
+
+511
+00:45:37,190 --> 00:45:42,130
+بنات هيجيت cosine الزاوية عندكم معلومة أكيدة انه
+
+512
+00:45:42,130 --> 00:45:46,190
+مستحيل تكون أكبر من واحد معلومة معروفة هي من سفر
+
+513
+00:45:46,190 --> 00:45:53,860
+لواحد قال لي هذه الحلوةبقدر اقول ان a ضد بي مستحيل
+
+514
+00:45:53,860 --> 00:45:58,500
+تكون اكبر من a في بي مش مستحيل ليش مستحيل تكون
+
+515
+00:45:58,500 --> 00:46:02,460
+اكبر عشان تكون اكبر لازم تكون هدى اكبر من واحد لكن
+
+516
+00:46:02,460 --> 00:46:08,220
+بقدر اقول ممكن تسوى اذا كسان السفر واحد وممكن تكون
+
+517
+00:46:08,220 --> 00:46:13,420
+اصغر اذا الزاوية من السفرالزاوية اللي بتحديت تطلع
+
+518
+00:46:13,420 --> 00:46:16,500
+ليك ويز ايش بيقول بيقول which of the following
+
+519
+00:46:16,500 --> 00:46:19,320
+statements is true عظم ان هذه الجملة معروفة
+
+520
+00:46:19,320 --> 00:46:23,460
+بالانجليزي ايش من هذه الجملة التالية صحيحة بيقول
+
+521
+00:46:23,460 --> 00:46:28,260
+لي a بط ال b is larger than magnitude ال a في ال b
+
+522
+00:46:28,260 --> 00:46:32,720
+بيقول له و لا ممكن و لا ممكن لأنه عمريش سمعت
+
+523
+00:46:32,720 --> 00:46:38,690
+cosine زاوية أكبر من واحد ولا في حد سمعه يدلناA
+
+524
+00:46:38,690 --> 00:46:43,310
+بطول B is smaller than FB بقوله مش بالضرورة ممكن
+
+525
+00:46:43,310 --> 00:46:50,370
+يتساوى اذا برضه هذه مش دقيقة صحيحيك ولا لأ هذه مثل
+
+526
+00:46:50,370 --> 00:46:55,070
+اللي عارفين اشلوله مرة اكبر و مرة اصغر مستحيل
+
+527
+00:46:55,070 --> 00:47:02,070
+بيشوف الأخيرة A بطول B could be equal يعني ممكن
+
+528
+00:47:02,070 --> 00:47:06,670
+تكون مساوية بقوله اه اذا كانت الزاويةzero اذا هذا
+
+529
+00:47:06,670 --> 00:47:12,470
+صحيح طبعا انتوا اتعلمتوا لان لما شفتوا الكوزات انه
+
+530
+00:47:12,470 --> 00:47:15,530
+في من الكوزات اللي امه دا عياله بيطلع واحد من هدول
+
+531
+00:47:15,530 --> 00:47:22,110
+صح اه انتوا ماطلعكيش ماطلعكيش لأ هدول موجودين
+
+532
+00:47:22,110 --> 00:47:26,750
+مغزعين جوا فمرات بيطلع هو نفسه و مرات بيطلع تغيير
+
+533
+00:47:26,750 --> 00:47:31,370
+بسيط اما فيه يطلع علم نفسه اللي بيعمله مرضه شكله
+
+534
+00:47:31,370 --> 00:47:37,740
+مش طالع عليك انترجع حالك و علاقتك مع أمك قبل ما
+
+535
+00:47:37,740 --> 00:47:47,420
+تموتي على ال quiz روح يقولي لأمك ادعيلي تمام هل
+
+536
+00:47:47,420 --> 00:47:50,240
+جيت عشان ال quiz فيه ملو كان لأن الخميس ال quiz في
+
+537
+00:47:50,240 --> 00:47:53,760
+كل أحوال بغض النظر عن الإجازة عشان ماتقولوش هذا
+
+538
+00:47:53,760 --> 00:47:57,980
+ماخدنهوش cross product او vector product ال vector
+
+539
+00:47:57,980 --> 00:48:00,840
+product يا بنا سمته vector product عشان النتج
+
+540
+00:48:00,840 --> 00:48:05,820
+vectorالناتج ماله vector اذا بيقول لي طبعا انا
+
+541
+00:48:05,820 --> 00:48:10,860
+هعيده يوم السبت او يوم الأربعة لكن بدي اسلجه شويه
+
+542
+00:48:10,860 --> 00:48:16,340
+عشان ال quiz تمام فاتحملونيبقول إذا vector product
+
+543
+00:48:16,340 --> 00:48:19,520
+of two vectors a and b هذا لازم يكون between two
+
+544
+00:48:19,520 --> 00:48:25,160
+vectors أيضا written as كيف بنكتب a cross ال b is
+
+545
+00:48:25,160 --> 00:48:30,140
+a third vector إذا لنا نتيج ماله vector with ما
+
+546
+00:48:30,140 --> 00:48:32,680
+زال vector بدك تديني إليه تنتين magnitude و
+
+547
+00:48:32,680 --> 00:48:37,490
+direction صح؟ ال magnitude تبقى هذا هومجنتيودي
+
+548
+00:48:37,490 --> 00:48:41,590
+الـC اللي هو مجنتيودي الـA في الـB بيسوي A في B في
+
+549
+00:48:41,590 --> 00:48:46,870
+صيني الزاوية تمام؟ بدي ال direction قال ليه ال
+
+550
+00:48:46,870 --> 00:48:52,630
+vector C له direction لازم يكون عمودي على مستوى
+
+551
+00:48:52,630 --> 00:48:56,690
+التنين A وB ولمّا يكون عمودي على المستوى معناته
+
+552
+00:48:56,690 --> 00:48:59,850
+عمودي على كل الخطوط جوا المستوى مش هي كانت في
+
+553
+00:48:59,850 --> 00:49:05,660
+نظرية؟ تمام إذا C عمودي على A ولا لأ؟و C عمودي على
+
+554
+00:49:05,660 --> 00:49:12,780
+B ولا لأ قطع العمودي على التنين قال لي طيب بنات هي
+
+555
+00:49:12,780 --> 00:49:20,020
+A و هي B التنين عاللوح بدي أضربهم أطلع C cross
+
+556
+00:49:20,020 --> 00:49:23,740
+product بدي أطلع عندي لازم عمودي على التنين في
+
+557
+00:49:23,740 --> 00:49:28,860
+عندي احتمالين لا عليكم لا علوحبنتعلم كيف نعرف انه
+
+558
+00:49:28,860 --> 00:49:31,920
+عليكم ولا علي اللوح قاللي في قاعدة اليدي اليمنى
+
+559
+00:49:31,920 --> 00:49:36,280
+بتعرفوها حلو كلكم بتعرفوها هيها أصابعك الأربع
+
+560
+00:49:36,280 --> 00:49:41,620
+افردهم وحطهم باتجاه ال A أصابعنا الأربع حطوناهم في
+
+561
+00:49:41,620 --> 00:49:47,480
+اتجاه ال A ولف باتجاه ال B لفهم أصابعك الأربع بعد
+
+562
+00:49:47,480 --> 00:49:54,080
+كده هيهم شايفينها هي A و هي B اتفقنا أصابع الأربعة
+
+563
+00:49:54,080 --> 00:50:00,630
+هيهمبلف هيك هيك بلتفه للخارج
+
+564
+00:50:00,630 --> 00:50:05,670
+طيب بدي بي cross ال a بي إذا أنا أصابعي الأربعة مع
+
+565
+00:50:05,670 --> 00:50:10,650
+مين مع بي مع بي بدي ألفه معناته لازم يكون بيبقى من
+
+566
+00:50:10,650 --> 00:50:14,230
+دوا إيش بيدل بيقولي a cross ال b بيساوي سالب بي
+
+567
+00:50:14,230 --> 00:50:22,370
+cross ال a إذا لو عكسته هتحط شعر سالب أمين حلو صين
+
+568
+00:50:22,370 --> 00:50:28,110
+السفر قداشسفر وصاني سفر واحد وصاني سفر سفر وصاني
+
+569
+00:50:28,110 --> 00:50:35,210
+تسعين حلو معناته I X I I X I I X I I X I I X I I I
+
+570
+00:50:35,210 --> 00:50:35,450
+X I I I X I I I X I I I X I I I X I I I X I I I X
+
+571
+00:50:35,450 --> 00:50:37,690
+I I I X I I I X I I I X I I I X I I I X I I I X I
+
+572
+00:50:37,690 --> 00:50:40,950
+I I X I I I X I I I X I I I X I I I X I I I X I I
+
+573
+00:50:40,950 --> 00:50:41,590
+I X I I I X I I I X I I I X I I I X I I I X I I I
+
+574
+00:50:41,590 --> 00:50:44,530
+X I I I X I I I X I I I X I I I X I I I X I I I X
+
+575
+00:50:44,530 --> 00:50:45,970
+I I I X I I I X I I I X I I I X I I I X I I I X I
+
+576
+00:50:45,970 --> 00:50:52,080
+I I X I I I X I I I X I I I X I I X I I IK يعني K
+
+577
+00:50:52,080 --> 00:50:58,660
+إذاً I cross الـ J بيعطي K J cross ال I سالب K صح
+
+578
+00:50:58,660 --> 00:51:06,780
+ولا .. طب تتوقعوا J cross ال K I J cross ال K I
+
+579
+00:51:06,780 --> 00:51:11,800
+تمام هذه القاعدة من جيبها بعد كده اتطلع واحد هذه
+
+580
+00:51:11,800 --> 00:51:18,160
+القاعدة التي ادربنا قال لي في عنديكيف تجيب I x J x
+
+581
+00:51:18,160 --> 00:51:22,220
+K؟ قال لي هاي I و J و K شايفينهم؟ بدي أضرب كل
+
+582
+00:51:22,220 --> 00:51:25,780
+التنين مع بعض يطلع للتالت قطعا ولا لأ؟ بدي يطلع
+
+583
+00:51:25,780 --> 00:51:30,020
+التالت I x J بدي يطلع K أو سلب K مظبوط؟ J x K بدي
+
+584
+00:51:30,020 --> 00:51:34,800
+يطلع معاك I أو سلب I K x J ال I بدي يطلعك J أو سلب
+
+585
+00:51:34,800 --> 00:51:37,660
+J كيف تبقى أعرف موجة بولا سلب؟ قاللي طلع القاعدة
+
+586
+00:51:37,660 --> 00:51:42,220
+الحلوة و حطهم على رأس مثلث حطناهم و قولي .. و
+
+587
+00:51:42,220 --> 00:51:47,490
+اعملي يوم هيكها هجيت انت ماشي بدك تضرب sorry I
+
+588
+00:51:47,490 --> 00:51:51,490
+cross ال J بقول I cross ال J انا ماشي و كاين معاقر
+
+589
+00:51:51,490 --> 00:51:56,190
+بالساعة بطلع التالت موجب لو بدي اقول J cross ال I
+
+590
+00:51:56,190 --> 00:52:02,390
+بصير اقلافف بطلع سالب K طيب J cross .. هي طلعت J
+
+591
+00:52:02,390 --> 00:52:04,630
+cross ال K I
+
+592
+00:52:07,780 --> 00:52:14,000
+كي .. لو .. كي كروس الجي سالب اي تمام كي كروس الاي
+
+593
+00:52:14,000 --> 00:52:21,040
+جي اي كروس الكي سالب ممولة تمام هذه حلوين بعدين
+
+594
+00:52:21,040 --> 00:52:26,580
+بنكملها عشان نغلب كورس هذا حال نرجعله تفصيل و هذا
+
+595
+00:52:26,580 --> 00:52:33,530
+بدنا نرجعله تفصيل بدي ال quiz بسبقولي which of the
+
+596
+00:52:33,530 --> 00:52:37,230
+following is always zero؟ واطلعوا الخيارات تبعتي
+
+597
+00:52:37,230 --> 00:52:41,330
+يا بنات وانتبهوا عشان لو إيجي زيه في ال quiz a
+
+598
+00:52:41,330 --> 00:52:46,010
+cross ال b cross ال a كيف سفر ماعرفش نيجي لهدا
+
+599
+00:52:46,010 --> 00:52:50,490
+انتبهولي a cross ال b طلع victory جديد صح عمودي
+
+600
+00:52:50,490 --> 00:52:55,840
+على هدا مش عمودي على التانية أناو عمودي على هذا طب
+
+601
+00:52:55,840 --> 00:52:59,720
+ما زال هذا عمودي عليه معناته هذا و هذا عموديات و
+
+602
+00:52:59,720 --> 00:53:03,980
+ضد product cosine و cosine التسعين صفر اذا هذا صفر
+
+603
+00:53:03,980 --> 00:53:11,580
+طب لو a cross ال b ضد ال bبرضه severe برضه severe
+
+604
+00:53:11,580 --> 00:53:15,800
+هذا و هذا ماليش دعوة فيهم طلع هادى الحلو قال لي
+
+605
+00:53:15,800 --> 00:53:20,360
+هذا أصلا الأعمى اللى بيصدقك لأن هادى ايه ضد ال big
+
+606
+00:53:20,360 --> 00:53:24,640
+scalar و scalar و مع vector ممنوع تحط cross إذا
+
+607
+00:53:24,640 --> 00:53:29,100
+هادى أصلا كتبته غلط إذا مين من هدول اللي دايما
+
+608
+00:53:29,100 --> 00:53:35,250
+zeroب فهمتوا يا بنات هذا بيأكد انه دايما لما اضرب
+
+609
+00:53:35,250 --> 00:53:37,630
+to vectors cross product الناجي ايش يجب ان يكون
+
+610
+00:53:37,630 --> 00:53:42,750
+عمودي ع التنين خيار دي انت حكيت انه .. مخلط تمام
+
+611
+00:53:42,750 --> 00:53:46,570
+dot معي scanner ومافعش اتحد cross طبعا طب هلأ لما
+
+612
+00:53:46,570 --> 00:53:50,430
+انا اضرب a في b خيار دي طب هو هيطلع ليه scanner من
+
+613
+00:53:50,430 --> 00:53:54,150
+هنا هذا scalar و vector vector اه vector بتكون ضد
+
+614
+00:53:54,150 --> 00:53:59,900
+ال scalar من scalar هذا scalarهذا vector هذا كتابة
+
+615
+00:53:59,900 --> 00:54:05,900
+صحيحة تمام احنا وياكم والعربعة بفصل بيننا في إجازة
+
+616
+00:54:05,900 --> 00:54:10,060
+ولا لأ إذا في إجازة بنشوفكم السبت مافيش إجازة
+
+617
+00:54:10,060 --> 00:54:14,020
+بنشوفكم العربعة يعطيكوا
+
+618
+00:54:14,020 --> 00:54:14,460
+العافية
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/jn4ooM4Kee0_postprocess.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/jn4ooM4Kee0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..56c9e8705fd29f178554a579d294bd912f4bb725
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/jn4ooM4Kee0_postprocess.srt
@@ -0,0 +1,1480 @@
+1
+00:00:05,360 --> 00:00:08,520
+تمام يا بنات اليوم ان شاء الله بدنا نسمر هذا ال
+
+2
+00:00:08,520 --> 00:00:13,780
+chapter و ننهيه ال chapter الماضي او المحاضرة
+
+3
+00:00:13,780 --> 00:00:19,980
+الماضية استقلنا احنا وياكم اربع معادلات بتحكم
+
+4
+00:00:19,980 --> 00:00:27,300
+الحركة بتسارع ثابت و المعادلات كانت التالت Vfinal
+
+5
+00:00:27,300 --> 00:00:34,670
+بتساوي D-A-Tو X final نخس X initial بيسوي V
+
+6
+00:00:34,670 --> 00:00:39,950
+initial في T زائد نص AT تربيع صح ولا لأ؟ وقلنا
+
+7
+00:00:39,950 --> 00:00:44,330
+هدول معادلتي الأساسيتين التالتين منهم .. مش تقتمان
+
+8
+00:00:44,330 --> 00:00:50,510
+تلتين منهم X final نخس X initial بيسوي نص V
+
+9
+00:00:50,510 --> 00:00:56,730
+initial زايد V final في Tوالاخيرة Vfinal تربيع
+
+10
+00:00:56,730 --> 00:01:03,470
+بتسوي Vinitial تربيع ذات 2AXfinal-Xinitial مظبوط
+
+11
+00:01:03,470 --> 00:01:08,330
+ولا لأ؟ كنا هدول ثلاث معادلات شرط استخدامهم بأن
+
+12
+00:01:08,330 --> 00:01:12,470
+يكون A constant صح ولا لأ؟ هذا الشرط الواعي إذا في
+
+13
+00:01:12,470 --> 00:01:18,340
+هذه المحاضرةبدنا نكمل تقريبا نفس المحاضرة السابقة
+
+14
+00:01:18,340 --> 00:01:25,340
+وهي حركة خطية بتسارق ثابت هذه الحركة بنسميها سقوط
+
+15
+00:01:25,340 --> 00:01:30,520
+الحر ايش يعني سقوط حر واحنا حكينا لكل مسمى من اسمه
+
+16
+00:01:30,520 --> 00:01:36,960
+نصيب سموها free كلمة free حر يعني ماعليهوش قيد ولا
+
+17
+00:01:36,960 --> 00:01:43,490
+لأوعلمياً قيد يعني قوة ماعلهوش قوة إلا قوة واحدة
+
+18
+00:01:43,490 --> 00:01:48,730
+ربانية طبيعية هي قوة الجاذبية العرضية إذا بيقولي
+
+19
+00:01:48,730 --> 00:01:57,310
+any object moving freely يتحرك بحرية بدون أي قوة
+
+20
+00:01:57,310 --> 00:02:04,410
+بس تحت تأثير under the influence تحت تأثير of
+
+21
+00:02:04,410 --> 00:02:08,870
+gravity gravity يعني جاذبيةوفي الـ Gravity is said
+
+22
+00:02:08,870 --> 00:02:12,250
+to be in free-falling motion. اذا free-falling
+
+23
+00:02:12,250 --> 00:02:16,870
+motion يسم عليه فقط قوة جاذبية. هذه معناتها
+
+24
+00:02:16,870 --> 00:02:21,930
+بالبلدين. وباقي القوة ممنوع تكون موجودة. أي قوة
+
+25
+00:02:21,930 --> 00:02:25,730
+موجودة بيبطل free-falling. مقاومة الهواء بيبطل
+
+26
+00:02:25,730 --> 00:02:30,640
+free-falling.بس في قوة ولا لأ ارتطن بالأرض بيبطل
+
+27
+00:02:30,640 --> 00:02:34,000
+free falling في صيغ قوة جيدة فهمتوا عليها كيف؟ اذا
+
+28
+00:02:34,000 --> 00:02:39,200
+بس قوة الجاذبية ده اللي معناته تصارع الجسم هو
+
+29
+00:02:39,200 --> 00:02:43,720
+تصارع الجاذبية صح؟ و تصارع الجاذبية ثابت ولا
+
+30
+00:02:43,720 --> 00:02:47,920
+مالثابت؟ ثابت اذا هدول القوانين صحيحين تصارع
+
+31
+00:02:47,920 --> 00:02:52,480
+الجاذبية ثابت بس ايه بتبطل مرة عشرة و مرة تمانية و
+
+32
+00:02:52,480 --> 00:02:59,210
+مرة ستة الها كم قيمة؟ واحدة اذا بيقوليassuming
+
+33
+00:02:59,210 --> 00:03:05,530
+that the gravitational acceleration تسارع الجاذبية
+
+34
+00:03:05,530 --> 00:03:10,610
+اللى يرمز لها بالرمز G denoted by G بتعرف اللى
+
+35
+00:03:10,610 --> 00:03:14,590
+رمزها ولا لأ؟ denoted by G طب ليش قلتلي assuming
+
+36
+00:03:14,590 --> 00:03:18,590
+is constant؟ قاللي لأنه هي مش ثابتة بالمكان يعني
+
+37
+00:03:18,590 --> 00:03:23,970
+بمعنى أخر لو أنت جيست في غزة 9.8 وروحت جيستها في
+
+38
+00:03:23,970 --> 00:03:28,310
+رمال اللى ممكن تلاقيها 9.7أجل من غزة لو روحت على
+
+39
+00:03:28,310 --> 00:03:32,690
+أريحة هتلاقي هي أكتر من غزة طبعا رمالها أعلى من
+
+40
+00:03:32,690 --> 00:03:37,950
+غزة ولا لأ وريحها أوطى إذا تختلف من حسب المكان ولو
+
+41
+00:03:37,950 --> 00:03:43,450
+جثتهافي أقصى شمال الكورة الأرضية عند Helsinki ولا
+
+42
+00:03:43,450 --> 00:03:47,010
+عند Stockholm غير لما تجسى في الخرطوم الخرطوم
+
+43
+00:03:47,010 --> 00:03:51,650
+حوالين خط الاستواع إذا في اختلاف بس احنا بنعتبر
+
+44
+00:03:51,650 --> 00:03:55,930
+همالنا ثالثة وقداش قيمتها تسعة بون تمانية هذا اللي
+
+45
+00:03:55,930 --> 00:04:01,970
+بدنا نعتبره افتراضا تمامنقول إنها مستمرة ونعتبر
+
+46
+00:04:01,970 --> 00:04:12,210
+أنها مستمرة ونعتبر أنها مستمرة
+
+47
+00:04:12,210 --> 00:04:14,770
+ونعتبر أنها مستمرة ونعتبر أنها مستمرة ونعتبر أنها
+
+48
+00:04:14,770 --> 00:04:16,490
+مستمرة ونعتبر أنها مستمرة ونعتبر أنها مستمرة
+
+49
+00:04:16,490 --> 00:04:17,090
+ونعتبر أنها مستمرة ونعتبر أنها مستمرة ونعتبر أنها
+
+50
+00:04:17,090 --> 00:04:17,310
+مستمرة ونعتبر أنها مستمرة ونعتبر أنها مستمرة
+
+51
+00:04:17,310 --> 00:04:18,550
+ونعتبر أنها مستمرة ونعتبر أنها مستمرة ونعتبر أنها
+
+52
+00:04:18,550 --> 00:04:26,050
+مستمرة ونعتبر أنها مستمرة ونعتبر أنهاعشان واحد
+
+53
+00:04:26,050 --> 00:04:30,830
+يقول طب انا بيني و بين ال Y طار بحب اش خلّي X مش
+
+54
+00:04:30,830 --> 00:04:34,930
+مشكلة تمام؟ لكن ال default ان كل حاجة عمودية
+
+55
+00:04:34,930 --> 00:04:41,030
+بناخدها Y ولا لأ حلو اذا بقول جي بتسوى 9.8 متر per
+
+56
+00:04:41,030 --> 00:04:44,950
+second تربيع أو بتسوى 32 foot per second تربيع
+
+57
+00:04:44,950 --> 00:04:50,130
+بالنظام البريطاني 32 تمام؟ شوفوا انتوا عشان نؤسس
+
+58
+00:04:50,130 --> 00:04:53,510
+احنا اشهد بدنيا منكم شوفوا 9.8 في حدا منكم مش
+
+59
+00:04:53,510 --> 00:04:57,900
+حافظهمش كلكم حظينه بالرغم من ذلك بنقولكم بنقش
+
+60
+00:04:57,900 --> 00:05:01,920
+جميلتكم تحفظوهوش بنديكم إياه في الامتحان نكتبه في
+
+61
+00:05:01,920 --> 00:05:05,060
+وراج الامتحان بس عشان تفهموا إنه إيش بدياه منكم
+
+62
+00:05:05,060 --> 00:05:09,480
+أنا بديش ياكم تحفظوا أرقامأحنا بدنا ياكم هذا يشتغل
+
+63
+00:05:09,480 --> 00:05:14,340
+و بس و كل حاجة حفظ علينا تمام الشغلات الأساسية ما
+
+64
+00:05:14,340 --> 00:05:18,140
+بنقولكم إيش هي بيقول since the motion is vertical
+
+65
+00:05:18,140 --> 00:05:23,320
+بما إنه الحركة عمودية we take our axis to be the y
+
+66
+00:05:23,320 --> 00:05:27,440
+-axis محول راح يكون بالأعلى واحد مش x فيها مشكلة
+
+67
+00:05:27,440 --> 00:05:31,320
+ولا فيها أي مشكلة with the positive since is
+
+68
+00:05:31,320 --> 00:05:36,160
+upward اتجاهك الموجة بالأعلى إيش جيد ماحنا عارفين
+
+69
+00:05:36,160 --> 00:05:41,970
+تمامجلسوه جلّي هدول المعادلات الحلوين و بيبقى تعمل
+
+70
+00:05:41,970 --> 00:05:47,550
+عليهم تبديلين وين في X حط محلها Y؟ في مشكلة؟ لأ
+
+71
+00:05:47,550 --> 00:05:54,510
+وين في A حط سالب G و ليش سالب؟ لأنها لأسفل و أنت
+
+72
+00:05:54,510 --> 00:06:00,270
+بتقول كل شي لأعلى؟موجب موجب and a by minus g قال
+
+73
+00:06:00,270 --> 00:06:05,810
+لي حلو قال لي the negative sign هي بيأكد عليها is
+
+74
+00:06:05,810 --> 00:06:10,450
+because the gravitational acceleration is always
+
+75
+00:06:10,450 --> 00:06:15,230
+downward always مظبوطة او لأ دايما طبعا هذه خيارة
+
+76
+00:06:15,230 --> 00:06:19,450
+ربنا في حد تغيرها ممكن الحد يغيرها دايما downward
+
+77
+00:06:19,450 --> 00:06:24,360
+قال لي إذا هذه المعادلة الأربع طلعوا عليهاشوفوا
+
+78
+00:06:24,360 --> 00:06:29,580
+إيش الفرق وإن في X حطيت Y وإن في A حطيت ثالث جيه
+
+79
+00:06:29,580 --> 00:06:44,260
+فيه شي جيد ولا شي جيد بدي
+
+80
+00:06:44,260 --> 00:06:49,140
+ال A نقل جيه مظبوط هيك؟ والمحور عشانها بس عشان
+
+81
+00:06:49,140 --> 00:06:55,580
+صاضية عشانها عمودية صاضيةتمام؟ أي سفسة أخر؟ حلو
+
+82
+00:06:55,580 --> 00:07:00,900
+بيقولي الريمارك اتفق ان احنا بنركز على شغلات معينة
+
+83
+00:07:00,900 --> 00:07:04,220
+في الريمارك مظبوط ولا لأ؟ بيقولي remember that اذا
+
+84
+00:07:04,220 --> 00:07:09,280
+ذكر انه وحطها في مخك شغل عارفها انت that the
+
+85
+00:07:09,280 --> 00:07:14,100
+gravitational acceleration g is constant في اشي
+
+86
+00:07:14,100 --> 00:07:18,340
+جديد؟و لما تقول ال constant معناته ثابت بشكل تاني
+
+87
+00:07:18,340 --> 00:07:21,840
+لان هذه الها magnitude و الها direction الها مقدار
+
+88
+00:07:21,840 --> 00:07:25,880
+و اتجاه فهي ثابتة بكلا ال magnitude و ال direction
+
+89
+00:07:25,880 --> 00:07:31,900
+in magnitude and direction and this means that the
+
+90
+00:07:31,900 --> 00:07:36,480
+negative sign of g in the last equation will not
+
+91
+00:07:36,480 --> 00:07:40,870
+be changed ممنوع تغيرهwill not be changed unless
+
+92
+00:07:40,870 --> 00:07:46,790
+الا إذا انت قلت انا بديش اللي فوق هو يكون موجب بدي
+
+93
+00:07:46,790 --> 00:07:50,710
+اللي تحت يكون موجب ساعتها بتجرب كل شي صح ساعتها كل
+
+94
+00:07:50,710 --> 00:07:54,810
+حاجة الأعلى بتخليها سالبة مظبوط ولا وكل حاجة
+
+95
+00:07:54,810 --> 00:07:58,070
+الأسفل بصير موجب لكن أنا بانصحش تعملوا هذه الشغل
+
+96
+00:07:58,070 --> 00:08:01,090
+لسه بدري علينا خلينا زي ما احنا ال default
+
+97
+00:08:01,090 --> 00:08:05,990
+وبالتالي هذه المعادلات بدك تاخدها زي ما هي ال G
+
+98
+00:08:05,990 --> 00:08:12,140
+دايما قدامها سالب اتفجنا؟تمام بقولني unless الا
+
+99
+00:08:12,140 --> 00:08:16,420
+إذا will not be changed unless you change your
+
+100
+00:08:16,420 --> 00:08:19,460
+positive sense إلى اللي إذا غيرت اتجاهك الموجد
+
+101
+00:08:19,460 --> 00:08:24,080
+regardless of the motion .. regardless of the
+
+102
+00:08:24,080 --> 00:08:27,420
+direction of motion يعني بيغضي النظر الجسم طالع
+
+103
+00:08:27,420 --> 00:08:33,600
+ولا نازل طالع ولا نازل جي إلى أسفل صح ولا لأ تمام
+
+104
+00:08:33,600 --> 00:08:39,700
+وسلبة بتبقى حلوحكينا من أكام جلمة لأ كلمة ايه؟
+
+105
+00:08:39,700 --> 00:08:44,940
+بنشوف عربي ولا صيني تامه؟ بقول الـ a ball is
+
+106
+00:08:44,940 --> 00:08:50,460
+thrown upward إيه فيه falling motion؟ قذفتها لأعلى
+
+107
+00:08:50,460 --> 00:08:58,080
+لو بدي أسألكم السرعة الإبتدائية موجبة ولا سلبة؟
+
+108
+00:08:58,080 --> 00:09:04,350
+ليش؟ لأنها لأعلىتما كذفت إلى أعلى إذا السرعة
+
+109
+00:09:04,350 --> 00:09:08,690
+الإبتدائية موجبة لو جالي قذفتها إلى أسفل السرعة
+
+110
+00:09:08,690 --> 00:09:11,830
+الإبتدائية بيصير سالبة حلو أنت مش سائلني عن السرعة
+
+111
+00:09:11,830 --> 00:09:14,330
+الإبتدائية إيش بدها بيقولي it's acceleration
+
+112
+00:09:14,330 --> 00:09:17,390
+بيسألني عن ال acceleration تعالي تشوفوا إيش حاطط
+
+113
+00:09:17,390 --> 00:09:19,490
+ليه الخيارات
+
+114
+00:09:25,190 --> 00:09:30,170
+مظبوط ولا لأ؟ فيها شك؟ ولا نقعد يفكر إيش هي؟ مات
+
+115
+00:09:30,170 --> 00:09:35,250
+بتقوللي تسارعة ثابت؟ مالثابت؟ مازال حاجة الجسم
+
+116
+00:09:35,250 --> 00:09:38,770
+طالع النزل شوي فيه، أنت بتسألني عن تسارعة،
+
+117
+00:09:38,770 --> 00:09:43,780
+فالتسارعة ثابت، إذا إيش خياري؟Stays constant.
+
+118
+00:09:44,600 --> 00:09:48,480
+تمام؟ يعني هو بده يضحك عليّ، بيقول طالع عفوج و لا
+
+119
+00:09:48,480 --> 00:09:51,920
+تغل، مش اللي فيها، أنت بتحكي عن acceleration و
+
+120
+00:09:51,920 --> 00:09:54,180
+free-falling، ما زال free-falling، إذا الـ
+
+121
+00:09:54,180 --> 00:09:58,380
+acceleration ما لها، constant. حلو، لأنه طيب، نغير
+
+122
+00:09:58,380 --> 00:10:02,560
+السؤال، نطلب حاجة تانية، بس نفس السؤال. A ball is
+
+123
+00:10:02,560 --> 00:10:05,860
+thrown upward in a free-falling motion. بيقول،
+
+124
+00:10:05,860 --> 00:10:10,160
+بيدي سرعتها.ما جالش سرعتها ابتدائية جالي سرعتها
+
+125
+00:10:10,160 --> 00:10:15,100
+كلها قلتله شوف الخيارات جالي و هي طالعة سرعتها إيش
+
+126
+00:10:15,100 --> 00:10:21,040
+بيصير فيها؟ و هي طالعة بتنجس مش ابتجه في الأخر
+
+127
+00:10:21,040 --> 00:10:28,440
+بتنجس بعدها بتعود تزيد إذا بتنجس ثم بتزيد تمام؟
+
+128
+00:10:28,440 --> 00:10:33,620
+إذا أي خيار قلتله decreases and then increases صح
+
+129
+00:10:33,620 --> 00:10:35,860
+ولا لأ؟ أي صفصة؟
+
+130
+00:10:39,440 --> 00:10:45,920
+هدا هال gate هادى free falling motion سقوط حر ماهو
+
+131
+00:10:45,920 --> 00:10:55,460
+تصاروحها مافيش ثابت تصاروح هيك جوابتي هيك سقوها
+
+132
+00:10:55,460 --> 00:11:04,860
+شوفي free falling هدا هي غيرها تمام يا بنات كل هي
+
+133
+00:11:04,860 --> 00:11:07,140
+معلمتين مش فيه أيش
+
+134
+00:11:10,640 --> 00:11:15,080
+السؤال المشهور يمكن يمر عليكم في صفحة 10 قال لي
+
+135
+00:11:15,080 --> 00:11:21,200
+هذا زلمة واقف على سطح مبنى و بدى يخذف stone ايش
+
+136
+00:11:21,200 --> 00:11:26,120
+يعني stone؟ حجر a stone is thrown from the top of
+
+137
+00:11:26,120 --> 00:11:30,440
+a building من قمة مبنى وهذا وين واقف في المبنى؟
+
+138
+00:11:30,440 --> 00:11:35,770
+على حفة المبنىخبط الحجر اللي فوق It is thrown from
+
+139
+00:11:35,770 --> 00:11:38,810
+the top of a building with an initial velocity
+
+140
+00:11:38,810 --> 00:11:42,310
+سرعية ابتدائية مقدارها عشرين متر per second
+
+141
+00:11:42,310 --> 00:11:45,950
+straight upward إذا قذفها لأعلى ولا لأ إذا سرعية
+
+142
+00:11:45,950 --> 00:11:51,810
+ابتدائية مجملة مظبوط ولا لأ؟ حلو بيقوللي the stone
+
+143
+00:11:51,810 --> 00:11:58,160
+is launched اطلقت اطلق هنا معناته launchأُطلقت من
+
+144
+00:11:58,160 --> 00:12:02,080
+ارتفاع خمسين متر above the ground المبنى كان
+
+145
+00:12:02,080 --> 00:12:06,780
+ارتفاعه خمسين متر تمام؟ يلّا ماشيين توق في منكم
+
+146
+00:12:06,780 --> 00:12:14,620
+حصير مهندسات المستقبل؟ أكم طابق الخمسين متر؟ اهو
+
+147
+00:12:14,620 --> 00:12:20,280
+حسب أيه؟ مافيه standard عالمي علي
+
+148
+00:12:20,280 --> 00:12:26,460
+صوتكطوابق واحد؟ معناته العمارة اللي .. اللي عشر
+
+149
+00:12:26,460 --> 00:12:32,300
+طوابق واصل السماء؟
+
+150
+00:12:32,300 --> 00:12:36,440
+هذا النيح اللي قلت انا، عشر متر؟ انتوا مش عارفين
+
+151
+00:12:36,440 --> 00:12:41,520
+ايش معنى عشر متر؟ بنات، عمركوش، شفتوا أبوكم لماشي
+
+152
+00:12:41,520 --> 00:12:46,710
+الاستارة كم متر بشريها؟ عشان تغطيها دي؟بس تلاتة
+
+153
+00:12:46,710 --> 00:12:50,750
+متر و أقل كمان تلاتة متر قبل ما يتبلط و لما يتبلط
+
+154
+00:12:50,750 --> 00:12:55,630
+و نحط رمل بيصير 2.8 أصلا كل الجماش اللي فيه اللي
+
+155
+00:12:55,630 --> 00:13:01,070
+بتنش الاسطرات maximum مترين و تمانين صنطي ليش
+
+156
+00:13:01,070 --> 00:13:04,270
+بيقولوا ما هو مابحقلهاش يتجروا على أرض مش بيجيسوا
+
+157
+00:13:04,270 --> 00:13:09,350
+و بيخلوا يكونوا منتفعة شوية إذا هذه حوالى 16 طعبك
+
+158
+00:13:09,350 --> 00:13:18,590
+عرفتوا أكان طعبك؟بديك بص طابجين انت؟ تمام اذا هاد
+
+159
+00:13:18,590 --> 00:13:22,550
+يقولش عشان بيناقشوها .. ما أنا قولتلكم بيناحس ..
+
+160
+00:13:22,550 --> 00:13:24,330
+بيناحس .. بيناحس .. بيناحس .. بيناحس .. بيناحس ..
+
+161
+00:13:24,330 --> 00:13:24,370
+بيناحس .. بيناحس .. بيناحس .. بيناحس .. بيناحس ..
+
+162
+00:13:24,370 --> 00:13:24,390
+بيناحس .. بيناحس .. بيناحس .. بيناحس .. بيناحس ..
+
+163
+00:13:24,390 --> 00:13:25,370
+بيناحس .. بيناحس .. بيناحس .. بيناحس .. بيناحس ..
+
+164
+00:13:25,370 --> 00:13:31,230
+بيناحس .. بيناحس .. بيناحس
+
+165
+00:13:31,230 --> 00:13:39,210
+.. بيناحس .. بيناحس
+
+166
+00:13:39,500 --> 00:13:44,860
+اننا نكون في 6 متر و لا اي شي تمام؟ حلو بنا شوية
+
+167
+00:13:44,860 --> 00:13:50,100
+شوية نحس بال .. بال .. بالامطار والمسافات تمام؟
+
+168
+00:13:50,100 --> 00:13:52,840
+بحكي لك اقولنا المرة دي مش واحد رايح الشجعية بيفكر
+
+169
+00:13:52,840 --> 00:13:59,460
+حاله رايح تلبيب ولا رايح حيفة لأ اللي هي هنا تمام؟
+
+170
+00:13:59,460 --> 00:14:03,260
+the stone is launched fifty meters above the
+
+171
+00:14:03,260 --> 00:14:09,010
+ground تمام؟and the stone just missed the edge of
+
+172
+00:14:09,010 --> 00:14:12,270
+the roof in its way down as shown in the figure
+
+173
+00:14:12,270 --> 00:14:15,690
+قال لي الحجر بعد ما طلع فوق و نزل ما سجتش على
+
+174
+00:14:15,690 --> 00:14:19,450
+الحثة دلوا مهوت نزل تحت على الأرض طبعا الله
+
+175
+00:14:19,450 --> 00:14:23,210
+الحراصنة هاي الحجر يا بنات كان عنده نقطة إيه وصل
+
+176
+00:14:23,210 --> 00:14:26,530
+بيه أقصى ارتفاع نزل نزل على الطاولة هنا ولا دلوا
+
+177
+00:14:26,530 --> 00:14:30,630
+ننزل لمّا وصل للأرض طب ايش اللي بدك ايه؟ قال لي
+
+178
+00:14:30,630 --> 00:14:37,500
+بدي من الخمس مطالب واحدdetermine حدد the time at
+
+179
+00:14:37,500 --> 00:14:42,160
+which the stone reaches its maximum height أقصى
+
+180
+00:14:42,160 --> 00:14:46,800
+ارتفاع يعني عند النقطة B شايفينه؟ جديش السرعة
+
+181
+00:14:46,800 --> 00:14:51,680
+النهائية؟ سفر، مظبوط ولا لأ؟ إذا السرعة النهائية
+
+182
+00:14:51,680 --> 00:14:55,600
+هناك سفر، بدا كل زمان، بدي كل زمان، هذا أول مطلوب،
+
+183
+00:14:55,600 --> 00:15:01,240
+اتنين، واحدة واحدةFind the maximum height بدي
+
+184
+00:15:01,240 --> 00:15:06,400
+الارتفاع يعني بدي why why final تمام واحدة واحدة
+
+185
+00:15:06,400 --> 00:15:11,800
+سنة شوية determine the velocity of the stone when
+
+186
+00:15:11,800 --> 00:15:15,560
+it returns to the height from which it was thrown
+
+187
+00:15:15,560 --> 00:15:19,920
+لما رجع لنفس النقطة اللي انطلق منها لنفس الارتفاع
+
+188
+00:15:19,920 --> 00:15:22,000
+اللي انطلق منه يعني النقطة C
+
+189
+00:15:30,840 --> 00:15:34,540
+عند النقطة C تتوقع السرعة النهائية تكون موجبة ولا
+
+190
+00:15:34,540 --> 00:15:38,780
+سالبة؟ سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+191
+00:15:38,780 --> 00:15:41,260
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+192
+00:15:41,260 --> 00:15:43,780
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+193
+00:15:43,780 --> 00:15:46,020
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+194
+00:15:46,020 --> 00:15:46,440
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+195
+00:15:46,440 --> 00:15:46,640
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+196
+00:15:46,640 --> 00:15:47,820
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+197
+00:15:47,820 --> 00:15:51,350
+سالبة، سزي لما بيجيبوا زمان وطلع سالب ترضوا فيها
+
+198
+00:15:51,350 --> 00:15:56,530
+وهذه نفس العملية استني شوية واحدة واحدة جاييكي
+
+199
+00:15:56,530 --> 00:16:03,550
+جاييكي find the velocity and the position of the
+
+200
+00:16:03,550 --> 00:16:10,470
+stone بعد خمس ثواني أمين أمين find هذا المطلوب
+
+201
+00:16:10,470 --> 00:16:15,110
+الخامسthe velocity of the stone just before
+
+202
+00:16:15,110 --> 00:16:18,930
+hitting the ground just باللغة الإنجليزية معناته
+
+203
+00:16:18,930 --> 00:16:26,310
+هنا لحظات ما ضرب الأرض زي لما نقول هال gate في عند
+
+204
+00:16:26,310 --> 00:16:29,750
+بنت outside this room outside إيش يعني outside؟
+
+205
+00:16:29,750 --> 00:16:33,870
+ممكن تكون في رفح ولا لأ؟ أه لكن لما أقول just
+
+206
+00:16:33,870 --> 00:16:37,510
+outside this room ممكن هو واقف على الباب عرفتوا
+
+207
+00:16:37,510 --> 00:16:41,090
+إيش معنى just؟ just outside يعني واقف على الباب
+
+208
+00:16:41,950 --> 00:16:46,130
+وهان قبل ما يضرب الأرض مباشرة بقول لإن لو بعد ما
+
+209
+00:16:46,130 --> 00:16:48,930
+ضربت الأرض بتبطل الـfree falling بيصير فيه قوة
+
+210
+00:16:48,930 --> 00:16:53,670
+جديدة قوة الأرض تذكرين التصادم؟ حد بيصير في قوة
+
+211
+00:16:53,670 --> 00:16:56,430
+جديدة بيبطل الـfree falling بيصير جثة جديدة مالكاش
+
+212
+00:16:56,430 --> 00:17:01,810
+دعوة فيها بدي وكأنه سرعتها عند النقطة إيه قبل ما
+
+213
+00:17:01,810 --> 00:17:08,280
+تلمس الأرض اتفجلي يا بنات هذه مطالبيبدنا نبدأ ها
+
+214
+00:17:08,280 --> 00:17:16,540
+نمحي هدون و نبدأ ب E B C D هاي ايه ايه ايش بده ده
+
+215
+00:17:16,540 --> 00:17:22,600
+اللي بد الزمن بد الزمن لما يصل لأقفى ارتفاع نقطة
+
+216
+00:17:22,600 --> 00:17:26,200
+البداية معروفة و نقطة النهاية سرعتها الابتدائية
+
+217
+00:17:26,200 --> 00:17:31,960
+سفرو G بعرفها ولا بعرفهاش بعرفها بقوله لو قلتلك V
+
+218
+00:17:31,960 --> 00:17:38,460
+final بساوي V initial نقص GT بحللك المشكلة ولا
+
+219
+00:17:38,460 --> 00:17:44,880
+بحلليش اذا حط محل V final سفر وهدي عشرين وهدي تسعة
+
+220
+00:17:44,880 --> 00:17:51,210
+point تمانية وهيتي في مجهول غيرتي طلعتيإذا انت
+
+221
+00:17:51,210 --> 00:17:58,050
+بتسوي 2.04 متر per second و لو حد كتب اتنين صح
+
+222
+00:17:58,050 --> 00:18:05,890
+second فكرت الصوابعة برا عليكم second أيه الصفسر
+
+223
+00:18:05,890 --> 00:18:13,390
+يا بنات؟ في مشكلة؟ فش مشكلة بيقول
+
+224
+00:18:13,390 --> 00:18:21,210
+للآنبدي Y صح؟ Y final حلو بقول له فالتك من هذه
+
+225
+00:18:21,210 --> 00:18:24,410
+لحظة تكون هذه غلط بديش أستخدمها لحظة تكون غلط
+
+226
+00:18:24,410 --> 00:18:28,770
+مظبوط ولا لأ طبعا ممكن أستخدمها لإنه T إيه عندي؟
+
+227
+00:18:28,770 --> 00:18:33,350
+قللي لو كتبتلك V final تربيع بيسوي V initial تربيع
+
+228
+00:18:33,350 --> 00:18:40,370
+ناقص 2G Y final ناقص Y initial بحل مشكلتك بقوله
+
+229
+00:18:40,370 --> 00:18:50,430
+بحل مشكلتي بقول له هذه قداش0 هدى 420 تربيع ناقص 2
+
+230
+00:18:50,430 --> 00:19:00,390
+في G 19.6 9.8 في 2 why final و هدى 0 انا بديت من
+
+231
+00:19:00,390 --> 00:19:05,230
+هنا شايفين ال origin من هنا بديت اذا هدى 0 ايش
+
+232
+00:19:05,230 --> 00:19:09,410
+المجهول الوحيد في الرسمة why final هى هى طلعتلك
+
+233
+00:19:09,410 --> 00:19:12,930
+why final طلعت حوالى 20
+
+234
+00:19:15,920 --> 00:19:21,660
+عشرين point اربعة متر كمان مرة اي واحد بدها تسألكي
+
+235
+00:19:21,660 --> 00:19:28,180
+اسأله على طول احكي اه حسب انت مرجعيتك وين بدك
+
+236
+00:19:28,180 --> 00:19:33,940
+مرجعيتك انا خدت هناك انا خدت النقطة ايه بديكي
+
+237
+00:19:33,940 --> 00:19:40,960
+تغيري من غير نعم ممكن تكون أرض صحيح اذا كانت الأرض
+
+238
+00:19:40,960 --> 00:19:47,630
+بالصير خمسين بتطلع واي فاين السبعينزائتها صح؟ صح
+
+239
+00:19:47,630 --> 00:19:53,610
+هي وكأنه أقصى ارتفاع بيبعد عشرين متر عن سطح المبنى
+
+240
+00:19:53,610 --> 00:19:57,650
+وعن الأرض كدهش؟ سبعين سبعين، بتجمعنا الخمسين، اذا
+
+241
+00:19:57,650 --> 00:19:59,930
+حسب المرجعية اللي أخدتها، و هي المرجعية اللي
+
+242
+00:19:59,930 --> 00:20:02,550
+أخدتها، قلتلك عنها، و هي اللي أخدتها على الرسمة
+
+243
+00:20:02,550 --> 00:20:07,290
+المرجعية اختياري، بس أنا حددته، انه جُلت نقطة إيه؟
+
+244
+00:20:07,290 --> 00:20:13,010
+نقطة الانطلاق، غاها كنا
+
+245
+00:20:13,010 --> 00:20:18,390
+بننهز، صح، بنهز راسنااتفجنا هذا سؤال بدنا نحله و
+
+246
+00:20:18,390 --> 00:20:24,570
+احنا نفهميه ايش بنعمل تمام C بيقوللي ايش بده
+
+247
+00:20:24,570 --> 00:20:29,470
+قولتله بدي سرعة لما الجسم ريجي على نقطة انا عارفها
+
+248
+00:20:29,470 --> 00:20:34,510
+صح هجيت انا نقطة المرجعية تبعت النقطة ايه سفر
+
+249
+00:20:34,510 --> 00:20:39,690
+اخدتها طب النقطة C ايش بيكون برضه سفر مش سفر مش
+
+250
+00:20:39,690 --> 00:20:45,180
+ايه نفسك مش كبالهاأحلو بقول له انا initial قال انك
+
+251
+00:20:45,180 --> 00:20:48,680
+بدك V final قلت له اه والله بدي V final بتسوي V
+
+252
+00:20:48,680 --> 00:20:53,460
+initial تربيع نقص اتنين G Y final نقص Y initial
+
+253
+00:20:53,460 --> 00:20:59,300
+صحيك؟ هذا قبل ما كنا بنعرفه تمام قال ليه جداش V
+
+254
+00:20:59,300 --> 00:21:08,020
+initial تربيع 400 اتنين في G تسعتاش point ستة يلا
+
+255
+00:21:10,100 --> 00:21:14,600
+حلو براو عليكي سفر ناقص سفر معناته حتى دي روحت
+
+256
+00:21:14,600 --> 00:21:20,880
+سمنا شوية بقى الشيخ طلعت طلعت هنا يلا بال
+
+257
+00:21:20,880 --> 00:21:26,960
+calculator دي بيقول ايه؟ لأن
+
+258
+00:21:26,960 --> 00:21:30,980
+جزر التربيع إلى الخمسة وعشرين ممنوع تقول خمسة لادى
+
+259
+00:21:30,980 --> 00:21:36,900
+يكون موجة في خمسة او ناقص خمسة صح؟ طيب انت هنا في
+
+260
+00:21:36,900 --> 00:21:42,110
+سؤال ما انت فاهمه ولا مش فاهمه؟فهمه عند النقطة C
+
+261
+00:21:42,110 --> 00:21:48,590
+وصلها هو طالع له و هو نازل إذا من هنا
+
+262
+00:21:48,590 --> 00:21:53,870
+بتقول the final بيساوي سالب عشرين متر per second
+
+263
+00:21:53,870 --> 00:21:57,450
+مظبوط
+
+264
+00:21:57,450 --> 00:22:05,030
+هيك ولا لأ؟ تم؟ ليش مبلمتوا؟
+
+265
+00:22:05,030 --> 00:22:14,310
+تقدر تقولي هيك احكيها منتيحلو وين كان الرسمة عنده
+
+266
+00:22:14,310 --> 00:22:18,610
+نقطة ايه صح وين صار عنده نقطة C مش هو بقولك لما
+
+267
+00:22:18,610 --> 00:22:23,290
+وصل لنفس المستوى اذا النقطة A صفر النقطة C ايش
+
+268
+00:22:23,290 --> 00:22:30,070
+عرفتي ليه ايش غيرها دكتور اللي انا عامليه هو نقطة
+
+269
+00:22:30,070 --> 00:22:33,230
+B احنا حكينا ان هو حددلي من النقطة A عشان ايه
+
+270
+00:22:33,230 --> 00:22:38,130
+اخدنا ال final صفر اه تمام اللي هو بحدد لكن لو لا
+
+271
+00:22:38,130 --> 00:22:42,130
+بيه برضهأه طبعا النقطة بيه أقصى ارتفاع هو الجلي
+
+272
+00:22:42,130 --> 00:22:47,850
+طبعا هذه معطيات احكي هل
+
+273
+00:22:47,850 --> 00:22:53,410
+determined the velocity of the stone when .. لما
+
+274
+00:22:53,410 --> 00:22:58,870
+تقولي بطلت أفهم قولي when it returns رجع to the
+
+275
+00:22:58,870 --> 00:23:03,010
+height للارتفاع from which it was thrown للارتفاع
+
+276
+00:23:03,010 --> 00:23:09,450
+اللي انطلق منه واضحة؟إذن فهمت من هذه الجملة انه
+
+277
+00:23:09,450 --> 00:23:13,970
+بده عنده نقطة C من نفس الارتفاع اللي انطلق منه
+
+278
+00:23:13,970 --> 00:23:22,110
+غيرها يعني
+
+279
+00:23:22,110 --> 00:23:28,190
+بدك تقدره بزمن الصعود في اتنين اه
+
+280
+00:23:28,190 --> 00:23:32,330
+بس أنا مابديش اخد شغلة اختراع بدي اخد من معطية
+
+281
+00:23:32,330 --> 00:23:36,430
+السؤال عشان كده أخدت القانون هذا بتطلع نفس الإجابة
+
+282
+00:23:39,350 --> 00:23:44,790
+تمام خلصنا ايه بي سي نجلدى بقولى انا الآن الزمن
+
+283
+00:23:44,790 --> 00:23:50,250
+بتدلكى جاهز منيح اكمل زمان خمس ثوانى بدي تجيبلى
+
+284
+00:23:50,250 --> 00:23:56,610
+السرعة و تجيبلى موضعه حلو السرعة هي دى يا بنات
+
+285
+00:23:57,880 --> 00:24:04,260
+Vfinal بيساوي Vinitial ناقص GT إيش بدي؟ بدي Vfinal
+
+286
+00:24:04,260 --> 00:24:10,240
+هذه عشرين ناقص تسعة point تمانية في خمسة يلا يا
+
+287
+00:24:10,240 --> 00:24:16,640
+كاب كوريتا طلعتلي موجب ولا سالب؟ هيها حوالي خمسين
+
+288
+00:24:16,640 --> 00:24:20,920
+و هدك عشرين حوالي ناقص سلتين أظن أقل من .. ناقص
+
+289
+00:24:20,920 --> 00:24:26,180
+تسعة و عشرين متر per second هتجهد هذه الإشارة
+
+290
+00:24:26,180 --> 00:24:31,450
+الحلوةاللي هي السالب، أيها معنى فيزيائي ولا لا؟
+
+291
+00:24:31,450 --> 00:24:36,310
+إنها نازلة، صح؟ لو واحد قال ليه، ممكن تكون عند
+
+292
+00:24:36,310 --> 00:24:40,530
+النقطة هذه؟ ولا ممكن، لأن عند النقطة هذه طالعة
+
+293
+00:24:40,530 --> 00:24:45,070
+وانت طلعت معاك الإجابة؟ سالبة، بقوله هنا ممكن وهنا
+
+294
+00:24:45,070 --> 00:24:49,250
+ممكن، صح؟ هل جيت هنا ولا هنا، بتعتمد على ال
+
+295
+00:24:49,250 --> 00:24:53,660
+positionانت أخدت السفر هنا ولا لأ؟ كل نقطة تحت
+
+296
+00:24:53,660 --> 00:24:57,520
+السفر ايش المفروض تكون؟ سالبة وكل نقطة فوق السفر
+
+297
+00:24:57,520 --> 00:25:03,160
+موجة بيه يجرب انها تحته ولا فوقه ايش بدك كمان؟ ده
+
+298
+00:25:03,160 --> 00:25:08,900
+اللي بديه Y final بقول Y final نقص Y initial اللي
+
+299
+00:25:08,900 --> 00:25:16,240
+هو القانون بتساوي V initial Vt نقص نص GT تربية مش
+
+300
+00:25:16,240 --> 00:25:21,470
+في قانون زيها ده؟ حلوy initial اعتبرته 0 اذا y
+
+301
+00:25:21,470 --> 00:25:30,510
+final بيسوي 20 في 5 ناقص 4.9 نص جيه في 25 اللي هو
+
+302
+00:25:30,510 --> 00:25:36,230
+T تربيع صح بقى عوض يلا بال calculator هذه حوالي
+
+303
+00:25:36,230 --> 00:25:44,170
+100 صح؟ و هذه 5 في 25 اكتر 125 تقريبا حوالي سالب
+
+304
+00:25:44,170 --> 00:25:50,980
+22.5 مترطلعت سالبة معناته تحت نقطة الأصل ولا فوق
+
+305
+00:25:50,980 --> 00:25:58,820
+تحت إذا المعناته هذه النقطة هنا ال C
+
+306
+00:25:58,820 --> 00:26:02,800
+و أنا شينا في ال C
+
+307
+00:26:02,800 --> 00:26:08,760
+أرقمها
+
+308
+00:26:08,760 --> 00:26:13,320
+يعني انت شفت ان الصراع أكبر تمام احنا بدنا مقالة
+
+309
+00:26:13,320 --> 00:26:13,920
+مباشرة
+
+310
+00:26:17,980 --> 00:26:24,440
+أكبر اكبر من 4 اكبر من 4 لانه 2 و 2 اربع طبعا بس
+
+311
+00:26:24,440 --> 00:26:31,540
+احنا بدنا الشغلات المباشرة عاموجة
+
+312
+00:26:31,540 --> 00:26:37,340
+فوق نقطة الاصل يعني فوق ال ايه حتى لو كانت نازلة
+
+313
+00:26:37,340 --> 00:26:42,550
+ال position مالوش ده عوض الصرعةالـ Position غير عن
+
+314
+00:26:42,550 --> 00:26:46,010
+الصرعة لما يكون نازل الصرعة سلبة الـ Position
+
+315
+00:26:46,010 --> 00:26:50,390
+مالهوش دعوة هجيت عند النقطة هذه يا بنتي هذه النقطة
+
+316
+00:26:50,390 --> 00:26:55,290
+هذه شفاها صرعتها كيش بيبقى تكون لكن الـ Position
+
+317
+00:26:55,290 --> 00:27:01,870
+هو موجودة مالهوش دعوة هذه غير عن هذه تمام يا بنتي؟
+
+318
+00:27:01,870 --> 00:27:11,820
+تمام غيره حلو جلل زوايا جلد ديE sorry ايش بدك
+
+319
+00:27:11,820 --> 00:27:16,340
+اجلبدي السرعة قبل ما يرتطن بالأرض مباشرة بطلع
+
+320
+00:27:16,340 --> 00:27:20,100
+بقوله يعني عنده النقطة ايه ولا لا عند النقطة ايه
+
+321
+00:27:20,100 --> 00:27:25,040
+بقاعدي بقوله E ايش بدك اجلبدي V final صح ولا لأ
+
+322
+00:27:25,040 --> 00:27:30,640
+بقوله V final بنجيبها في عند V final تربيع بيساوي
+
+323
+00:27:30,640 --> 00:27:36,220
+V initial تربيع نقص اتنين G وY final نقص Y initial
+
+324
+00:27:36,220 --> 00:27:42,970
+اطلع الفلجل كله معطفاللي هادي مش معطية هدي جديش
+
+325
+00:27:42,970 --> 00:27:48,870
+قال يا 400 نقص 2 في G 19.6 أف تحجوز وينيش لما
+
+326
+00:27:48,870 --> 00:27:52,930
+اتفقن سفر ولا لأ طب واي فينا مني ولي جديش احكي
+
+327
+00:27:52,930 --> 00:27:58,650
+الوا سالب خمسين bravo عليكي سالب خمسين قولت سالب
+
+328
+00:27:58,650 --> 00:28:03,550
+خمسين مش خمسين سالب خمسين لأ انا تحت اذا سالب
+
+329
+00:28:03,550 --> 00:28:11,700
+خمسين نقص سفر خلصت تمام طلع جواببدي اخد اجازة
+
+330
+00:28:11,700 --> 00:28:17,220
+تربيع تبعه هجيت ارتطم الأرض وانصاحي ومصحصح و هو
+
+331
+00:28:17,220 --> 00:28:21,940
+طالع ولا هو نازل اذا بدي اخد السالب بدي اخد السالب
+
+332
+00:28:21,940 --> 00:28:29,040
+جدش طلع الجواب في اللعب السالب قصد 37.4 متر per
+
+333
+00:28:29,040 --> 00:28:33,280
+second مش
+
+334
+00:28:33,280 --> 00:28:39,460
+4 يعني point one أي صف صار
+
+335
+00:28:42,950 --> 00:28:46,710
+أه وإينيش السفر متفاجئين ولا لأ؟ لأنه أنا عم أتبع
+
+336
+00:28:46,710 --> 00:28:49,990
+السفر طب و هي ال final وين؟ هي ال final هي شخصية
+
+337
+00:28:49,990 --> 00:28:54,550
+مجهولة ولا معروفة النقطة مش وصلت الأرض طيب الأرض
+
+338
+00:28:54,550 --> 00:29:00,470
+كانت أوطى من نقطة البداية ولا أعلى أو طبع كم متر؟
+
+339
+00:29:00,470 --> 00:29:04,570
+خمسين هو وعشانها أوطى حطت ثالث
+
+340
+00:29:08,080 --> 00:29:11,800
+أي هو طول هذا الزلمة خمسين متر كله مترين مابديش ..
+
+341
+00:29:11,800 --> 00:29:16,540
+تمام؟ تمام .. هو اعتبر و كأنه من .. من إيدي الزلمة
+
+342
+00:29:16,540 --> 00:29:20,000
+ليناك الخمسين .. ماهي تقريب .. حسب طول البرج يعني
+
+343
+00:29:20,000 --> 00:29:24,160
+عبارة إنه سالب طول البرج؟ أه .. هو موضع مش طول ..
+
+344
+00:29:24,160 --> 00:29:28,780
+أنا بدي موضع الحجر لما وصل للأرض .. بقوله كموضع
+
+345
+00:29:28,780 --> 00:29:34,110
+تحت نقطة الأصل ولا لأ .. أخدته سالب ..موضع مش طول
+
+346
+00:29:34,110 --> 00:29:37,430
+لان الطول مينفعش يكون سالب لكن كموضع بنقول سالب
+
+347
+00:29:37,430 --> 00:29:48,170
+غيرها احكي اه مش
+
+348
+00:29:48,170 --> 00:29:57,070
+طول موضع position صح هذه
+
+349
+00:29:57,070 --> 00:30:01,870
+النقطة جديش حد يثير ثصابي النقطة هذه
+
+350
+00:30:08,630 --> 00:30:11,810
+Y initial سفر وY final
+
+351
+00:30:24,940 --> 00:30:29,520
+أمين؟ هجيت؟ انغششكم إيه السؤال اللي جابلكم الشباب
+
+352
+00:30:29,520 --> 00:30:33,340
+ذهجون صبحيات الساعة تمانية و هم يسألوا قالوا في
+
+353
+00:30:33,340 --> 00:30:36,200
+عيننا قانون بيقول زمن الصعود بيساوي زمن الهبوط
+
+354
+00:30:36,200 --> 00:30:38,980
+دايما لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+355
+00:30:38,980 --> 00:30:39,860
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+356
+00:30:39,860 --> 00:30:40,400
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+357
+00:30:40,400 --> 00:30:52,520
+لأ لأ لأ لأ لأ
+
+358
+00:30:52,990 --> 00:30:56,090
+بصى مونيافى توجيهى بيقول جزء تربيع اتنين GH
+
+359
+00:30:56,090 --> 00:31:01,870
+بيقولوا ازحقوا تستخدموا ازحقوا تستخدموا ممنوع
+
+360
+00:31:01,870 --> 00:31:10,480
+تستخدموا محنة تمام يا بنات مافيش قانون اسمه هيكأه
+
+361
+00:31:10,480 --> 00:31:13,880
+أه .. و الحالة الخاصة مش قانون .. ما زالت ورتي
+
+362
+00:31:13,880 --> 00:31:16,920
+حالة خاصة بطل القانون .. القانون شغل عامة يا بنات
+
+363
+00:31:16,920 --> 00:31:20,620
+.. فانتقوا منه .. اه انسيه .. انا بدي .. اه بس انا
+
+364
+00:31:20,620 --> 00:31:23,780
+احفظ الشغلات الأساسية بدي قاعد أحفظ ميت سا قانون
+
+365
+00:31:23,780 --> 00:31:27,960
+.. كل شغل قانون .. إذا أنا ده مش قانون .. مش قانون
+
+366
+00:31:27,960 --> 00:31:28,740
+..
+
+367
+00:31:33,140 --> 00:31:36,940
+أه بس اللي هو 100 شرط فيه شروط كتيرة زي ما جالت
+
+368
+00:31:36,940 --> 00:31:40,460
+حلقات خاصة كتيرة فهذه حلقة خاصة مش موجودة أنا
+
+369
+00:31:40,460 --> 00:31:44,600
+مغششكم إيش جالوا الطلاب يعني يسألوني تمام يا بنات؟
+
+370
+00:31:44,600 --> 00:31:48,660
+أيه السفسار؟ خلصي ال chapter
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/jn4ooM4Kee0_raw.json b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/jn4ooM4Kee0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..d7bb3d1b094e5cba9d11e3dea7f118a4f0bd7127
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/jn4ooM4Kee0_raw.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/jn4ooM4Kee0_raw.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/jn4ooM4Kee0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f8c5c94ae810d31fd1155379311dce6491a6d7e9
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/jn4ooM4Kee0_raw.srt
@@ -0,0 +1,1496 @@
+1
+00:00:05,360 --> 00:00:08,520
+تمام يا بنات اليوم ان شاء الله بدنا نسمر هذا ال
+
+2
+00:00:08,520 --> 00:00:13,780
+chapter و ننهيه ال chapter الماضي او المحاضرة
+
+3
+00:00:13,780 --> 00:00:19,980
+الماضية استقلنا احنا وياكم اربع معادلات بتحكم
+
+4
+00:00:19,980 --> 00:00:27,300
+الحركة بتسارع ثابت و المعادلات كانت التالت Vfinal
+
+5
+00:00:27,300 --> 00:00:34,670
+بتساوي D-A-Tو X final نخس X initial بيسوي V
+
+6
+00:00:34,670 --> 00:00:39,950
+initial في T زائد نص AT تربيع صح ولا لأ؟ وقلنا
+
+7
+00:00:39,950 --> 00:00:44,330
+هدول معادلتي الأساسيتين التالتين منهم .. مش تقتمان
+
+8
+00:00:44,330 --> 00:00:50,510
+تلتين منهم X final نخس X initial بيسوي نص V
+
+9
+00:00:50,510 --> 00:00:56,730
+initial زايد V final في Tوالاخيرة Vfinal تربيع
+
+10
+00:00:56,730 --> 00:01:03,470
+بتسوي Vinitial تربيع ذات 2AXfinal-Xinitial مظبوط
+
+11
+00:01:03,470 --> 00:01:08,330
+ولا لأ؟ كنا هدول ثلاث معادلات شرط استخدامهم بأن
+
+12
+00:01:08,330 --> 00:01:12,470
+يكون A constant صح ولا لأ؟ هذا الشرط الواعي إذا في
+
+13
+00:01:12,470 --> 00:01:18,340
+هذه المحاضرةبدنا نكمل تقريبا نفس المحاضرة السابقة
+
+14
+00:01:18,340 --> 00:01:25,340
+وهي حركة خطية بتسارق ثابت هذه الحركة بنسميها سقوط
+
+15
+00:01:25,340 --> 00:01:30,520
+الحر ايش يعني سقوط حر واحنا حكينا لكل مسمى من اسمه
+
+16
+00:01:30,520 --> 00:01:36,960
+نصيب سموها free كلمة free حر يعني ماعليهوش قيد ولا
+
+17
+00:01:36,960 --> 00:01:43,490
+لأوعلمياً قيد يعني قوة ماعلهوش قوة إلا قوة واحدة
+
+18
+00:01:43,490 --> 00:01:48,730
+ربانية طبيعية هي قوة الجاذبية العرضية إذا بيقولي
+
+19
+00:01:48,730 --> 00:01:57,310
+any object moving freely يتحرك بحرية بدون أي قوة
+
+20
+00:01:57,310 --> 00:02:04,410
+بس تحت تأثير under the influence تحت تأثير of
+
+21
+00:02:04,410 --> 00:02:08,870
+gravity gravity يعني جاذبيةوفي الـ Gravity is said
+
+22
+00:02:08,870 --> 00:02:12,250
+to be in free-falling motion. اذا free-falling
+
+23
+00:02:12,250 --> 00:02:16,870
+motion يسم عليه فقط قوة جاذبية. هذه معناتها
+
+24
+00:02:16,870 --> 00:02:21,930
+بالبلدين. وباقي القوة ممنوع تكون موجودة. أي قوة
+
+25
+00:02:21,930 --> 00:02:25,730
+موجودة بيبطل free-falling. مقاومة الهواء بيبطل
+
+26
+00:02:25,730 --> 00:02:30,640
+free-falling.بس في قوة ولا لأ ارتطن بالأرض بيبطل
+
+27
+00:02:30,640 --> 00:02:34,000
+free falling في صيغ قوة جيدة فهمتوا عليها كيف؟ اذا
+
+28
+00:02:34,000 --> 00:02:39,200
+بس قوة الجاذبية ده اللي معناته تصارع الجسم هو
+
+29
+00:02:39,200 --> 00:02:43,720
+تصارع الجاذبية صح؟ و تصارع الجاذبية ثابت ولا
+
+30
+00:02:43,720 --> 00:02:47,920
+مالثابت؟ ثابت اذا هدول القوانين صحيحين تصارع
+
+31
+00:02:47,920 --> 00:02:52,480
+الجاذبية ثابت بس ايه بتبطل مرة عشرة و مرة تمانية و
+
+32
+00:02:52,480 --> 00:02:59,210
+مرة ستة الها كم قيمة؟ واحدة اذا بيقوليassuming
+
+33
+00:02:59,210 --> 00:03:05,530
+that the gravitational acceleration تسارع الجاذبية
+
+34
+00:03:05,530 --> 00:03:10,610
+اللى يرمز لها بالرمز G denoted by G بتعرف اللى
+
+35
+00:03:10,610 --> 00:03:14,590
+رمزها ولا لأ؟ denoted by G طب ليش قلتلي assuming
+
+36
+00:03:14,590 --> 00:03:18,590
+is constant؟ قاللي لأنه هي مش ثابتة بالمكان يعني
+
+37
+00:03:18,590 --> 00:03:23,970
+بمعنى أخر لو أنت جيست في غزة 9.8 وروحت جيستها في
+
+38
+00:03:23,970 --> 00:03:28,310
+رمال اللى ممكن تلاقيها 9.7أجل من غزة لو روحت على
+
+39
+00:03:28,310 --> 00:03:32,690
+أريحة هتلاقي هي أكتر من غزة طبعا رمالها أعلى من
+
+40
+00:03:32,690 --> 00:03:37,950
+غزة ولا لأ وريحها أوطى إذا تختلف من حسب المكان ولو
+
+41
+00:03:37,950 --> 00:03:43,450
+جثتهافي أقصى شمال الكورة الأرضية عند Helsinki ولا
+
+42
+00:03:43,450 --> 00:03:47,010
+عند Stockholm غير لما تجسى في الخرطوم الخرطوم
+
+43
+00:03:47,010 --> 00:03:51,650
+حوالين خط الاستواع إذا في اختلاف بس احنا بنعتبر
+
+44
+00:03:51,650 --> 00:03:55,930
+همالنا ثالثة وقداش قيمتها تسعة بون تمانية هذا اللي
+
+45
+00:03:55,930 --> 00:04:01,970
+بدنا نعتبره افتراضا تمامنقول إنها مستمرة ونعتبر
+
+46
+00:04:01,970 --> 00:04:12,210
+أنها مستمرة ونعتبر أنها مستمرة
+
+47
+00:04:12,210 --> 00:04:14,770
+ونعتبر أنها مستمرة ونعتبر أنها مستمرة ونعتبر أنها
+
+48
+00:04:14,770 --> 00:04:16,490
+مستمرة ونعتبر أنها مستمرة ونعتبر أنها مستمرة
+
+49
+00:04:16,490 --> 00:04:17,090
+ونعتبر أنها مستمرة ونعتبر أنها مستمرة ونعتبر أنها
+
+50
+00:04:17,090 --> 00:04:17,310
+مستمرة ونعتبر أنها مستمرة ونعتبر أنها مستمرة
+
+51
+00:04:17,310 --> 00:04:17,310
+ونعتبر أنها مستمرة ونعتبر أنها مستمرة ونعتبر أنها
+
+52
+00:04:17,310 --> 00:04:17,310
+مستمرة ونعتبر أنها مستمرة ونعتبر أنها مستمرة
+
+53
+00:04:17,310 --> 00:04:18,550
+ونعتبر أنها مستمرة ونعتبر أنها مستمرة ونعتبر أنها
+
+54
+00:04:18,550 --> 00:04:26,050
+مستمرة ونعتبر أنها مستمرة ونعتبر أنهاعشان واحد
+
+55
+00:04:26,050 --> 00:04:30,830
+يقول طب انا بيني و بين ال Y طار بحب اش خلّي X مش
+
+56
+00:04:30,830 --> 00:04:34,930
+مشكلة تمام؟ لكن ال default ان كل حاجة عمودية
+
+57
+00:04:34,930 --> 00:04:41,030
+بناخدها Y ولا لأ حلو اذا بقول جي بتسوى 9.8 متر per
+
+58
+00:04:41,030 --> 00:04:44,950
+second تربيع أو بتسوى 32 foot per second تربيع
+
+59
+00:04:44,950 --> 00:04:50,130
+بالنظام البريطاني 32 تمام؟ شوفوا انتوا عشان نؤسس
+
+60
+00:04:50,130 --> 00:04:53,510
+احنا اشهد بدنيا منكم شوفوا 9.8 في حدا منكم مش
+
+61
+00:04:53,510 --> 00:04:57,900
+حافظهمش كلكم حظينه بالرغم من ذلك بنقولكم بنقش
+
+62
+00:04:57,900 --> 00:05:01,920
+جميلتكم تحفظوهوش بنديكم إياه في الامتحان نكتبه في
+
+63
+00:05:01,920 --> 00:05:05,060
+وراج الامتحان بس عشان تفهموا إنه إيش بدياه منكم
+
+64
+00:05:05,060 --> 00:05:09,480
+أنا بديش ياكم تحفظوا أرقامأحنا بدنا ياكم هذا يشتغل
+
+65
+00:05:09,480 --> 00:05:14,340
+و بس و كل حاجة حفظ علينا تمام الشغلات الأساسية ما
+
+66
+00:05:14,340 --> 00:05:18,140
+بنقولكم إيش هي بيقول since the motion is vertical
+
+67
+00:05:18,140 --> 00:05:23,320
+بما إنه الحركة عمودية we take our axis to be the y
+
+68
+00:05:23,320 --> 00:05:27,440
+-axis محول راح يكون بالأعلى واحد مش x فيها مشكلة
+
+69
+00:05:27,440 --> 00:05:31,320
+ولا فيها أي مشكلة with the positive since is
+
+70
+00:05:31,320 --> 00:05:36,160
+upward اتجاهك الموجة بالأعلى إيش جيد ماحنا عارفين
+
+71
+00:05:36,160 --> 00:05:41,970
+تمامجلسوه جلّي هدول المعادلات الحلوين و بيبقى تعمل
+
+72
+00:05:41,970 --> 00:05:47,550
+عليهم تبديلين وين في X حط محلها Y؟ في مشكلة؟ لأ
+
+73
+00:05:47,550 --> 00:05:54,510
+وين في A حط سالب G و ليش سالب؟ لأنها لأسفل و أنت
+
+74
+00:05:54,510 --> 00:06:00,270
+بتقول كل شي لأعلى؟موجب موجب and a by minus g قال
+
+75
+00:06:00,270 --> 00:06:05,810
+لي حلو قال لي the negative sign هي بيأكد عليها is
+
+76
+00:06:05,810 --> 00:06:10,450
+because the gravitational acceleration is always
+
+77
+00:06:10,450 --> 00:06:15,230
+downward always مظبوطة او لأ دايما طبعا هذه خيارة
+
+78
+00:06:15,230 --> 00:06:19,450
+ربنا في حد تغيرها ممكن الحد يغيرها دايما downward
+
+79
+00:06:19,450 --> 00:06:24,360
+قال لي إذا هذه المعادلة الأربع طلعوا عليهاشوفوا
+
+80
+00:06:24,360 --> 00:06:29,580
+إيش الفرق وإن في X حطيت Y وإن في A حطيت ثالث جيه
+
+81
+00:06:29,580 --> 00:06:44,260
+فيه شي جيد ولا شي جيد بدي
+
+82
+00:06:44,260 --> 00:06:49,140
+ال A نقل جيه مظبوط هيك؟ والمحور عشانها بس عشان
+
+83
+00:06:49,140 --> 00:06:55,580
+صاضية عشانها عمودية صاضيةتمام؟ أي سفسة أخر؟ حلو
+
+84
+00:06:55,580 --> 00:07:00,900
+بيقولي الريمارك اتفق ان احنا بنركز على شغلات معينة
+
+85
+00:07:00,900 --> 00:07:04,220
+في الريمارك مظبوط ولا لأ؟ بيقولي remember that اذا
+
+86
+00:07:04,220 --> 00:07:09,280
+ذكر انه وحطها في مخك شغل عارفها انت that the
+
+87
+00:07:09,280 --> 00:07:14,100
+gravitational acceleration g is constant في اشي
+
+88
+00:07:14,100 --> 00:07:18,340
+جديد؟و لما تقول ال constant معناته ثابت بشكل تاني
+
+89
+00:07:18,340 --> 00:07:21,840
+لان هذه الها magnitude و الها direction الها مقدار
+
+90
+00:07:21,840 --> 00:07:25,880
+و اتجاه فهي ثابتة بكلا ال magnitude و ال direction
+
+91
+00:07:25,880 --> 00:07:31,900
+in magnitude and direction and this means that the
+
+92
+00:07:31,900 --> 00:07:36,480
+negative sign of g in the last equation will not
+
+93
+00:07:36,480 --> 00:07:40,870
+be changed ممنوع تغيرهwill not be changed unless
+
+94
+00:07:40,870 --> 00:07:46,790
+الا إذا انت قلت انا بديش اللي فوق هو يكون موجب بدي
+
+95
+00:07:46,790 --> 00:07:50,710
+اللي تحت يكون موجب ساعتها بتجرب كل شي صح ساعتها كل
+
+96
+00:07:50,710 --> 00:07:54,810
+حاجة الأعلى بتخليها سالبة مظبوط ولا وكل حاجة
+
+97
+00:07:54,810 --> 00:07:58,070
+الأسفل بصير موجب لكن أنا بانصحش تعملوا هذه الشغل
+
+98
+00:07:58,070 --> 00:08:01,090
+لسه بدري علينا خلينا زي ما احنا ال default
+
+99
+00:08:01,090 --> 00:08:05,990
+وبالتالي هذه المعادلات بدك تاخدها زي ما هي ال G
+
+100
+00:08:05,990 --> 00:08:12,140
+دايما قدامها سالب اتفجنا؟تمام بقولني unless الا
+
+101
+00:08:12,140 --> 00:08:16,420
+إذا will not be changed unless you change your
+
+102
+00:08:16,420 --> 00:08:19,460
+positive sense إلى اللي إذا غيرت اتجاهك الموجد
+
+103
+00:08:19,460 --> 00:08:24,080
+regardless of the motion .. regardless of the
+
+104
+00:08:24,080 --> 00:08:27,420
+direction of motion يعني بيغضي النظر الجسم طالع
+
+105
+00:08:27,420 --> 00:08:33,600
+ولا نازل طالع ولا نازل جي إلى أسفل صح ولا لأ تمام
+
+106
+00:08:33,600 --> 00:08:39,700
+وسلبة بتبقى حلوحكينا من أكام جلمة لأ كلمة ايه؟
+
+107
+00:08:39,700 --> 00:08:44,940
+بنشوف عربي ولا صيني تامه؟ بقول الـ a ball is
+
+108
+00:08:44,940 --> 00:08:50,460
+thrown upward إيه فيه falling motion؟ قذفتها لأعلى
+
+109
+00:08:50,460 --> 00:08:58,080
+لو بدي أسألكم السرعة الإبتدائية موجبة ولا سلبة؟
+
+110
+00:08:58,080 --> 00:09:04,350
+ليش؟ لأنها لأعلىتما كذفت إلى أعلى إذا السرعة
+
+111
+00:09:04,350 --> 00:09:08,690
+الإبتدائية موجبة لو جالي قذفتها إلى أسفل السرعة
+
+112
+00:09:08,690 --> 00:09:11,830
+الإبتدائية بيصير سالبة حلو أنت مش سائلني عن السرعة
+
+113
+00:09:11,830 --> 00:09:14,330
+الإبتدائية إيش بدها بيقولي it's acceleration
+
+114
+00:09:14,330 --> 00:09:17,390
+بيسألني عن ال acceleration تعالي تشوفوا إيش حاطط
+
+115
+00:09:17,390 --> 00:09:19,490
+ليه الخيارات
+
+116
+00:09:25,190 --> 00:09:30,170
+مظبوط ولا لأ؟ فيها شك؟ ولا نقعد يفكر إيش هي؟ مات
+
+117
+00:09:30,170 --> 00:09:35,250
+بتقوللي تسارعة ثابت؟ مالثابت؟ مازال حاجة الجسم
+
+118
+00:09:35,250 --> 00:09:38,770
+طالع النزل شوي فيه، أنت بتسألني عن تسارعة،
+
+119
+00:09:38,770 --> 00:09:43,780
+فالتسارعة ثابت، إذا إيش خياري؟Stays constant.
+
+120
+00:09:44,600 --> 00:09:48,480
+تمام؟ يعني هو بده يضحك عليّ، بيقول طالع عفوج و لا
+
+121
+00:09:48,480 --> 00:09:51,920
+تغل، مش اللي فيها، أنت بتحكي عن acceleration و
+
+122
+00:09:51,920 --> 00:09:54,180
+free-falling، ما زال free-falling، إذا الـ
+
+123
+00:09:54,180 --> 00:09:58,380
+acceleration ما لها، constant. حلو، لأنه طيب، نغير
+
+124
+00:09:58,380 --> 00:10:02,560
+السؤال، نطلب حاجة تانية، بس نفس السؤال. A ball is
+
+125
+00:10:02,560 --> 00:10:05,860
+thrown upward in a free-falling motion. بيقول،
+
+126
+00:10:05,860 --> 00:10:10,160
+بيدي سرعتها.ما جالش سرعتها ابتدائية جالي سرعتها
+
+127
+00:10:10,160 --> 00:10:15,100
+كلها قلتله شوف الخيارات جالي و هي طالعة سرعتها إيش
+
+128
+00:10:15,100 --> 00:10:21,040
+بيصير فيها؟ و هي طالعة بتنجس مش ابتجه في الأخر
+
+129
+00:10:21,040 --> 00:10:28,440
+بتنجس بعدها بتعود تزيد إذا بتنجس ثم بتزيد تمام؟
+
+130
+00:10:28,440 --> 00:10:33,620
+إذا أي خيار قلتله decreases and then increases صح
+
+131
+00:10:33,620 --> 00:10:35,860
+ولا لأ؟ أي صفصة؟
+
+132
+00:10:39,440 --> 00:10:45,920
+هدا هال gate هادى free falling motion سقوط حر ماهو
+
+133
+00:10:45,920 --> 00:10:55,460
+تصاروحها مافيش ثابت تصاروح هيك جوابتي هيك سقوها
+
+134
+00:10:55,460 --> 00:11:04,860
+شوفي free falling هدا هي غيرها تمام يا بنات كل هي
+
+135
+00:11:04,860 --> 00:11:07,140
+معلمتين مش فيه أيش
+
+136
+00:11:10,640 --> 00:11:15,080
+السؤال المشهور يمكن يمر عليكم في صفحة 10 قال لي
+
+137
+00:11:15,080 --> 00:11:21,200
+هذا زلمة واقف على سطح مبنى و بدى يخذف stone ايش
+
+138
+00:11:21,200 --> 00:11:26,120
+يعني stone؟ حجر a stone is thrown from the top of
+
+139
+00:11:26,120 --> 00:11:30,440
+a building من قمة مبنى وهذا وين واقف في المبنى؟
+
+140
+00:11:30,440 --> 00:11:35,770
+على حفة المبنىخبط الحجر اللي فوق It is thrown from
+
+141
+00:11:35,770 --> 00:11:38,810
+the top of a building with an initial velocity
+
+142
+00:11:38,810 --> 00:11:42,310
+سرعية ابتدائية مقدارها عشرين متر per second
+
+143
+00:11:42,310 --> 00:11:45,950
+straight upward إذا قذفها لأعلى ولا لأ إذا سرعية
+
+144
+00:11:45,950 --> 00:11:51,810
+ابتدائية مجملة مظبوط ولا لأ؟ حلو بيقوللي the stone
+
+145
+00:11:51,810 --> 00:11:58,160
+is launched اطلقت اطلق هنا معناته launchأُطلقت من
+
+146
+00:11:58,160 --> 00:12:02,080
+ارتفاع خمسين متر above the ground المبنى كان
+
+147
+00:12:02,080 --> 00:12:06,780
+ارتفاعه خمسين متر تمام؟ يلّا ماشيين توق في منكم
+
+148
+00:12:06,780 --> 00:12:14,620
+حصير مهندسات المستقبل؟ أكم طابق الخمسين متر؟ اهو
+
+149
+00:12:14,620 --> 00:12:20,280
+حسب أيه؟ مافيه standard عالمي علي
+
+150
+00:12:20,280 --> 00:12:26,460
+صوتكطوابق واحد؟ معناته العمارة اللي .. اللي عشر
+
+151
+00:12:26,460 --> 00:12:32,300
+طوابق واصل السماء؟
+
+152
+00:12:32,300 --> 00:12:36,440
+هذا النيح اللي قلت انا، عشر متر؟ انتوا مش عارفين
+
+153
+00:12:36,440 --> 00:12:41,520
+ايش معنى عشر متر؟ بنات، عمركوش، شفتوا أبوكم لماشي
+
+154
+00:12:41,520 --> 00:12:46,710
+الاستارة كم متر بشريها؟ عشان تغطيها دي؟بس تلاتة
+
+155
+00:12:46,710 --> 00:12:50,750
+متر و أقل كمان تلاتة متر قبل ما يتبلط و لما يتبلط
+
+156
+00:12:50,750 --> 00:12:55,630
+و نحط رمل بيصير 2.8 أصلا كل الجماش اللي فيه اللي
+
+157
+00:12:55,630 --> 00:13:01,070
+بتنش الاسطرات maximum مترين و تمانين صنطي ليش
+
+158
+00:13:01,070 --> 00:13:04,270
+بيقولوا ما هو مابحقلهاش يتجروا على أرض مش بيجيسوا
+
+159
+00:13:04,270 --> 00:13:09,350
+و بيخلوا يكونوا منتفعة شوية إذا هذه حوالى 16 طعبك
+
+160
+00:13:09,350 --> 00:13:18,590
+عرفتوا أكان طعبك؟بديك بص طابجين انت؟ تمام اذا هاد
+
+161
+00:13:18,590 --> 00:13:22,550
+يقولش عشان بيناقشوها .. ما أنا قولتلكم بيناحس ..
+
+162
+00:13:22,550 --> 00:13:24,330
+بيناحس .. بيناحس .. بيناحس .. بيناحس .. بيناحس ..
+
+163
+00:13:24,330 --> 00:13:24,370
+بيناحس .. بيناحس .. بيناحس .. بيناحس .. بيناحس ..
+
+164
+00:13:24,370 --> 00:13:24,390
+بيناحس .. بيناحس .. بيناحس .. بيناحس .. بيناحس ..
+
+165
+00:13:24,390 --> 00:13:24,390
+بيناحس .. بيناحس .. بيناحس .. بيناحس .. بيناحس ..
+
+166
+00:13:24,390 --> 00:13:25,370
+بيناحس .. بيناحس .. بيناحس .. بيناحس .. بيناحس ..
+
+167
+00:13:25,370 --> 00:13:31,230
+بيناحس .. بيناحس .. بيناحس
+
+168
+00:13:31,230 --> 00:13:39,210
+.. بيناحس .. بيناحس
+
+169
+00:13:39,500 --> 00:13:44,860
+اننا نكون في 6 متر و لا اي شي تمام؟ حلو بنا شوية
+
+170
+00:13:44,860 --> 00:13:50,100
+شوية نحس بال .. بال .. بالامطار والمسافات تمام؟
+
+171
+00:13:50,100 --> 00:13:52,840
+بحكي لك اقولنا المرة دي مش واحد رايح الشجعية بيفكر
+
+172
+00:13:52,840 --> 00:13:59,460
+حاله رايح تلبيب ولا رايح حيفة لأ اللي هي هنا تمام؟
+
+173
+00:13:59,460 --> 00:14:03,260
+the stone is launched fifty meters above the
+
+174
+00:14:03,260 --> 00:14:09,010
+ground تمام؟and the stone just missed the edge of
+
+175
+00:14:09,010 --> 00:14:12,270
+the roof in its way down as shown in the figure
+
+176
+00:14:12,270 --> 00:14:15,690
+قال لي الحجر بعد ما طلع فوق و نزل ما سجتش على
+
+177
+00:14:15,690 --> 00:14:19,450
+الحثة دلوا مهوت نزل تحت على الأرض طبعا الله
+
+178
+00:14:19,450 --> 00:14:23,210
+الحراصنة هاي الحجر يا بنات كان عنده نقطة إيه وصل
+
+179
+00:14:23,210 --> 00:14:26,530
+بيه أقصى ارتفاع نزل نزل على الطاولة هنا ولا دلوا
+
+180
+00:14:26,530 --> 00:14:30,630
+ننزل لمّا وصل للأرض طب ايش اللي بدك ايه؟ قال لي
+
+181
+00:14:30,630 --> 00:14:37,500
+بدي من الخمس مطالب واحدdetermine حدد the time at
+
+182
+00:14:37,500 --> 00:14:42,160
+which the stone reaches its maximum height أقصى
+
+183
+00:14:42,160 --> 00:14:46,800
+ارتفاع يعني عند النقطة B شايفينه؟ جديش السرعة
+
+184
+00:14:46,800 --> 00:14:51,680
+النهائية؟ سفر، مظبوط ولا لأ؟ إذا السرعة النهائية
+
+185
+00:14:51,680 --> 00:14:55,600
+هناك سفر، بدا كل زمان، بدي كل زمان، هذا أول مطلوب،
+
+186
+00:14:55,600 --> 00:15:01,240
+اتنين، واحدة واحدةFind the maximum height بدي
+
+187
+00:15:01,240 --> 00:15:06,400
+الارتفاع يعني بدي why why final تمام واحدة واحدة
+
+188
+00:15:06,400 --> 00:15:11,800
+سنة شوية determine the velocity of the stone when
+
+189
+00:15:11,800 --> 00:15:15,560
+it returns to the height from which it was thrown
+
+190
+00:15:15,560 --> 00:15:19,920
+لما رجع لنفس النقطة اللي انطلق منها لنفس الارتفاع
+
+191
+00:15:19,920 --> 00:15:22,000
+اللي انطلق منه يعني النقطة C
+
+192
+00:15:30,840 --> 00:15:34,540
+عند النقطة C تتوقع السرعة النهائية تكون موجبة ولا
+
+193
+00:15:34,540 --> 00:15:38,780
+سالبة؟ سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+194
+00:15:38,780 --> 00:15:41,260
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+195
+00:15:41,260 --> 00:15:43,780
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+196
+00:15:43,780 --> 00:15:46,020
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+197
+00:15:46,020 --> 00:15:46,440
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+198
+00:15:46,440 --> 00:15:46,640
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+199
+00:15:46,640 --> 00:15:47,820
+سالبة، سالبة، سالبة، سالبة، سالبة، سالبة، سالبة،
+
+200
+00:15:47,820 --> 00:15:51,350
+سالبة، سزي لما بيجيبوا زمان وطلع سالب ترضوا فيها
+
+201
+00:15:51,350 --> 00:15:56,530
+وهذه نفس العملية استني شوية واحدة واحدة جاييكي
+
+202
+00:15:56,530 --> 00:16:03,550
+جاييكي find the velocity and the position of the
+
+203
+00:16:03,550 --> 00:16:10,470
+stone بعد خمس ثواني أمين أمين find هذا المطلوب
+
+204
+00:16:10,470 --> 00:16:15,110
+الخامسthe velocity of the stone just before
+
+205
+00:16:15,110 --> 00:16:18,930
+hitting the ground just باللغة الإنجليزية معناته
+
+206
+00:16:18,930 --> 00:16:26,310
+هنا لحظات ما ضرب الأرض زي لما نقول هال gate في عند
+
+207
+00:16:26,310 --> 00:16:29,750
+بنت outside this room outside إيش يعني outside؟
+
+208
+00:16:29,750 --> 00:16:33,870
+ممكن تكون في رفح ولا لأ؟ أه لكن لما أقول just
+
+209
+00:16:33,870 --> 00:16:37,510
+outside this room ممكن هو واقف على الباب عرفتوا
+
+210
+00:16:37,510 --> 00:16:41,090
+إيش معنى just؟ just outside يعني واقف على الباب
+
+211
+00:16:41,950 --> 00:16:46,130
+وهان قبل ما يضرب الأرض مباشرة بقول لإن لو بعد ما
+
+212
+00:16:46,130 --> 00:16:48,930
+ضربت الأرض بتبطل الـfree falling بيصير فيه قوة
+
+213
+00:16:48,930 --> 00:16:53,670
+جديدة قوة الأرض تذكرين التصادم؟ حد بيصير في قوة
+
+214
+00:16:53,670 --> 00:16:56,430
+جديدة بيبطل الـfree falling بيصير جثة جديدة مالكاش
+
+215
+00:16:56,430 --> 00:17:01,810
+دعوة فيها بدي وكأنه سرعتها عند النقطة إيه قبل ما
+
+216
+00:17:01,810 --> 00:17:08,280
+تلمس الأرض اتفجلي يا بنات هذه مطالبيبدنا نبدأ ها
+
+217
+00:17:08,280 --> 00:17:16,540
+نمحي هدون و نبدأ ب E B C D هاي ايه ايه ايش بده ده
+
+218
+00:17:16,540 --> 00:17:22,600
+اللي بد الزمن بد الزمن لما يصل لأقفى ارتفاع نقطة
+
+219
+00:17:22,600 --> 00:17:26,200
+البداية معروفة و نقطة النهاية سرعتها الابتدائية
+
+220
+00:17:26,200 --> 00:17:31,960
+سفرو G بعرفها ولا بعرفهاش بعرفها بقوله لو قلتلك V
+
+221
+00:17:31,960 --> 00:17:38,460
+final بساوي V initial نقص GT بحللك المشكلة ولا
+
+222
+00:17:38,460 --> 00:17:44,880
+بحلليش اذا حط محل V final سفر وهدي عشرين وهدي تسعة
+
+223
+00:17:44,880 --> 00:17:51,210
+point تمانية وهيتي في مجهول غيرتي طلعتيإذا انت
+
+224
+00:17:51,210 --> 00:17:58,050
+بتسوي 2.04 متر per second و لو حد كتب اتنين صح
+
+225
+00:17:58,050 --> 00:18:05,890
+second فكرت الصوابعة برا عليكم second أيه الصفسر
+
+226
+00:18:05,890 --> 00:18:13,390
+يا بنات؟ في مشكلة؟ فش مشكلة بيقول
+
+227
+00:18:13,390 --> 00:18:21,210
+للآنبدي Y صح؟ Y final حلو بقول له فالتك من هذه
+
+228
+00:18:21,210 --> 00:18:24,410
+لحظة تكون هذه غلط بديش أستخدمها لحظة تكون غلط
+
+229
+00:18:24,410 --> 00:18:28,770
+مظبوط ولا لأ طبعا ممكن أستخدمها لإنه T إيه عندي؟
+
+230
+00:18:28,770 --> 00:18:33,350
+قللي لو كتبتلك V final تربيع بيسوي V initial تربيع
+
+231
+00:18:33,350 --> 00:18:40,370
+ناقص 2G Y final ناقص Y initial بحل مشكلتك بقوله
+
+232
+00:18:40,370 --> 00:18:50,430
+بحل مشكلتي بقول له هذه قداش0 هدى 420 تربيع ناقص 2
+
+233
+00:18:50,430 --> 00:19:00,390
+في G 19.6 9.8 في 2 why final و هدى 0 انا بديت من
+
+234
+00:19:00,390 --> 00:19:05,230
+هنا شايفين ال origin من هنا بديت اذا هدى 0 ايش
+
+235
+00:19:05,230 --> 00:19:09,410
+المجهول الوحيد في الرسمة why final هى هى طلعتلك
+
+236
+00:19:09,410 --> 00:19:12,930
+why final طلعت حوالى 20
+
+237
+00:19:15,920 --> 00:19:21,660
+عشرين point اربعة متر كمان مرة اي واحد بدها تسألكي
+
+238
+00:19:21,660 --> 00:19:28,180
+اسأله على طول احكي اه حسب انت مرجعيتك وين بدك
+
+239
+00:19:28,180 --> 00:19:33,940
+مرجعيتك انا خدت هناك انا خدت النقطة ايه بديكي
+
+240
+00:19:33,940 --> 00:19:40,960
+تغيري من غير نعم ممكن تكون أرض صحيح اذا كانت الأرض
+
+241
+00:19:40,960 --> 00:19:47,630
+بالصير خمسين بتطلع واي فاين السبعينزائتها صح؟ صح
+
+242
+00:19:47,630 --> 00:19:53,610
+هي وكأنه أقصى ارتفاع بيبعد عشرين متر عن سطح المبنى
+
+243
+00:19:53,610 --> 00:19:57,650
+وعن الأرض كدهش؟ سبعين سبعين، بتجمعنا الخمسين، اذا
+
+244
+00:19:57,650 --> 00:19:59,930
+حسب المرجعية اللي أخدتها، و هي المرجعية اللي
+
+245
+00:19:59,930 --> 00:20:02,550
+أخدتها، قلتلك عنها، و هي اللي أخدتها على الرسمة
+
+246
+00:20:02,550 --> 00:20:07,290
+المرجعية اختياري، بس أنا حددته، انه جُلت نقطة إيه؟
+
+247
+00:20:07,290 --> 00:20:13,010
+نقطة الانطلاق، غاها كنا
+
+248
+00:20:13,010 --> 00:20:18,390
+بننهز، صح، بنهز راسنااتفجنا هذا سؤال بدنا نحله و
+
+249
+00:20:18,390 --> 00:20:24,570
+احنا نفهميه ايش بنعمل تمام C بيقوللي ايش بده
+
+250
+00:20:24,570 --> 00:20:29,470
+قولتله بدي سرعة لما الجسم ريجي على نقطة انا عارفها
+
+251
+00:20:29,470 --> 00:20:34,510
+صح هجيت انا نقطة المرجعية تبعت النقطة ايه سفر
+
+252
+00:20:34,510 --> 00:20:39,690
+اخدتها طب النقطة C ايش بيكون برضه سفر مش سفر مش
+
+253
+00:20:39,690 --> 00:20:45,180
+ايه نفسك مش كبالهاأحلو بقول له انا initial قال انك
+
+254
+00:20:45,180 --> 00:20:48,680
+بدك V final قلت له اه والله بدي V final بتسوي V
+
+255
+00:20:48,680 --> 00:20:53,460
+initial تربيع نقص اتنين G Y final نقص Y initial
+
+256
+00:20:53,460 --> 00:20:59,300
+صحيك؟ هذا قبل ما كنا بنعرفه تمام قال ليه جداش V
+
+257
+00:20:59,300 --> 00:21:08,020
+initial تربيع 400 اتنين في G تسعتاش point ستة يلا
+
+258
+00:21:10,100 --> 00:21:14,600
+حلو براو عليكي سفر ناقص سفر معناته حتى دي روحت
+
+259
+00:21:14,600 --> 00:21:20,880
+سمنا شوية بقى الشيخ طلعت طلعت هنا يلا بال
+
+260
+00:21:20,880 --> 00:21:26,960
+calculator دي بيقول ايه؟ لأن
+
+261
+00:21:26,960 --> 00:21:30,980
+جزر التربيع إلى الخمسة وعشرين ممنوع تقول خمسة لادى
+
+262
+00:21:30,980 --> 00:21:36,900
+يكون موجة في خمسة او ناقص خمسة صح؟ طيب انت هنا في
+
+263
+00:21:36,900 --> 00:21:42,110
+سؤال ما انت فاهمه ولا مش فاهمه؟فهمه عند النقطة C
+
+264
+00:21:42,110 --> 00:21:48,590
+وصلها هو طالع له و هو نازل إذا من هنا
+
+265
+00:21:48,590 --> 00:21:53,870
+بتقول the final بيساوي سالب عشرين متر per second
+
+266
+00:21:53,870 --> 00:21:57,450
+مظبوط
+
+267
+00:21:57,450 --> 00:22:05,030
+هيك ولا لأ؟ تم؟ ليش مبلمتوا؟
+
+268
+00:22:05,030 --> 00:22:14,310
+تقدر تقولي هيك احكيها منتيحلو وين كان الرسمة عنده
+
+269
+00:22:14,310 --> 00:22:18,610
+نقطة ايه صح وين صار عنده نقطة C مش هو بقولك لما
+
+270
+00:22:18,610 --> 00:22:23,290
+وصل لنفس المستوى اذا النقطة A صفر النقطة C ايش
+
+271
+00:22:23,290 --> 00:22:30,070
+عرفتي ليه ايش غيرها دكتور اللي انا عامليه هو نقطة
+
+272
+00:22:30,070 --> 00:22:33,230
+B احنا حكينا ان هو حددلي من النقطة A عشان ايه
+
+273
+00:22:33,230 --> 00:22:38,130
+اخدنا ال final صفر اه تمام اللي هو بحدد لكن لو لا
+
+274
+00:22:38,130 --> 00:22:42,130
+بيه برضهأه طبعا النقطة بيه أقصى ارتفاع هو الجلي
+
+275
+00:22:42,130 --> 00:22:47,850
+طبعا هذه معطيات احكي هل
+
+276
+00:22:47,850 --> 00:22:53,410
+determined the velocity of the stone when .. لما
+
+277
+00:22:53,410 --> 00:22:58,870
+تقولي بطلت أفهم قولي when it returns رجع to the
+
+278
+00:22:58,870 --> 00:23:03,010
+height للارتفاع from which it was thrown للارتفاع
+
+279
+00:23:03,010 --> 00:23:09,450
+اللي انطلق منه واضحة؟إذن فهمت من هذه الجملة انه
+
+280
+00:23:09,450 --> 00:23:13,970
+بده عنده نقطة C من نفس الارتفاع اللي انطلق منه
+
+281
+00:23:13,970 --> 00:23:22,110
+غيرها يعني
+
+282
+00:23:22,110 --> 00:23:28,190
+بدك تقدره بزمن الصعود في اتنين اه
+
+283
+00:23:28,190 --> 00:23:32,330
+بس أنا مابديش اخد شغلة اختراع بدي اخد من معطية
+
+284
+00:23:32,330 --> 00:23:36,430
+السؤال عشان كده أخدت القانون هذا بتطلع نفس الإجابة
+
+285
+00:23:39,350 --> 00:23:44,790
+تمام خلصنا ايه بي سي نجلدى بقولى انا الآن الزمن
+
+286
+00:23:44,790 --> 00:23:50,250
+بتدلكى جاهز منيح اكمل زمان خمس ثوانى بدي تجيبلى
+
+287
+00:23:50,250 --> 00:23:56,610
+السرعة و تجيبلى موضعه حلو السرعة هي دى يا بنات
+
+288
+00:23:57,880 --> 00:24:04,260
+Vfinal بيساوي Vinitial ناقص GT إيش بدي؟ بدي Vfinal
+
+289
+00:24:04,260 --> 00:24:10,240
+هذه عشرين ناقص تسعة point تمانية في خمسة يلا يا
+
+290
+00:24:10,240 --> 00:24:16,640
+كاب كوريتا طلعتلي موجب ولا سالب؟ هيها حوالي خمسين
+
+291
+00:24:16,640 --> 00:24:20,920
+و هدك عشرين حوالي ناقص سلتين أظن أقل من .. ناقص
+
+292
+00:24:20,920 --> 00:24:26,180
+تسعة و عشرين متر per second هتجهد هذه الإشارة
+
+293
+00:24:26,180 --> 00:24:31,450
+الحلوةاللي هي السالب، أيها معنى فيزيائي ولا لا؟
+
+294
+00:24:31,450 --> 00:24:36,310
+إنها نازلة، صح؟ لو واحد قال ليه، ممكن تكون عند
+
+295
+00:24:36,310 --> 00:24:40,530
+النقطة هذه؟ ولا ممكن، لأن عند النقطة هذه طالعة
+
+296
+00:24:40,530 --> 00:24:45,070
+وانت طلعت معاك الإجابة؟ سالبة، بقوله هنا ممكن وهنا
+
+297
+00:24:45,070 --> 00:24:49,250
+ممكن، صح؟ هل جيت هنا ولا هنا، بتعتمد على ال
+
+298
+00:24:49,250 --> 00:24:53,660
+positionانت أخدت السفر هنا ولا لأ؟ كل نقطة تحت
+
+299
+00:24:53,660 --> 00:24:57,520
+السفر ايش المفروض تكون؟ سالبة وكل نقطة فوق السفر
+
+300
+00:24:57,520 --> 00:25:03,160
+موجة بيه يجرب انها تحته ولا فوقه ايش بدك كمان؟ ده
+
+301
+00:25:03,160 --> 00:25:08,900
+اللي بديه Y final بقول Y final نقص Y initial اللي
+
+302
+00:25:08,900 --> 00:25:16,240
+هو القانون بتساوي V initial Vt نقص نص GT تربية مش
+
+303
+00:25:16,240 --> 00:25:21,470
+في قانون زيها ده؟ حلوy initial اعتبرته 0 اذا y
+
+304
+00:25:21,470 --> 00:25:30,510
+final بيسوي 20 في 5 ناقص 4.9 نص جيه في 25 اللي هو
+
+305
+00:25:30,510 --> 00:25:36,230
+T تربيع صح بقى عوض يلا بال calculator هذه حوالي
+
+306
+00:25:36,230 --> 00:25:44,170
+100 صح؟ و هذه 5 في 25 اكتر 125 تقريبا حوالي سالب
+
+307
+00:25:44,170 --> 00:25:50,980
+22.5 مترطلعت سالبة معناته تحت نقطة الأصل ولا فوق
+
+308
+00:25:50,980 --> 00:25:58,820
+تحت إذا المعناته هذه النقطة هنا ال C
+
+309
+00:25:58,820 --> 00:26:02,800
+و أنا شينا في ال C
+
+310
+00:26:02,800 --> 00:26:08,760
+أرقمها
+
+311
+00:26:08,760 --> 00:26:13,320
+يعني انت شفت ان الصراع أكبر تمام احنا بدنا مقالة
+
+312
+00:26:13,320 --> 00:26:13,920
+مباشرة
+
+313
+00:26:17,980 --> 00:26:24,440
+أكبر اكبر من 4 اكبر من 4 لانه 2 و 2 اربع طبعا بس
+
+314
+00:26:24,440 --> 00:26:31,540
+احنا بدنا الشغلات المباشرة عاموجة
+
+315
+00:26:31,540 --> 00:26:37,340
+فوق نقطة الاصل يعني فوق ال ايه حتى لو كانت نازلة
+
+316
+00:26:37,340 --> 00:26:42,550
+ال position مالوش ده عوض الصرعةالـ Position غير عن
+
+317
+00:26:42,550 --> 00:26:46,010
+الصرعة لما يكون نازل الصرعة سلبة الـ Position
+
+318
+00:26:46,010 --> 00:26:50,390
+مالهوش دعوة هجيت عند النقطة هذه يا بنتي هذه النقطة
+
+319
+00:26:50,390 --> 00:26:55,290
+هذه شفاها صرعتها كيش بيبقى تكون لكن الـ Position
+
+320
+00:26:55,290 --> 00:27:01,870
+هو موجودة مالهوش دعوة هذه غير عن هذه تمام يا بنتي؟
+
+321
+00:27:01,870 --> 00:27:11,820
+تمام غيره حلو جلل زوايا جلد ديE sorry ايش بدك
+
+322
+00:27:11,820 --> 00:27:16,340
+اجلبدي السرعة قبل ما يرتطن بالأرض مباشرة بطلع
+
+323
+00:27:16,340 --> 00:27:20,100
+بقوله يعني عنده النقطة ايه ولا لا عند النقطة ايه
+
+324
+00:27:20,100 --> 00:27:25,040
+بقاعدي بقوله E ايش بدك اجلبدي V final صح ولا لأ
+
+325
+00:27:25,040 --> 00:27:30,640
+بقوله V final بنجيبها في عند V final تربيع بيساوي
+
+326
+00:27:30,640 --> 00:27:36,220
+V initial تربيع نقص اتنين G وY final نقص Y initial
+
+327
+00:27:36,220 --> 00:27:42,970
+اطلع الفلجل كله معطفاللي هادي مش معطية هدي جديش
+
+328
+00:27:42,970 --> 00:27:48,870
+قال يا 400 نقص 2 في G 19.6 أف تحجوز وينيش لما
+
+329
+00:27:48,870 --> 00:27:52,930
+اتفقن سفر ولا لأ طب واي فينا مني ولي جديش احكي
+
+330
+00:27:52,930 --> 00:27:58,650
+الوا سالب خمسين bravo عليكي سالب خمسين قولت سالب
+
+331
+00:27:58,650 --> 00:28:03,550
+خمسين مش خمسين سالب خمسين لأ انا تحت اذا سالب
+
+332
+00:28:03,550 --> 00:28:11,700
+خمسين نقص سفر خلصت تمام طلع جواببدي اخد اجازة
+
+333
+00:28:11,700 --> 00:28:17,220
+تربيع تبعه هجيت ارتطم الأرض وانصاحي ومصحصح و هو
+
+334
+00:28:17,220 --> 00:28:21,940
+طالع ولا هو نازل اذا بدي اخد السالب بدي اخد السالب
+
+335
+00:28:21,940 --> 00:28:29,040
+جدش طلع الجواب في اللعب السالب قصد 37.4 متر per
+
+336
+00:28:29,040 --> 00:28:33,280
+second مش
+
+337
+00:28:33,280 --> 00:28:39,460
+4 يعني point one أي صف صار
+
+338
+00:28:42,950 --> 00:28:46,710
+أه وإينيش السفر متفاجئين ولا لأ؟ لأنه أنا عم أتبع
+
+339
+00:28:46,710 --> 00:28:49,990
+السفر طب و هي ال final وين؟ هي ال final هي شخصية
+
+340
+00:28:49,990 --> 00:28:54,550
+مجهولة ولا معروفة النقطة مش وصلت الأرض طيب الأرض
+
+341
+00:28:54,550 --> 00:29:00,470
+كانت أوطى من نقطة البداية ولا أعلى أو طبع كم متر؟
+
+342
+00:29:00,470 --> 00:29:04,570
+خمسين هو وعشانها أوطى حطت ثالث
+
+343
+00:29:08,080 --> 00:29:11,800
+أي هو طول هذا الزلمة خمسين متر كله مترين مابديش ..
+
+344
+00:29:11,800 --> 00:29:16,540
+تمام؟ تمام .. هو اعتبر و كأنه من .. من إيدي الزلمة
+
+345
+00:29:16,540 --> 00:29:20,000
+ليناك الخمسين .. ماهي تقريب .. حسب طول البرج يعني
+
+346
+00:29:20,000 --> 00:29:24,160
+عبارة إنه سالب طول البرج؟ أه .. هو موضع مش طول ..
+
+347
+00:29:24,160 --> 00:29:28,780
+أنا بدي موضع الحجر لما وصل للأرض .. بقوله كموضع
+
+348
+00:29:28,780 --> 00:29:34,110
+تحت نقطة الأصل ولا لأ .. أخدته سالب ..موضع مش طول
+
+349
+00:29:34,110 --> 00:29:37,430
+لان الطول مينفعش يكون سالب لكن كموضع بنقول سالب
+
+350
+00:29:37,430 --> 00:29:48,170
+غيرها احكي اه مش
+
+351
+00:29:48,170 --> 00:29:57,070
+طول موضع position صح هذه
+
+352
+00:29:57,070 --> 00:30:01,870
+النقطة جديش حد يثير ثصابي النقطة هذه
+
+353
+00:30:08,630 --> 00:30:11,810
+Y initial سفر وY final
+
+354
+00:30:24,940 --> 00:30:29,520
+أمين؟ هجيت؟ انغششكم إيه السؤال اللي جابلكم الشباب
+
+355
+00:30:29,520 --> 00:30:33,340
+ذهجون صبحيات الساعة تمانية و هم يسألوا قالوا في
+
+356
+00:30:33,340 --> 00:30:36,200
+عيننا قانون بيقول زمن الصعود بيساوي زمن الهبوط
+
+357
+00:30:36,200 --> 00:30:38,980
+دايما لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+358
+00:30:38,980 --> 00:30:39,860
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+359
+00:30:39,860 --> 00:30:40,400
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+360
+00:30:40,400 --> 00:30:40,400
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+361
+00:30:40,400 --> 00:30:52,520
+لأ لأ لأ لأ لأ
+
+362
+00:30:52,990 --> 00:30:56,090
+بصى مونيافى توجيهى بيقول جزء تربيع اتنين GH
+
+363
+00:30:56,090 --> 00:31:01,870
+بيقولوا ازحقوا تستخدموا ازحقوا تستخدموا ممنوع
+
+364
+00:31:01,870 --> 00:31:10,480
+تستخدموا محنة تمام يا بنات مافيش قانون اسمه هيكأه
+
+365
+00:31:10,480 --> 00:31:13,880
+أه .. و الحالة الخاصة مش قانون .. ما زالت ورتي
+
+366
+00:31:13,880 --> 00:31:16,920
+حالة خاصة بطل القانون .. القانون شغل عامة يا بنات
+
+367
+00:31:16,920 --> 00:31:20,620
+.. فانتقوا منه .. اه انسيه .. انا بدي .. اه بس انا
+
+368
+00:31:20,620 --> 00:31:23,780
+احفظ الشغلات الأساسية بدي قاعد أحفظ ميت سا قانون
+
+369
+00:31:23,780 --> 00:31:27,960
+.. كل شغل قانون .. إذا أنا ده مش قانون .. مش قانون
+
+370
+00:31:27,960 --> 00:31:28,740
+..
+
+371
+00:31:33,140 --> 00:31:36,940
+أه بس اللي هو 100 شرط فيه شروط كتيرة زي ما جالت
+
+372
+00:31:36,940 --> 00:31:40,460
+حلقات خاصة كتيرة فهذه حلقة خاصة مش موجودة أنا
+
+373
+00:31:40,460 --> 00:31:44,600
+مغششكم إيش جالوا الطلاب يعني يسألوني تمام يا بنات؟
+
+374
+00:31:44,600 --> 00:31:48,660
+أيه السفسار؟ خلصي ال chapter
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/lL45YY9Z9j0.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/lL45YY9Z9j0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..495a8e90595a2753f03e4f055a37860e8ad3bdef
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/lL45YY9Z9j0.srt
@@ -0,0 +1,902 @@
+1
+00:00:05,800 --> 00:00:09,640
+تمام يا بنات، نسمي باسم الله ونبدأ بالchapter
+
+2
+00:00:09,640 --> 00:00:15,660
+الرابع، عنوانه motion. كلمة motion بنعرفها ولا لأ؟
+
+3
+00:00:15,660 --> 00:00:20,540
+عنوان الchapter الثاني برضه motion، بس هناك كان
+
+4
+00:00:20,540 --> 00:00:26,580
+one dimension، هنا two dimensions، in two dimensions.
+
+5
+00:00:26,580 --> 00:00:34,120
+طيب، motion حركة. حركة الموضع بيظل زي ما هو، إذاً بدي
+
+6
+00:00:34,120 --> 00:00:39,980
+أعيد تعريف الموضوع، بس الآن يا بنات، بتتحركش في خط
+
+7
+00:00:39,980 --> 00:00:45,560
+واحد، بتتحرك في مستوى، وبدي أعيد الvelocity، وبدي
+
+8
+00:00:45,560 --> 00:00:49,880
+أعيد الacceleration، وإذا الacceleration ثابتة،
+
+9
+00:00:49,880 --> 00:00:53,340
+بدي أعيد اشتقاق الثلاث معادلات أو الأربع معادلات.
+
+10
+00:00:53,340 --> 00:00:58,580
+ذاكرينهم؟ تمام. إذا ما اتذكرتوهم، بدي أدرسهم، بدي أدرس
+
+11
+00:00:59,420 --> 00:01:03,900
+position، velocity، and acceleration. مروا علينا ولا
+
+12
+00:01:03,900 --> 00:01:10,120
+لأ؟ بعدين، لما تكون الacceleration constant، two
+
+13
+00:01:10,120 --> 00:01:15,770
+dimensional motion. تمام؟ هيك بيسموها، دي من
+
+14
+00:01:15,770 --> 00:01:20,550
+dimension with constant acceleration. العلاقات اللي
+
+15
+00:01:20,550 --> 00:01:24,450
+اشتقتهم أنا وإياكم، جالوا لما أنت حكيت عن الحركة
+
+16
+00:01:24,450 --> 00:01:28,470
+الخطية في chapter اثنين، كان في مثال مشهور اسمه سقوط
+
+17
+00:01:28,470 --> 00:01:32,850
+الحر، برضه في الحركة الtwo dimensions، في مثال
+
+18
+00:01:32,850 --> 00:01:38,850
+مشهور، هي حركة المقذوفات، الprojectile motion. تمام؟
+
+19
+00:01:38,850 --> 00:01:42,470
+قال لي كمان، في حركة مشهورة جداً في الحركة المستوية،
+
+20
+00:01:42,470 --> 00:01:48,190
+هي الحركة الدائرية، Circular، من Circle، Circle دائرة.
+
+21
+00:01:48,190 --> 00:01:52,090
+Circular، دائري. قال لي فيه نوعين، حاجة بنسميها
+
+22
+00:01:52,090 --> 00:01:55,730
+uniform، منتظمة، وnon uniform، غير منتظمة. إيش
+
+23
+00:01:55,730 --> 00:01:59,390
+معناتها لما نيجي لها؟ ارتكزنا. قال لي، آخر حاجة في
+
+24
+00:01:59,390 --> 00:02:05,830
+حاجة اسمها سرعة نسبية، سرعة نسبية. طبعاً، وإحنا بنقول
+
+25
+00:02:05,830 --> 00:02:11,810
+الchapter الرابع، هو بداية الشغل الحقيقي، لأنه chapter
+
+26
+00:02:11,810 --> 00:02:17,750
+اثنين، عشان أغششكم، بيشملوا chapter أربعة. يعني بكرة في
+
+27
+00:02:17,750 --> 00:02:21,350
+الfinal، واحد بدو يدرس، ما يدرسش اثنين، يدرس أربعة.
+
+28
+00:02:21,350 --> 00:02:26,090
+ما هو تلقائي، لأ، أنا اثنين، إحنا بندرس ثلاثة، ثلاثة
+
+29
+00:02:26,090 --> 00:02:29,990
+هيندرس غصب عن عمك، هيتكرر معك كتير، بس اثنين ليش
+
+30
+00:02:29,990 --> 00:02:32,250
+هيدرس اثنين، أو هيدرس أربعة؟ ما ندرس أربعة، بيكون
+
+31
+00:02:32,250 --> 00:02:38,980
+ندرس اثنين وأربعة، جاكل اثنين. تمام؟ بالظبط، ابطلوا
+
+32
+00:02:38,980 --> 00:02:41,800
+عشان هيك؟ شوفوا الrecommended problems، ما شاء الله
+
+33
+00:02:41,800 --> 00:02:48,040
+عليهم أسماء أكثر، لأنه chapter حقيقي، الآن هذا شغل
+
+34
+00:02:48,040 --> 00:02:53,780
+chapter اثنين، كنا ساهلين فيه، كانوا بدلعونا، خلصنا منه.
+
+35
+00:02:53,780 --> 00:03:00,710
+تمام؟ يلا يا بنات، إيش في عندي plane؟ قلت لها اللوح
+
+36
+00:03:00,710 --> 00:03:05,050
+الplane ولا مش الplane؟ أي جسم بيمشي على اللوح،
+
+37
+00:03:05,050 --> 00:03:08,250
+على اللوح، بقول بأضمن إنه two-dimensional motion.
+
+38
+00:03:08,250 --> 00:03:12,650
+ولا لأ؟ تمام يا بنات، أنا أخذت مثال في الشعب اللي
+
+39
+00:03:12,650 --> 00:03:15,910
+جابته، لو خلينا على نفس المثال، عشان ما يقولوش غش
+
+40
+00:03:15,910 --> 00:03:21,470
+للي جاي، بيصور معهم، في نملة بتمشي على اللوح، نملة
+
+41
+00:03:21,470 --> 00:03:24,830
+تمام. طبعاً النملة اللي جيبتها صغيرة، عشان كلمة
+
+42
+00:03:24,830 --> 00:03:29,290
+particle، particle، جسم صغير. تمام. حاجة النملة، وهي
+
+43
+00:03:29,290 --> 00:03:33,990
+بتمشي، بتقدروا تقولوا هي نملة ماشية خط مستقيم، عم تمشي
+
+44
+00:03:33,990 --> 00:03:37,390
+هي، بتمشي صح ولا لأ؟ بتمشي لها خط أيّ مكان ممكن
+
+45
+00:03:37,390 --> 00:03:42,930
+تكون. قال لي، هذه النملة، هي الخط اللي ماشية فيه، هيك ماشية
+
+46
+00:03:42,930 --> 00:03:49,470
+هيك. هل ماشية سين؟ الخط الأحمر سين؟ لأ. إذا سين،
+
+47
+00:03:49,470 --> 00:03:55,540
+صفر. يا نملة، بدنا ندرس حركتك، اتفقنا؟ استنى شوية،
+
+48
+00:03:55,540 --> 00:04:02,560
+وقفت. قالت، والله كنت هنا، هذا موضعها الحقيقي الابتدائي،
+
+49
+00:04:02,560 --> 00:04:05,420
+امشي، ماشي. تلو عند هنا، هذا موضعها الحقيقي النهائي.
+
+50
+00:04:06,150 --> 00:04:10,410
+الحركات بتعطي position تبعك. الposition دائماً
+
+51
+00:04:10,410 --> 00:04:15,430
+متعودين نحدده بناءً على نقطة أصل، ولا لأ؟ جالوا
+
+52
+00:04:15,430 --> 00:04:18,710
+نقطة أصل، أنا برسمها لكم. كيف بدكم تجيبوا موضعها؟
+
+53
+00:04:18,710 --> 00:04:24,010
+قولوا، من هنا لأصل هنا. صح ولا لأ؟ هاي الposition
+
+54
+00:04:24,010 --> 00:04:29,310
+تبعها initially، وهذا الposition تبعها finally. صح
+
+55
+00:04:29,310 --> 00:04:32,510
+ومظبوط ولا لأ؟ طيب، اتطلعوا لي على الposition الـ
+
+56
+00:04:32,510 --> 00:04:38,960
+initial. هذا الخط المستقيم، فين؟ الأزرق، شايفينه؟ سين؟
+
+57
+00:04:38,960 --> 00:04:43,840
+لأ. طيب، بقدر أقول إنه إله مركبة سينية، وإله مركبة
+
+58
+00:04:43,840 --> 00:04:48,500
+صينية، أو لأ؟ يا عيني عليكم! يا عيني، اتّفقنا. قلت له،
+
+59
+00:04:48,500 --> 00:04:51,640
+هاي مركبتها السينية، وهاي مركبتها الصادية. صفتوا
+
+60
+00:04:51,640 --> 00:04:56,040
+مركبتين، الحمر هدول؟ السينية بتحط جنبه i ولا لأ؟
+
+61
+00:04:56,040 --> 00:04:59,600
+والصادية بتحط جنبه j ولا لأ؟ مش هيك اتعلمنا؟ قال لي،
+
+62
+00:04:59,600 --> 00:05:05,640
+هاي r initial، قال لي، وr final، هيها نفس الشيء.
+
+63
+00:05:08,610 --> 00:05:12,350
+جالي حلو. بدي الdisplacement. جالوا الdisplacement
+
+64
+00:05:12,350 --> 00:05:18,030
+بتجيبه من بداية للنهاية. مظبوط؟ أو Δx، أو Δ
+
+65
+00:05:18,030 --> 00:05:21,850
+أي حاجة. مش بتساوي final ناقص initial. وقال لي، بدّي
+
+66
+00:05:21,850 --> 00:05:27,010
+دلتا الr. طبعاً، أنا قدرت أسميه x ولا y؟ إيش الرمز
+
+67
+00:05:27,010 --> 00:05:30,370
+اللي اتفقنا عليه؟ قالوا r. قال لي، بدي الآن الـ
+
+68
+00:05:30,370 --> 00:05:34,710
+displacement. قلت له، يعني بدك دلتا r. دلتا r بتساوي r
+
+69
+00:05:34,710 --> 00:05:39,270
+final ناقص r initial. final ناقص initial. a ناقص b.
+
+70
+00:05:39,270 --> 00:05:44,350
+اتعلمنا كيف نطرح ونجمع vectors ولا لأ؟ جالوا، آه. جالوا
+
+71
+00:05:44,350 --> 00:05:46,970
+الcase بتجمع وبتطرح الvectors. جالوا، السينية مع
+
+72
+00:05:46,970 --> 00:05:52,090
+السينية، والصادية مع الصادية. هادي ناقص هادي، وهادي ناقص
+
+73
+00:05:52,090 --> 00:05:56,510
+هادي، ولا لأ؟ جالوا، هيّها. جمعيها. اتطلعت هنا، قلت له، هادي
+
+74
+00:05:56,510 --> 00:06:01,470
+ممكن أسميها Δx، وممكن هادي أسميها Δy. آه.
+
+75
+00:06:01,470 --> 00:06:09,350
+إذا هادي، هادي هي Δx. إذا الإزاحة، كم مركبة
+
+76
+00:06:09,350 --> 00:06:12,050
+إلها؟ مركبتين سينية. أحكي.
+
+77
+00:06:15,030 --> 00:06:22,750
+لأ، لأ، حلو. أنتِ قلتِ هذا، ليش رسمتِه؟ صح؟ هيّها، ماشي
+
+78
+00:06:22,750 --> 00:06:29,270
+هيك. شوف الخط الأحمر هذا، هذا الخط الأحمر هو خط سير
+
+79
+00:06:29,270 --> 00:06:34,990
+النملة، خط سير النملة،  ماشي. هل جيت النملة كانت هنا؟
+
+80
+00:06:34,990 --> 00:06:39,230
+ماشيت وجت هنا؟ لما أنتِ بدك إزاحتها، إزاحتها مش
+
+81
+00:06:39,230 --> 00:06:43,190
+مسافتها، إيش بتسوين؟ بتقولي وين كانت، و وين صارت؟ أو
+
+82
+00:06:43,190 --> 00:06:46,710
+بتجيبي خط مستقيم من بداية لنهاية ولا لأ؟ إذا هذه
+
+83
+00:06:46,710 --> 00:06:51,650
+الإزاحة، مش خط سيرها. نرجع لقانون اسمه المغازي؟ نرجع
+
+84
+00:06:51,650 --> 00:06:59,050
+لقانون اسمه المغازي، ذاكرتيه؟ تمام؟ حلّو. جالي حلو، إذا
+
+85
+00:06:59,050 --> 00:07:04,070
+الإزاحة صار لها مركبتين، سينية وصادية. نيجي لها
+
+86
+00:07:04,070 --> 00:07:08,710
+السرعة. جالنا. السرعة، أعطتني شغلتين، سرعة متوسطة و
+
+87
+00:07:08,710 --> 00:07:12,490
+سرعة لحظية. ذاكرينها؟ جالي، السرعة المتوسطة، عرفتيلي
+
+88
+00:07:12,490 --> 00:07:15,950
+إياها، إنه Δ، إزاحة على Δ، زمان. كان زمان
+
+89
+00:07:15,950 --> 00:07:19,530
+الإزاحة x، بس. Δ إزاحة على Δ زمان. قلت له،
+
+90
+00:07:19,530 --> 00:07:24,630
+الإزاحة، قدرت مش x يا ابني، ولا y، r. صح ولا لأ؟ إذا
+
+91
+00:07:24,630 --> 00:07:30,950
+معناته بدك تقولي، دلتا ال v average. مش هاي إشارة
+
+92
+00:07:30,950 --> 00:07:33,790
+الaverage، هال gate، بدك تكون حاطط لي إشارة الـ
+
+93
+00:07:33,790 --> 00:07:41,730
+vector بالمرة. بقول، بتساوي Δr على Δt. في
+
+94
+00:07:41,730 --> 00:07:47,770
+مشكلة؟ هاي تعريف السرعة المتوسطة، إزاحة على زمان.
+
+95
+00:07:47,770 --> 00:07:54,840
+إيش هي رمز إزاحتك؟ r. حطيتها، دي اللي بالمقام، هي كمية
+
+96
+00:07:54,840 --> 00:07:59,400
+فيزيائية مشهورة، الشيء، زمان، scalar ولا vector؟
+
+97
+00:07:59,400 --> 00:08:02,400
+scalar. لما نضرب scalar في vector، عشان نضرب
+
+98
+00:08:02,400 --> 00:08:06,480
+المركبات كلها. طيب، هذه المركبات هيها، يعني هذه
+
+99
+00:08:06,480 --> 00:08:13,340
+بتصير Δx على Δt<sub>i</sub> زائد Δy على Δ
+
+100
+00:08:13,340 --> 00:08:17,200
+t<sub>j</sub>. ولا لأ؟ ال Δt ضربتها في ال two components.
+
+101
+00:08:17,200 --> 00:08:23,320
+اللي طلعت. هادي أخدناها في chapter 2، هادي v average
+
+102
+00:08:23,320 --> 00:08:29,140
+بالسينية، وهادي v average بالصادية. عشان سينية، صادية،
+
+103
+00:08:29,140 --> 00:08:29,760
+بتحطي
+
+104
+00:08:32,480 --> 00:08:37,220
+إذا السرعة المتوسطة أيضاً إلها كم مركبة؟
+
+105
+00:08:37,220 --> 00:08:43,400
+اثنتين، واحدة سينية، واحدة صادية. إذا قال لي، Now the
+
+106
+00:08:43,400 --> 00:08:46,100
+average velocity of the particle، قال لي هذا هي
+
+107
+00:08:46,940 --> 00:08:51,160
+سينية زائد صادية. جالي، طيب، السرعة اللحظية. جالي، السرعة
+
+108
+00:08:51,160 --> 00:08:55,360
+اللحظية، إيش عرفتها؟ قلت له، السرعة اللحظية مش سرعة
+
+109
+00:08:55,360 --> 00:08:59,920
+الإزاحة بالنسبالي الزمن. مظبوط ولا لأ؟ طيب، وين
+
+110
+00:08:59,920 --> 00:09:03,940
+الإزاحة؟ ده اللي والله إلها سين وصاد. فصارت بالساوي
+
+111
+00:09:03,940 --> 00:09:12,000
+dx على dt<sub>i</sub> زائد dy على dt<sub>g</sub>. جالي، هذه مش سرعة لحظية
+
+112
+00:09:12,000 --> 00:09:19,500
+سينية، وهذه سرعة لحظية صادية. بتساوي v<sub>xi</sub> زائد v<sub>yj</sub>.
+
+113
+00:09:19,500 --> 00:09:29,060
+صفتنا في إيش؟ ولا نعستي؟ تمام؟ إذا برضه السرعة
+
+114
+00:09:29,060 --> 00:09:36,570
+اللحظية، مركبتين. قال لي، similarly، بنفس المفهوم، إيش
+
+115
+00:09:36,570 --> 00:09:41,770
+بتتوقعوا، التسارع المتوسط، إله كم مركبة؟ ولا لأ؟ و
+
+116
+00:09:41,770 --> 00:09:45,930
+التسارع، والتسارع اللحظي، نفس القضية. قال لي، تخص
+
+117
+00:09:45,930 --> 00:09:51,050
+بلاش نحفظ اشتقاقات ونغلب حالنا. إيش اللي بدنا إياه؟ ده اللي
+
+118
+00:09:51,050 --> 00:09:56,730
+اللي معناته، بتقدر تقول إن الحركة المستوية، أو
+
+119
+00:09:56,730 --> 00:10:01,260
+الحركة في الtwo dimensions، هي مجموعة حركتين، سينية
+
+120
+00:10:01,260 --> 00:10:07,280
+وصادية. إذا هي مجموعة حركتين. وكأنه بقول لي، كل سؤال
+
+121
+00:10:07,280 --> 00:10:10,620
+في هذا الchapter، عبارة عن سؤالين من chapter اثنين.
+
+122
+00:10:10,620 --> 00:10:15,620
+كل سؤال بنقسمه لسؤالين، واحد سيني، واحد صادي. واحد سيني،
+
+123
+00:10:15,620 --> 00:10:22,300
+واحد صادي بس، وكل اللي بدنا إياه زي ما هو. حلو. أجراها
+
+124
+00:10:22,300 --> 00:10:27,720
+بس عشان التصوير. it is clear now that the planar
+
+125
+00:10:27,720 --> 00:10:31,970
+motion، الحركة المستوية، can be considered... ممكن
+
+126
+00:10:31,970 --> 00:10:36,790
+تعتبر، as a vector sum of two perpendicular linear
+
+127
+00:10:36,790 --> 00:10:40,770
+motions، هي مجموعة حركتين خطيتين، ولا... ولا لأ؟
+
+128
+00:10:40,770 --> 00:10:44,830
+ومتعامدتين، لأن واحدة سينية، واحدة صادية. one along
+
+129
+00:10:44,830 --> 00:10:49,090
+the x-axis and the other along the y-axis. إذا
+
+130
+00:10:49,090 --> 00:10:55,660
+دائماً بيقول لي، في هذا، بدك تعملي جدول. هذا جسمتي
+
+131
+00:10:55,660 --> 00:11:01,460
+الحركة. كم جسم؟ اثنين. تقولي، هذه x، وهذه y، في كل
+
+132
+00:11:01,460 --> 00:11:05,980
+الأسئلة. طيب.
+
+133
+00:11:05,980 --> 00:11:12,560
+جالي، نبدأ. جالي، افترض أن التسارع ثابت. جالي، في شغل
+
+134
+00:11:12,560 --> 00:11:17,620
+ثابت، وبيكون أحد مركباته متغير؟ مش ممكن. إذا أنتَ
+
+135
+00:11:17,620 --> 00:11:20,620
+بتقولي، كل التسارع ثابت، مع أن المركبة الثانية مالها
+
+136
+00:11:21,210 --> 00:11:25,170
+ثابتة، والمركبة الصادية ثابتة، فإذا المركبة
+
+137
+00:11:25,170 --> 00:11:28,550
+السينية ثابتة. فطب ما أنا وإياك اشتقينا، قلنا v
+
+138
+00:11:28,550 --> 00:11:34,530
+final بتساوي v initial زائد at. ذاكرينه؟ قال لي، بس
+
+139
+00:11:34,530 --> 00:11:40,690
+عشان هادي x، بدي أحط x. v<sub>x</sub> final، v<sub>x</sub> initial، a. قلت له،
+
+140
+00:11:40,690 --> 00:11:45,950
+طب ما هادي ثابتة. قلت له، حلو. v<sub>y</sub> final بتساوي v<sub>y</sub>
+
+141
+00:11:45,950 --> 00:11:52,120
+initial زائد a<sub>y</sub>t. نفس المعادلة ولا لأ؟ نفس المعادلة.
+
+142
+00:11:52,120 --> 00:11:56,520
+ده اللي فيه كمان قانون، كان بيقول، x final ناقص x
+
+143
+00:11:56,520 --> 00:12:02,380
+initial بيساوي v initial أو x initial t زائد نص a
+
+144
+00:12:02,380 --> 00:12:06,600
+x t تربيع. ذاكرينهم؟ وفي معادلة t مشتقة من هدول،
+
+145
+00:12:06,600 --> 00:12:10,280
+كيف نكون هدول؟ وهنا، ده اللي بدل الx بتحط
+
+146
+00:12:10,280 --> 00:12:16,420
+y. y ناقص y initial بيساوي v<sub>y</sub> initial في t زائد نص الـ
+
+147
+00:12:16,420 --> 00:12:22,010
+a<sub>y</sub> في t تربيع. والمعادلات كانت ثانية زيهم. اتفقنا هيك؟
+
+148
+00:12:22,010 --> 00:12:27,810
+إذا ما فيش شيء جديد... ما فيش شيء جديد، بس الشغل قاعد
+
+149
+00:12:27,810 --> 00:12:33,470
+بنعمله double، بكرره مرتين، مرة سين، ومرة صاد.
+
+150
+00:12:33,470 --> 00:12:39,590
+اتفقنا يا بنات؟ اتفقنا. شايفين الجدول؟ طبعاً هنا بس
+
+151
+00:12:39,590 --> 00:12:43,410
+بنجمعهم. بلدكم من التجميع. حاجة بديهية، من شوف التجميع.
+
+152
+00:12:43,410 --> 00:12:50,430
+تمام؟ هنشوف هذا المثال. قال لي، يلّا حلّ. قال لي، هاي
+
+153
+00:12:50,430 --> 00:12:57,830
+نملة، particle، بتتحرك، أحسن من صورة صورة. لأ، تمام.
+
+154
+00:12:57,830 --> 00:13:03,450
+نملة بتتحرك، moves in the XY plane، يعني في اللوح، ع
+
+155
+00:13:03,450 --> 00:13:08,790
+الشاشة، قاعدة بتمشي. قال لي، in the XY plane، starting
+
+156
+00:13:08,790 --> 00:13:12,870
+from the origin، يعني x initial صفر، وy initial صفر،
+
+157
+00:13:12,870 --> 00:13:19,220
+ولا لأ؟ حلو. إذا معناته، هدول نخليهم هيك. هي أيّ
+
+158
+00:13:19,220 --> 00:13:25,500
+example، example. تشوف المعطيات. جالي، x initial، قد إيش؟
+
+159
+00:13:25,500 --> 00:13:32,500
+و y initial. هاي أول معطى. تمام. starting from the
+
+160
+00:13:32,500 --> 00:13:37,260
+origin with an initial velocity، v initial، having
+
+161
+00:13:37,260 --> 00:13:45,160
+v<sub>x</sub> initial، v<sub>x</sub> initial، بتساوي عشرين متر per second، و
+
+162
+00:13:45,160 --> 00:13:52,770
+v<sub>y</sub> initial، بتساوي سالب خمسة عشر متر per second. شوفوا
+
+163
+00:13:52,770 --> 00:14:00,210
+هدول، ممكن أكتبهم، هيّاها، بصيغة ثانية. v initial، ما بدّي
+
+164
+00:14:00,210 --> 00:14:05,550
+
+223
+00:19:08,070 --> 00:19:13,270
+جيبلي بس الأحداث الصينية وخلاص؟ بنفع؟ لازم أديكي
+
+224
+00:19:13,270 --> 00:19:17,930
+محدثين إذا بدي ال position جالي حلو، جالي هادي؟
+
+225
+00:19:18,700 --> 00:19:23,680
+بتطلع لك X Final ولا لأ؟ حسب المعطيات خلّيني أمحي
+
+226
+00:19:23,680 --> 00:19:28,540
+هذه لإنه خلصناها آه هذي Ey بيبنيها Ey بالساوية سفر
+
+227
+00:19:28,540 --> 00:19:35,140
+يلا يا بناة X Final ايش هتحط محله هذه؟ سفر بتساوي
+
+228
+00:19:35,140 --> 00:19:42,180
+عشرين في خمسة زائد أربعة على اتنين في خمسة وعشرين
+
+229
+00:19:42,180 --> 00:19:48,920
+عشرين في خمسة مئة وخمسين  اين عليك احصل من ال
+
+230
+00:19:48,920 --> 00:19:57,180
+calculator مئة وخمسين متر صح نجيها تلوها Y final
+
+231
+00:19:57,180 --> 00:20:04,760
+لأن هذه سفر يا بنات بتساوي ناقص خمسة عشر في خمسة هذه
+
+232
+00:20:04,760 --> 00:20:10,020
+جد أيش سفر ناقص خمسة عشر في خمسة ناقص خمسة وسبعين
+
+233
+00:20:10,020 --> 00:20:10,380
+متر
+
+234
+00:20:13,410 --> 00:20:17,330
+بدي اكتبها ال Y جبتها ولا ما جبتهاش؟ آه يعني جبتها
+
+235
+00:20:17,330 --> 00:20:22,890
+مَزعجْتاش لأن إذا زعلتها بنوع مني علامات صح ولا لا؟
+
+236
+00:20:22,890 --> 00:20:28,190
+ما بحبش أزعل حدا نحنا تمام إذا ما بقدر أقول هي ال G R
+
+237
+00:20:28,190 --> 00:20:34,830
+اللي هو رمز ال position بالساوية 150 I ناقص 75 J
+
+238
+00:20:34,830 --> 00:20:45,050
+متر على متر صح ولا لأ؟ صح سهلة سهلة جداً آخر حاجة بس
+
+239
+00:20:45,050 --> 00:20:52,590
+ال جيجا بس بديه هتخلصنا منه بس
+
+240
+00:20:52,590 --> 00:20:55,950
+عشان التصوير يجيبه عشان  مشيلنا باللي اللي بديه
+
+241
+00:20:55,950 --> 00:21:04,510
+يحضرنا ده كله حكيناه آخر حاجة قال لي في عندي يسمين
+
+242
+00:21:04,510 --> 00:21:10,960
+كورتين مسكهم أنا في إيدوفي نفس الارتفاع تمام؟ نفس
+
+243
+00:21:10,960 --> 00:21:17,540
+الارتفاع بدي أطلقهم بنفس اللحظة two poles are
+
+244
+00:21:17,540 --> 00:21:21,660
+projected قُذفوا يعني at the same instant في نفس
+
+245
+00:21:21,660 --> 00:21:25,360
+اللحظة from the same height  إذا نفس الارتفاع ولا
+
+246
+00:21:25,360 --> 00:21:31,380
+لأ؟ وفي نفس اللحظة بدوا كيف ضربتهم جالي واحد سجّت
+
+247
+00:21:31,380 --> 00:21:38,110
+سجوت والتاني خبطه بشكل أفقي واحد سجّت سجوت والتاني
+
+248
+00:21:38,110 --> 00:21:42,730
+قذفت وادته سرعة ابتدائية يعني بس كيف قال لي سينية
+
+249
+00:21:42,730 --> 00:21:47,830
+من وين عرفت سينية horizontally بقول ايه is
+
+250
+00:21:47,830 --> 00:21:52,990
+projected horizontally طيب هجتش السؤال أنا قذفت
+
+251
+00:21:52,990 --> 00:21:56,490
+واحد باتجاه سيني هذه سرعة ابتدائية ولا لأ ماهي
+
+252
+00:21:56,490 --> 00:22:04,050
+السرعة الابتدائية الصادية سفر مظبط ولا لأ سرعتها
+
+253
+00:22:04,050 --> 00:22:08,990
+الابتدائية السينية لكنها صادية من أين عرفت؟ من هذه
+
+254
+00:22:08,990 --> 00:22:14,290
+الكلمة بي قال بي بس فلتها بي سرعتها الابتدائية
+
+255
+00:22:14,290 --> 00:22:18,690
+السينية سفر والصادية صفر والصادية صفر لكن في نهاية
+
+256
+00:22:18,690 --> 00:22:22,270
+ركزنا على الصادية صادية صفر ولا لأ ولا ايه برضه
+
+257
+00:22:22,270 --> 00:22:29,530
+صفر حلو طيب assuming the only acceleration acting
+
+258
+00:22:29,530 --> 00:22:32,230
+on the two poles is the acceleration of gravity
+
+259
+00:22:33,040 --> 00:22:36,140
+التصارع اللي سجّته التنين جاذبية ولا مش جاذبية؟
+
+260
+00:22:36,140 --> 00:22:39,140
+والجاذبية بنعتبرها ثابتة ولا مش ثابتة؟ وكيف
+
+261
+00:22:39,140 --> 00:22:45,060
+اتجاهها؟ سينية ولا صادية؟ صادية، صادية، صادية،
+
+262
+00:22:45,060 --> 00:22:45,220
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+263
+00:22:45,220 --> 00:22:47,420
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+264
+00:22:47,420 --> 00:22:49,080
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+265
+00:22:49,080 --> 00:22:49,820
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+266
+00:22:49,820 --> 00:22:52,380
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+267
+00:22:52,380 --> 00:22:58,660
+صادية، صادية،
+
+268
+00:22:58,660 --> 00:23:05,140
+صح  من نفس الارتفاع بفرق ال Y إذا الاتنين يلهم
+
+269
+00:23:05,140 --> 00:23:12,800
+نفس ال Y صح السرعة الابتدائية الصادية للإثنين واحد
+
+270
+00:23:12,800 --> 00:23:18,420
+00 مع أن الأولى إلها سرعة ابتدائية سينية بس أنت
+
+271
+00:23:18,420 --> 00:23:25,300
+بتتعود هنا إيش Y  جديش لل Y 0 ولا B 0 حلو ها
+
+272
+00:23:25,300 --> 00:23:32,070
+للإثنين G نقش G لكن ايه؟ إذا هدول زي بعض و هدول زي
+
+273
+00:23:32,070 --> 00:23:36,610
+بعض و هد زي بعض إذا تلك الإثنين زي بعض ولا لا؟ إذا
+
+274
+00:23:36,610 --> 00:23:41,670
+بدهم يصلوا بنفس الزمن إذا بدهم يصلوا بنفس الزمن
+
+275
+00:23:41,670 --> 00:23:45,210
+أنتِ
+
+276
+00:23:45,210 --> 00:23:51,530
+مش مسدقة طبعاً مش مسدقة روحي اعملي تجارب و
+
+277
+00:23:51,530 --> 00:23:53,990
+جيبي أهلك كلهم يحسبوا معاكي
+
+278
+00:23:57,900 --> 00:24:03,900
+آه هو من الذي بضل رايحة ع رفعها .. هي ال details
+
+279
+00:24:03,900 --> 00:24:09,960
+هضيها لسينية .. تجربيش لصادية .. تجربيش لصادية شوف محل
+
+280
+00:24:09,960 --> 00:24:16,460
+العلم ..المعادلات صحيحة لكن أنتِ مش .. مش بلعها ..
+
+281
+00:24:16,460 --> 00:24:21,520
+مش بلعها لأ صحيحة المعادلات بتجيل بالتالي طلعوش
+
+282
+00:24:21,520 --> 00:24:27,340
+المطلوب they will reach together مع بعض ولا واحد
+
+283
+00:24:27,340 --> 00:24:32,940
+أحد اسمه جيت ثانية ثمانية بنات؟ بكرا quiz من الستة
+
+284
+00:24:32,940 --> 00:24:33,480
+صباحاً
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/lL45YY9Z9j0_postprocess.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/lL45YY9Z9j0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..485ddb6e3f39a992a98635df46bbaa1de9db7473
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/lL45YY9Z9j0_postprocess.srt
@@ -0,0 +1,1136 @@
+1
+00:00:05,800 --> 00:00:09,640
+تمام يا بنات انسمى باسم الله ونبدأ بال chapter
+
+2
+00:00:09,640 --> 00:00:15,660
+الرابع عنوانه motion كلمة motion بنعرفها ولا لأ
+
+3
+00:00:15,660 --> 00:00:20,540
+عنوان ال chapter التاني برضه motion بس هناك كان
+
+4
+00:00:20,540 --> 00:00:26,580
+one dimension هنا two dimensions in two dimensions
+
+5
+00:00:26,580 --> 00:00:34,120
+طيب motion حركة حركة الموضع بيظل زي ما هوإذاً بدي
+
+6
+00:00:34,120 --> 00:00:39,980
+أعيد تعريف الموضوع بس الآن يا بنات بتتحركش في قط
+
+7
+00:00:39,980 --> 00:00:45,560
+واحد بتتحرك في مستوى و بدي أعيد ال velocity و بدي
+
+8
+00:00:45,560 --> 00:00:49,880
+أعيد ال acceleration و إذا ال acceleration ثابتة
+
+9
+00:00:49,880 --> 00:00:53,340
+بدي أعيد اشتقاق التلت معادلات أو الأربع معادلات
+
+10
+00:00:53,340 --> 00:00:58,580
+ذاكرينهم؟ تمام إذا اتطلعش بدي أدرس بدي أدرس
+
+11
+00:00:59,420 --> 00:01:03,900
+position velocity and acceleration مروا علينا ولا
+
+12
+00:01:03,900 --> 00:01:10,120
+لأ بعدين لما تكون ال acceleration constant two
+
+13
+00:01:10,120 --> 00:01:15,770
+dimensional motionتمام؟ هيك بيسموها دي من
+
+14
+00:01:15,770 --> 00:01:20,550
+dimension with constant acceleration العلاقات اللي
+
+15
+00:01:20,550 --> 00:01:24,450
+اشتقتهم انا وياكم جالي لما انت حكيت عن الحركة
+
+16
+00:01:24,450 --> 00:01:28,470
+الخطية في شطر اتنين كان في مثال مشهور اسمه سقوط
+
+17
+00:01:28,470 --> 00:01:32,850
+الحر برضه في الحركة ال two dimensions في مثال
+
+18
+00:01:32,850 --> 00:01:38,850
+مشهور هي حركة المقذوفات ال projectile motionتمام؟
+
+19
+00:01:38,850 --> 00:01:42,470
+قال لي كمان في حركة مشهورة جدا في الحركة المستوية
+
+20
+00:01:42,470 --> 00:01:48,190
+هي الحركة الدائرية Circular من Circle Circle دائرة
+
+21
+00:01:48,190 --> 00:01:52,090
+Circular دائري قال لي فيه نوعين حاجة بنسميها
+
+22
+00:01:52,090 --> 00:01:55,730
+uniform منتظمة و non uniform غير منتظمة ايش
+
+23
+00:01:55,730 --> 00:01:59,390
+معناتها لما نجيها؟ ارتسأل نصر قال لي اخر حاجة في
+
+24
+00:01:59,390 --> 00:02:05,830
+حاجة اسمها سرعة نسبية سرعة نسبيةطبعا واحنا بنقول
+
+25
+00:02:05,830 --> 00:02:11,810
+الشبتر الرابع هو بداية الشغل الحقيقي لأنه شبتر
+
+26
+00:02:11,810 --> 00:02:17,750
+اتنين عشان اغششكم بيبلعوا شبتر اربعة يعني بكرا في
+
+27
+00:02:17,750 --> 00:02:21,350
+ال final واحد بدي يدرس مايدرسش اتنين يدرس اربعة
+
+28
+00:02:21,350 --> 00:02:26,090
+ماهو تلقائي لأ انا اتنين احنا بندرس ثلاثة ثلاثة
+
+29
+00:02:26,090 --> 00:02:29,990
+هيندرس غصب من عمك هيتكرر معاك كتير بس اتنين ليش
+
+30
+00:02:29,990 --> 00:02:32,250
+هدرس اتنين و او هدرس اربعة مانبدرس اربعة بكون
+
+31
+00:02:32,250 --> 00:02:38,980
+اندرس اتنينأربعة جاكل اتنين تمام؟ بالظبط ابطلوا
+
+32
+00:02:38,980 --> 00:02:41,800
+عشان كده؟ شوف ال recommended problem ما شاء الله
+
+33
+00:02:41,800 --> 00:02:48,040
+عليهم اسمان اكتر لأنه chapter حقيقي الآن هذا شغل
+
+34
+00:02:48,040 --> 00:02:53,780
+chapter اتنين كنا ساخن فيه كانوا بدلعونه خلصنا منه
+
+35
+00:02:53,780 --> 00:03:00,710
+تمام؟ يلا يا بناتإيش في عندى plane؟ قلتله اللوح
+
+36
+00:03:00,710 --> 00:03:05,050
+الـplane ولا مش الـplane؟ أي جسم بيمشي في اللوح،
+
+37
+00:03:05,050 --> 00:03:08,250
+على اللوح، بقول بأضمن إنه two-dimensional motion
+
+38
+00:03:08,250 --> 00:03:12,650
+ولا لأ؟ تمام يا بنات، أنا أخدت مثال في الشعب اللي
+
+39
+00:03:12,650 --> 00:03:15,910
+جابي، لو خلّيني على نفس المثال، عشان مايقولوش غوزة
+
+40
+00:03:15,910 --> 00:03:21,470
+للي جاعل بيصور معهم، في نملة بتمشي على اللوح،نملة
+
+41
+00:03:21,470 --> 00:03:24,830
+تمام طبعا النملة اللي جيبتها صغيرة عشان كلمة
+
+42
+00:03:24,830 --> 00:03:29,290
+particle particle جسم صغير تمام حاجة النملة و هي
+
+43
+00:03:29,290 --> 00:03:33,990
+بتمشي بتقدروا تقولوا هي نملة ماشي خط مستقيم عمزاج
+
+44
+00:03:33,990 --> 00:03:37,390
+هي بتمشي صح ولا لأ تمشي لها خط أي وين مكان ممكن
+
+45
+00:03:37,390 --> 00:03:42,930
+تكون قال لي هذه النملة هي خط ماشيها هيك ماشيها
+
+46
+00:03:42,930 --> 00:03:49,470
+أشواء هل ماشية سيني خط الأحمر صاضي لأ إذا سينه
+
+47
+00:03:49,470 --> 00:03:55,540
+صاضييا نبلة بدنا ندرس حركتك، اتفقنا؟ استنى شوية،
+
+48
+00:03:55,540 --> 00:04:02,560
+وقفت، قولت والله كنت هنا، هذا موضوع حال ابتدائي،
+
+49
+00:04:02,560 --> 00:04:05,420
+امشي، ماشي تلو عند الهنا، هذا موضوع حال نهائي
+
+50
+00:04:06,150 --> 00:04:10,410
+الحاجات بتدي position تبعك ال position دائما
+
+51
+00:04:10,410 --> 00:04:15,430
+متعودين ان احددوا بناء على نقطة أصل ولا لأ جالي
+
+52
+00:04:15,430 --> 00:04:18,710
+نقطة أصل انا ارسملك إياها كيف بديك تجيب موضوحها؟
+
+53
+00:04:18,710 --> 00:04:24,010
+قول من هنا بصل هنا صح ولا لأ؟ هاي ال position
+
+54
+00:04:24,010 --> 00:04:29,310
+تبحها initially وهذا ال position تبحها finally صح
+
+55
+00:04:29,310 --> 00:04:32,510
+ومظبوط ولا لأ؟ طيب اتطلعولي على ال position ال
+
+56
+00:04:32,510 --> 00:04:38,960
+initial هذا خط مستقيم فيني؟الأزرق شايفينه؟ صاضي؟
+
+57
+00:04:38,960 --> 00:04:43,840
+لأ طيب بقدر أقول إنه إله مراكبة صينية وإله مراكبة
+
+58
+00:04:43,840 --> 00:04:48,500
+صاضية أو لا؟ يا عيني عليكم يا عيني اتويلوا قولتله
+
+59
+00:04:48,500 --> 00:04:51,640
+هاي مراكبتها الصينية وهاي مراكبتها الصاضية صفتوا
+
+60
+00:04:51,640 --> 00:04:56,040
+مراكبتان الحمر هدول؟ الصيني بتحط جنبه I ولا لأ؟
+
+61
+00:04:56,040 --> 00:04:59,600
+والصاضي بتحط جنبه J ولا لأ؟ مش هيك اتعلمنا؟ قاللي
+
+62
+00:04:59,600 --> 00:05:05,640
+هاي R initial قاللي وR final هيها نفس الاشي
+
+63
+00:05:08,610 --> 00:05:12,350
+جاليه حلو بدي ال displacement جالي ال displacement
+
+64
+00:05:12,350 --> 00:05:18,030
+بتجيب من بداية للنهاية مظبوط او Delta X او Delta
+
+65
+00:05:18,030 --> 00:05:21,850
+اي حاجة مش بتسوي final نقص initialو قال لي بدّي
+
+66
+00:05:21,850 --> 00:05:27,010
+دلتة الأن R طبعا أنا قدرت أسمي X ولا Y إيش الرمز
+
+67
+00:05:27,010 --> 00:05:30,370
+اللي اتفجوا عليه قالوا R قال لي بدّي الآن ال
+
+68
+00:05:30,370 --> 00:05:34,710
+displacement قلتله يعني بدك دلتة R دلتة R بسوي R
+
+69
+00:05:34,710 --> 00:05:39,270
+final ناقص R initial final ناقص initial A ناقص B
+
+70
+00:05:39,270 --> 00:05:44,350
+اتعلمنا كيف نطح و نجمع vectors ولا لأ؟جالي اه جالي
+
+71
+00:05:44,350 --> 00:05:46,970
+ال case بتجمع و بتطرح ال vectors جالي الصيني مع
+
+72
+00:05:46,970 --> 00:05:52,090
+الصيني و الصاضي مع الصاضي هادي نقص هادي و هادي نقص
+
+73
+00:05:52,090 --> 00:05:56,510
+هادي ولا لأ جالي هايني جمعي اتطلعت هنا قلت له هادي
+
+74
+00:05:56,510 --> 00:06:01,470
+ممكن أسميها delta X و ممكن هادي أسميها delta Y اه
+
+75
+00:06:01,470 --> 00:06:09,350
+إذا هادي هدا هي delta X إذا الإزاحة أكم مركبة
+
+76
+00:06:09,350 --> 00:06:12,050
+إليها تنتهي سنية أحكي
+
+77
+00:06:15,030 --> 00:06:22,750
+لأ لأ حلو انت قلتي هذا ليش رسمته؟ صح؟ هيها ماشي
+
+78
+00:06:22,750 --> 00:06:29,270
+هيك شوف الخط الأحمر هذا، هذا الخط الأحمر هو خط سير
+
+79
+00:06:29,270 --> 00:06:34,990
+النملة، خط سير النملة، مياههل جيت النملة كانت هنا؟
+
+80
+00:06:34,990 --> 00:06:39,230
+ماشيت و جت هنا؟ لما انت بدك إذاحتها، إذاحتها مش
+
+81
+00:06:39,230 --> 00:06:43,190
+مسافتها، إيش بتسوي؟ بتقولي وين كانت و وين صارت؟ أو
+
+82
+00:06:43,190 --> 00:06:46,710
+بتجيبي خط مستقيم من بداية لنهاية ولا لأ؟ إذا هذه
+
+83
+00:06:46,710 --> 00:06:51,650
+الإزاحة مش خط صيرها، نرجع لقانون اسم المغازي؟ نرجع
+
+84
+00:06:51,650 --> 00:06:59,050
+لقانون اسم المغازي، ذاكرها؟ تمام؟ حلوجيلي حلو إذا
+
+85
+00:06:59,050 --> 00:07:04,070
+الإزاحة صار لها مركبتين سنية وصادرية ميجي لها
+
+86
+00:07:04,070 --> 00:07:08,710
+السرعة جالسانة السرعة أدتني شغلتين سرعة متوسطة و
+
+87
+00:07:08,710 --> 00:07:12,490
+سرعة لحظية ذاكرينها جلي السرعة المتوسطة عرفتيلي
+
+88
+00:07:12,490 --> 00:07:15,950
+إياها إنه Delta إزاحة على Delta زمان كان زمان
+
+89
+00:07:15,950 --> 00:07:19,530
+الإزاحة X بس Delta إزاحة على Delta زمان قولتله
+
+90
+00:07:19,530 --> 00:07:24,630
+الإزاحة قدت مش X يا ابني ولا Y R صح ولا لأ إذا
+
+91
+00:07:24,630 --> 00:07:30,950
+معناته بدك تقولليدال الـ V average مش هاي إشارة
+
+92
+00:07:30,950 --> 00:07:33,790
+الـ Average هال gate بدك تكون حاطيللي إشارة ال
+
+93
+00:07:33,790 --> 00:07:41,730
+vector بالمرة بقول بتساوي Delta R على Delta T في
+
+94
+00:07:41,730 --> 00:07:47,770
+مشكلة؟ هاي التعريف السرعة المتوسطة إزاحة على زمان
+
+95
+00:07:47,770 --> 00:07:54,840
+إيش أيه رمز إزاحتك؟ R هطيتها دي لي المقام هدىكمية
+
+96
+00:07:54,840 --> 00:07:59,400
+فيزيائية مشهورة الشيية زمان scalar ولا vector؟
+
+97
+00:07:59,400 --> 00:08:02,400
+scalar لما نضرب scalar في vector عشان نضرب
+
+98
+00:08:02,400 --> 00:08:06,480
+المراكبات كلها طب هذه المراكبات هيها يعني هذه
+
+99
+00:08:06,480 --> 00:08:13,340
+بتصيرDelta X على Delta Ti زائد Delta Y على Delta
+
+100
+00:08:13,340 --> 00:08:17,200
+Tj ولا لأ ال Delta T ضربتها في ال two components
+
+101
+00:08:17,200 --> 00:08:23,320
+اللي اتطلع هادي أخدتها في chapter 2 هادي V average
+
+102
+00:08:23,320 --> 00:08:29,140
+بالسمية و هادي V average بالصدية عشان سمية صدية
+
+103
+00:08:29,140 --> 00:08:29,760
+بتحطي
+
+104
+00:08:32,480 --> 00:08:37,220
+إذا السرعة المتوسطة أيضًا إلها أكام مُركّبة،
+
+105
+00:08:37,220 --> 00:08:43,400
+تنتين، واحدة سينية واحدة صينية، إذا قال لي Now the
+
+106
+00:08:43,400 --> 00:08:46,100
+average velocity of the particle، قال لي هذا هي
+
+107
+00:08:46,940 --> 00:08:51,160
+سيني زيات صاضي جالي طب الصراع اللحظية جالي الصراع
+
+108
+00:08:51,160 --> 00:08:55,360
+اللحظية إيش عرفتها قولتلي الصراع اللحظية مش ثقة
+
+109
+00:08:55,360 --> 00:08:59,920
+الإذاعة بالنسبالي الزمن مظبوط ولا لأ طب وين
+
+110
+00:08:59,920 --> 00:09:03,940
+الإذاعة ده اللي والله إلها سين وصاضي فصارت بالساوي
+
+111
+00:09:03,940 --> 00:09:12,000
+DX على DTI زيات DY على DTG جالي هذه مش صراع لحظية
+
+112
+00:09:12,000 --> 00:09:19,500
+سينية وهذه صراع لحظية صاضيةبتساوي VXI زائد VYJ
+
+113
+00:09:19,500 --> 00:09:29,060
+صفنا في إيش؟ و لا نعستي؟ تمام؟ إذا برضه السرعة
+
+114
+00:09:29,060 --> 00:09:36,570
+اللحظيةمركبتين قال لي similarly بنفس المفهوم ايه
+
+115
+00:09:36,570 --> 00:09:41,770
+بتتوقع التسارع ان المتوسط كله مركبتين ولا لا و
+
+116
+00:09:41,770 --> 00:09:45,930
+التسارع و التسارع اللحظي نفس القضية قال لي تخص
+
+117
+00:09:45,930 --> 00:09:51,050
+بلاش نحفظ اشتقاقات و نغلب حالنا ايش اللي بدك هي ده
+
+118
+00:09:51,050 --> 00:09:56,730
+اللي معناته بتقدر تقول ان الحركة المستوية او
+
+119
+00:09:56,730 --> 00:10:01,260
+الحركة في ال two dimensions هي مجموعة حركتينسينية
+
+120
+00:10:01,260 --> 00:10:07,280
+وصادية إذا هي مجموعة حركتين وكأنه بقول ليه كل سؤال
+
+121
+00:10:07,280 --> 00:10:10,620
+في هذا ال chapter عبارة عن سؤالين من chapter اتنين
+
+122
+00:10:10,620 --> 00:10:15,620
+كل سؤال بنقسم سؤالين واحد سيني واحد صادي واحد سيني
+
+123
+00:10:15,620 --> 00:10:22,300
+واحد صادي بس وكل اللي بدك يبدو زي ما هو حلو أجراها
+
+124
+00:10:22,300 --> 00:10:27,720
+بس عشان التصوير it is clear now that the planar
+
+125
+00:10:27,720 --> 00:10:31,970
+motion الحركة المستويةcan be considered .. ممكن
+
+126
+00:10:31,970 --> 00:10:36,790
+تعتبر as a vector sum of two perpendicular linear
+
+127
+00:10:36,790 --> 00:10:40,770
+motions هي مجموح حركتين خطيتين ولا .. ولا لأ؟
+
+128
+00:10:40,770 --> 00:10:44,830
+ومتعامدتين لأن واحدة سينية واحدة صادية one along
+
+129
+00:10:44,830 --> 00:10:49,090
+the x-axis and the other along the y-axis اذا
+
+130
+00:10:49,090 --> 00:10:55,660
+دائما بيقوللي في هدا بدت تعملي جدول هداجسمتي
+
+131
+00:10:55,660 --> 00:11:01,460
+الحركة أكمل جسم؟ اتنين تقولي هذه X وهذه Y في كل
+
+132
+00:11:01,460 --> 00:11:05,980
+الأسئلة طيب
+
+133
+00:11:05,980 --> 00:11:12,560
+جالي نبدأ جالي هب ان التصارع ثابت جالي في شغل
+
+134
+00:11:12,560 --> 00:11:17,620
+ثابتة و بيكون أحد مراكباتها متغير؟ مش ممكن إذا انت
+
+135
+00:11:17,620 --> 00:11:20,620
+بتقولي كل التصارع ثابت مع أن المراكبة ثانية مالها
+
+136
+00:11:21,210 --> 00:11:25,170
+ثابتة و المراكبة الصادية ثابتة فإذا المراكبة
+
+137
+00:11:25,170 --> 00:11:28,550
+الصينية ثابتة فطب ما انا و إياك اشتقين اقولنا V
+
+138
+00:11:28,550 --> 00:11:34,530
+Final بتسوى V Initial زائد At ذاكرينه قال لي بس
+
+139
+00:11:34,530 --> 00:11:40,690
+عشان هادي X بدي أحط X V X Final X Initial A قلتلي
+
+140
+00:11:40,690 --> 00:11:45,950
+طب ما هادي ثابتة قولتله حلو V Y Final بتسوى V Y
+
+141
+00:11:45,950 --> 00:11:52,120
+Initial زائد Aytنفس المعادلة ولا لأ؟ نفس المعادلة
+
+142
+00:11:52,120 --> 00:11:56,520
+ده اللي فيه كمان قانون كان يقول X final نقص X
+
+143
+00:11:56,520 --> 00:12:02,380
+initial بيساوي V initial او X initial T زائد نص A
+
+144
+00:12:02,380 --> 00:12:06,600
+X T تربيع، ذاكرينهم؟ وفي معادلة T مش تقي من هدول،
+
+145
+00:12:06,600 --> 00:12:10,280
+كيف يكون هدول هالجان؟ وهنا، ده اللي بدل ال X بتحط
+
+146
+00:12:10,280 --> 00:12:16,420
+Y ناقص Y initial بيساوي VY initial في T زائد نص ال
+
+147
+00:12:16,420 --> 00:12:22,010
+Y في T تربيعوالمعادلات كانت تانية زيهم اتفجنا هيك
+
+148
+00:12:22,010 --> 00:12:27,810
+إذا مافيش شي جديد .. مافيش شي جديد بس الشغل قاعد
+
+149
+00:12:27,810 --> 00:12:33,470
+بعملها double بكررها مرتين مرة سين و مرة ساطر
+
+150
+00:12:33,470 --> 00:12:39,590
+اتفجنا يا بنات اتفجنا شايفين الجدول؟ طبعا هنا بس
+
+151
+00:12:39,590 --> 00:12:43,410
+جمّعهم بلدكم من التجميع حاجة بعضية من شوف التجميع
+
+152
+00:12:43,410 --> 00:12:50,430
+تمام؟ هنشوف هذا المثالقال لي يلّا حل قال لي هاي
+
+153
+00:12:50,430 --> 00:12:57,830
+نملة particle بتتحرك أحسن من صصورة صصورة لأ تمام
+
+154
+00:12:57,830 --> 00:13:03,450
+نملة بتتحرك moves in the XY plane يعني في اللوح ع
+
+155
+00:13:03,450 --> 00:13:08,790
+الشاشة قاعدة بتمشي قال لي in the XY plane starting
+
+156
+00:13:08,790 --> 00:13:12,870
+from the origin يعني X initial صفر و Y initial صفر
+
+157
+00:13:12,870 --> 00:13:19,220
+ولا لأ حلو إذا معناته ههدول خلّيهم هجيت هاي اي
+
+158
+00:13:19,220 --> 00:13:25,500
+example example تشوف المعطيات جالي x initial جديش
+
+159
+00:13:25,500 --> 00:13:32,500
+و y initial هاي اول معطر تمام starting from the
+
+160
+00:13:32,500 --> 00:13:37,260
+origin with an initial velocity V initial having
+
+161
+00:13:37,260 --> 00:13:45,160
+Vx initial Vx initial بسوء عشرين متر per second و
+
+162
+00:13:45,160 --> 00:13:52,770
+Vy initialبتساوي سالب خمستاش متر per second شوفوا
+
+163
+00:13:52,770 --> 00:14:00,210
+هدول ممكن اكتبكمياها بصيغة تانية V initial بديش
+
+164
+00:14:00,210 --> 00:14:05,550
+اقول XY كلها اقول هاي vector بتساوي عشرين I ناقص
+
+165
+00:14:05,550 --> 00:14:08,870
+خمستاش RJ متر per second بصحيح اللي اكتب هيك ولا
+
+166
+00:14:08,870 --> 00:14:13,560
+لأ؟لو اللي أزرق هذا يقولولكم ما هي المركبة الصينية
+
+167
+00:14:13,560 --> 00:14:18,020
+للصراع التدعية والمركبة الصادية سالب خمس عشر نفس
+
+168
+00:14:18,020 --> 00:14:24,600
+الشيء أولا لأ؟ حلوطيب .. the particle .. هاد اللي
+
+169
+00:14:24,600 --> 00:14:27,360
+ساعة اللي نعمل نقرأ السؤال و ناخد منه معطيات the
+
+170
+00:14:27,360 --> 00:14:32,100
+particle experiences an acceleration بتأثر بتسارع
+
+171
+00:14:32,100 --> 00:14:35,940
+أو عنده تسارع إيش مقداره؟ قال لي in the X
+
+172
+00:14:35,940 --> 00:14:40,580
+direction best seen إيش مقداره؟ قال لي AX بيساوي
+
+173
+00:14:40,580 --> 00:14:45,100
+أربعة متر per second تربية نرجع بقوله AX بيساوي
+
+174
+00:14:45,100 --> 00:14:49,930
+أربعة متر per second تربيةقال لي حاجة عن ال Y قال
+
+175
+00:14:49,930 --> 00:14:54,790
+لي فيه هي في الشيشة سينية يعني الصدية مالها ايه Y
+
+176
+00:14:54,790 --> 00:15:00,270
+بتساوي سفر معطيات هو قال هيك مش واحد يقولي ليش
+
+177
+00:15:00,270 --> 00:15:07,250
+عملت هيك هو بده هيك تمام؟ حلو هاي معطيات سؤال ايش
+
+178
+00:15:07,250 --> 00:15:14,470
+بدك؟ بيقولي calculate the velocity and the speed
+
+179
+00:15:16,430 --> 00:15:19,430
+إيش معناته يا جوجل سبيت قلي سرعة و إيش معاك
+
+180
+00:15:19,430 --> 00:15:24,150
+Velocity قلي سرعة؟ إيش الفرق بينهم؟ Bravo إذا
+
+181
+00:15:24,150 --> 00:15:28,910
+Velocity بديها ك vector يعني حطيلي حاجة I و حاجة J
+
+182
+00:15:28,910 --> 00:15:34,520
+لكن بديه ال speedبدي أجيب ال magnitude لأن نسبية
+
+183
+00:15:34,520 --> 00:15:39,420
+تعريفها عرفناها في الشبطر 2 هي ال magnitude بتاعة
+
+184
+00:15:39,420 --> 00:15:44,880
+ال velocity ولا لأ حلو تمام و بعدين بنجيب بيه أول
+
+185
+00:15:44,880 --> 00:15:48,400
+نخلص واحدة واحدة find the velocity of T بالساوية
+
+186
+00:15:48,400 --> 00:15:51,500
+five second يعني بيدو V final ولا لأ هذه ال V
+
+187
+00:15:51,500 --> 00:15:55,380
+final في واحدة سينية واحدة صادية ده بتجيب السينية
+
+188
+00:15:55,380 --> 00:15:59,480
+و الصادية و بعدين تحطها يلا هذي بتجيبها هذي ولا
+
+189
+00:15:59,480 --> 00:16:08,850
+بتجيبهاشVx final ايش اعوض هنا براوالينا زاد ايش
+
+190
+00:16:08,850 --> 00:16:13,350
+اعوض محل ايه اربع اربع اربع انت ضربتي من المرة
+
+191
+00:16:13,350 --> 00:16:17,630
+اللي قالت عشانيه وش ال T طلعت اربعين متر per
+
+192
+00:16:17,630 --> 00:16:26,190
+second صح هتشوف القانون هذا Vy final قدش Vy
+
+193
+00:16:26,190 --> 00:16:35,680
+initial سالب خمستاشسفر اذا متر per second اتغيرتوا
+
+194
+00:16:35,680 --> 00:16:40,500
+السرعات الصادرية جالهو مين بيغير السرعات تسارع في
+
+195
+00:16:40,500 --> 00:16:45,980
+تسارع مش التسارع تعريفه اتغير سرعة اتغيرها ايجابا
+
+196
+00:16:45,980 --> 00:16:50,560
+او سلبا تباطؤا او زيادة مافيش تسارعة بتتوقع ان
+
+197
+00:16:50,560 --> 00:16:54,980
+تتغير السرعة دلت زي ما هي انت ايش بالجد جاله بده
+
+198
+00:16:54,980 --> 00:17:04,020
+السرعة جيتله هذه final بتساوي اربعينI-15Jm per
+
+199
+00:17:04,020 --> 00:17:09,260
+second نص المطبوب طلعته هذه velocity هذه velocity
+
+200
+00:17:09,260 --> 00:17:13,680
+بدى ال speed و كأنه بيقولي اودي دي ال magnitude
+
+201
+00:17:13,680 --> 00:17:17,960
+لهذا ال vector اودي دي ال magnitude لأن ال speed
+
+202
+00:17:17,960 --> 00:17:21,240
+هي ال magnitude تحت ال velocity ولا لأ قلت ال
+
+203
+00:17:21,240 --> 00:17:29,570
+speed بتساوي the final magnitude هيترجمهامش شكلها
+
+204
+00:17:29,570 --> 00:17:38,210
+تسبيد؟ تمام جاليها دي بتساوي 40 تربيع زائد 15
+
+205
+00:17:38,210 --> 00:17:46,130
+تربيع طبعا هنا في ناقص مافرجش اظن طبعا 43 تمام؟
+
+206
+00:17:46,130 --> 00:17:55,390
+في اي صفرار؟ صوت عالي اكيد؟ احكيه ال
+
+207
+00:17:55,390 --> 00:17:59,510
+average سويدي اللي بتحكي عنهاالدي اه ال average
+
+208
+00:17:59,510 --> 00:18:02,290
+speed اللي بتحكي عنها لكن لما يقولك او دي دي
+
+209
+00:18:02,290 --> 00:18:04,950
+velocity عند نقطة معينة وبعدين او دي دي ال speed
+
+210
+00:18:04,950 --> 00:18:08,230
+هي ال magnitude تحت ال velocity اما دي ال average
+
+211
+00:18:08,230 --> 00:18:15,410
+speed مختلفة غيرها هديك
+
+212
+00:18:15,410 --> 00:18:17,970
+قاللي ال average speed لاتساوي magnitude ال
+
+213
+00:18:17,970 --> 00:18:21,550
+average velocity لكن ال speed بتساوي ال magnitude
+
+214
+00:18:21,550 --> 00:18:23,450
+تحت ال velocity غيرها
+
+215
+00:18:26,040 --> 00:18:29,920
+تمام؟ هذه الأسئلة حلوة عشان ما تخربطنيش هنا
+
+216
+00:18:29,920 --> 00:18:34,400
+بنحكيها براحتنا ومخصومش علامات على الأسئلة إذا
+
+217
+00:18:34,400 --> 00:18:38,380
+خربطنا في الامتحان بناكل هوى صحيح؟ بالتالي ناخد
+
+218
+00:18:38,380 --> 00:18:42,920
+راحتنا الآن نسأل كل حاجة بتنط في المخ تطلع على
+
+219
+00:18:42,920 --> 00:18:49,260
+الإسان تظلي جوا تمام إيش بدك؟ قال لي بدي ال
+
+220
+00:18:49,260 --> 00:18:57,470
+position بدي X وYتقولي ليش X؟ هدبلين؟ بزعل منك ال
+
+221
+00:18:57,470 --> 00:19:03,930
+Y؟ ليش ال X و ال Y لأ؟ بده position إذا بدي X و Y
+
+222
+00:19:03,930 --> 00:19:08,070
+ولا لأ؟ هجيت أنا لما أقولكم حددولي موضع نقطة تقولي
+
+223
+00:19:08,070 --> 00:19:13,270
+جيبلي بس الأحداث الصيني و خلاص؟ بنفع؟ لازم أديكي
+
+224
+00:19:13,270 --> 00:19:17,930
+محدثيين إذا بدي ال position جالي حلو، جالي هادي؟
+
+225
+00:19:18,700 --> 00:19:23,680
+بتطلع لك X Final ولا لأ؟ حسب المعطيات خلّيني أمحي
+
+226
+00:19:23,680 --> 00:19:28,540
+هذه لإنه خلصناها اه هذي Ey بيبنيها Ey بالساوية سفر
+
+227
+00:19:28,540 --> 00:19:35,140
+يلا يا بناك X Final ايش هتحط محله هذه؟ سفر بتساوي
+
+228
+00:19:35,140 --> 00:19:42,180
+عشرين في خمسة زائد أربعة ع اتنين في خمسة وعشرين
+
+229
+00:19:42,180 --> 00:19:48,920
+عشرين في خمسة ميةمية و خمسين اين عليك احصل من ال
+
+230
+00:19:48,920 --> 00:19:57,180
+calculator مية و خمسين متر صح نجيها تلوها Y final
+
+231
+00:19:57,180 --> 00:20:04,760
+لأن هذه سفر يا بنات بتساوي ناقص خمستعش في خمسة هذه
+
+232
+00:20:04,760 --> 00:20:10,020
+جد أيش سفر ناقص خمستعش في خمسة ناقص خمسة و سبعين
+
+233
+00:20:10,020 --> 00:20:10,380
+متر
+
+234
+00:20:13,410 --> 00:20:17,330
+بدي اكتبها ال Y جبتها ولا ماتجبتاش؟ اه يعني جبتها
+
+235
+00:20:17,330 --> 00:20:22,890
+مزعلتاش لان اذا زعلتها بنوع مني علامات صح ولا لا؟
+
+236
+00:20:22,890 --> 00:20:28,190
+ماحبش نزعل حدا نحنا تمام اذا مابقدر اقول هي ال G R
+
+237
+00:20:28,190 --> 00:20:34,830
+اللي هو رمز ال position بالساوي 150 I ناقص 75 J
+
+238
+00:20:34,830 --> 00:20:45,050
+متر على متر صح ولا لأ؟صح سهلة سهلة جدا اخر حاجة بس
+
+239
+00:20:45,050 --> 00:20:52,590
+ال جيجا بس بديه هتخلصنا منه بس
+
+240
+00:20:52,590 --> 00:20:55,950
+عشان التصوير يجيبه عشان مشيلنا باللي اللي بديه
+
+241
+00:20:55,950 --> 00:21:04,510
+يحضرنا ده كله حكيناه اخر حاجة قال لي في عندي يسمين
+
+242
+00:21:04,510 --> 00:21:10,960
+كورتين مسكهم انا في ايديوفي نفس الارتفاع تمام؟ نفس
+
+243
+00:21:10,960 --> 00:21:17,540
+الارتفاع بدي أطلقهم بنفس اللحظة two poles are
+
+244
+00:21:17,540 --> 00:21:21,660
+projected قدفوا يعني at the same instant في نفس
+
+245
+00:21:21,660 --> 00:21:25,360
+اللحظة from the same height إذا نفس الارتفاع ولا
+
+246
+00:21:25,360 --> 00:21:31,380
+لأ؟ وفي نفس اللحظة بدوا كيف ضربتهم جالي واحد سجت
+
+247
+00:21:31,380 --> 00:21:38,110
+سجوت والتاني خبطه بشكل أفقيواحد سجت تسجوت والتانى
+
+248
+00:21:38,110 --> 00:21:42,730
+قذفت وادته سرعة ابتدائية يعنى بس كيف قال لي سينية
+
+249
+00:21:42,730 --> 00:21:47,830
+من وين عرفت سينية horizontally بقول ايه is
+
+250
+00:21:47,830 --> 00:21:52,990
+projected horizontally طيب هجتش السؤال انا قذفت
+
+251
+00:21:52,990 --> 00:21:56,490
+واحد باتجاه سينى هذه سرعة ابتدائية ولا لأ ماهي
+
+252
+00:21:56,490 --> 00:22:04,050
+السرعة الابتدائية الصادية سفر مظبط ولا لأسرعتها
+
+253
+00:22:04,050 --> 00:22:08,990
+الابتدائية السنية لكنها صادية من أين عرفت؟ من هذه
+
+254
+00:22:08,990 --> 00:22:14,290
+الكلمة بي قال بي بس فلتها بي سرعتها الابتدائية
+
+255
+00:22:14,290 --> 00:22:18,690
+السنية سفر والصادية سفر والصادية سفر لكن في نهاية
+
+256
+00:22:18,690 --> 00:22:22,270
+ركزنا على الصادية صادية سفر ولا لأ ولا ايه برضه
+
+257
+00:22:22,270 --> 00:22:29,530
+سفر حلو طيب assuming the only acceleration acting
+
+258
+00:22:29,530 --> 00:22:32,230
+on the two poles is the acceleration of gravity
+
+259
+00:22:33,040 --> 00:22:36,140
+التصارع اللي سجّهت التنين جاذبية ولا مش جاذبية؟
+
+260
+00:22:36,140 --> 00:22:39,140
+والجاذبية بنعتبرها ثابتة ولا مش ثابتة؟ وكيف
+
+261
+00:22:39,140 --> 00:22:45,060
+اتجاهها؟ سنية ولا صادية؟ صادية، صادية، صادية،
+
+262
+00:22:45,060 --> 00:22:45,220
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+263
+00:22:45,220 --> 00:22:47,420
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+264
+00:22:47,420 --> 00:22:49,080
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+265
+00:22:49,080 --> 00:22:49,820
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+266
+00:22:49,820 --> 00:22:52,380
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+267
+00:22:52,380 --> 00:22:58,660
+صادية، صادية،
+
+268
+00:22:58,660 --> 00:23:05,140
+صحلو من نفس الارتفاع بفرق ال Y إذا الاتنين يلهم
+
+269
+00:23:05,140 --> 00:23:12,800
+نفس ال Y صح السرعة الإبتدائية الصادية للإتنين واحد
+
+270
+00:23:12,800 --> 00:23:18,420
+00 مع أن الأولى إلها سرعة إبتدائية سنية بس إنت
+
+271
+00:23:18,420 --> 00:23:25,300
+بتتعود هنا إيش Y جديش لل Y 0 ولا B 0 حلو ها
+
+272
+00:23:25,300 --> 00:23:32,070
+للإتنين G نقش Gلكن ايه؟ اذا هدول زي بعض و هدول زي
+
+273
+00:23:32,070 --> 00:23:36,610
+بعض و هد زي بعض اذا تلك تنتين زي بعض ولا لا؟ اذا
+
+274
+00:23:36,610 --> 00:23:41,670
+بدهم يصلوا بنفس الزمن اذا بدهم يصلوا بنفس الزمن
+
+275
+00:23:41,670 --> 00:23:45,210
+انت
+
+276
+00:23:45,210 --> 00:23:51,530
+مش مسدقة طبعا مش مسدقة روحي عضها و بعملي تجارب و
+
+277
+00:23:51,530 --> 00:23:53,990
+جيبي أهلك كلهم يحسبوا معاكي
+
+278
+00:23:57,900 --> 00:24:03,900
+اه هو من الذى بضل رايحة ع رفعها .. هي ال details
+
+279
+00:24:03,900 --> 00:24:09,960
+هضيها لصينية .. تجربيش لصاد .. تجربيش لصاد شوف محل
+
+280
+00:24:09,960 --> 00:24:16,460
+العلم ..المعادلات صحيحة لكن انت مش .. مش بلعها ..
+
+281
+00:24:16,460 --> 00:24:21,520
+مش بلعها لأ صحيحة المعادلات بتجيل بالتالت طلعوش
+
+282
+00:24:21,520 --> 00:24:27,340
+المطلوب they will reach together مع بعض ولا واحد
+
+283
+00:24:27,340 --> 00:24:32,940
+احد اسمه جيت تانية تمانية بنات؟ بكرا quiz من الستة
+
+284
+00:24:32,940 --> 00:24:33,480
+صباحا
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/lL45YY9Z9j0_raw.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/lL45YY9Z9j0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..485ddb6e3f39a992a98635df46bbaa1de9db7473
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/lL45YY9Z9j0_raw.srt
@@ -0,0 +1,1136 @@
+1
+00:00:05,800 --> 00:00:09,640
+تمام يا بنات انسمى باسم الله ونبدأ بال chapter
+
+2
+00:00:09,640 --> 00:00:15,660
+الرابع عنوانه motion كلمة motion بنعرفها ولا لأ
+
+3
+00:00:15,660 --> 00:00:20,540
+عنوان ال chapter التاني برضه motion بس هناك كان
+
+4
+00:00:20,540 --> 00:00:26,580
+one dimension هنا two dimensions in two dimensions
+
+5
+00:00:26,580 --> 00:00:34,120
+طيب motion حركة حركة الموضع بيظل زي ما هوإذاً بدي
+
+6
+00:00:34,120 --> 00:00:39,980
+أعيد تعريف الموضوع بس الآن يا بنات بتتحركش في قط
+
+7
+00:00:39,980 --> 00:00:45,560
+واحد بتتحرك في مستوى و بدي أعيد ال velocity و بدي
+
+8
+00:00:45,560 --> 00:00:49,880
+أعيد ال acceleration و إذا ال acceleration ثابتة
+
+9
+00:00:49,880 --> 00:00:53,340
+بدي أعيد اشتقاق التلت معادلات أو الأربع معادلات
+
+10
+00:00:53,340 --> 00:00:58,580
+ذاكرينهم؟ تمام إذا اتطلعش بدي أدرس بدي أدرس
+
+11
+00:00:59,420 --> 00:01:03,900
+position velocity and acceleration مروا علينا ولا
+
+12
+00:01:03,900 --> 00:01:10,120
+لأ بعدين لما تكون ال acceleration constant two
+
+13
+00:01:10,120 --> 00:01:15,770
+dimensional motionتمام؟ هيك بيسموها دي من
+
+14
+00:01:15,770 --> 00:01:20,550
+dimension with constant acceleration العلاقات اللي
+
+15
+00:01:20,550 --> 00:01:24,450
+اشتقتهم انا وياكم جالي لما انت حكيت عن الحركة
+
+16
+00:01:24,450 --> 00:01:28,470
+الخطية في شطر اتنين كان في مثال مشهور اسمه سقوط
+
+17
+00:01:28,470 --> 00:01:32,850
+الحر برضه في الحركة ال two dimensions في مثال
+
+18
+00:01:32,850 --> 00:01:38,850
+مشهور هي حركة المقذوفات ال projectile motionتمام؟
+
+19
+00:01:38,850 --> 00:01:42,470
+قال لي كمان في حركة مشهورة جدا في الحركة المستوية
+
+20
+00:01:42,470 --> 00:01:48,190
+هي الحركة الدائرية Circular من Circle Circle دائرة
+
+21
+00:01:48,190 --> 00:01:52,090
+Circular دائري قال لي فيه نوعين حاجة بنسميها
+
+22
+00:01:52,090 --> 00:01:55,730
+uniform منتظمة و non uniform غير منتظمة ايش
+
+23
+00:01:55,730 --> 00:01:59,390
+معناتها لما نجيها؟ ارتسأل نصر قال لي اخر حاجة في
+
+24
+00:01:59,390 --> 00:02:05,830
+حاجة اسمها سرعة نسبية سرعة نسبيةطبعا واحنا بنقول
+
+25
+00:02:05,830 --> 00:02:11,810
+الشبتر الرابع هو بداية الشغل الحقيقي لأنه شبتر
+
+26
+00:02:11,810 --> 00:02:17,750
+اتنين عشان اغششكم بيبلعوا شبتر اربعة يعني بكرا في
+
+27
+00:02:17,750 --> 00:02:21,350
+ال final واحد بدي يدرس مايدرسش اتنين يدرس اربعة
+
+28
+00:02:21,350 --> 00:02:26,090
+ماهو تلقائي لأ انا اتنين احنا بندرس ثلاثة ثلاثة
+
+29
+00:02:26,090 --> 00:02:29,990
+هيندرس غصب من عمك هيتكرر معاك كتير بس اتنين ليش
+
+30
+00:02:29,990 --> 00:02:32,250
+هدرس اتنين و او هدرس اربعة مانبدرس اربعة بكون
+
+31
+00:02:32,250 --> 00:02:38,980
+اندرس اتنينأربعة جاكل اتنين تمام؟ بالظبط ابطلوا
+
+32
+00:02:38,980 --> 00:02:41,800
+عشان كده؟ شوف ال recommended problem ما شاء الله
+
+33
+00:02:41,800 --> 00:02:48,040
+عليهم اسمان اكتر لأنه chapter حقيقي الآن هذا شغل
+
+34
+00:02:48,040 --> 00:02:53,780
+chapter اتنين كنا ساخن فيه كانوا بدلعونه خلصنا منه
+
+35
+00:02:53,780 --> 00:03:00,710
+تمام؟ يلا يا بناتإيش في عندى plane؟ قلتله اللوح
+
+36
+00:03:00,710 --> 00:03:05,050
+الـplane ولا مش الـplane؟ أي جسم بيمشي في اللوح،
+
+37
+00:03:05,050 --> 00:03:08,250
+على اللوح، بقول بأضمن إنه two-dimensional motion
+
+38
+00:03:08,250 --> 00:03:12,650
+ولا لأ؟ تمام يا بنات، أنا أخدت مثال في الشعب اللي
+
+39
+00:03:12,650 --> 00:03:15,910
+جابي، لو خلّيني على نفس المثال، عشان مايقولوش غوزة
+
+40
+00:03:15,910 --> 00:03:21,470
+للي جاعل بيصور معهم، في نملة بتمشي على اللوح،نملة
+
+41
+00:03:21,470 --> 00:03:24,830
+تمام طبعا النملة اللي جيبتها صغيرة عشان كلمة
+
+42
+00:03:24,830 --> 00:03:29,290
+particle particle جسم صغير تمام حاجة النملة و هي
+
+43
+00:03:29,290 --> 00:03:33,990
+بتمشي بتقدروا تقولوا هي نملة ماشي خط مستقيم عمزاج
+
+44
+00:03:33,990 --> 00:03:37,390
+هي بتمشي صح ولا لأ تمشي لها خط أي وين مكان ممكن
+
+45
+00:03:37,390 --> 00:03:42,930
+تكون قال لي هذه النملة هي خط ماشيها هيك ماشيها
+
+46
+00:03:42,930 --> 00:03:49,470
+أشواء هل ماشية سيني خط الأحمر صاضي لأ إذا سينه
+
+47
+00:03:49,470 --> 00:03:55,540
+صاضييا نبلة بدنا ندرس حركتك، اتفقنا؟ استنى شوية،
+
+48
+00:03:55,540 --> 00:04:02,560
+وقفت، قولت والله كنت هنا، هذا موضوع حال ابتدائي،
+
+49
+00:04:02,560 --> 00:04:05,420
+امشي، ماشي تلو عند الهنا، هذا موضوع حال نهائي
+
+50
+00:04:06,150 --> 00:04:10,410
+الحاجات بتدي position تبعك ال position دائما
+
+51
+00:04:10,410 --> 00:04:15,430
+متعودين ان احددوا بناء على نقطة أصل ولا لأ جالي
+
+52
+00:04:15,430 --> 00:04:18,710
+نقطة أصل انا ارسملك إياها كيف بديك تجيب موضوحها؟
+
+53
+00:04:18,710 --> 00:04:24,010
+قول من هنا بصل هنا صح ولا لأ؟ هاي ال position
+
+54
+00:04:24,010 --> 00:04:29,310
+تبحها initially وهذا ال position تبحها finally صح
+
+55
+00:04:29,310 --> 00:04:32,510
+ومظبوط ولا لأ؟ طيب اتطلعولي على ال position ال
+
+56
+00:04:32,510 --> 00:04:38,960
+initial هذا خط مستقيم فيني؟الأزرق شايفينه؟ صاضي؟
+
+57
+00:04:38,960 --> 00:04:43,840
+لأ طيب بقدر أقول إنه إله مراكبة صينية وإله مراكبة
+
+58
+00:04:43,840 --> 00:04:48,500
+صاضية أو لا؟ يا عيني عليكم يا عيني اتويلوا قولتله
+
+59
+00:04:48,500 --> 00:04:51,640
+هاي مراكبتها الصينية وهاي مراكبتها الصاضية صفتوا
+
+60
+00:04:51,640 --> 00:04:56,040
+مراكبتان الحمر هدول؟ الصيني بتحط جنبه I ولا لأ؟
+
+61
+00:04:56,040 --> 00:04:59,600
+والصاضي بتحط جنبه J ولا لأ؟ مش هيك اتعلمنا؟ قاللي
+
+62
+00:04:59,600 --> 00:05:05,640
+هاي R initial قاللي وR final هيها نفس الاشي
+
+63
+00:05:08,610 --> 00:05:12,350
+جاليه حلو بدي ال displacement جالي ال displacement
+
+64
+00:05:12,350 --> 00:05:18,030
+بتجيب من بداية للنهاية مظبوط او Delta X او Delta
+
+65
+00:05:18,030 --> 00:05:21,850
+اي حاجة مش بتسوي final نقص initialو قال لي بدّي
+
+66
+00:05:21,850 --> 00:05:27,010
+دلتة الأن R طبعا أنا قدرت أسمي X ولا Y إيش الرمز
+
+67
+00:05:27,010 --> 00:05:30,370
+اللي اتفجوا عليه قالوا R قال لي بدّي الآن ال
+
+68
+00:05:30,370 --> 00:05:34,710
+displacement قلتله يعني بدك دلتة R دلتة R بسوي R
+
+69
+00:05:34,710 --> 00:05:39,270
+final ناقص R initial final ناقص initial A ناقص B
+
+70
+00:05:39,270 --> 00:05:44,350
+اتعلمنا كيف نطح و نجمع vectors ولا لأ؟جالي اه جالي
+
+71
+00:05:44,350 --> 00:05:46,970
+ال case بتجمع و بتطرح ال vectors جالي الصيني مع
+
+72
+00:05:46,970 --> 00:05:52,090
+الصيني و الصاضي مع الصاضي هادي نقص هادي و هادي نقص
+
+73
+00:05:52,090 --> 00:05:56,510
+هادي ولا لأ جالي هايني جمعي اتطلعت هنا قلت له هادي
+
+74
+00:05:56,510 --> 00:06:01,470
+ممكن أسميها delta X و ممكن هادي أسميها delta Y اه
+
+75
+00:06:01,470 --> 00:06:09,350
+إذا هادي هدا هي delta X إذا الإزاحة أكم مركبة
+
+76
+00:06:09,350 --> 00:06:12,050
+إليها تنتهي سنية أحكي
+
+77
+00:06:15,030 --> 00:06:22,750
+لأ لأ حلو انت قلتي هذا ليش رسمته؟ صح؟ هيها ماشي
+
+78
+00:06:22,750 --> 00:06:29,270
+هيك شوف الخط الأحمر هذا، هذا الخط الأحمر هو خط سير
+
+79
+00:06:29,270 --> 00:06:34,990
+النملة، خط سير النملة، مياههل جيت النملة كانت هنا؟
+
+80
+00:06:34,990 --> 00:06:39,230
+ماشيت و جت هنا؟ لما انت بدك إذاحتها، إذاحتها مش
+
+81
+00:06:39,230 --> 00:06:43,190
+مسافتها، إيش بتسوي؟ بتقولي وين كانت و وين صارت؟ أو
+
+82
+00:06:43,190 --> 00:06:46,710
+بتجيبي خط مستقيم من بداية لنهاية ولا لأ؟ إذا هذه
+
+83
+00:06:46,710 --> 00:06:51,650
+الإزاحة مش خط صيرها، نرجع لقانون اسم المغازي؟ نرجع
+
+84
+00:06:51,650 --> 00:06:59,050
+لقانون اسم المغازي، ذاكرها؟ تمام؟ حلوجيلي حلو إذا
+
+85
+00:06:59,050 --> 00:07:04,070
+الإزاحة صار لها مركبتين سنية وصادرية ميجي لها
+
+86
+00:07:04,070 --> 00:07:08,710
+السرعة جالسانة السرعة أدتني شغلتين سرعة متوسطة و
+
+87
+00:07:08,710 --> 00:07:12,490
+سرعة لحظية ذاكرينها جلي السرعة المتوسطة عرفتيلي
+
+88
+00:07:12,490 --> 00:07:15,950
+إياها إنه Delta إزاحة على Delta زمان كان زمان
+
+89
+00:07:15,950 --> 00:07:19,530
+الإزاحة X بس Delta إزاحة على Delta زمان قولتله
+
+90
+00:07:19,530 --> 00:07:24,630
+الإزاحة قدت مش X يا ابني ولا Y R صح ولا لأ إذا
+
+91
+00:07:24,630 --> 00:07:30,950
+معناته بدك تقولليدال الـ V average مش هاي إشارة
+
+92
+00:07:30,950 --> 00:07:33,790
+الـ Average هال gate بدك تكون حاطيللي إشارة ال
+
+93
+00:07:33,790 --> 00:07:41,730
+vector بالمرة بقول بتساوي Delta R على Delta T في
+
+94
+00:07:41,730 --> 00:07:47,770
+مشكلة؟ هاي التعريف السرعة المتوسطة إزاحة على زمان
+
+95
+00:07:47,770 --> 00:07:54,840
+إيش أيه رمز إزاحتك؟ R هطيتها دي لي المقام هدىكمية
+
+96
+00:07:54,840 --> 00:07:59,400
+فيزيائية مشهورة الشيية زمان scalar ولا vector؟
+
+97
+00:07:59,400 --> 00:08:02,400
+scalar لما نضرب scalar في vector عشان نضرب
+
+98
+00:08:02,400 --> 00:08:06,480
+المراكبات كلها طب هذه المراكبات هيها يعني هذه
+
+99
+00:08:06,480 --> 00:08:13,340
+بتصيرDelta X على Delta Ti زائد Delta Y على Delta
+
+100
+00:08:13,340 --> 00:08:17,200
+Tj ولا لأ ال Delta T ضربتها في ال two components
+
+101
+00:08:17,200 --> 00:08:23,320
+اللي اتطلع هادي أخدتها في chapter 2 هادي V average
+
+102
+00:08:23,320 --> 00:08:29,140
+بالسمية و هادي V average بالصدية عشان سمية صدية
+
+103
+00:08:29,140 --> 00:08:29,760
+بتحطي
+
+104
+00:08:32,480 --> 00:08:37,220
+إذا السرعة المتوسطة أيضًا إلها أكام مُركّبة،
+
+105
+00:08:37,220 --> 00:08:43,400
+تنتين، واحدة سينية واحدة صينية، إذا قال لي Now the
+
+106
+00:08:43,400 --> 00:08:46,100
+average velocity of the particle، قال لي هذا هي
+
+107
+00:08:46,940 --> 00:08:51,160
+سيني زيات صاضي جالي طب الصراع اللحظية جالي الصراع
+
+108
+00:08:51,160 --> 00:08:55,360
+اللحظية إيش عرفتها قولتلي الصراع اللحظية مش ثقة
+
+109
+00:08:55,360 --> 00:08:59,920
+الإذاعة بالنسبالي الزمن مظبوط ولا لأ طب وين
+
+110
+00:08:59,920 --> 00:09:03,940
+الإذاعة ده اللي والله إلها سين وصاضي فصارت بالساوي
+
+111
+00:09:03,940 --> 00:09:12,000
+DX على DTI زيات DY على DTG جالي هذه مش صراع لحظية
+
+112
+00:09:12,000 --> 00:09:19,500
+سينية وهذه صراع لحظية صاضيةبتساوي VXI زائد VYJ
+
+113
+00:09:19,500 --> 00:09:29,060
+صفنا في إيش؟ و لا نعستي؟ تمام؟ إذا برضه السرعة
+
+114
+00:09:29,060 --> 00:09:36,570
+اللحظيةمركبتين قال لي similarly بنفس المفهوم ايه
+
+115
+00:09:36,570 --> 00:09:41,770
+بتتوقع التسارع ان المتوسط كله مركبتين ولا لا و
+
+116
+00:09:41,770 --> 00:09:45,930
+التسارع و التسارع اللحظي نفس القضية قال لي تخص
+
+117
+00:09:45,930 --> 00:09:51,050
+بلاش نحفظ اشتقاقات و نغلب حالنا ايش اللي بدك هي ده
+
+118
+00:09:51,050 --> 00:09:56,730
+اللي معناته بتقدر تقول ان الحركة المستوية او
+
+119
+00:09:56,730 --> 00:10:01,260
+الحركة في ال two dimensions هي مجموعة حركتينسينية
+
+120
+00:10:01,260 --> 00:10:07,280
+وصادية إذا هي مجموعة حركتين وكأنه بقول ليه كل سؤال
+
+121
+00:10:07,280 --> 00:10:10,620
+في هذا ال chapter عبارة عن سؤالين من chapter اتنين
+
+122
+00:10:10,620 --> 00:10:15,620
+كل سؤال بنقسم سؤالين واحد سيني واحد صادي واحد سيني
+
+123
+00:10:15,620 --> 00:10:22,300
+واحد صادي بس وكل اللي بدك يبدو زي ما هو حلو أجراها
+
+124
+00:10:22,300 --> 00:10:27,720
+بس عشان التصوير it is clear now that the planar
+
+125
+00:10:27,720 --> 00:10:31,970
+motion الحركة المستويةcan be considered .. ممكن
+
+126
+00:10:31,970 --> 00:10:36,790
+تعتبر as a vector sum of two perpendicular linear
+
+127
+00:10:36,790 --> 00:10:40,770
+motions هي مجموح حركتين خطيتين ولا .. ولا لأ؟
+
+128
+00:10:40,770 --> 00:10:44,830
+ومتعامدتين لأن واحدة سينية واحدة صادية one along
+
+129
+00:10:44,830 --> 00:10:49,090
+the x-axis and the other along the y-axis اذا
+
+130
+00:10:49,090 --> 00:10:55,660
+دائما بيقوللي في هدا بدت تعملي جدول هداجسمتي
+
+131
+00:10:55,660 --> 00:11:01,460
+الحركة أكمل جسم؟ اتنين تقولي هذه X وهذه Y في كل
+
+132
+00:11:01,460 --> 00:11:05,980
+الأسئلة طيب
+
+133
+00:11:05,980 --> 00:11:12,560
+جالي نبدأ جالي هب ان التصارع ثابت جالي في شغل
+
+134
+00:11:12,560 --> 00:11:17,620
+ثابتة و بيكون أحد مراكباتها متغير؟ مش ممكن إذا انت
+
+135
+00:11:17,620 --> 00:11:20,620
+بتقولي كل التصارع ثابت مع أن المراكبة ثانية مالها
+
+136
+00:11:21,210 --> 00:11:25,170
+ثابتة و المراكبة الصادية ثابتة فإذا المراكبة
+
+137
+00:11:25,170 --> 00:11:28,550
+الصينية ثابتة فطب ما انا و إياك اشتقين اقولنا V
+
+138
+00:11:28,550 --> 00:11:34,530
+Final بتسوى V Initial زائد At ذاكرينه قال لي بس
+
+139
+00:11:34,530 --> 00:11:40,690
+عشان هادي X بدي أحط X V X Final X Initial A قلتلي
+
+140
+00:11:40,690 --> 00:11:45,950
+طب ما هادي ثابتة قولتله حلو V Y Final بتسوى V Y
+
+141
+00:11:45,950 --> 00:11:52,120
+Initial زائد Aytنفس المعادلة ولا لأ؟ نفس المعادلة
+
+142
+00:11:52,120 --> 00:11:56,520
+ده اللي فيه كمان قانون كان يقول X final نقص X
+
+143
+00:11:56,520 --> 00:12:02,380
+initial بيساوي V initial او X initial T زائد نص A
+
+144
+00:12:02,380 --> 00:12:06,600
+X T تربيع، ذاكرينهم؟ وفي معادلة T مش تقي من هدول،
+
+145
+00:12:06,600 --> 00:12:10,280
+كيف يكون هدول هالجان؟ وهنا، ده اللي بدل ال X بتحط
+
+146
+00:12:10,280 --> 00:12:16,420
+Y ناقص Y initial بيساوي VY initial في T زائد نص ال
+
+147
+00:12:16,420 --> 00:12:22,010
+Y في T تربيعوالمعادلات كانت تانية زيهم اتفجنا هيك
+
+148
+00:12:22,010 --> 00:12:27,810
+إذا مافيش شي جديد .. مافيش شي جديد بس الشغل قاعد
+
+149
+00:12:27,810 --> 00:12:33,470
+بعملها double بكررها مرتين مرة سين و مرة ساطر
+
+150
+00:12:33,470 --> 00:12:39,590
+اتفجنا يا بنات اتفجنا شايفين الجدول؟ طبعا هنا بس
+
+151
+00:12:39,590 --> 00:12:43,410
+جمّعهم بلدكم من التجميع حاجة بعضية من شوف التجميع
+
+152
+00:12:43,410 --> 00:12:50,430
+تمام؟ هنشوف هذا المثالقال لي يلّا حل قال لي هاي
+
+153
+00:12:50,430 --> 00:12:57,830
+نملة particle بتتحرك أحسن من صصورة صصورة لأ تمام
+
+154
+00:12:57,830 --> 00:13:03,450
+نملة بتتحرك moves in the XY plane يعني في اللوح ع
+
+155
+00:13:03,450 --> 00:13:08,790
+الشاشة قاعدة بتمشي قال لي in the XY plane starting
+
+156
+00:13:08,790 --> 00:13:12,870
+from the origin يعني X initial صفر و Y initial صفر
+
+157
+00:13:12,870 --> 00:13:19,220
+ولا لأ حلو إذا معناته ههدول خلّيهم هجيت هاي اي
+
+158
+00:13:19,220 --> 00:13:25,500
+example example تشوف المعطيات جالي x initial جديش
+
+159
+00:13:25,500 --> 00:13:32,500
+و y initial هاي اول معطر تمام starting from the
+
+160
+00:13:32,500 --> 00:13:37,260
+origin with an initial velocity V initial having
+
+161
+00:13:37,260 --> 00:13:45,160
+Vx initial Vx initial بسوء عشرين متر per second و
+
+162
+00:13:45,160 --> 00:13:52,770
+Vy initialبتساوي سالب خمستاش متر per second شوفوا
+
+163
+00:13:52,770 --> 00:14:00,210
+هدول ممكن اكتبكمياها بصيغة تانية V initial بديش
+
+164
+00:14:00,210 --> 00:14:05,550
+اقول XY كلها اقول هاي vector بتساوي عشرين I ناقص
+
+165
+00:14:05,550 --> 00:14:08,870
+خمستاش RJ متر per second بصحيح اللي اكتب هيك ولا
+
+166
+00:14:08,870 --> 00:14:13,560
+لأ؟لو اللي أزرق هذا يقولولكم ما هي المركبة الصينية
+
+167
+00:14:13,560 --> 00:14:18,020
+للصراع التدعية والمركبة الصادية سالب خمس عشر نفس
+
+168
+00:14:18,020 --> 00:14:24,600
+الشيء أولا لأ؟ حلوطيب .. the particle .. هاد اللي
+
+169
+00:14:24,600 --> 00:14:27,360
+ساعة اللي نعمل نقرأ السؤال و ناخد منه معطيات the
+
+170
+00:14:27,360 --> 00:14:32,100
+particle experiences an acceleration بتأثر بتسارع
+
+171
+00:14:32,100 --> 00:14:35,940
+أو عنده تسارع إيش مقداره؟ قال لي in the X
+
+172
+00:14:35,940 --> 00:14:40,580
+direction best seen إيش مقداره؟ قال لي AX بيساوي
+
+173
+00:14:40,580 --> 00:14:45,100
+أربعة متر per second تربية نرجع بقوله AX بيساوي
+
+174
+00:14:45,100 --> 00:14:49,930
+أربعة متر per second تربيةقال لي حاجة عن ال Y قال
+
+175
+00:14:49,930 --> 00:14:54,790
+لي فيه هي في الشيشة سينية يعني الصدية مالها ايه Y
+
+176
+00:14:54,790 --> 00:15:00,270
+بتساوي سفر معطيات هو قال هيك مش واحد يقولي ليش
+
+177
+00:15:00,270 --> 00:15:07,250
+عملت هيك هو بده هيك تمام؟ حلو هاي معطيات سؤال ايش
+
+178
+00:15:07,250 --> 00:15:14,470
+بدك؟ بيقولي calculate the velocity and the speed
+
+179
+00:15:16,430 --> 00:15:19,430
+إيش معناته يا جوجل سبيت قلي سرعة و إيش معاك
+
+180
+00:15:19,430 --> 00:15:24,150
+Velocity قلي سرعة؟ إيش الفرق بينهم؟ Bravo إذا
+
+181
+00:15:24,150 --> 00:15:28,910
+Velocity بديها ك vector يعني حطيلي حاجة I و حاجة J
+
+182
+00:15:28,910 --> 00:15:34,520
+لكن بديه ال speedبدي أجيب ال magnitude لأن نسبية
+
+183
+00:15:34,520 --> 00:15:39,420
+تعريفها عرفناها في الشبطر 2 هي ال magnitude بتاعة
+
+184
+00:15:39,420 --> 00:15:44,880
+ال velocity ولا لأ حلو تمام و بعدين بنجيب بيه أول
+
+185
+00:15:44,880 --> 00:15:48,400
+نخلص واحدة واحدة find the velocity of T بالساوية
+
+186
+00:15:48,400 --> 00:15:51,500
+five second يعني بيدو V final ولا لأ هذه ال V
+
+187
+00:15:51,500 --> 00:15:55,380
+final في واحدة سينية واحدة صادية ده بتجيب السينية
+
+188
+00:15:55,380 --> 00:15:59,480
+و الصادية و بعدين تحطها يلا هذي بتجيبها هذي ولا
+
+189
+00:15:59,480 --> 00:16:08,850
+بتجيبهاشVx final ايش اعوض هنا براوالينا زاد ايش
+
+190
+00:16:08,850 --> 00:16:13,350
+اعوض محل ايه اربع اربع اربع انت ضربتي من المرة
+
+191
+00:16:13,350 --> 00:16:17,630
+اللي قالت عشانيه وش ال T طلعت اربعين متر per
+
+192
+00:16:17,630 --> 00:16:26,190
+second صح هتشوف القانون هذا Vy final قدش Vy
+
+193
+00:16:26,190 --> 00:16:35,680
+initial سالب خمستاشسفر اذا متر per second اتغيرتوا
+
+194
+00:16:35,680 --> 00:16:40,500
+السرعات الصادرية جالهو مين بيغير السرعات تسارع في
+
+195
+00:16:40,500 --> 00:16:45,980
+تسارع مش التسارع تعريفه اتغير سرعة اتغيرها ايجابا
+
+196
+00:16:45,980 --> 00:16:50,560
+او سلبا تباطؤا او زيادة مافيش تسارعة بتتوقع ان
+
+197
+00:16:50,560 --> 00:16:54,980
+تتغير السرعة دلت زي ما هي انت ايش بالجد جاله بده
+
+198
+00:16:54,980 --> 00:17:04,020
+السرعة جيتله هذه final بتساوي اربعينI-15Jm per
+
+199
+00:17:04,020 --> 00:17:09,260
+second نص المطبوب طلعته هذه velocity هذه velocity
+
+200
+00:17:09,260 --> 00:17:13,680
+بدى ال speed و كأنه بيقولي اودي دي ال magnitude
+
+201
+00:17:13,680 --> 00:17:17,960
+لهذا ال vector اودي دي ال magnitude لأن ال speed
+
+202
+00:17:17,960 --> 00:17:21,240
+هي ال magnitude تحت ال velocity ولا لأ قلت ال
+
+203
+00:17:21,240 --> 00:17:29,570
+speed بتساوي the final magnitude هيترجمهامش شكلها
+
+204
+00:17:29,570 --> 00:17:38,210
+تسبيد؟ تمام جاليها دي بتساوي 40 تربيع زائد 15
+
+205
+00:17:38,210 --> 00:17:46,130
+تربيع طبعا هنا في ناقص مافرجش اظن طبعا 43 تمام؟
+
+206
+00:17:46,130 --> 00:17:55,390
+في اي صفرار؟ صوت عالي اكيد؟ احكيه ال
+
+207
+00:17:55,390 --> 00:17:59,510
+average سويدي اللي بتحكي عنهاالدي اه ال average
+
+208
+00:17:59,510 --> 00:18:02,290
+speed اللي بتحكي عنها لكن لما يقولك او دي دي
+
+209
+00:18:02,290 --> 00:18:04,950
+velocity عند نقطة معينة وبعدين او دي دي ال speed
+
+210
+00:18:04,950 --> 00:18:08,230
+هي ال magnitude تحت ال velocity اما دي ال average
+
+211
+00:18:08,230 --> 00:18:15,410
+speed مختلفة غيرها هديك
+
+212
+00:18:15,410 --> 00:18:17,970
+قاللي ال average speed لاتساوي magnitude ال
+
+213
+00:18:17,970 --> 00:18:21,550
+average velocity لكن ال speed بتساوي ال magnitude
+
+214
+00:18:21,550 --> 00:18:23,450
+تحت ال velocity غيرها
+
+215
+00:18:26,040 --> 00:18:29,920
+تمام؟ هذه الأسئلة حلوة عشان ما تخربطنيش هنا
+
+216
+00:18:29,920 --> 00:18:34,400
+بنحكيها براحتنا ومخصومش علامات على الأسئلة إذا
+
+217
+00:18:34,400 --> 00:18:38,380
+خربطنا في الامتحان بناكل هوى صحيح؟ بالتالي ناخد
+
+218
+00:18:38,380 --> 00:18:42,920
+راحتنا الآن نسأل كل حاجة بتنط في المخ تطلع على
+
+219
+00:18:42,920 --> 00:18:49,260
+الإسان تظلي جوا تمام إيش بدك؟ قال لي بدي ال
+
+220
+00:18:49,260 --> 00:18:57,470
+position بدي X وYتقولي ليش X؟ هدبلين؟ بزعل منك ال
+
+221
+00:18:57,470 --> 00:19:03,930
+Y؟ ليش ال X و ال Y لأ؟ بده position إذا بدي X و Y
+
+222
+00:19:03,930 --> 00:19:08,070
+ولا لأ؟ هجيت أنا لما أقولكم حددولي موضع نقطة تقولي
+
+223
+00:19:08,070 --> 00:19:13,270
+جيبلي بس الأحداث الصيني و خلاص؟ بنفع؟ لازم أديكي
+
+224
+00:19:13,270 --> 00:19:17,930
+محدثيين إذا بدي ال position جالي حلو، جالي هادي؟
+
+225
+00:19:18,700 --> 00:19:23,680
+بتطلع لك X Final ولا لأ؟ حسب المعطيات خلّيني أمحي
+
+226
+00:19:23,680 --> 00:19:28,540
+هذه لإنه خلصناها اه هذي Ey بيبنيها Ey بالساوية سفر
+
+227
+00:19:28,540 --> 00:19:35,140
+يلا يا بناك X Final ايش هتحط محله هذه؟ سفر بتساوي
+
+228
+00:19:35,140 --> 00:19:42,180
+عشرين في خمسة زائد أربعة ع اتنين في خمسة وعشرين
+
+229
+00:19:42,180 --> 00:19:48,920
+عشرين في خمسة ميةمية و خمسين اين عليك احصل من ال
+
+230
+00:19:48,920 --> 00:19:57,180
+calculator مية و خمسين متر صح نجيها تلوها Y final
+
+231
+00:19:57,180 --> 00:20:04,760
+لأن هذه سفر يا بنات بتساوي ناقص خمستعش في خمسة هذه
+
+232
+00:20:04,760 --> 00:20:10,020
+جد أيش سفر ناقص خمستعش في خمسة ناقص خمسة و سبعين
+
+233
+00:20:10,020 --> 00:20:10,380
+متر
+
+234
+00:20:13,410 --> 00:20:17,330
+بدي اكتبها ال Y جبتها ولا ماتجبتاش؟ اه يعني جبتها
+
+235
+00:20:17,330 --> 00:20:22,890
+مزعلتاش لان اذا زعلتها بنوع مني علامات صح ولا لا؟
+
+236
+00:20:22,890 --> 00:20:28,190
+ماحبش نزعل حدا نحنا تمام اذا مابقدر اقول هي ال G R
+
+237
+00:20:28,190 --> 00:20:34,830
+اللي هو رمز ال position بالساوي 150 I ناقص 75 J
+
+238
+00:20:34,830 --> 00:20:45,050
+متر على متر صح ولا لأ؟صح سهلة سهلة جدا اخر حاجة بس
+
+239
+00:20:45,050 --> 00:20:52,590
+ال جيجا بس بديه هتخلصنا منه بس
+
+240
+00:20:52,590 --> 00:20:55,950
+عشان التصوير يجيبه عشان مشيلنا باللي اللي بديه
+
+241
+00:20:55,950 --> 00:21:04,510
+يحضرنا ده كله حكيناه اخر حاجة قال لي في عندي يسمين
+
+242
+00:21:04,510 --> 00:21:10,960
+كورتين مسكهم انا في ايديوفي نفس الارتفاع تمام؟ نفس
+
+243
+00:21:10,960 --> 00:21:17,540
+الارتفاع بدي أطلقهم بنفس اللحظة two poles are
+
+244
+00:21:17,540 --> 00:21:21,660
+projected قدفوا يعني at the same instant في نفس
+
+245
+00:21:21,660 --> 00:21:25,360
+اللحظة from the same height إذا نفس الارتفاع ولا
+
+246
+00:21:25,360 --> 00:21:31,380
+لأ؟ وفي نفس اللحظة بدوا كيف ضربتهم جالي واحد سجت
+
+247
+00:21:31,380 --> 00:21:38,110
+سجوت والتاني خبطه بشكل أفقيواحد سجت تسجوت والتانى
+
+248
+00:21:38,110 --> 00:21:42,730
+قذفت وادته سرعة ابتدائية يعنى بس كيف قال لي سينية
+
+249
+00:21:42,730 --> 00:21:47,830
+من وين عرفت سينية horizontally بقول ايه is
+
+250
+00:21:47,830 --> 00:21:52,990
+projected horizontally طيب هجتش السؤال انا قذفت
+
+251
+00:21:52,990 --> 00:21:56,490
+واحد باتجاه سينى هذه سرعة ابتدائية ولا لأ ماهي
+
+252
+00:21:56,490 --> 00:22:04,050
+السرعة الابتدائية الصادية سفر مظبط ولا لأسرعتها
+
+253
+00:22:04,050 --> 00:22:08,990
+الابتدائية السنية لكنها صادية من أين عرفت؟ من هذه
+
+254
+00:22:08,990 --> 00:22:14,290
+الكلمة بي قال بي بس فلتها بي سرعتها الابتدائية
+
+255
+00:22:14,290 --> 00:22:18,690
+السنية سفر والصادية سفر والصادية سفر لكن في نهاية
+
+256
+00:22:18,690 --> 00:22:22,270
+ركزنا على الصادية صادية سفر ولا لأ ولا ايه برضه
+
+257
+00:22:22,270 --> 00:22:29,530
+سفر حلو طيب assuming the only acceleration acting
+
+258
+00:22:29,530 --> 00:22:32,230
+on the two poles is the acceleration of gravity
+
+259
+00:22:33,040 --> 00:22:36,140
+التصارع اللي سجّهت التنين جاذبية ولا مش جاذبية؟
+
+260
+00:22:36,140 --> 00:22:39,140
+والجاذبية بنعتبرها ثابتة ولا مش ثابتة؟ وكيف
+
+261
+00:22:39,140 --> 00:22:45,060
+اتجاهها؟ سنية ولا صادية؟ صادية، صادية، صادية،
+
+262
+00:22:45,060 --> 00:22:45,220
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+263
+00:22:45,220 --> 00:22:47,420
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+264
+00:22:47,420 --> 00:22:49,080
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+265
+00:22:49,080 --> 00:22:49,820
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+266
+00:22:49,820 --> 00:22:52,380
+صادية، صادية، صادية، صادية، صادية، صادية، صادية،
+
+267
+00:22:52,380 --> 00:22:58,660
+صادية، صادية،
+
+268
+00:22:58,660 --> 00:23:05,140
+صحلو من نفس الارتفاع بفرق ال Y إذا الاتنين يلهم
+
+269
+00:23:05,140 --> 00:23:12,800
+نفس ال Y صح السرعة الإبتدائية الصادية للإتنين واحد
+
+270
+00:23:12,800 --> 00:23:18,420
+00 مع أن الأولى إلها سرعة إبتدائية سنية بس إنت
+
+271
+00:23:18,420 --> 00:23:25,300
+بتتعود هنا إيش Y جديش لل Y 0 ولا B 0 حلو ها
+
+272
+00:23:25,300 --> 00:23:32,070
+للإتنين G نقش Gلكن ايه؟ اذا هدول زي بعض و هدول زي
+
+273
+00:23:32,070 --> 00:23:36,610
+بعض و هد زي بعض اذا تلك تنتين زي بعض ولا لا؟ اذا
+
+274
+00:23:36,610 --> 00:23:41,670
+بدهم يصلوا بنفس الزمن اذا بدهم يصلوا بنفس الزمن
+
+275
+00:23:41,670 --> 00:23:45,210
+انت
+
+276
+00:23:45,210 --> 00:23:51,530
+مش مسدقة طبعا مش مسدقة روحي عضها و بعملي تجارب و
+
+277
+00:23:51,530 --> 00:23:53,990
+جيبي أهلك كلهم يحسبوا معاكي
+
+278
+00:23:57,900 --> 00:24:03,900
+اه هو من الذى بضل رايحة ع رفعها .. هي ال details
+
+279
+00:24:03,900 --> 00:24:09,960
+هضيها لصينية .. تجربيش لصاد .. تجربيش لصاد شوف محل
+
+280
+00:24:09,960 --> 00:24:16,460
+العلم ..المعادلات صحيحة لكن انت مش .. مش بلعها ..
+
+281
+00:24:16,460 --> 00:24:21,520
+مش بلعها لأ صحيحة المعادلات بتجيل بالتالت طلعوش
+
+282
+00:24:21,520 --> 00:24:27,340
+المطلوب they will reach together مع بعض ولا واحد
+
+283
+00:24:27,340 --> 00:24:32,940
+احد اسمه جيت تانية تمانية بنات؟ بكرا quiz من الستة
+
+284
+00:24:32,940 --> 00:24:33,480
+صباحا
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2ffe67712f05b56b2ef91f40f25be0c0caebcccb
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4.srt
@@ -0,0 +1,1981 @@
+1
+00:00:05,280 --> 00:00:09,540
+طبعا يا بنات خلينا نستكمل المثال أو نعيد المثال
+
+2
+00:00:09,540 --> 00:00:15,600
+حلقنا و بدينا نحله و قلنا إنه في عندي هدف بدي
+
+3
+00:00:15,600 --> 00:00:21,640
+أصيده و هان اللي بدي أصيده بدي ينشل هال gate بدي
+
+4
+00:00:21,640 --> 00:00:26,660
+أثبت إنه عشان يقدر يصيده لازم أول ما ينطلق يكون على
+
+5
+00:00:26,660 --> 00:00:31,820
+نفس الخط مع الهدف قبل ما ينزل مع الهدف الثابت
+
+6
+00:00:31,820 --> 00:00:37,730
+وبالتالي قلت إنه نفترض إنه بدي نصيبه من هنا إذا
+
+7
+00:00:37,730 --> 00:00:42,170
+قطعا بدي يكون موضعين زي بعض ولا لأ هذا هو الـtrick
+
+8
+00:00:42,170 --> 00:00:47,230
+السؤال قال لي حلو أنا بأقذف أنا بدي أقذف قذيفة
+
+9
+00:00:47,230 --> 00:00:53,630
+عشان نصيبها بأقذف بزاوية هذه الزاوية بعتبرها θ  في
+
+10
+00:00:53,630 --> 00:00:57,630
+زاوية تابعة للخط لما رسمت ونشنت اللي بدي اعتبرها
+
+11
+00:00:57,630 --> 00:01:00,830
+α  هجيت أنا بدي أثبت أن θ و α نفس الزاوية
+
+12
+00:01:00,830 --> 00:01:05,750
+ولا لأ هذا هو اللي بدي أثبته  قلت في عندي
+
+13
+00:01:05,750 --> 00:01:10,250
+حركتين هذا عبارة عن الـtarget الهدف اللي بدي أصيبه
+
+14
+00:01:10,250 --> 00:01:17,220
+وهذا الـprojectile اللي هي اللي قذفتها تمام هيك؟
+
+15
+00:01:17,220 --> 00:01:23,140
+حلو قلت الـtarget بده ينزل سقوط حر قطعي بده ينزل
+
+16
+00:01:23,140 --> 00:01:27,080
+سقوط حر وبالتالي في السقوط الحر كان في عندي قانون
+
+17
+00:01:27,080 --> 00:01:32,500
+بيقول Y final ناقص Y initial بتساوي VY initial في T
+
+18
+00:01:32,500 --> 00:01:37,700
+ناقص نص GT تربيع ذاكرينه؟ قلت يبدأ يشتغل فيه طبعا
+
+19
+00:01:37,700 --> 00:01:42,310
+المحاور تبعتي أنا بدي أشتغل بناءً على هيك، إن هاي
+
+20
+00:01:42,310 --> 00:01:47,430
+المحاولة هي الدنياها، إذاً معناته هي الـOrigin،
+
+21
+00:01:47,430 --> 00:01:52,610
+وبالتالي، بداية أنا أسقطت سقوطاً، معناته السرعة
+
+22
+00:01:52,610 --> 00:01:56,490
+الابتدائية تبعته بديش، هذا هو الهدف، إن أنا بدي
+
+23
+00:01:56,490 --> 00:02:00,090
+أسقط وهو بدي يقذف، هو بدي يقذف بسرعة ابتدائية
+
+24
+00:02:00,090 --> 00:02:03,630
+معينة، لكن أنا الهدف بدي أن أنزل وأنزل، معناته
+
+25
+00:02:03,630 --> 00:02:10,830
+هان، هذه صفر، تمام  Y final وين بده المصيد و بعيد
+
+26
+00:02:10,830 --> 00:02:15,570
+هنا Y final بده يعتبره Y تمام إذا Y final هي
+
+27
+00:02:15,570 --> 00:02:22,310
+Y طب وين كان بداية المشروع؟ إذا ناقص H تمام
+
+28
+00:02:22,310 --> 00:02:33,250
+بتساوي صفر ناقص نص جي تي تربيع صحيح احكيه اللي بدك
+
+29
+00:02:33,250 --> 00:02:42,150
+إيه تمام حلو من هنا قدرت أقول إنه H بدأنا نقول H
+
+30
+00:02:42,150 --> 00:02:50,570
+هنا وهذه H صارت Y زائد نص GT تربيع خلاص قفلنا هذه
+
+31
+00:02:50,570 --> 00:02:57,320
+جيبناها العلاقة نشوف المقذوف المقذوف قذفتها حسب
+
+32
+00:02:57,320 --> 00:03:01,380
+الرسمة بزاوية أنت اعتبرتها θ  صح ولا لأ إذا أنا
+
+33
+00:03:01,380 --> 00:03:05,720
+في المقذوفات قلت أول حاجة بقول V initial x بتساوي
+
+34
+00:03:05,720 --> 00:03:11,180
+V initial cos θ و V initial y بتساوي V initial sin
+
+35
+00:03:11,180 --> 00:03:16,880
+θ بعملها لكل حركة المقذوفات بجسم معطياتي إلى سينية
+
+36
+00:03:16,880 --> 00:03:24,110
+وصادية تمام قال لي في عندك قانون برضه هنا بيقول هذا
+
+37
+00:03:24,110 --> 00:03:28,550
+الـprojectile Y final ناقص Y initial بيساوي VY
+
+38
+00:03:28,550 --> 00:03:32,910
+initial في T ناقص نص GT تربيع ولا لأ نفس الشغل
+
+39
+00:03:32,910 --> 00:03:38,430
+هذا القانون الصادي قال لي الآن Y final والله نفس
+
+40
+00:03:38,430 --> 00:03:42,790
+الـY ماشي التانية نقلهم نفس الـY؟ طب initial الـ
+
+41
+00:03:42,790 --> 00:03:47,750
+projectile من وين بدأ؟ من صفر إذا هذا بدأ من صفر
+
+42
+00:03:47,750 --> 00:03:53,490
+بتساوي ... قدّيش هذه هيها؟ V initial sin
+
+43
+00:03:53,490 --> 00:03:59,910
+θ ناقص نص GT تربيع صحيح ولا لأ؟ اتطلعوا أنتو
+
+44
+00:03:59,910 --> 00:04:05,740
+هنا إيش عملت لنا؟ هجيت هذه Y غير عن Y هذه؟ ولا نفسه
+
+45
+00:04:05,740 --> 00:04:09,440
+لأنه عشان يصيدوا بعض لازم يكون اللي هو نفسه الـY
+
+46
+00:04:09,440 --> 00:04:14,080
+إذا معناته بصح اللي هادي أجيبها وأحطها محل هادي
+
+47
+00:04:14,080 --> 00:04:16,000
+ولا لأ إذا بقوله
+
+48
+00:04:19,450 --> 00:04:24,610
+في هذا الـT مظبوط كلامكم تمام إذا هذا الـY جيبها
+
+49
+00:04:24,610 --> 00:04:32,450
+هنا قلت له إذا صار H بتساوي  V initial sin
+
+50
+00:04:32,450 --> 00:04:37,750
+θ في T هذا زائد وهذا ناقص بيروحوا مع بعض قال لي
+
+51
+00:04:37,750 --> 00:04:41,510
+حلو طلعت لي H قال لي أنت إيش اللي بدك تثبته؟ بدي
+
+52
+00:04:41,510 --> 00:04:44,990
+أقول له بدي أثبت إن α و θ إخوة نفس الزاوية
+
+53
+00:04:44,990 --> 00:04:48,890
+قلت له طلع لي على الرسمة بتقدر تقولي من الرسمة أن
+
+54
+00:04:48,890 --> 00:04:55,810
+تان α هي عبارة عن مقابل على مجاور H على X صح
+
+55
+00:04:55,810 --> 00:05:01,170
+ولا لأ؟ H والله جبتها  ده اللي كيف بدك تجيب X؟
+
+56
+00:05:01,170 --> 00:05:03,610
+قلت له X لأن الـprojectile motion اللي فيه قانون بيقول
+
+57
+00:05:03,610 --> 00:05:09,550
+X final ناقص X initial بتساوي V initial X في T
+
+58
+00:05:09,550 --> 00:05:14,110
+ذاكرينه؟ هذا الـprojectile motion القانون الوحيد
+
+59
+00:05:14,110 --> 00:05:19,130
+في الحركة السينية بيقول كله طاير X final هي X اللي
+
+60
+00:05:19,130 --> 00:05:25,250
+بتقول عنها و X initial صفر إذا X و V initial X وين
+
+61
+00:05:25,250 --> 00:05:33,110
+ها هي V initial cos θ T هاي X  قال لي يلّا عوض هاي H
+
+62
+00:05:33,110 --> 00:05:38,930
+وهاي X إذا هذه بتساوي  اعوض V initial sin θ في
+
+63
+00:05:38,930 --> 00:05:44,090
+T على V initial cos θ في T V initial مع V initial
+
+64
+00:05:44,090 --> 00:05:49,090
+بتروح sin θ على cos θ تان θ تان α بتساوي
+
+65
+00:05:49,090 --> 00:05:53,690
+تان θ إذا θ هي نفس α والمطلوب
+
+66
+00:05:53,690 --> 00:06:00,680
+إثباته كمان يا بنات؟ هذا المثال خلصناه هانا عملتها
+
+67
+00:06:00,680 --> 00:06:06,500
+زي ما أنا كتبتها حطيت الـtarget على اعتبار أنه في
+
+68
+00:06:06,500 --> 00:06:10,700
+falling حطيتها على المجموعة هذا هذا الحل على أساس أنه
+
+69
+00:06:10,700 --> 00:06:14,120
+لو  تخوضوا عينيكم في الورق والـprojector اللي هي
+
+70
+00:06:14,120 --> 00:06:20,660
+القذيفة اللي قذفتها حطيت قوانينها وبعد كده قلت بعد
+
+71
+00:06:20,660 --> 00:06:24,620
+ما حطيتها وجبت H و X وقلت it is necessary for the
+
+72
+00:06:24,620 --> 00:06:27,480
+projectile that for the projectile to hit the
+
+73
+00:06:27,480 --> 00:06:30,920
+target they must have the same position لازم
+
+74
+00:06:30,920 --> 00:06:36,100
+يضربوا بعض في نفس المكان وبالتالي جيبت Y وجيبت H
+
+75
+00:06:36,100 --> 00:06:41,740
+وجيبت X ومنها قلت إذا θ هي نفس الـα تمام؟ وحل
+
+76
+00:06:41,740 --> 00:06:46,760
+الكتاب بين أيديكم مختلف شوية مش قضية حد خلصناه؟
+
+77
+00:06:46,760 --> 00:06:49,960
+شوفوا هالسؤال
+
+78
+00:06:52,820 --> 00:06:59,380
+جالي متزلج بتعرفوها رياضة التزلج بيروحوا بينطوا نطة وبعدين
+
+79
+00:06:59,380 --> 00:07:02,340
+بعدين في الآخر نازلين على الثلج ولا مش نازلين
+
+80
+00:07:02,340 --> 00:07:07,490
+نازلين مين بينزله؟ الجاذبية إذا هي projectile motion
+
+81
+00:07:07,490 --> 00:07:12,090
+لأن اللي بتحكم فيهم هي الجاذبية الأرضية وهي
+
+82
+00:07:12,090 --> 00:07:17,310
+تعريفه projectile motion جالي a sky jumper بيقفز
+
+83
+00:07:17,310 --> 00:07:26,610
+من قفز التزلج leaves the sky track المسار تبع التزلج
+
+84
+00:07:26,610 --> 00:07:30,810
+track مسار هو لما يترك المسار  بس ما يشوف الهواء
+
+85
+00:07:32,330 --> 00:07:35,470
+بقى عبث وبيروح في الهواء وبعدين بنزل إذا هو
+
+86
+00:07:35,470 --> 00:07:40,890
+projectile motion leaves the sky track moving
+
+87
+00:07:40,890 --> 00:07:47,010
+horizontally قال لي أول ما يترك المسار في الهواء طلع
+
+88
+00:07:47,010 --> 00:07:53,950
+بسرعة أفقية فقط يعني V initial Y قد ايش؟ صفر قال لي
+
+89
+00:07:53,950 --> 00:07:58,030
+هذه حركة مقذوفات وفي حركة المقذوفات احنا متعودين
+
+90
+00:07:58,030 --> 00:08:03,790
+أن نجسم الحركة سينية وصادية ولا لأ حلو هاي بدنا
+
+91
+00:08:03,790 --> 00:08:07,790
+نجسمها هاي بدنا نقول X motion
+
+92
+00:08:11,550 --> 00:08:17,950
+Y  مش الحركة السينية والصادية تمام نجي على السؤال
+
+93
+00:08:17,950 --> 00:08:22,970
+كل حاجة معطاة بتشوفها سينية ولا صادية  ولي لا هي هيك
+
+94
+00:08:22,970 --> 00:08:27,330
+ولا هي هيك بدي أحللها مش هيك اتفاقنا  حلو جالي
+
+95
+00:08:27,330 --> 00:08:33,430
+قُدِفَت بسرعة أفقية معناته V Y Initial  صفر
+
+96
+00:08:33,430 --> 00:08:41,660
+صفر لأنه مافيش سرعة ابتدائية صادية هو قال لي سينية
+
+97
+00:08:41,660 --> 00:08:46,900
+فقط كيف عرفتي أنه سينية من كلمة horizontally صحيح؟
+
+98
+00:08:46,900 --> 00:08:53,520
+V X initial قال لي والله خمسة وعشرين هذه أول معطى
+
+99
+00:08:53,520 --> 00:09:01,250
+بتفجيني هيك؟ حلو قال لي رسمة  أشوف يا جماعة هذا الرسم
+
+100
+00:09:01,250 --> 00:09:03,990
+من معطيات السؤال ولا لأ؟ يا جماعة اتطلعوا الـorigin
+
+101
+00:09:03,990 --> 00:09:07,950
+أين هو اللي منطلقيها هنا إذا هو بدأ من هنا من نقطة الـ
+
+102
+00:09:07,950 --> 00:09:13,090
+origin يعني X initial قد ايش؟ و Y initial صفر إذا
+
+103
+00:09:13,090 --> 00:09:19,570
+بقول له X initial ها X initial صفر و Y initial صفر
+
+104
+00:09:20,860 --> 00:09:24,980
+إيش بدك؟ بقول لي where does the landing inclined
+
+105
+00:09:24,980 --> 00:09:29,320
+below her falls off with a slope of 35 degrees
+
+106
+00:09:29,320 --> 00:09:34,860
+قال لي المسار اللي بتسقط عليه مش عدل بيميل بزاوية 35
+
+107
+00:09:34,860 --> 00:09:41,080
+درجة شايفين الرسمة؟ إذا هو أو هي لما طارت بدأت تنزل
+
+108
+00:09:41,080 --> 00:09:45,900
+على الثلج والمسار هذا ميل  قد ايش الزاوية ميلانه؟ قال
+
+109
+00:09:45,900 --> 00:09:51,740
+لي 35 درجة قال لي هيها 35 طب احنا بمعلومات المدرسة
+
+110
+00:09:51,740 --> 00:09:55,480
+بنقدر نقول هذه الزاوية هي نفسها هذه بالتبادل ولا
+
+111
+00:09:55,480 --> 00:10:01,500
+لأ؟ إذا هذه الزاوية  قد ايش؟ 35 وين بده ينزل؟ قال
+
+112
+00:10:01,500 --> 00:10:02,920
+لي نفترض أنه بينزل هذه
+
+113
+00:10:11,160 --> 00:10:17,140
+بتقدر تقول إيه إذا هذه الزاوية في المثلث  sorry
+
+114
+00:10:17,140 --> 00:10:20,760
+سايني φ خلينا نقول واحدة واحدة كوسايني φ
+
+115
+00:10:20,760 --> 00:10:27,960
+اللي هي 35 بتساوي مجاور على وتر  المجاور X ولا لأ إذا
+
+116
+00:10:27,960 --> 00:10:38,020
+X على D cos φ بتساوي Y على D طبعا بنيجي هجيت للموضع
+
+117
+00:10:38,020 --> 00:10:46,600
+معناته بقدر أجيب هنا X final بتساوي D cos φ؟ صح
+
+118
+00:10:46,600 --> 00:10:53,860
+ولا لأ؟ طب الـY  دي  ربّاك تحت الـorigin تحت الـ
+
+119
+00:10:53,860 --> 00:10:57,640
+origin بالناقص إذا معناته بقول له هنا Y final
+
+120
+00:10:57,640 --> 00:11:06,750
+بتساوي سالب D sin φ  أفهمتوا إيه يا بنات؟ خلص إيش بده؟
+
+121
+00:11:06,750 --> 00:11:11,490
+جالي بدي D  قال لي يلّا نشوف نخبّص في القوانين اللي
+
+122
+00:11:11,490 --> 00:11:15,950
+عندنا الحركة السينية هي اللي هي قانون واحد X final
+
+123
+00:11:15,950 --> 00:11:19,910
+ناقص X initial بتساوي V initial X في T صح ولا لأ؟
+
+124
+00:11:19,910 --> 00:11:25,570
+اكتبوا قلت له ها X final ناقص X initial بتساوي V
+
+125
+00:11:25,570 --> 00:11:31,790
+initial X في T مش غيره نجي نعوض  قد ايش X final هاي
+
+126
+00:11:31,790 --> 00:11:39,210
+D cos φ وقد ايش  X initial  هاي؟ صفر قد ايش هذه؟
+
+127
+00:11:39,210 --> 00:11:44,870
+خمسة وعشرين T  هاي اللي قدرت أطلعه عليه قولوا يا خلينا
+
+128
+00:11:44,870 --> 00:11:47,050
+نجيب الزمن ما هو الزمن اللي بقدر أجيبه من هو
+
+129
+00:11:47,050 --> 00:11:51,930
+المكان مظبوط ولا سينية وصادية خلينا نجيب T بتساوي D
+
+130
+00:11:51,930 --> 00:11:56,590
+cos φ هذه D cos φ على خمسة
+
+131
+00:11:56,590 --> 00:12:01,260
+وعشرين هذه جهزناها نشوف الحركة الصادية خلصنا من
+
+132
+00:12:01,260 --> 00:12:05,200
+السينية اللي قدرنا نعمله فيه عملناه نجي لها وقال
+
+133
+00:12:05,200 --> 00:12:10,560
+والله في قانون بيقول Y final ناقص Y initial بتساوي V
+
+134
+00:12:10,560 --> 00:12:17,300
+initial  أو Y initial T ناقص نص GT تربيع ذاكرينه؟
+
+135
+00:12:17,300 --> 00:12:24,370
+ذي الله نعوض قد ايش Y final؟ سالب D sin φ
+
+136
+00:12:24,370 --> 00:12:30,530
+إذا سالب D sin 35  قد ايش Y initial؟
+
+137
+00:12:30,530 --> 00:12:38,290
+صفر بتساوي قد ايش V Y initial؟ صفر إذا بتساوي سالب
+
+138
+00:12:38,290 --> 00:12:46,290
+نص جي  قد ايش T تربيع؟ بينفعش حتى منها مش هي T نفس
+
+139
+00:12:46,290 --> 00:12:51,010
+السينية والصادية واحد إذا بدل ما تحط اللي T عوض يا
+
+140
+00:12:51,010 --> 00:12:58,690
+عمّ اعوضنا D cos 35 على خمسة وعشرين
+
+141
+00:12:58,690 --> 00:13:05,230
+كل تربيع مظبوط ولا لأ طلعوا على المعادلة إيش
+
+142
+00:13:05,230 --> 00:13:11,580
+المجهول الوحيد طلعنا D خلص السؤال نيجي نتطلع بقول
+
+143
+00:13:11,580 --> 00:13:17,060
+السالب مع السالب بيروح صح ها D D تربيع وهنا في
+
+144
+00:13:17,060 --> 00:13:27,220
+D إذا هذه D بتصير sin 35 بتساوي نص G cos تربيع 35
+
+145
+00:13:27,220 --> 00:13:38,350
+في D في D على 625 اللي هو 25 تربيع قال لي يلّا
+
+146
+00:13:38,350 --> 00:13:42,990
+وقلت له إذا D اللي بتدور عليها بتساوي هذه نص وهذه
+
+147
+00:13:42,990 --> 00:13:46,350
+625 يعني تضربها في 2 625
+
+148
+00:13:46,350 --> 00:13:49,630
+625 ألف و250 625 1250 اذا
+
+149
+00:13:49,630 --> 00:13:55,290
+ألف و 250 إذا ألف و 250 في sin
+
+150
+00:13:55,290 --> 00:14:02,730
+35 على G في cos تربيع 35  يلّا الـcalculator  طلعتها 109  صح ولا
+
+151
+00:14:07,030 --> 00:14:12,190
+لأ؟ وإذا طلعنا D  بقدر أجيب X final و Y final
+
+152
+00:14:12,190 --> 00:14:20,310
+خلاص هذا السؤال أي سفسار سهل  العملية تمام يا
+
+153
+00:14:20,310 --> 00:14:25,130
+بنات؟ هي حركة المقذوفات حركة المقذوفات حركة مهمة
+
+154
+00:14:25,130 --> 00:14:30,040
+وبتنط في كثير امتحانات كأسئلة  إيش كيف نشتغل
+
+155
+00:14:30,040 --> 00:14:32,760
+عليها؟ إيش الاستراتيجية؟ بقوله أول حاجة بدي أجسمها
+
+156
+00:14:32,760 --> 00:14:36,520
+حركتين سينية وصادية بروح بتطلع على المعطيات
+
+157
+00:14:36,520 --> 00:14:40,000
+المعطى السيني بحطه تحت السيني والصادي بحطه تحت
+
+158
+00:14:40,000 --> 00:14:44,240
+الصادي اللي لا هو سيني ولا هو صادي بدي أجسمه أحلله
+
+159
+00:14:44,240 --> 00:14:47,640
+إلى مركبة سينية ومركبة صادية وبعدين بدي أشتغل
+
+160
+00:14:47,640 --> 00:14:51,420
+إيش بدك؟ بدي مسافة سينية بروح أقارن السينية بدي
+
+161
+00:14:51,420 --> 00:14:55,390
+مسافة صادية بروح أقارن الصادية بدي زمن  انتحار روح
+
+162
+00:14:55,390 --> 00:14:58,310
+سيني أو روح صادي صح ولا لأ؟ وبنشتغل على هذه
+
+163
+00:14:58,310 --> 00:15:06,610
+الأساس تمام إذا أول حاجة جيب لي X final و Y final من
+
+164
+00:15:06,610 --> 00:15:10,710
+القانون اللي بنعرفه وبعدين  ده اللي في عندي X
+
+165
+00:15:10,710 --> 00:15:14,210
+final ناقص X initial اللي هي صفر بتساوي X initial
+
+166
+00:15:14,210 --> 00:15:20,430
+في T  طلّع لي إياها عوض ومنها بقدر أجيب T وأستخدم قانون
+
+167
+00:15:20,430 --> 00:15:25,250
+الـY بنفس الكيفية على اعتبار أن VY initial صفر
+
+168
+00:15:25,250 --> 00:15:32,450
+طلّعها قال لي Substituting  عوّض من T  هاللي
+
+169
+00:15:32,450 --> 00:15:37,090
+عملناه قال لي طلعت عندك المعادلة الحلوة هيها و
+
+170
+00:15:37,090 --> 00:15:41,210
+طلعت منها D طلعت 109 وبناء عليها جبت الـposition
+
+171
+00:15:41,210 --> 00:15:52,160
+تبع
+
+223
+00:19:51,160 --> 00:19:56,320
+although إيش معناته برغم من أنّه the speed is
+
+224
+00:19:56,320 --> 00:20:01,550
+constant،لسبيت constant  يجي واحد يقول لك الـ speed
+
+225
+00:20:01,550 --> 00:20:05,630
+constant، الـ acceleration يساوي صفر، لأ، لأنّ الـ
+
+226
+00:20:05,630 --> 00:20:10,990
+acceleration بتتبعش الـ speed، بتتبع الـ velocity، بيقول
+
+227
+00:20:10,990 --> 00:20:15,350
+although the speed is constant، We have an
+
+228
+00:20:15,350 --> 00:20:19,950
+acceleration. من وين إجت؟ It's due to the change
+
+229
+00:20:19,950 --> 00:20:23,050
+of the direction of the velocity. إذن، في عندي
+
+230
+00:20:23,050 --> 00:20:27,690
+تسارع بينتج فقط من تغير الـ direction تبع
+
+231
+00:20:27,690 --> 00:20:33,170
+الـ velocity. طب هذا إيش صفاته؟ قال لي هذا إله اشتقاق
+
+232
+00:20:33,170 --> 00:20:37,190
+مش مطموض بإنه في هذا المستوى. لو اشتقيت هذا التسارع
+
+233
+00:20:37,190 --> 00:20:39,970
+اللي جاي من تغير الـ direction، حيكون اتجاهه باتجاه
+
+234
+00:20:39,970 --> 00:20:44,580
+المركز. اتجاه التسارع كيف؟ باتجاه المركزي، بيقول
+
+235
+00:20:44,580 --> 00:20:49,040
+this acceleration is directed اتجاهها towards the
+
+236
+00:20:49,040 --> 00:20:52,780
+center، طب واحد باتجاه الـ center إيش هسميه؟ قالوا
+
+237
+00:20:52,780 --> 00:20:57,100
+سمّوه مركزي عشان ما حد يخربط فيه، ليش مركزي؟ لأنّ
+
+238
+00:20:57,100 --> 00:21:01,540
+اتجاهه باتجاه مين؟ المركز، تمام؟ طبعاً اتفقنا أنّه
+
+239
+00:21:01,540 --> 00:21:05,180
+إثبات رياضي، بس لسه شوية مهل عليكم عشان نديكم
+
+240
+00:21:05,180 --> 00:21:09,120
+إثباته في سنة ثانية، بصيروا تقدروا تعملوا له إثبات
+
+241
+00:21:09,120 --> 00:21:13,650
+تفصيلي، تمام، centripetal acceleration يعني تسارع
+
+242
+00:21:13,650 --> 00:21:19,550
+مركزي، and is given by، طب كيف مقداره؟ قالوا برضه هذه
+
+243
+00:21:19,550 --> 00:21:23,050
+الإثبات الرياضي بيطلع لك المقدار بيساوي V تربيع على
+
+244
+00:21:23,050 --> 00:21:26,230
+R، ذاكرين لما خدنا الـ dimensions وقلنا لكم هذا
+
+245
+00:21:26,230 --> 00:21:31,810
+التسارع المركزي إثبات
+
+246
+00:21:31,810 --> 00:21:36,880
+الهندسي مش الرياضي، الإثبات الهندسي اللي أخدته صحيح،
+
+247
+00:21:36,880 --> 00:21:40,080
+بعرف اللي هو، عشان كده لأ، أنا جاي بهدا و لأ أنا جاي
+
+248
+00:21:40,080 --> 00:21:43,460
+بهدا اللي أخدته في المدرسة سهل، وبالتالي كبرتوا
+
+249
+00:21:43,460 --> 00:21:45,920
+عليه، واللي أخدت.. اللي بتاخدوه رياضي لسه أنتو
+
+250
+00:21:45,920 --> 00:21:52,140
+بدري عليكم، الإثبات الرياضي حلو، A C C يعني
+
+251
+00:21:52,140 --> 00:21:56,680
+centripetal، صح ولا لأ؟ طيب احنا أخدنا رموز كثيرة، A
+
+252
+00:21:56,680 --> 00:22:03,860
+X إيش يعنيه؟ سينية، طب و Y صادية، طب لو كتبت لك هيك
+
+253
+00:22:03,860 --> 00:22:12,640
+إيش بتتوقع هذه R؟ ذاكرين الإحداثيات القطبية كان
+
+254
+00:22:12,640 --> 00:22:18,280
+فيها R و θ، R يعني نص قطر، عمركم سمعتوا نص قطر؟ بومرش
+
+255
+00:22:18,280 --> 00:22:22,320
+في المركز، إذن المراد اللي ما أقول مركزي بيكتبوها R
+
+256
+00:22:23,130 --> 00:22:27,630
+مش نفس الشيء، أو ولا في نص قطر بيمر في المركز، إذن
+
+257
+00:22:27,630 --> 00:22:31,670
+المرات هنكتبها R، و المرات هنكتبها C، واحدة ولا لأ؟
+
+258
+00:22:31,670 --> 00:22:35,070
+واحدة، نفس العملية، بدأ ما أكتب X و Y، بدأ أكتب R
+
+259
+00:22:35,070 --> 00:22:39,290
+وقعدنا هنكتب كمان فيتا اللي أنتو عارفينها، كما
+
+260
+00:22:39,290 --> 00:22:44,920
+شايفين الأسهم الخضراء الخضراء الخضراء؟ هدول اتجاه
+
+261
+00:22:44,920 --> 00:22:48,420
+التسارع، كلهم باتجاه المركز ولا لأ؟ لكن مرة صيني و
+
+262
+00:22:48,420 --> 00:22:53,420
+مرة شادي، شايفينها؟ تتغير تماماً حسب النقطة، المهم
+
+263
+00:22:53,420 --> 00:23:00,080
+تكون باتجاه المركز، أحسن شوية، لسه بدل علينا هذا
+
+264
+00:23:00,080 --> 00:23:06,080
+بدنا نيوتن، آه، لسه نيوتن مش في طريق اللي وراه، تمام؟
+
+265
+00:23:06,080 --> 00:23:11,260
+حلو، بس مهل، واحدة واحدة بنمشي، دادة دادة، هذا نيوتن
+
+266
+00:23:11,260 --> 00:23:15,570
+هيك بيقولوا، لسه عن نيوتن ما جيناهوش، و أنا قلت ما هو
+
+267
+00:23:15,570 --> 00:23:20,450
+المظبوط، بس أنا قلت هيك، حكيتها، بس هو أصلاً مش أنا
+
+268
+00:23:20,450 --> 00:23:23,830
+اللي قلتها، نيوتن اللي جابها، عفواً، بتساوي m a، صحيح،
+
+269
+00:23:23,830 --> 00:23:30,890
+تمام، تمام، ده اللي ما زال في حركة دائرية، و الدائرة
+
+270
+00:23:30,890 --> 00:23:35,590
+بتخليها تلف ولا لأ؟ في تكرار، ما زال في تكرار
+
+271
+00:23:35,590 --> 00:23:37,810
+في المادة اللي أخدنا منها كمّاً من المصطلحات، بدي نعيده
+
+272
+00:23:37,810 --> 00:23:43,230
+احنا وياكم عارفينها، في تردد و زمن دوري، سمعتوا
+
+273
+00:23:43,230 --> 00:23:47,470
+فيهم؟ و هدول مرتبطين بالحركة الدائرية و الحركة
+
+274
+00:23:47,470 --> 00:23:52,310
+المتكررة، بنسميها، تمام؟ قال لي إيش تعريف الزمن الدوري؟
+
+275
+00:23:53,290 --> 00:23:58,230
+هو عبارة عن زمن الدورة الواحدة، مشاكل اتفجنا، تمام،
+
+276
+00:23:58,230 --> 00:24:02,730
+هاي الزمن الدوري، then the period، اللي هو الزمن
+
+277
+00:24:02,730 --> 00:24:06,630
+الدوري، يعني اللي رمزه capital T، is defined as the
+
+278
+00:24:06,630 --> 00:24:09,990
+time needed، هو الزمن اللازم، for the particle to
+
+279
+00:24:09,990 --> 00:24:14,110
+complete one revolution، revolution دورة، من يقول
+
+280
+00:24:14,110 --> 00:24:20,700
+يجي، إيش مسافة الدورة؟ 2πR، 2πR، هذي الزاوية تبعته، لكن
+
+281
+00:24:20,700 --> 00:24:25,280
+المسافة محيط، مضبوط، محيط، قال لي في أي بي تويتر قول لي
+
+282
+00:24:25,280 --> 00:24:29,540
+الزمن الدورة بيساوي مسافة الدورة على السرعة، ولا لأ؟
+
+283
+00:24:29,540 --> 00:24:36,420
+هذا هي مسافة الدورة اللي هو المحيط، أسرة، طيب إيش
+
+284
+00:24:36,420 --> 00:24:40,280
+مرتبط بالزمن الدوري؟ معكوس الزمن الدوري، التردد،
+
+285
+00:24:40,280 --> 00:24:44,760
+التردد، قالوا الـ frequency، the reciprocal، يعني
+
+286
+00:24:44,760 --> 00:24:48,380
+معكوس، reciprocal، يعني واحد على X، هذا مسمّيه
+
+287
+00:24:48,380 --> 00:24:51,460
+reciprocal، the reciprocal of the period is called
+
+288
+00:24:51,460 --> 00:24:54,620
+the frequency، which is defined as the number of
+
+289
+00:24:54,620 --> 00:24:58,660
+revolutions in one second، حاجات لما نقول وحدة التردد
+
+290
+00:24:58,660 --> 00:25:04,640
+في المدرسة كذا دورة أو كذا دورة في الثانية، مش
+
+291
+00:25:04,640 --> 00:25:09,040
+هيكون نكتب، أو years، كذا دورة في الثانية، والدورة
+
+292
+00:25:09,040 --> 00:25:12,200
+احنا عارفينها، طب أنا بدي دورة، بدي وحدة جديدة،
+
+293
+00:25:12,200 --> 00:25:19,900
+Radian، هو الدورة كم Radian؟ الدورة كم Radian؟ مش
+
+294
+00:25:19,900 --> 00:25:24,720
+تقول 360 درجة، 360، 2π، إذن عشان يتحول من دورة لكل ثانية إلى radian لكل ثانية
+
+295
+00:25:24,720 --> 00:25:32,360
+ضرب ليه في 2π، صحيح؟ إذن معناته بيقول لي because
+
+296
+00:25:32,360 --> 00:25:37,100
+when revolution، كل دورة، equals 2π radian، ليه 360
+
+297
+00:25:37,100 --> 00:25:42,080
+درجة، تمام، the angular speed، هو frequency جيد، بس
+
+298
+00:25:47,060 --> 00:25:50,540
+متعرف عليه برمز جيد، Omega، اسمه الـ Omega، أديكم
+
+299
+00:25:50,540 --> 00:25:56,160
+الرمز تبعه، سمعتوا في Omega هذه؟ Small Omega، بس هو
+
+300
+00:25:56,160 --> 00:25:58,980
+اتنين بقى في الـ frequency، ليه ضربتوا في اتنين بقى؟
+
+301
+00:25:58,980 --> 00:26:02,920
+عشان أحوّل من دورة لكل ثانية إلى radian لكل ثانية،
+
+302
+00:26:02,920 --> 00:26:05,600
+طب و الـ frequency مجردة بقى بالزمن، واحد على
+
+303
+00:26:05,600 --> 00:26:07,740
+اتنين، هاد يكونها المعلومات تحت المجلة، بس أنا بس
+
+304
+00:26:07,740 --> 00:26:13,620
+بتذكر حالنا فيها، تمّ، قال لي حلو، أنت إيش جبت لي حسب
+
+305
+00:26:13,620 --> 00:26:17,520
+هذا القانون، Omega، بيساوي V على R، و توّ قلت لي هادي
+
+306
+00:26:17,520 --> 00:26:22,950
+اللي هي A C بتساوي V تربيع على R، ولا لأ؟ حطّوا لي بدل
+
+307
+00:26:22,950 --> 00:26:27,530
+V، Omega في R، ما هي دي بتصير Omega تربيع R تربيع على
+
+308
+00:26:27,530 --> 00:26:31,810
+R، بتصير Omega تربيع في R، الشيء Omega ده اللي
+
+309
+00:26:31,810 --> 00:26:35,290
+بيسمّوها مرات سرعة زاوية، عشان نميّز بينها و بين الـ
+
+310
+00:26:35,290 --> 00:26:38,650
+frequency العادي، لكن لما نكبّر بنقول عنها frequency
+
+311
+00:26:38,650 --> 00:26:43,290
+برضه هي frequency، هي تردد زاوية، تمام، عشان نميّزه عن
+
+312
+00:26:43,290 --> 00:26:44,170
+الـ frequency العادي،
+
+313
+00:26:47,340 --> 00:26:52,580
+إذن هي الكتابة اللي كتبناها، حلو، قالوا إيش في أمثلة
+
+314
+00:26:52,580 --> 00:26:58,560
+ربانية في حركات دائرية؟ احنا كنا السيارة في الضوار،
+
+315
+00:26:58,560 --> 00:27:04,040
+لكن قبل السيارة، ربنا خلق الأرض تدور حول الشمس،
+
+316
+00:27:04,040 --> 00:27:09,120
+والقمر تدور حول الأرض، والإلكترون تدور حول النواة،
+
+317
+00:27:09,120 --> 00:27:14,860
+صح ولا لأ؟ هذي حركات ربانية، وعندكم علم أنّ علم الفلك من
+
+318
+00:27:14,860 --> 00:27:19,390
+أقدم العلوم، صحيح؟ شوفوا من وقتاش، من أيام سيدنا
+
+319
+00:27:19,390 --> 00:27:23,010
+إبراهيم.. ذاكرين الجدال اللي كان بينه و بين ربه، و
+
+320
+00:27:23,010 --> 00:27:26,170
+حاجة إبراهيم ربه، كل ما شاف القمر و شاف الشمس،
+
+321
+00:27:26,170 --> 00:27:31,050
+الإنسان بطبيعته دائماً بيحب يصطلع الكون اللي حواليه،
+
+322
+00:27:31,050 --> 00:27:36,010
+يعني بيصحى الواحد بيلاقيه إنّه طلعت الشمس، عادت صارت
+
+323
+00:27:36,010 --> 00:27:40,270
+شوبة، بعدين عولت بردت، بعدين غابت الشمس، صح ولا؟
+
+324
+00:27:40,270 --> 00:27:44,470
+فالإنسان قاعد يقعد يفكر، وبعدين هذا قمر، مرة بتصير
+
+325
+00:27:44,470 --> 00:27:49,210
+بضوء في الليل و مرة بتطفي، إذن هذا العلم من زمان،
+
+326
+00:27:49,210 --> 00:27:55,510
+الإنسان بدوّر عليه، و الآن أصبح شبه يقيني، عشان كده
+
+327
+00:27:55,510 --> 00:28:00,010
+جوالاتنا معانا، صح ولا لأ؟ و بنفتح الجزيرة، من وين
+
+328
+00:28:00,010 --> 00:28:03,710
+بتبث الجزيرة؟ من الدوحة، و بنفتح العربية بتبث من
+
+329
+00:28:03,710 --> 00:28:07,990
+دبي، و بنفتح، و بنفتح، كل هذا من وين إجا؟ قال لي والله
+
+330
+00:28:07,990 --> 00:28:11,530
+لا والله، أقمار الصناعية مش موجودة، لا معانا جوالات
+
+331
+00:28:11,530 --> 00:28:16,250
+ولا بنعرف نتفرج على أي محطة، تمام؟ إذن كل هذه
+
+332
+00:28:16,250 --> 00:28:22,390
+التكنولوجيا مبنية على علم جديد، اسمه علم الفلك، تمام،
+
+333
+00:28:22,390 --> 00:28:27,010
+و صار يقيني، مرات بتسمعوا أنّه بيصير عندنا كسوف أو
+
+334
+00:28:27,010 --> 00:28:32,070
+خسوف، و بيصير فيه إعلانات، و كل الناس بتصدق و
+
+335
+00:28:32,070 --> 00:28:35,670
+الحكومة بتصدق، و بتعمل احتياطاتها، ولا لا؟ بيقول لك
+
+336
+00:28:35,670 --> 00:28:39,130
+الكسوف بده يبدأ الساعة اتنين و عشر دقائق و
+
+337
+00:28:39,130 --> 00:28:42,670
+خمسة و عشرين ثانية، تصوّروا، ليش؟ اللي اتطلع عليه قعد
+
+338
+00:28:42,670 --> 00:28:47,670
+متأكد من صحّته، صح؟ إذن الحسابات دقيقة، بيقول لك هذا بيرجع
+
+339
+00:28:47,670 --> 00:28:51,130
+و قال لي ربع الساعة و اتخلص، وبعد ما عنصر جاب بعد ربع
+
+340
+00:28:51,130 --> 00:28:56,350
+الساعة ولا كأنه صار إيش؟ إذا صار عندنا من المعلومات
+
+341
+00:28:56,350 --> 00:29:03,500
+العلمية اللي وصلت إلى درجة اليقين، هي نجي، قال لي من
+
+342
+00:29:03,500 --> 00:29:07,480
+ضمن.. طبعاً احنا بنعرف في آية بتقول الشمس و القمر
+
+343
+00:29:07,480 --> 00:29:11,300
+بحسبها، الها حساباته ولا مالهاش حسابات؟ الها حساباته،
+
+344
+00:29:11,300 --> 00:29:16,340
+و الإنسان توصّل لحساباتها، بيقول the earth الأرض
+
+345
+00:29:16,340 --> 00:29:22,260
+revolves، بتدور، around the sun، حول الشمس، in an
+
+346
+00:29:22,260 --> 00:29:26,800
+orbit، بيقول يفترض أنّه دائرة، هو طبعاً بمدار بيكون
+
+347
+00:29:26,800 --> 00:29:32,130
+لكن أنا بعتبره دائرة تقريباً، نص قطر الدوران اللي هي
+
+348
+00:29:32,130 --> 00:29:35,670
+المسافة بين مركز الأرض إلى مركز الشمس، one point
+
+349
+00:29:35,670 --> 00:29:40,590
+five ten to power eleven متر، يعني حوالي مئة و خمسين
+
+350
+00:29:40,590 --> 00:29:46,870
+مليون كيلومتر، اتخيّل أنت، عادي تمّه.. روح طلع لك رحلة
+
+351
+00:29:46,870 --> 00:29:51,070
+من هون للشمس، وكتشوف، وكتنفكّ الاتصال تمّه.. and
+
+352
+00:29:51,070 --> 00:29:56,700
+complete one revolution، بكمل دورة كاملة كل سنة،
+
+353
+00:29:56,700 --> 00:30:00,300
+معلومة بنعرفها ولا لأ؟ ماشي، احنا شهر يناير، واحد
+
+354
+00:30:00,300 --> 00:30:03,760
+يناير، بعد سنة، نصير واحد يناير، معناته إنّ رجعت
+
+355
+00:30:03,760 --> 00:30:09,780
+الأرض لنفس النقطة اللي كانت منها للشمس، إذن كل سنة
+
+356
+00:30:09,780 --> 00:30:14,580
+الأرض بتكمل دورة واحدة، إذن هذا زمن دوري ولا لا
+
+357
+00:30:14,580 --> 00:30:18,160
+تبع الأرض؟ مش هي تعريف الزمن الدوري؟ الزمن الدوري
+
+358
+00:30:18,160 --> 00:30:21,540
+هو الزمن اللازم عشان أكمل دورة كاملة، في هذه الحالة،
+
+359
+00:30:21,540 --> 00:30:26,940
+القمر، الأرض بتكون لفت 360 درجة ولا لأ؟ 360 درجة
+
+360
+00:30:26,940 --> 00:30:32,980
+لفت، تمام؟ قال لي إيش بدك؟ قال لي بدي.. آه الأرض
+
+361
+00:30:32,980 --> 00:30:38,320
+بتعمل حركة دائرية، بنفع ما يكون لها تسارع إلا يكون
+
+362
+00:30:38,320 --> 00:30:42,000
+لها تسارع، بيقول أوجده، بيقول أوجده، what is the
+
+363
+00:30:42,000 --> 00:30:44,930
+centripetal acceleration of the earth؟ المثال اللي
+
+364
+00:30:44,930 --> 00:30:49,010
+ورا، أو المطبوع الثاني، قال لي فلتة من الأرض، نشوف كيف
+
+365
+00:30:49,010 --> 00:30:52,490
+بيصير رمضان و بيصير عيد و بيصير حج و بيصير بداية أشهر
+
+366
+00:30:52,490 --> 00:30:56,470
+و بتختلفوا، المسلمين، هذا صام وهذا ما صامش، مظبوط ولا
+
+367
+00:30:56,470 --> 00:31:02,130
+لأ؟ نشوف كيف احنا بنبدأ أشهرنا العربية؟ قالوا حسب
+
+368
+00:31:02,130 --> 00:31:06,070
+القمر، صح؟ طب القمر إيش بتحرك؟ قال لي والله حركة
+
+369
+00:31:06,070 --> 00:31:10,990
+معروفة، و ربنا خلقها، Find the acceleration of the
+
+370
+00:31:10,990 --> 00:31:15,890
+moon، آه، لأنّ الـ moon بيدور حوالي الأرض، تمام، بيقول لي
+
+371
+00:31:15,890 --> 00:31:18,210
+the moon towards the earth if the moon revolves
+
+372
+00:31:18,210 --> 00:31:22,670
+يدور، about the earth in an orbit، برضه في مدار، of
+
+373
+00:31:22,670 --> 00:31:25,550
+average radius، نص قطره، أظنّ هذه متر، مش كيلومتر،
+
+374
+00:31:25,550 --> 00:31:29,960
+بالخاطر، آه، هنا محطوطة كده لمكان، مش مشكلة، and mix
+
+375
+00:31:29,960 --> 00:31:35,100
+و بيعمل دورة كاملة، تشوفوا الأرض بتعمل كل سنة دورة،
+
+376
+00:31:35,100 --> 00:31:41,660
+القمر بيعمل كل شهر دورة، كل شهر، تطلع الشهر إيه كم
+
+377
+00:31:41,660 --> 00:31:47,900
+يوم؟ حاطّ، عمركم ما سمعتوا في شهر عربي 27 يوم ولا
+
+378
+00:31:47,900 --> 00:31:56,100
+28، عربي، عربي، ثمّ 28 يوم،
+
+380
+00:32:00,410 --> 00:32:07,110
+أنت بتعرف ما يسمّى أشهر عربية؟ محرم
+
+381
+00:32:07,110 --> 00:32:11,930
+و صفر و جمادى و ربيع و رمضان و شوال، هاي الأشهر
+
+382
+00:32:11,930 --> 00:32:16,090
+العربية، خلّيني أسألك، و أسأل أمّك و أبوك، عمّك، خالتك،
+
+383
+00:32:16,090 --> 00:32:22,450
+28 يوم؟ لأ، إمّا تسعة و عشرين أو تلاتين، صح؟ ليش بتحطّ لي
+
+384
+00:32:22,450 --> 00:32:26,330
+أنت سبعة و عشرين؟ هذا زمن دوري، المفروض يكون شهره
+
+385
+00:32:26,330 --> 00:32:30,270
+قدّم نحكي عنه، ليش هذا السبعة و عشرين؟ و كيف يصير
+
+386
+00:32:30,270 --> 00:32:35,230
+الشهر العربي إمّا تسعة و عشرين أو تلاتين؟ طيب، قال لي
+
+387
+00:32:35,230 --> 00:32:38,35
+
+445
+00:37:33,970 --> 00:37:38,970
+هذا التسارع الفلكي، هذا التسارع الفلكي
+
+446
+00:37:38,970 --> 00:37:44,970
+معلومات ثقافية أكثر، نجيء لهذا، ونرجع إليه نحن عشان
+
+447
+00:37:44,970 --> 00:37:51,250
+يبدأ الشهر العربي، لازم ينولد الهلال، بنسميه ولادة
+
+448
+00:37:51,250 --> 00:37:55,980
+الهلال، سمعتوا في هذا المصطلح؟ تمام، إيش معنى ولادة
+
+449
+00:37:55,980 --> 00:38:01,220
+الهلال؟ إنه لازم القمر يكون ما بين الأرض والشمس
+
+450
+00:38:01,220 --> 00:38:06,440
+على خط واحد، يعني هي الشمس شايفينها؟ هي مركزها، هي
+
+451
+00:38:06,440 --> 00:38:09,420
+مركز القمر، وهي مركز الأرض، لازم يكون في خط مستقيم
+
+452
+00:38:09,420 --> 00:38:16,420
+في هذه اللحظة، بقول إن ولد الهلال، إذا بدأ الشهر
+
+453
+00:38:16,420 --> 00:38:23,120
+فلكيًا، عشان يبدأ شرعيًا، في الحديث: صوموا لرؤيته، أفطروا لرؤيته
+
+454
+00:38:23,120 --> 00:38:26,920
+ولا رئيته، ذاكرينه؟ إذا لازم أشوف القمر طبعًا في
+
+455
+00:38:26,920 --> 00:38:32,260
+هذه اللحظة، القمر لا يراه لأن أشعة الشمس محجوبة
+
+456
+00:38:32,260 --> 00:38:37,000
+والأرض بتحجب القمر، تمام، كيف بدي أشوفه؟ هو القمر
+
+457
+00:38:37,000 --> 00:38:43,240
+بدي يلف، بدي يلف، هذه اللحظة لحظة اقتران أو ولادة
+
+458
+00:38:43,240 --> 00:38:47,760
+الهلال، هي لحظة ثابتة على جميع العالم، ولا واحد
+
+459
+00:38:47,760 --> 00:38:52,860
+بيختلف فيه، ربيعي الأول اللي إحنا فيه، كانت لحظة
+
+460
+00:38:52,860 --> 00:38:57,320
+ولادته موجودة بالساعة والدقيقة والثانية، وما فيش
+
+461
+00:38:57,320 --> 00:39:03,000
+عليها خلاف، ربيعي الثاني، بخشّ عنّه، بقول... بقول ليه
+
+462
+00:39:03,000 --> 00:39:07,820
+وقتيش بالظبط هيولد الهلال، هجيت بدينا ربيعي الأول
+
+463
+00:39:07,820 --> 00:39:12,880
+وبعد الشهر يمشي القمر، بدي يمشي القمر، بيمشي، بيمشي
+
+464
+00:39:12,880 --> 00:39:18,230
+بيمشي، وصل هنا، هجيت كمل دورة كاملة، أكمل زاوية ماشية
+
+465
+00:39:18,230 --> 00:39:23,630
+360 درجة، مش هي دورة كاملة، جالي حلو، جديش استهلك يوم
+
+466
+00:39:23,630 --> 00:39:27,370
+جالي سبعة وعشرين وثلاثة أرباع يوم، اللي مكتوب عندكم سبعة و
+
+467
+00:39:27,370 --> 00:39:31,330
+عشرين وثلاثة أرباع يوم، جالي، طب هيّا أكمل دورة كاملة، إن
+
+468
+00:39:31,330 --> 00:39:35,290
+ولد الهلال، تبقى الشهر القادم، بقول له: ليه؟ قال لي
+
+469
+00:39:35,290 --> 00:39:38,630
+لأنه مش عم يمشي في المستوى، ليه؟ قال لي: هو الأرض بتفكر
+
+470
+00:39:38,630 --> 00:39:41,410
+في السّنة وأنت بتمشي يا قمر؟ هي الأرض، ده، ده
+
+471
+00:39:41,410 --> 00:39:46,210
+السّنة والبداية كلو، البداية كلّها أو كام يوم
+
+472
+00:39:46,210 --> 00:39:48,550
+القمر قعد بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+473
+00:39:48,550 --> 00:39:48,630
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+474
+00:39:48,630 --> 00:39:49,090
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+475
+00:39:49,090 --> 00:39:49,790
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+476
+00:39:49,790 --> 00:39:53,470
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+477
+00:39:53,470 --> 00:39:58,210
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+478
+00:39:58,210 --> 00:40:06,510
+بـ بـ بـ بـ بـ بـ بـ
+
+479
+00:40:06,510 --> 00:40:14,530
+بـ
+
+480
+00:40:14,710 --> 00:40:18,190
+إذن، عشان كده سبعة وعشرين وشويا وكمان يومين وشويا
+
+481
+00:40:18,190 --> 00:40:22,830
+صاروا تسعة وعشرين وشويا، تسعة وعشرين وشويا، هي تسعة
+
+482
+00:40:22,830 --> 00:40:27,310
+وعشرين، عشان
+
+483
+00:40:27,310 --> 00:40:30,850
+كده بيقول الشهر إما تسعة وعشرين أو ثلاثين، ولازم
+
+484
+00:40:30,850 --> 00:40:34,960
+الثلاثينات يكونوا أكثر من التسعة والعشرين، لأن فيه
+
+485
+00:40:34,960 --> 00:40:40,700
+أكثر من الخمسة، لو هذه... كنت بحط رجل على رجل وب
+
+486
+00:40:40,700 --> 00:40:45,860
+بقول ما حد يستطلق شهر رمضان ثلاثين، إذا شوال تسعة و
+
+487
+00:40:45,860 --> 00:40:48,980
+عشرين، إذا نزل قعدة ثلاثين، إذا اللي وراه تسعة و
+
+488
+00:40:48,980 --> 00:40:53,560
+عشرين، مظبوط، لا تصير واحد واحد، بس ما حسن الحظ إن هنا
+
+489
+00:40:53,560 --> 00:40:58,620
+فيه أرقام، وبالتالي رمضان مرة بيكون ثلاثين ومرة
+
+490
+00:40:58,620 --> 00:41:05,680
+بيكون تسعة وعشرين، تمام؟ طبعًا، ولا ممكن هدول لما
+
+491
+00:41:05,680 --> 00:41:10,920
+يخربطوا البني آدمين اللي ما بيفهموش، هم بيخلّوا واحد
+
+492
+00:41:10,920 --> 00:41:17,420
+ثلاثين، أما إحنا شهرنا العربي لازم يكون إما تسعة و
+
+493
+00:41:17,420 --> 00:41:23,140
+عشرين أو ثلاثين، ولازم يكون عدد الشهور اللي ثلاثين
+
+494
+00:41:23,140 --> 00:41:27,680
+أكثر من عدد الشهور التسعة والعشرين، لأن هذه تسعة و
+
+495
+00:41:27,680 --> 00:41:31,960
+عشرين، وأكثر من النصف، معناته أنت أقرب للثلاثين من
+
+496
+00:41:31,960 --> 00:41:35,360
+التسعة والعشرين، فلازم عشان كده هذا الكلام اللي توي
+
+497
+00:41:35,360 --> 00:41:39,720
+حكيته، بيقول لي: note that in the period، لما لفّ هذا
+
+498
+00:41:39,720 --> 00:41:46,260
+أكمل دورة كاملة، الأرض دورت ثابتة ولا اتحركت لها
+
+499
+00:41:46,900 --> 00:41:51,120
+حوالي 27 درجة، معناته يا قمر عشان تنولد من أول و
+
+500
+00:41:51,120 --> 00:41:55,680
+جديد، مطلوب إنك تمشي هذه المسافة الزاوية، وهذه بدها
+
+501
+00:41:55,680 --> 00:42:00,880
+حوالي كمان يومين وشويا، فبيطلع الشهر الحقيقي اللي
+
+502
+00:42:00,880 --> 00:42:04,200
+بنتعامل معه، طبعًا برضه معلومة ثقافية، أنتو بتعرفوا
+
+503
+00:42:04,200 --> 00:42:08,340
+وقتيش بتطلّعوا عليه، لأن فيّه... وجيت الدهر ولا المغرب
+
+504
+00:42:08,340 --> 00:42:16,900
+المغرب، ليش إحنا؟ ليش يا بنات آخر يوم في شعبان مش
+
+505
+00:42:16,900 --> 00:42:21,020
+بنبدأ نصلي التراويح؟ ليش؟ بقول له: لأنه لما يأذن
+
+506
+00:42:21,020 --> 00:42:25,180
+المغرب، بدأ رمضان، لأنه شرعًا يبدأ اليوم، يأذن
+
+507
+00:42:25,180 --> 00:42:29,360
+المغرب، شرعًا آخر يوم في رمضان بنصلي التراويح لأنه
+
+508
+00:42:29,360 --> 00:42:33,320
+لما جاء الله أكبر وأفطرنا، خلص رمضان، وبالتالي
+
+509
+00:42:33,320 --> 00:42:37,160
+التراويح بعد العشاء، خشت في اليوم، ليش دي؟ يعني اليوم
+
+510
+00:42:37,160 --> 00:42:40,220
+شرعًا اليوم الثاني بعد يأذن المغرب، يصير التالت
+
+511
+00:42:41,890 --> 00:42:47,830
+تمام؟ عشان كده هيك الشرع بنشتغل عليها، وبتطلع، بأقول
+
+512
+00:42:47,830 --> 00:42:51,770
+تقويمنا الدينية كيف بنعمل فيها، تمام؟ يعني مثلًا
+
+513
+00:42:51,770 --> 00:42:54,790
+بتعرفوا أنتو في عيد الأضحى فيه تكبيرات، إحنا
+
+514
+00:42:54,790 --> 00:42:58,310
+بنكبر في كل الصّلوات، وما كنا بنخلص بعد صلاة العصر
+
+515
+00:42:58,310 --> 00:43:01,310
+رابع يوم العيد، والمغرب، ليش بنكبر؟ ليش بيقول خلص
+
+516
+00:43:01,310 --> 00:43:05,390
+العيد؟ لأنّ قد آن المغرب، خلص العيد، خلصنا، خلصنا،
+
+517
+00:43:05,390 --> 00:43:11,440
+ما فيش داعي نكبر، تمام؟ وبالتالي هذه المعلومات لازم
+
+518
+00:43:11,440 --> 00:43:14,840
+نكون عارفينها، عشان كده بنقول، كتير بنقول، لازم اللي
+
+519
+00:43:14,840 --> 00:43:17,420
+بدّيه يتطلع يكون، يأذن المغرب عشان نشوف اليوم بدأ
+
+520
+00:43:17,420 --> 00:43:21,440
+ولا ما بدّاش، طبعًا المعلومة اللي لازم نفهمها، هجيت
+
+521
+00:43:21,440 --> 00:43:26,380
+إحنا، واجهتنا، يأذن المغرب، اليوم عندنا ستّة ونصف جول
+
+522
+00:43:26,380 --> 00:43:31,440
+ستّة ونصف، لو اتخيلتوا مدينة زي الرباط، وين موقع
+
+523
+00:43:31,440 --> 00:43:36,010
+الرباط؟ في المغرب، غرب، جوركُم على الستّة ونصف بيكون
+
+524
+00:43:36,010 --> 00:43:40,690
+المغرب قدر عندهم، بيكون لسه تقريبًا الظهر، إذا بقدر
+
+525
+00:43:40,690 --> 00:43:44,930
+المغرب بعد ثلاث ساعات، أربع ساعات، معناته لو أنا شفت
+
+526
+00:43:44,930 --> 00:43:49,490
+القمر، معناته هو شايف القمر أكيد أكثر مني، ليش؟ لأن
+
+527
+00:43:49,490 --> 00:43:52,930
+هو كمان تلت، أربع ساعات، القمر بيكون عليه، بيكون
+
+528
+00:43:52,930 --> 00:43:59,350
+ماشي، وبالتالي لازم يشوفه، لكن لو أنا قلت: يجي واحد
+
+529
+00:43:59,350 --> 00:44:04,650
+نفترض في طهران، طهران وين موقعها؟ شرق، جال، آه في إيران
+
+530
+00:44:04,650 --> 00:44:08,390
+شرق، يعني جال: والله أنا ما شفتش القمر، بقول له: استنى
+
+531
+00:44:08,390 --> 00:44:11,990
+عليا أنا، يمكن أشوفه، ليش أنت لسه... أنا المغرب تبقى
+
+532
+00:44:11,990 --> 00:44:14,590
+أنت قد مغربك، أنا لسه بدي أربع ساعات لما يجي
+
+533
+00:44:14,590 --> 00:44:18,330
+المغرب، وبالتالي لما يجي المغرب بيكون القمر كبير
+
+534
+00:44:18,330 --> 00:44:22,830
+عندي، وممكن أشوفه، المعلومة اللي بدّي أكون تعرفها، إذا
+
+535
+00:44:22,830 --> 00:44:27,900
+واحد قاعد في القاهرة، أنا ما شفتش القمر، وكان عالم
+
+536
+00:44:27,900 --> 00:44:33,280
+بمعنى صحيح، ما حد يصدق واحد في دبي أو واحد في طهران
+
+537
+00:44:33,280 --> 00:44:36,930
+يقول: أنا شفت القمر، ولا ممكن... ولا ممكن، إذا كان اللي
+
+538
+00:44:36,930 --> 00:44:41,070
+في القاهرة اللي هو غرب هذه المدن، ما شافش القمر،
+
+539
+00:44:41,070 --> 00:44:45,870
+كيف أنت شفته؟ طب أنا كان كبير لما طلعت المغرب، أنت
+
+540
+00:44:45,870 --> 00:44:50,070
+لسه قمرك صغير، كيف شفته؟ ما ينفعش، لذا هذه
+
+541
+00:44:50,070 --> 00:44:53,870
+المعلومات اللي الشيوخ الآن حسموها، أغلب الشيوخ وخصوصًا
+
+542
+00:44:53,870 --> 00:44:58,650
+القرضاوي، قال، والعلماء قالوا: القمر لم يولد،
+
+543
+00:44:58,650 --> 00:45:02,720
+ما حد يصدق واحد يقول: شفته القمر، يقول: بقى بكرة رمضان
+
+544
+00:45:02,720 --> 00:45:08,020
+ولا ممكن، هذه خلاص معلومات يقينية، لما القمر يقول: لم
+
+545
+00:45:08,020 --> 00:45:12,560
+يولد، بمعنى آخر: صار على خط واحد، هي ولادة القمر، ما زال
+
+546
+00:45:12,560 --> 00:45:18,000
+هذه المعلومة اليقينية، ما كانت موجودة ساعة المغرب
+
+547
+00:45:18,000 --> 00:45:21,300
+نفترض إن إحنا ستّة ونصف، بقول: والله هذا القمر
+
+548
+00:45:21,300 --> 00:45:25,620
+بيصير في هذا الشكل، سبعة الأرباع، معناته عند المغرب
+
+549
+00:45:25,620 --> 00:45:29,890
+بلاقي قمر، بلا قمر، لأنه مش موجود في السماء أصلًا
+
+550
+00:45:29,890 --> 00:45:33,010
+وبالتالي يجي واحد يقول: طب أنا شفت، بقول لك: شفت لك حاجة
+
+551
+00:45:33,010 --> 00:45:39,590
+تانية، الله أعلم، اللي شفته، يمكن شفت نجمة، مرات
+
+552
+00:45:39,590 --> 00:45:43,770
+طبعًا في خلاف فقهي، إحنا ما عنا نخشّ عنه، إنّه توحيد
+
+553
+00:45:43,770 --> 00:45:47,450
+المطالع أو إنّه تفرقة المطالع، إنّه كل واحد، كل واحد
+
+554
+00:45:47,450 --> 00:45:50,090
+له مطلع مختلف، إحنا ما عنا نخشّ في الأمور الشرعية
+
+555
+00:45:50,090 --> 00:45:53,640
+إنّه في الأمور العلمية، أحكي، العلماء اللي بيختلفوا
+
+556
+00:45:53,640 --> 00:45:56,560
+عليه عشان نسمّي رمضان، إن هذه ولادة القمر، هذا اللي
+
+557
+00:45:56,560 --> 00:45:59,180
+بيختلفوا عليه، الرؤية؟ لأ، لأ، لأ، ما بيختلفوش على هذه
+
+558
+00:45:59,180 --> 00:46:02,400
+اللحظة، بيختلفوا على الرؤية، لأنّهم بيقولوا: ما يكفيش
+
+559
+00:46:02,400 --> 00:46:05,860
+ولادة القمر، لأنّ الحديث بيقول: صوموا لرؤيته، وأفطروا
+
+560
+00:46:05,860 --> 00:46:09,860
+لرؤيته، والمشكلة عند الرؤية، فبيصير يقول: مين شاف
+
+561
+00:46:09,860 --> 00:46:14,560
+ومين ما شافش، وبيصير الخلاف، طبعًا أغلب البلدان حسمت
+
+562
+00:46:14,560 --> 00:46:20,930
+الأمر، وما حد بيشوف، خلاص بيحسبوها، وأنا كنت في تركيا
+
+563
+00:46:20,930 --> 00:46:25,190
+في الثمانينات، من الثمانينات، إن عمره ما حد في تركيا قال: بدنا
+
+564
+00:46:25,190 --> 00:46:29,390
+نشوف القمر، وكتش رمضان بكرة، وكتش العيد بكرة، وكتش
+
+565
+00:46:29,390 --> 00:46:34,730
+العيد الأضحى معروف، مخطّط من هجرت، لو تخشّ على تقويم
+
+566
+00:46:34,730 --> 00:46:38,170
+خليني أقول وزارة الأوقات في تركيا، كمان خمس سنوات
+
+567
+00:46:38,170 --> 00:46:43,010
+وكتش العيد معروف، ما بدهم قمر ولا حاجة، كيف؟ حسب
+
+568
+00:46:43,010 --> 00:46:47,130
+الحسابات هذه، وهذه قطعية، مش فيها خلاف، وحسب قراءة
+
+569
+00:46:47,130 --> 00:46:53,150
+شرعية موجودة عندهم، قراءة شرعية، تمام، نشوف
+
+570
+00:46:53,150 --> 00:46:56,510
+tangential
+
+571
+00:46:56,510 --> 00:47:04,090
+and radial acceleration، هلجيت؟ أي vector، أي vector
+
+572
+00:47:04,090 --> 00:47:10,030
+ممكن أحلّله إلى مركبتين متعامدتين، سينية وصادية، صح؟ طيب
+
+573
+00:47:10,030 --> 00:47:13,670
+هو ما فيش اللي السيني والصادي متعامدات، مش فيه القطبية
+
+574
+00:47:13,670 --> 00:47:18,290
+هلجيتني، القطبية فيها نصف قطر، إيش اللي دائمًا عمودي عن
+
+575
+00:47:18,290 --> 00:47:26,430
+نصف القطر؟ المماس، المماس، ولا لأ؟ هدية المماس ونصف
+
+576
+00:47:26,430 --> 00:47:30,570
+القطر، بنفع نعتبرها محاور، اللي هي المحاور القطبية
+
+577
+00:47:30,570 --> 00:47:36,030
+لأنّهم متعامدات، ولا لأ؟ إذا كلّ شغلتين متعامدتين هما
+
+578
+00:47:36,030 --> 00:47:41,440
+إحداثيات، إذا الآن التسارع، بدي أنا أحلّله إلى
+
+579
+00:47:41,440 --> 00:47:45,620
+مركبتين متعامدتين، واحدة بدي أسمّيها نصف قطرية
+
+580
+00:47:45,620 --> 00:47:51,640
+radial، وواحدة tangential، مماسية، تمام يا بنات؟ حلو
+
+581
+00:47:51,640 --> 00:47:56,640
+النصف قطرية، سمّيتها مركزية، ولا لأ؟ قلت لك هذه بتجيء
+
+582
+00:47:56,640 --> 00:48:00,160
+من وين؟ من تغير الـdirection تبع السرعة، طب الآن
+
+583
+00:48:00,160 --> 00:48:04,580
+بدي أغيّر الـspeed، إذا إيش صار متغير في السرعة؟ الـ
+
+584
+00:48:04,580 --> 00:48:11,470
+magnitude، غصّم عنهم، الـdirection، بطلّع تسارع مركزي، طب و
+
+585
+00:48:11,470 --> 00:48:16,370
+الـmagnitude، بطلّع تسارع مماسّي، بطلّع تسارع مماسّي، إذا
+
+586
+00:48:16,370 --> 00:48:21,510
+بيقول لي: if the speed، السرعة اللي بتتغيّر من البرتقال
+
+587
+00:48:21,510 --> 00:48:28,750
+اللي بتتغيّر من البرتقال
+
+588
+00:48:28,750 --> 00:48:31,470
+اللي بتتغيّر من البرتقال، اللي بتتغيّر من البرتقال، اللي
+
+589
+00:48:31,470 --> 00:48:34,110
+بتتغيّر من البرتقال، اللي بتتغيّر من البرتقال، اللي
+
+590
+00:48:34,110 --> 00:48:34,690
+بتتغيّر من البرتقال، اللي بتتغيّر من البرتقال، اللي
+
+591
+00:48:34,690 --> 00:48:34,730
+بتتغيّر من البرتقال، اللي بتتغيّر من البرتقال، اللي
+
+592
+00:48:34,730 --> 00:48:36,630
+بتتغيّر من البرتقال، اللي بتتغيّر من البرتقال، اللي
+
+593
+00:48:36,630 --> 00:48:40,110
+بتتغيّر من البرتقال، اللي بتتغيّر من البرتقال، اللي تت
+
+594
+00:48:40,490 --> 00:48:44,670
+والتسارع المركزي بينتج عن تغير the direction of
+
+595
+00:48:44,670 --> 00:48:48,170
+the velocity، دخلة المعلومة، حنسأل عليها، عشان كده
+
+596
+00:48:48,170 --> 00:48:51,430
+أنا بركز عليها، حنسأل عليها بالـQ، إزاي؟ ده اللي
+
+597
+00:48:51,430 --> 00:48:54,930
+طبّق الـtotal acceleration، مش هي المركبتين جانب
+
+598
+00:48:54,930 --> 00:48:58,230
+بجانب، مش السيني زائد الصادي، إذا المعادلة تحت
+
+599
+00:48:58,230 --> 00:49:02,690
+تكتبها هيك، النسق القطبي والمماسّي، فبكتبها بدلالة
+
+600
+00:49:02,690 --> 00:49:07,450
+الـunit vectors I وJ، أسمع، عارفينهم ولا لأ؟ بنفع
+
+601
+00:49:07,450 --> 00:49:13,490
+أحطّ I وJ، وI ملزقة بالـX، وJ ملزقة بالـY، ولا لأ؟
+
+602
+00:49:13,490 --> 00:49:16,710
+طب هجيت، لا في X ولا في Y، إذا بدنا نستحدث unit
+
+603
+00:49:16,710 --> 00:49:22,070
+vector، الجيدة إيش هي؟ إذا معناته R والـθ، إذا
+
+604
+00:49:22,070 --> 00:49:26,470
+معناته هذه تكتب، طبعًا عادة بنرجّحها، إيش الـ
+
+605
+0
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4_postprocess.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..969bce6f1de4d4f77f15da6652cdf0417e987528
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4_postprocess.srt
@@ -0,0 +1,2464 @@
+1
+00:00:05,280 --> 00:00:09,540
+طبعا يا بنات خلينا نستكمل المثال أو نعيد المثال
+
+2
+00:00:09,540 --> 00:00:15,600
+حلقنا و بدينا نحله و قلنا إنه في عندى هدف بدي
+
+3
+00:00:15,600 --> 00:00:21,640
+أصيده و هان اللي بدي أصيده بدي ينشل هال gate بدي
+
+4
+00:00:21,640 --> 00:00:26,660
+أثبت إنه عشان يقدر يصيده لازم أول ما ينش يكون على
+
+5
+00:00:26,660 --> 00:00:31,820
+نفس الخط مع الهدف قبل ما ينزل مع الهدف الثابت
+
+6
+00:00:31,820 --> 00:00:37,730
+وبالتاليقلت إنه نفترض إنه بدي نصيبه بعض هنا إذا
+
+7
+00:00:37,730 --> 00:00:42,170
+قطعا بدي يكون موضعين زي بعض ولا لأ هذا هو trick
+
+8
+00:00:42,170 --> 00:00:47,230
+السؤال قال لي حلو أنا بأقذف أنا بدي أقذف قظيفة
+
+9
+00:00:47,230 --> 00:00:53,630
+عشان نصيب بأقذف بزاوية هذه الزاوية بعتبرها θيتاوفي
+
+10
+00:00:53,630 --> 00:00:57,630
+زاوية تابعة الخط لما رسمت ونشنت اللي بدي اعتبرها
+
+11
+00:00:57,630 --> 00:01:00,830
+Alpha هجيت انا بدي اثبت ان Theta و Alpha نفس زاوية
+
+12
+00:01:00,830 --> 00:01:05,750
+ولا لأ هذا هو اللي بدي اثبته واحد قلت في عندي
+
+13
+00:01:05,750 --> 00:01:10,250
+حركتين هذا عبارة عن ال target الهدف اللي بدي أصيبه
+
+14
+00:01:10,250 --> 00:01:17,220
+وهذا ال projectile اللي هياللي قدفتها تمام هيك؟
+
+15
+00:01:17,220 --> 00:01:23,140
+حلو قولت ال target بده ينزل سقوط حر قطعي بده ينزل
+
+16
+00:01:23,140 --> 00:01:27,080
+سقوط حر وبالتالي في السقوط الحر كان في عندي قانون
+
+17
+00:01:27,080 --> 00:01:32,500
+بيقول Y final مقص Y initial بتسوي VY initial في T
+
+18
+00:01:32,500 --> 00:01:37,700
+مقص نص GT تربيع ذاكرينه؟ قولت يبدأ يشتغل فيه طبعا
+
+19
+00:01:37,700 --> 00:01:42,310
+المحاور تبعتيأنا بدي أشتغل بناءً على هيك، إن هاي
+
+20
+00:01:42,310 --> 00:01:47,430
+المحاولة هو الدنياها، إذاً معناته هي الـOrigin،
+
+21
+00:01:47,430 --> 00:01:52,610
+وبالتالي، بداية أنا أسقطت سقوط، معناته السرعة
+
+22
+00:01:52,610 --> 00:01:56,490
+الإبتدائية تبعته بديش، هذا هو الهدف، إن أنا بدي
+
+23
+00:01:56,490 --> 00:02:00,090
+أسقط و هو بدي يقذف، هو بدي يقذف بسرعة إبتدائية
+
+24
+00:02:00,090 --> 00:02:03,630
+معينة، لكن أنا الهدف بدي أن أنزل و أنزل، معناته
+
+25
+00:02:03,630 --> 00:02:10,830
+هان، هذه Zero،تمام why final وين بده المصيد و بعيد
+
+26
+00:02:10,830 --> 00:02:15,570
+هنا why final بده اعتبره why تمام اذا why final هي
+
+27
+00:02:15,570 --> 00:02:22,310
+why طب وين كان بداية المشفوق اذا ناقص H تمام
+
+28
+00:02:22,310 --> 00:02:33,250
+بتساوي سفر ناقص نص جيل لتربية صحيح احكيه اللي بدك
+
+29
+00:02:33,250 --> 00:02:42,150
+هي تمامحلو من هنا اقدرت اقول انه H بدأنا نقول H
+
+30
+00:02:42,150 --> 00:02:50,570
+هنا وهذه H صارت Y زائد نص GT تربية خلاص قفلنا هذه
+
+31
+00:02:50,570 --> 00:02:57,320
+جيبناها العلاقة نشوف المخضوفةالمقظوفة قذفتها حسب
+
+32
+00:02:57,320 --> 00:03:01,380
+الرسمة بزاوية انت اعتبرتها θيتا صح ولا لأ اذا انا
+
+33
+00:03:01,380 --> 00:03:05,720
+في المقظوفات قلت اول حاجة بقول v initial x بتساوي
+
+34
+00:03:05,720 --> 00:03:11,180
+v initial cos θ و v initial y بتساوي v initial sin
+
+35
+00:03:11,180 --> 00:03:16,880
+θ بعملها لكل حركة المقظوفات بجسم معطياتي إلى سينية
+
+36
+00:03:16,880 --> 00:03:24,110
+وصادية تمقال لي في عندك قانون برضه هنا بيقول هذا
+
+37
+00:03:24,110 --> 00:03:28,550
+ال projectile Y final نقص Y initial بيسوي VY
+
+38
+00:03:28,550 --> 00:03:32,910
+initial في T minus half GT تربيع ولا لأ نفس الشغل
+
+39
+00:03:32,910 --> 00:03:38,430
+هذا القانون الصاضي قال لي الآن Y final و الله نفس
+
+40
+00:03:38,430 --> 00:03:42,790
+ال Y ماشي التانية نقلهم نفس ال Y؟ طب initial ال
+
+41
+00:03:42,790 --> 00:03:47,750
+projectile من وين بدأ؟من صفر إذا هذا بدأ من صفر
+
+42
+00:03:47,750 --> 00:03:53,490
+بتساوي .. قدّيش هذه هيها؟ the initial sine of
+
+43
+00:03:53,490 --> 00:03:59,910
+theta نقص half GT تربيع صحيك ولا لأ؟ اتطلع انتوا
+
+44
+00:03:59,910 --> 00:04:05,740
+هنا إيش عملتنا؟ هجيت هذه Y غير عن Y هذه؟ولا نفسه
+
+45
+00:04:05,740 --> 00:04:09,440
+لأنه عشان يصيدوا بعض لازم يكون اللي هو نفسه ال Y
+
+46
+00:04:09,440 --> 00:04:14,080
+إذا معناته بصح اللي هادي أجيبها و أحطها محل هادي
+
+47
+00:04:14,080 --> 00:04:16,000
+ولا لأ إذا بقوله
+
+48
+00:04:19,450 --> 00:04:24,610
+في هاد ال TV مظبوط كلامكم تمام إذا هاد ال Y جيبها
+
+49
+00:04:24,610 --> 00:04:32,450
+هنا قلتله إذا صار H بتثاوي طلعه V initial sine
+
+50
+00:04:32,450 --> 00:04:37,750
+theta في T هاد زائد و هاد ناقص بروحوا مع بعض قاللي
+
+51
+00:04:37,750 --> 00:04:41,510
+حلو طلعتلي H قاللي إنت إيش اللي بدك تثبته؟ بدي
+
+52
+00:04:41,510 --> 00:04:44,990
+قولله بدي أثبت إن Alpha و Theta إخوة نفس الزاوية
+
+53
+00:04:44,990 --> 00:04:48,890
+قلتله طلع ليه على الرسمةبتقدر تقولي من الرسمة أن
+
+54
+00:04:48,890 --> 00:04:55,810
+تاني الألفة هي عبارة عن مقابل ع ميوّر H على X صح
+
+55
+00:04:55,810 --> 00:05:01,170
+ولا لأ؟ H و الله جبتها ده اللي كيف بدك تجيب X؟
+
+56
+00:05:01,170 --> 00:05:03,610
+قلتله X لإن البروجيكت الموشي اللي فيه قانون بيقول
+
+57
+00:05:03,610 --> 00:05:09,550
+X final نغس X initial بتسوى V initial X في T
+
+58
+00:05:09,550 --> 00:05:14,110
+ذاكرينه؟هذه الـ projectile motion القانوني الوحيد
+
+59
+00:05:14,110 --> 00:05:19,130
+في الحلقة الصينية بيقول كله طاير X final هي X اللي
+
+60
+00:05:19,130 --> 00:05:25,250
+بتقول عنها و X initial صفر اذا X و V initial X وين
+
+61
+00:05:25,250 --> 00:05:33,110
+ها هي V initial cos θ T هاي Xجالي يلّا عوّط هاي H
+
+62
+00:05:33,110 --> 00:05:38,930
+و هاي X إذا هذه بتساوي ان عوّط V initial sin θ في
+
+63
+00:05:38,930 --> 00:05:44,090
+T على V initial cos θ في T V initial مع V initial
+
+64
+00:05:44,090 --> 00:05:49,090
+راحة sin θ على cos θ تان الثيتا تان الألفة بتساوي
+
+65
+00:05:49,090 --> 00:05:53,690
+تان الثيتا إذا الثيتا هي نفس الألفة و المطلوب
+
+66
+00:05:53,690 --> 00:06:00,680
+إثباته كمان يا بنات؟هذا المثال خلصنا هانا عملتها
+
+67
+00:06:00,680 --> 00:06:06,500
+زي ما أنا كتبتها حطيت ال target على اعتبار انه في
+
+68
+00:06:06,500 --> 00:06:10,700
+falling حطيتها على المجموعة هذا هذا الحل عساس انه
+
+69
+00:06:10,700 --> 00:06:14,120
+لو مخوض عينكم في الورق و ال projector اللي هي
+
+70
+00:06:14,120 --> 00:06:20,660
+القذيفة اللي قذفتها حطيت قوامينها و بعد كده قلتبعد
+
+71
+00:06:20,660 --> 00:06:24,620
+ما حطيتها وجيبت H و X وقالت it is not from the
+
+72
+00:06:24,620 --> 00:06:27,480
+projectile that for the projectile to hit the
+
+73
+00:06:27,480 --> 00:06:30,920
+target they must have the same position لازم
+
+74
+00:06:30,920 --> 00:06:36,100
+يضربوا بعض في نفس المكان وبالتالي جيبت Y وجيبت H
+
+75
+00:06:36,100 --> 00:06:41,740
+وجيبت X ومنها قلت اذا θ هي نفس ال alpha تمام؟ وحل
+
+76
+00:06:41,740 --> 00:06:46,760
+الكتاب بين ايديكم مختلف شوية مش قضية حد خلصناه؟
+
+77
+00:06:46,760 --> 00:06:49,960
+شوف هالسؤال
+
+78
+00:06:52,820 --> 00:06:59,380
+جلي متزلج بتعرفوها رياضة التزلج بروحوا بنط و نطة و
+
+79
+00:06:59,380 --> 00:07:02,340
+بعدين في الأخر نازلين على التلج ولا مش نازلين
+
+80
+00:07:02,340 --> 00:07:07,490
+نازلين مين ننزله؟الجاذبية إذا هي projectile motion
+
+81
+00:07:07,490 --> 00:07:12,090
+لأن اللي بتحكم فيهم هي الجاذبية الأرضية و هي
+
+82
+00:07:12,090 --> 00:07:17,310
+تعريفه projectile motion جالي a sky jumper بيقفز
+
+83
+00:07:17,310 --> 00:07:26,610
+قافظ التلج leaves the sky track المسار تبع التلج
+
+84
+00:07:26,610 --> 00:07:30,810
+track مسار هو لما يفلكي المسار بس ما تشوفي الهواء
+
+85
+00:07:32,330 --> 00:07:35,470
+بقى عبث و بيروح في الهو و بعدين بنزل اذا فار
+
+86
+00:07:35,470 --> 00:07:40,890
+project الموشي leavesThe sky track moving
+
+87
+00:07:40,890 --> 00:07:47,010
+horizontally قال لي أول ما طرع أسار في الهوى طلع
+
+88
+00:07:47,010 --> 00:07:53,950
+بسرعة أفقية فقط يعني V Initial Y جديش سفر قال لي
+
+89
+00:07:53,950 --> 00:07:58,030
+هذه حركة مغظوفات وفي حركة المغظوفات احنا متعودين
+
+90
+00:07:58,030 --> 00:08:03,790
+ان نجسم الحركة لسنية وصادرية ولا لأ حلو هاي بدنا
+
+91
+00:08:03,790 --> 00:08:07,790
+نجسم هاي بدنا نقول X motion
+
+92
+00:08:11,550 --> 00:08:17,950
+Why مش الحركة الصينية والصاضية تم نجي على السؤال
+
+93
+00:08:17,950 --> 00:08:22,970
+كل حاجة معطية بتشوفها صيني ولا صاضي ولي لا هي هيك
+
+94
+00:08:22,970 --> 00:08:27,330
+ولا هي هيك بدي أحللها مش هيك اتفاقناها حلو جالي
+
+95
+00:08:27,330 --> 00:08:33,430
+قُدِفَت بسرعة أفوخية معناته V Y Initial Gradiation
+
+96
+00:08:33,430 --> 00:08:41,660
+سفرلأنه مافيش صرعة ابتدائية صادية هو قاللي صينية
+
+97
+00:08:41,660 --> 00:08:46,900
+فقط كيف عرفتي انه صينية من كلمة horizontally صحيح؟
+
+98
+00:08:46,900 --> 00:08:53,520
+V X initial قاللي و الله خمسة و عشرين هاي أول معطف
+
+99
+00:08:53,520 --> 00:09:01,250
+بتفجيني هيك؟ حلو قاللي رسمةأشون يا جلّي هذا الرصم
+
+100
+00:09:01,250 --> 00:09:03,990
+من معطيات السؤال ولا لأ؟ يا جلّي اتطلع ال origin
+
+101
+00:09:03,990 --> 00:09:07,950
+أنوة اللي مضيكيها هنا إذا هو بدأ من هنا من نقطة ال
+
+102
+00:09:07,950 --> 00:09:13,090
+origin يعني x initial قداش و y initial سفر إذا
+
+103
+00:09:13,090 --> 00:09:19,570
+بقوله x initial ها x initial سفر و y initial سفر
+
+104
+00:09:20,860 --> 00:09:24,980
+أيش بدك؟ بقولي where does اه The landing inclined
+
+105
+00:09:24,980 --> 00:09:29,320
+below her falls off with a slope of 35 degree
+
+106
+00:09:29,320 --> 00:09:34,860
+قاللي المسار اللي بتسجط عليه مش عدل بيميل بزاوي 35
+
+107
+00:09:34,860 --> 00:09:41,080
+درجة شايفين الرسمة؟إذا هو أو هي لما طارت بدى تنزل
+
+108
+00:09:41,080 --> 00:09:45,900
+على التلج والمصار هاد ميل جديه الزاوية ميلانه؟ قال
+
+109
+00:09:45,900 --> 00:09:51,740
+لي 35 درجة قال لي هيها 35 طب احنا بمعلومات المدرسة
+
+110
+00:09:51,740 --> 00:09:55,480
+بنقدر نقول هادي الزاوية هي نفسها هادي بالتبادل ولا
+
+111
+00:09:55,480 --> 00:10:01,500
+لأ؟ إذا هادي الزاوية كدهش؟ 35 وين ودها تنزل؟ قال
+
+112
+00:10:01,500 --> 00:10:02,920
+لي نفترض ان بتنزل هادي
+
+113
+00:10:11,160 --> 00:10:17,140
+بتقدر تقول إيه إذا هذه الزاوية في تاني الفاي sorry
+
+114
+00:10:17,140 --> 00:10:20,760
+سايني الفاي خلينا نقول واحدة واحدة كوسايني الفاي
+
+115
+00:10:20,760 --> 00:10:27,960
+اللي هي 35 بتساوي مجاور أواطر المجاور X ولا لأ إذا
+
+116
+00:10:27,960 --> 00:10:38,020
+X على Dcos φ بتساوي y على d طبعا بنيجي هجيت للموضع
+
+117
+00:10:38,020 --> 00:10:46,600
+معناته بقدر أجوبكم هنا x final بتساوي d cos ف؟ صح
+
+118
+00:10:46,600 --> 00:10:53,860
+ولا لأ طب ال y بس دي رباكم تحت ال origin تحت ال
+
+119
+00:10:53,860 --> 00:10:57,640
+origin بال minus إذا معناته بقوله هنا y final
+
+120
+00:10:57,640 --> 00:11:06,750
+بساوي سالب d sin فاتفجن أيه يا بنات؟ خلص ايش بده؟
+
+121
+00:11:06,750 --> 00:11:11,490
+جالي بدي دي جالي يلّا نشوف نخبص في القوانين اللي
+
+122
+00:11:11,490 --> 00:11:15,950
+عندنا الحركة السنية هي اللي هي قانون واحدة X final
+
+123
+00:11:15,950 --> 00:11:19,910
+نقص X initial بتساوي V initial X في T صح ولا لأ؟
+
+124
+00:11:19,910 --> 00:11:25,570
+اكتبوا قولتله ها X final نقص X initial بتساوي V
+
+125
+00:11:25,570 --> 00:11:31,790
+initial X في T مش غيرهنجي معاول جدّيش X فاين هاي
+
+126
+00:11:31,790 --> 00:11:39,210
+دي وهاي قصاني الفاين جدّيش هذي؟ Zero جدّيش هذي؟
+
+127
+00:11:39,210 --> 00:11:44,870
+خمسة وعشرين T هاي اللي قدرتها عليه قولوا يا خلينا
+
+128
+00:11:44,870 --> 00:11:47,050
+نجيب الزمن ما هو الزمن اللي بقدر أشحته من هو
+
+129
+00:11:47,050 --> 00:11:51,930
+المكان مظبوط ولا سيني وصاضي خلينا نجهزه T بتسوي D
+
+130
+00:11:51,930 --> 00:11:56,590
+قصين هذي الفاين خمسة وتلاتين ولا لأ على خمسة
+
+131
+00:11:56,590 --> 00:12:01,260
+وعشرين هذي جهزتهوشوف الحركة الصادرية خلصنا من
+
+132
+00:12:01,260 --> 00:12:05,200
+الصينية اللي قدرنا نعمله فيه عملناه نجيلها وقال
+
+133
+00:12:05,200 --> 00:12:10,560
+والله في قانون بيقول y final ناقص y initial سواء v
+
+134
+00:12:10,560 --> 00:12:17,300
+initial او y initial t ناقص half gt تربيه ذاكرينه؟
+
+135
+00:12:17,300 --> 00:12:24,370
+ذي الله نعوضجدّيش y final؟ سالب دي sign ال five
+
+136
+00:12:24,370 --> 00:12:30,530
+إذا سالب دي sign الخمسة و تلاتين جدّيش y initial؟
+
+137
+00:12:30,530 --> 00:12:38,290
+سفر بتساوي جدّيش دي y initial؟ سفر إذا بتساوي سالب
+
+138
+00:12:38,290 --> 00:12:46,290
+نص جي إيش أدي؟T تربية بينفعش حتى منها مش هي T نفس
+
+139
+00:12:46,290 --> 00:12:51,010
+السنية وسادية واحد اذا بدل ما تحط اللي T اعوض يا
+
+140
+00:12:51,010 --> 00:12:58,690
+عم اعوضنا دي كوسايم الخمسة وتلاتين على خمسة وعشرين
+
+141
+00:12:58,690 --> 00:13:05,230
+كل تربية مظبوذك ولا لأ طلعوا على المعادلة ايش
+
+142
+00:13:05,230 --> 00:13:11,580
+المجهول الوحيد طلعنا ديخلص السؤال نيجي نتطلع بقول
+
+143
+00:13:11,580 --> 00:13:17,060
+السالب مع السالب روحه صح ها دي دي تربيع و هنا في
+
+144
+00:13:17,060 --> 00:13:27,220
+دي اذا ها دي بتصير sin 35 بساوي نص g cos تربيع 35
+
+145
+00:13:27,220 --> 00:13:38,350
+في دي في دي على 625 اللي هو 25 تربيعجالي يلّا و
+
+146
+00:13:38,350 --> 00:13:42,990
+قولتله إذا دي اللي بتدور عليها بتثوي هذه نص و هذه
+
+147
+00:13:42,990 --> 00:13:46,350
+ستمية و خمسة و عشرين يعني تدورها في اتنين ستمية و
+
+148
+00:13:46,350 --> 00:13:49,630
+ستمية ألف و متين و خمسة و عشرين و خمسة و عشرين إذا
+
+149
+00:13:49,630 --> 00:13:55,290
+ألف و متين و خمسين إذا ألف و متين و خمسين في sin
+
+150
+00:13:55,290 --> 00:14:02,730
+الخمسة و تلاتين على جي في cosine تربيع الخمسة و
+
+151
+00:14:02,730 --> 00:14:07,030
+تلاتين يلّا ال calculator طلعتها مية و تسعةصح ولا
+
+152
+00:14:07,030 --> 00:14:12,190
+لا؟ وإذا طلعنا دي يي بقدر أجيب X final و Y final
+
+153
+00:14:12,190 --> 00:14:20,310
+خلاص هاي السؤال أي السفسار سهل العملية تمام يا
+
+154
+00:14:20,310 --> 00:14:25,130
+بنات؟ هي حركة المغضوفات حركة المغضوفات حركة مهمة
+
+155
+00:14:25,130 --> 00:14:30,040
+وبتنط في كتير امتحانات كأسئلةإيش .. كيف نشتغل
+
+156
+00:14:30,040 --> 00:14:32,760
+عليها؟ إيش الستراتيجية؟ بقوله أول حاجة بدي أجسمها
+
+157
+00:14:32,760 --> 00:14:36,520
+حركتين صينية و صادية بروح بتطلع على المعطيات
+
+158
+00:14:36,520 --> 00:14:40,000
+المعطل الصيني بحطه تحت الصيني و الصادي بحطه تحت
+
+159
+00:14:40,000 --> 00:14:44,240
+الصادي اللي لا هو صيني ولا هو صادي بدي أجسمه أحلله
+
+160
+00:14:44,240 --> 00:14:47,640
+إلى مركبة صينية و مركبة صادية و بعدين بدي أشتغل
+
+161
+00:14:47,640 --> 00:14:51,420
+إيش بدك؟ بدي مسافة صينية بروح أقارن الصينية بدي
+
+162
+00:14:51,420 --> 00:14:55,390
+مسافة صادية بروح أقارن الصادية بدي زمان انتحارروح
+
+163
+00:14:55,390 --> 00:14:58,310
+صيني أو روح صادي صح ولا لأ؟ و بنشتغل على هذه
+
+164
+00:14:58,310 --> 00:15:06,610
+الأساس تمه اذا أول حاجة جيبني X final و Y final من
+
+165
+00:15:06,610 --> 00:15:10,710
+القانون اللي بنعرفه و بعدين ده اللي في عندي X
+
+166
+00:15:10,710 --> 00:15:14,210
+final ناقص X initial اللي هي سفر بيسوي X initial
+
+167
+00:15:14,210 --> 00:15:20,430
+في T طلعليهاأعوض و منها بقدر أجيب T و استخدم قانون
+
+168
+00:15:20,430 --> 00:15:25,250
+ال Y بنفس الكيفية على اعتبار ان VY initial صفر
+
+169
+00:15:25,250 --> 00:15:32,450
+طلحها قال لي Substituting عوض من T هالها اللي
+
+170
+00:15:32,450 --> 00:15:37,090
+عملناه قال لي طلعت عندك المعادلة الحلوة هايها و
+
+171
+00:15:37,090 --> 00:15:41,210
+طلعت منها D طلعت 109 وبناء عليها جبت ال position
+
+172
+00:15:41,210 --> 00:15:52,160
+تبع الالرياضية لما نزلت على الأرض تمى أنواننا
+
+173
+00:15:52,160 --> 00:15:58,120
+التالي هو نوع من أنواع الحركة المستوية ويسمى
+
+174
+00:15:58,120 --> 00:16:04,160
+circular من circle مظبوط ولا لأ حركة دائرية كل جسم
+
+175
+00:16:04,160 --> 00:16:08,260
+بدور بقول عنه بتحرك حركة دائرية بدور تمى
+
+176
+00:16:10,360 --> 00:16:14,380
+في الشوارع يعني فيه دوارات بتعرف الدوار؟ السيارة
+
+177
+00:16:14,380 --> 00:16:17,160
+لما تخش الدوار على طول بقول صارت حركتها حركة
+
+178
+00:16:17,160 --> 00:16:21,860
+دائرية لأنها بدأت لف تمه هاجيت يا بنات في الحركة
+
+179
+00:16:21,860 --> 00:16:26,960
+الدائرية تصورولي معاه هيك في مجال واحد يتحرك حركة
+
+180
+00:16:26,960 --> 00:16:35,320
+دائرية ويخل اتجاه صرعته ثابت اتجاه صرعته هو إيش
+
+181
+00:16:35,320 --> 00:16:39,650
+لازم يسوي مش هو لازم يميل؟ لازم يظل يميلولّا لو
+
+182
+00:16:39,650 --> 00:16:44,330
+دلّه اتجاه صرعته ثابت بطلت الحركة دائرية فانا بمشي
+
+183
+00:16:44,330 --> 00:16:49,810
+خط مصطقين تمام إذا في الحركة الدائرية اتجاه الصرعة
+
+184
+00:16:49,810 --> 00:16:54,790
+دائما متغير ولا لأ؟طب حلو انشوف ايش تعريف الـ
+
+185
+00:16:54,790 --> 00:16:59,890
+acceleration معدل تغير سرعة بالنسبالي الزمن اتغيرت
+
+186
+00:16:59,890 --> 00:17:03,850
+السرعة اذا في acceleration طب في حركة دائرية مسموح
+
+187
+00:17:03,850 --> 00:17:07,470
+لل velocity تظلها ثابتة اقل ال direction تبعها
+
+188
+00:17:07,470 --> 00:17:11,230
+متغير ولا لأ لأن ال velocity عبارة عن direction و
+
+189
+00:17:11,230 --> 00:17:16,150
+speedاتغير واحد منهم، إذا هي متغيرة، اتغير التانية
+
+190
+00:17:16,150 --> 00:17:21,250
+من باب أولى، تمام، إذا في الحركة الدائرية في مجال
+
+191
+00:17:21,250 --> 00:17:26,610
+يكون مافيش تسارع، ولا ممكن، ولا ممكن، بيصير فيه
+
+192
+00:17:26,610 --> 00:17:31,210
+تناقض، كيف حركة دائرية مافيش تسارع؟طبعا؟ إذا
+
+193
+00:17:31,210 --> 00:17:35,090
+معناته إيش بيقوللي طب وقت إيش بتسميها uniform و
+
+194
+00:17:35,090 --> 00:17:39,210
+وقت إيش بتسميها non uniform بيقوللي when an object
+
+195
+00:17:39,210 --> 00:17:46,150
+أي جسم moves on a circular path مصار دائري with
+
+196
+00:17:46,150 --> 00:17:52,650
+constant speed بقدر يقول constant velocity؟بالصحيح
+
+197
+00:17:52,650 --> 00:17:56,250
+لأنه بيبقى في تناقض بالكلام بجهود لأن كيف circular
+
+198
+00:17:56,250 --> 00:18:00,150
+بيحظر في constant velocity أما constant speed مسمح
+
+199
+00:18:00,150 --> 00:18:04,050
+لك بيبقى الاشي يتغير ال direction إذا كانت ال
+
+200
+00:18:04,050 --> 00:18:08,910
+speed constant بيقول هذه حركة دائرية بس منطلمة طيب
+
+201
+00:18:08,910 --> 00:18:11,770
+وإذا ال speed مش constant بتبطى ال uniform it's a
+
+202
+00:18:11,770 --> 00:18:16,810
+non uniform circular motion if the speed is
+
+203
+00:18:16,810 --> 00:18:19,750
+constant the object is said to be in a uniform
+
+204
+00:18:19,750 --> 00:18:23,820
+circular motion طيبهذه حركة دائرية مش عادي دائرة
+
+205
+00:18:23,820 --> 00:18:29,660
+وهذا الجسم بنخليه يلف في
+
+206
+00:18:29,660 --> 00:18:33,220
+نقطة من النقاط لو بدي أرسم المماثل هي السرعة
+
+207
+00:18:33,220 --> 00:18:39,040
+اتجاهها زي جابلها ولا ممكن ولا ممكن معناته كيف
+
+208
+00:18:39,040 --> 00:18:43,520
+اتجاه السرعات بقوله اتجاه السرعات هي هيك و هيك و
+
+209
+00:18:43,520 --> 00:18:48,780
+هيك و هيك صح؟ في سهم من الأسهم الأربعة اتجاهه زي
+
+210
+00:18:48,780 --> 00:18:58,070
+أخوإذن دائما اتجاه سرعة ماله متغير تمام؟ حلو بقول
+
+211
+00:18:58,070 --> 00:19:02,010
+لي as the velocity is always tangent to the path
+
+212
+00:19:02,010 --> 00:19:05,510
+flowed طبعا دائما السرعة لازم يكون مماس انتوا
+
+213
+00:19:05,510 --> 00:19:10,330
+عارفين ان السرعة مشتقة X؟ومش تقّمعها من المماس؟
+
+214
+00:19:10,330 --> 00:19:15,050
+إذا المماس تمام وهي واضحة يعني إن واحد ماشي صرعته
+
+215
+00:19:15,050 --> 00:19:19,250
+معاه وبالتالي هو بلف صوت و بتلف معاه بقول بما إن
+
+216
+00:19:19,250 --> 00:19:24,290
+الصوعة دايما tangent مماس للمسار اللي فيه شغال
+
+217
+00:19:24,290 --> 00:19:27,730
+عليه the direction of the velocity in uniform
+
+218
+00:19:27,730 --> 00:19:32,670
+circular motion always changing دائما متغيرة إيش
+
+219
+00:19:32,670 --> 00:19:37,020
+اللي خلّها متغيرة؟ ال direction صح؟لأن انت بتغير
+
+220
+00:19:37,020 --> 00:19:39,820
+ال direction قاعدة إذا انت فاهمة ان السرعة مالها
+
+221
+00:19:39,820 --> 00:19:46,520
+متغيرة حلو اتغيرت السرعة ايش اتولد تسارق صح مازال
+
+222
+00:19:46,520 --> 00:19:51,160
+اتغيرت السرعة صار في عندك تسارق بقول لي although
+
+223
+00:19:51,160 --> 00:19:56,320
+although ايش معناته برغم من انه the speed is
+
+224
+00:19:56,320 --> 00:20:01,550
+constantلسبيت constant يجي واحد يقول لك ال speed
+
+225
+00:20:01,550 --> 00:20:05,630
+constant ال acceleration يساوي سفير لأ لأن ال
+
+226
+00:20:05,630 --> 00:20:10,990
+acceleration بتتبعش ال speed بتتبع velocity بيقول
+
+227
+00:20:10,990 --> 00:20:15,350
+although the speed is constantWe have an
+
+228
+00:20:15,350 --> 00:20:19,950
+acceleration. من وين إجت؟ It's due to the change
+
+229
+00:20:19,950 --> 00:20:23,050
+of the direction of the velocity.إذن، في عندي
+
+230
+00:20:23,050 --> 00:20:27,690
+تسارع بينتج فقط من تغير الـdirection تبع
+
+231
+00:20:27,690 --> 00:20:33,170
+الـvelocity.طب هذا إيش صفاته؟ قاللي هذا إله اشتقاق
+
+232
+00:20:33,170 --> 00:20:37,190
+مش مطموض بإنه في هذا المستوى.لو اشتقيت هذا التسارع
+
+233
+00:20:37,190 --> 00:20:39,970
+اللي جاي من تغير الـdirection، حيكون اتجاهه باتجاه
+
+234
+00:20:39,970 --> 00:20:44,580
+المركز.اتجاه التسارع كيف؟ باتجاه المركزي بيقول
+
+235
+00:20:44,580 --> 00:20:49,040
+this acceleration is directed اتجاهها towards the
+
+236
+00:20:49,040 --> 00:20:52,780
+center طب واحد باتجاه ال center ايش هسميه؟ قالوا
+
+237
+00:20:52,780 --> 00:20:57,100
+سموه مركزي عشان ما حد يخربطيه ليش مركزي؟ لأن
+
+238
+00:20:57,100 --> 00:21:01,540
+اتجاهه باتجاه مين؟ المركز تمام؟ طبعا اتفقنا انه
+
+239
+00:21:01,540 --> 00:21:05,180
+إثبات رياضي بس لسه شوية مهل عليكم عشان نديكم
+
+240
+00:21:05,180 --> 00:21:09,120
+إثباته في سنة تانية بصيروا تقدروا تعملوله إثبات
+
+241
+00:21:09,120 --> 00:21:13,650
+تفصيلي تمامcentripetal acceleration يعني تسارع
+
+242
+00:21:13,650 --> 00:21:19,550
+مركزي and is given by طب كيف مقداره قالوا برضه هذه
+
+243
+00:21:19,550 --> 00:21:23,050
+الإثبات البياضي بيطلعلك المقدار بيساوي V تربيع على
+
+244
+00:21:23,050 --> 00:21:26,230
+R ذاكرين لما خدنا ال dimensions وقلنا لكم هذا
+
+245
+00:21:26,230 --> 00:21:31,810
+التسارع المركزي إثبات
+
+246
+00:21:31,810 --> 00:21:36,880
+الهندسيمش الرياضي الإثبات الهندس اللي أخدتيه صحيح
+
+247
+00:21:36,880 --> 00:21:40,080
+بعرف اللي هو عشان كده لأ أنا جاي بهدا و لأ أنا جاي
+
+248
+00:21:40,080 --> 00:21:43,460
+بهدا اللي أخدتيه في المدرسة سهل وبالتالي كبرتوا
+
+249
+00:21:43,460 --> 00:21:45,920
+عليه و اللي أخدت .. اللي بتاخدوه رياضي لسه أنتوا
+
+250
+00:21:45,920 --> 00:21:52,140
+بدري عليكم الإثبات الرياضي حلو A C C يعني
+
+251
+00:21:52,140 --> 00:21:56,680
+centripetal صح ولا لأ طيب احنا أخدنا رموز كتيرة A
+
+252
+00:21:56,680 --> 00:22:03,860
+X إيش يعنيسينية طب و why صادية طب لو كتبتلك هيك
+
+253
+00:22:03,860 --> 00:22:12,640
+ايش بتتوقع هذه R ذاكرين الاحداثيات القطبية كان
+
+254
+00:22:12,640 --> 00:22:18,280
+فيها R و θ R يعني نص خطر عمركم سمعتوا نص خطر بومرش
+
+255
+00:22:18,280 --> 00:22:22,320
+في المركز اذا المراد اللي ما اقول مركزي بيكتبوها R
+
+256
+00:22:23,130 --> 00:22:27,630
+مش نفس الشيء او ولا في نص خطر بمرش في المركز اذا
+
+257
+00:22:27,630 --> 00:22:31,670
+المرات هنكتبها R و المرات هنكتبها C واحدة ولا لأ؟
+
+258
+00:22:31,670 --> 00:22:35,070
+واحدة نفس العملية بدأ ما اكتب X وY بدأ اكتب R
+
+259
+00:22:35,070 --> 00:22:39,290
+وقعدنا هنكتب كمان فيتا اللي انتوا عارفينها كما
+
+260
+00:22:39,290 --> 00:22:44,920
+شايفين الأشهر الخضاء الخضراء الخضاءهدوله اتجاه
+
+261
+00:22:44,920 --> 00:22:48,420
+التسارع كلهم باتجاه المركز ولا لا؟ لكن مرة صيني و
+
+262
+00:22:48,420 --> 00:22:53,420
+مرة شاضي شايفينها؟ تتغير تمام حسب النقطة المهم
+
+263
+00:22:53,420 --> 00:23:00,080
+تكون باتجاه المركز احسن شويه لسه بدل علينا هذا
+
+264
+00:23:00,080 --> 00:23:06,080
+بدنا نيوتن اه لسه نيوتن مش في طريق اللي وراه تمام؟
+
+265
+00:23:06,080 --> 00:23:11,260
+حلو بس مهل واحدة واحدة بنمشي دادة دادة هذا نيوتن
+
+266
+00:23:11,260 --> 00:23:15,570
+هيك بقولو لسه عن نيوتن ما جيناهوش و أنا قلت ما هو
+
+267
+00:23:15,570 --> 00:23:20,450
+المظبوط بس أنا قلت هيك حكيتها بس هو اصلا مش انا
+
+268
+00:23:20,450 --> 00:23:23,830
+اللي قلتها نيوتن اللي جات عفوا بتساوي ام ايه صحيح
+
+269
+00:23:23,830 --> 00:23:30,890
+تمام تمام ده اللي ما زال في حركة دائريةوالدائرة
+
+270
+00:23:30,890 --> 00:23:35,590
+بتدلها تدلها تلف ولا لأ؟ في تكرار ما زال في تكرار
+
+271
+00:23:35,590 --> 00:23:37,810
+في المادة اللي أخدنا منها كمها المصطلح بدي نعيده
+
+272
+00:23:37,810 --> 00:23:43,230
+احنا وياكم عارفينها في تردد و زمن دوري سمعتوا
+
+273
+00:23:43,230 --> 00:23:47,470
+فيهم؟ و هدول مرتبطين بالحركة الدائرية والحركة
+
+274
+00:23:47,470 --> 00:23:52,310
+المتكررة بنسميها تمام؟ قال ليش تعرفي الزمن الدوري؟
+
+275
+00:23:53,290 --> 00:23:58,230
+هو عبارة عن زمن الدورة الواحدة مشاكل اتفجنا تمام
+
+276
+00:23:58,230 --> 00:24:02,730
+هاي الزمن الدوري then the period اللي هو الزمن
+
+277
+00:24:02,730 --> 00:24:06,630
+الدوري يعني اللي رمزه capital T is defined as the
+
+278
+00:24:06,630 --> 00:24:09,990
+time needed هو الزمن اللازم for the particle to
+
+279
+00:24:09,990 --> 00:24:14,110
+complete one revolution revolution دورة من يقول
+
+280
+00:24:14,110 --> 00:24:20,700
+يجديش مسافة الدورة؟2XR 2XR هذي الزاوية تبعته لكن
+
+281
+00:24:20,700 --> 00:24:25,280
+المسافة محيط مظموش محيط قال لي في اي بي تويتر قولي
+
+282
+00:24:25,280 --> 00:24:29,540
+الزمن الدورة بساوي مسافة الدورة على السرعة ولا لأ
+
+283
+00:24:29,540 --> 00:24:36,420
+هذا هيمسافة الدورة اللي هو المحيط أسرة طيب إيش
+
+284
+00:24:36,420 --> 00:24:40,280
+مرتبط بالزمن الدوري معكوس الزمن الدوري التردد
+
+285
+00:24:40,280 --> 00:24:44,760
+التردد قالوا ال frequency the reciprocal يعني
+
+286
+00:24:44,760 --> 00:24:48,380
+معكوس reciprocal يعني واحد على X هذا مسميه
+
+287
+00:24:48,380 --> 00:24:51,460
+reciprocal the reciprocal of the period is called
+
+288
+00:24:51,460 --> 00:24:54,620
+the frequency which is defined as the number of
+
+289
+00:24:54,620 --> 00:24:58,660
+revolution in one secondحاجات لما نقول وحدة التردد
+
+290
+00:24:58,660 --> 00:25:04,640
+في المدرسة كذا دورة أو كذا دورة في الثانية مش
+
+291
+00:25:04,640 --> 00:25:09,040
+هيكون نكتب او years كذا دورة في الثانية والدورة
+
+292
+00:25:09,040 --> 00:25:12,200
+احنا عارفينها طب انا بديش دورة بدي وحدة جديدة
+
+293
+00:25:12,200 --> 00:25:19,900
+Radian هو الدورة أكم Radian الدورة أكم Radianمش
+
+294
+00:25:19,900 --> 00:25:24,720
+تقول تلت مية و ستين درجة تلت مية و ستين اتنين باى
+
+295
+00:25:24,720 --> 00:25:32,360
+اذا عشان يتحول من دورةلكل ثانية إلى رديا لكل ثانية
+
+296
+00:25:32,360 --> 00:25:37,100
+ضرب ليه في 2π صحيح؟ اذا معناته بيقول ليه because
+
+297
+00:25:37,100 --> 00:25:42,080
+when revolution كل دورة equals 2π رديا لليه 360
+
+298
+00:25:42,080 --> 00:25:47,060
+درجة تمام the angular speed هو frequency جيد بس
+
+299
+00:25:47,060 --> 00:25:50,540
+متعرف عليه برمز جيد Omega اسمه الـ Omega أديكم
+
+300
+00:25:50,540 --> 00:25:56,160
+الرمز تبعهسمعتوا فيها Omega هذه؟ Small Omega بس هو
+
+301
+00:25:56,160 --> 00:25:58,980
+اتنين بقى في ال frequency ليه ضورتوا في اتنين بقى؟
+
+302
+00:25:58,980 --> 00:26:02,920
+عشان احوّن من دورة لكل ثانية إلى radian لكل ثانية
+
+303
+00:26:02,920 --> 00:26:05,600
+طب و ال frequency مش مجردة بقى بالزمن واحد على
+
+304
+00:26:05,600 --> 00:26:07,740
+اتين هاد يكونها المعلومات تحت المجلة بس أنا بس
+
+305
+00:26:07,740 --> 00:26:13,620
+بتذكر حالنا فيها تمى قاللي حلو انت ايش جبتلي حسب
+
+306
+00:26:13,620 --> 00:26:17,520
+هذا القانون Omega بسوة V على R و توي قلتلي هادي
+
+307
+00:26:17,520 --> 00:26:22,950
+اللي هي ACبتساوي V تربيع على R ولا لأ؟ حطولي بديل
+
+308
+00:26:22,950 --> 00:26:27,530
+V Omega في R مايه دي بتصير Omega تربيع R تربيع على
+
+309
+00:26:27,530 --> 00:26:31,810
+R بتصير Omega تربيع في R الشيء Omega ده اللي
+
+310
+00:26:31,810 --> 00:26:35,290
+بيسميها مرات سرعة زاوية عشان نميز بينها و بين ال
+
+311
+00:26:35,290 --> 00:26:38,650
+frequency العادى لكن لما نكبر بنقول عنها frequency
+
+312
+00:26:38,650 --> 00:26:43,290
+برضه هي frequency هي تردد زاوية تمام عشان نميزه عن
+
+313
+00:26:43,290 --> 00:26:44,170
+ال frequency العادى
+
+314
+00:26:47,340 --> 00:26:52,580
+إذن هي الكتابة اللي كتبناها حلو قالوا إيش في أمثلة
+
+315
+00:26:52,580 --> 00:26:58,560
+ربانية في حركات دائرية احنا كنا السيارة في الضوار
+
+316
+00:26:58,560 --> 00:27:04,040
+لكن قبل السيارة ربنا خلق الأرض تدور حول الشمس
+
+317
+00:27:04,040 --> 00:27:09,120
+والجمر تدور حول الأرض والإلكترون تدور حول النواة
+
+318
+00:27:09,120 --> 00:27:14,860
+صح ولا هذي حركات ربانية وعندكم علم إن علم الفلك من
+
+319
+00:27:14,860 --> 00:27:19,390
+أقدم العلومصحيح؟ شوفوا من وقتاش من أيام سيدنا
+
+320
+00:27:19,390 --> 00:27:23,010
+إبراهيم .. ذاكرين الجدال اللي كان بينه و بين ربه و
+
+321
+00:27:23,010 --> 00:27:26,170
+حاجة إبراهيم ربها كل ما شاف الجمر و شاف الشمس
+
+322
+00:27:26,170 --> 00:27:31,050
+الإنسان بطبيعته دائما بحب يصطلع الكون اللي حواليه
+
+323
+00:27:31,050 --> 00:27:36,010
+يعني بصحى الواحد بلاجئه انه طلعت الشمسعودت صارت
+
+324
+00:27:36,010 --> 00:27:40,270
+شوب، بعدين عوّلت بردت، بعدين غابت الشمس، صح ولا؟
+
+325
+00:27:40,270 --> 00:27:44,470
+فالإنسان قاعد يقعد يفكر، و بعدين هذا جمر مرة بتصير
+
+326
+00:27:44,470 --> 00:27:49,210
+بضوء في الليل و مرة بتطفي، اذا هذا العلم من زمان
+
+327
+00:27:49,210 --> 00:27:55,510
+الإنسان بدور عليه، و الآن أصبح شبههيقيني عشان كده
+
+328
+00:27:55,510 --> 00:28:00,010
+جوالاتنا معانا صح ولا لأ و بنفتح الجزيرة من وين
+
+329
+00:28:00,010 --> 00:28:03,710
+بتبث الجزيرة؟ من الدوحة و بنفتح العربية بتبث من
+
+330
+00:28:03,710 --> 00:28:07,990
+دبي و بنفتح و بنفتح كل هذا من وين إجا؟ قالي والله
+
+331
+00:28:07,990 --> 00:28:11,530
+لا والله أقمار الصناعية مش موجودة لا معانا جوالات
+
+332
+00:28:11,530 --> 00:28:16,250
+ولا بنعرف نتفرج على أي محطة تمام؟ اذا كل هذه
+
+333
+00:28:16,250 --> 00:28:22,390
+التكنولوجيا مبنية على علم جديد اسمه علم الفلكتمام
+
+334
+00:28:22,390 --> 00:28:27,010
+وصار يقيني مرات بتسمعوا انه بيصير عندنا كسوف او
+
+335
+00:28:27,010 --> 00:28:32,070
+خصوف و بيصير فيه اعلانات و كل الناس بتصدق و
+
+336
+00:28:32,070 --> 00:28:35,670
+الحكومة بتصدق و بتعمل احتياطاتها ولا لا بيقولك
+
+337
+00:28:35,670 --> 00:28:39,130
+الكسوف بدي يبدأ الساعة اتنين اتين و عشر دقايق و
+
+338
+00:28:39,130 --> 00:28:42,670
+خمسة و عشرين ثانية تصوروا ليش؟ اللي اتطلع ليه قعدت
+
+339
+00:28:42,670 --> 00:28:47,670
+متولا صدقهصح؟ إذن الحسابات دقيقة بيقولّك هذا بترجع
+
+340
+00:28:47,670 --> 00:28:51,130
+وقالي ربع الساعة و اتخلص وبعد ما عنصر جات بعد ربع
+
+341
+00:28:51,130 --> 00:28:56,350
+الساعة ولا كأنه صار إيش إذا صار عندنا من المعلومات
+
+342
+00:28:56,350 --> 00:29:03,500
+العلمية اللي اتصل إلى درجة اليقينهي نيجي قال لي من
+
+343
+00:29:03,500 --> 00:29:07,480
+ضمن .. طبعا احنا بنعرف في آية بتقول الشمس والقمر
+
+344
+00:29:07,480 --> 00:29:11,300
+بحسبها الها حساباته ولا مالاش حسابات؟ الها حساباته
+
+345
+00:29:11,300 --> 00:29:16,340
+وهي الإنسان توصل لحساباتها بيقول the earth الأرض
+
+346
+00:29:16,340 --> 00:29:22,260
+revolves بتدور around the sun حول الشمس in an
+
+347
+00:29:22,260 --> 00:29:26,800
+orbit بيقول يفترض إنه دائرة هو طبعا بيداوي بيكون
+
+348
+00:29:26,800 --> 00:29:32,130
+لكن أنا بتعتبره دائرة تقريبانص قطر الدوران اللي هي
+
+349
+00:29:32,130 --> 00:29:35,670
+المسافة بين مركز الأرض إلى مركز الشمس one point
+
+350
+00:29:35,670 --> 00:29:40,590
+five ten to power eleven متر يعني حوالي مية وخمسين
+
+351
+00:29:40,590 --> 00:29:46,870
+مليون كيلومتر اتخيل انت عادي تمه .. روح طلعلك رحلة
+
+352
+00:29:46,870 --> 00:29:51,070
+من هال الشمس وكتينشوف وكتينفك اتصال تمه .. and
+
+353
+00:29:51,070 --> 00:29:56,700
+complete one revolutionبكمل دورة كاملة كل سنة،
+
+354
+00:29:56,700 --> 00:30:00,300
+معلومة بنعرفها ولا لا؟ ماشي احنا شهر يناير، واحد
+
+355
+00:30:00,300 --> 00:30:03,760
+يناير، بعد سنة، نصير واحد يناير، معناه ان رجعت
+
+356
+00:30:03,760 --> 00:30:09,780
+الأرض عن نفس النقطة اللي كانت من الشمس، اذا كل سنة
+
+357
+00:30:09,780 --> 00:30:14,580
+الأرض بتكمل دورة واحدة كإذا هذا زمان الدوري ولا لا
+
+358
+00:30:14,580 --> 00:30:18,160
+تبع الأرض؟مش هي تعريف الزمن الدوري؟ الزمن الدوري
+
+359
+00:30:18,160 --> 00:30:21,540
+هو الزمن اللازم عشان اكمل دورة كاملة في هذه الحالة
+
+360
+00:30:21,540 --> 00:30:26,940
+القمع الارض بتكون لفت 360 درجة ولا لا؟ 360 درجة
+
+361
+00:30:26,940 --> 00:30:32,980
+لفت تمام؟ جالي ايش بدك؟ جالي بدي .. اه الارض
+
+362
+00:30:32,980 --> 00:30:38,320
+بتتخلق حركة دائرية بنفع مايكون لها تسارع إلا يكون
+
+363
+00:30:38,320 --> 00:30:42,000
+لها تسارع بقول اوجده بقول اوجده what is the
+
+364
+00:30:42,000 --> 00:30:44,930
+centripetal acceleration of the earth؟المثال اللي
+
+365
+00:30:44,930 --> 00:30:49,010
+ورا أو المطبوب التاني قاللي فلتك من الأرض نشوف كيف
+
+366
+00:30:49,010 --> 00:30:52,490
+يصير رمضان ويصير عيد ويصير حج ويصير بداية أشهر
+
+367
+00:30:52,490 --> 00:30:56,470
+وبتجاتلوا المسلمين هذا صام وهذا ماصامش، مظبوط ولا
+
+368
+00:30:56,470 --> 00:31:02,130
+لأ؟ نشوف كيف احنا بنبدأ أشهرنا العربية؟ قالوا حسب
+
+369
+00:31:02,130 --> 00:31:06,070
+الجمر، صح؟ طب الجمر إيش بتحرك؟ قاللي والله حركة
+
+370
+00:31:06,070 --> 00:31:10,990
+معروفة وربنا خلقهاFind the acceleration of the
+
+371
+00:31:10,990 --> 00:31:15,890
+moon اه لأن الـ moon بلوف حوالي الأرض تمام بقولي
+
+372
+00:31:15,890 --> 00:31:18,210
+the moon towards the earth if the moon revolves
+
+373
+00:31:18,210 --> 00:31:22,670
+بلوف about the earth in an orbit برضه في مدار of
+
+374
+00:31:22,670 --> 00:31:25,550
+average radius نسقطه أظن هذه متر مش كيلومتر
+
+375
+00:31:25,550 --> 00:31:29,960
+بالخاطر اه هنا محطوطة كده لمكان مش مشكلةand mix
+
+376
+00:31:29,960 --> 00:31:35,100
+وبيعمل دورة كاملة تشوفوا الأرض بتعمل كل سنة دورة
+
+377
+00:31:35,100 --> 00:31:41,660
+الجمر بيعمل كل شهر دورة كل شهر تطلع الشهر ايه كم
+
+378
+00:31:41,660 --> 00:31:47,900
+يوم حاطه عمركم ما اسمعتوا في شهر عربي 27 يوم ولا
+
+379
+00:31:47,900 --> 00:31:56,100
+28 عربي عربي ثم 28 يوم
+
+380
+00:32:00,410 --> 00:32:07,110
+انت بتعرفش ما يسمى أشهر عربية؟ محرم
+
+381
+00:32:07,110 --> 00:32:11,930
+و سفر و جماد و ربيع و رمضان و شوال هاي الأشهر
+
+382
+00:32:11,930 --> 00:32:16,090
+العربية خليني أسألك و اسأليه أمك و أبوك عمكم سبت و
+
+383
+00:32:16,090 --> 00:32:22,450
+28 يوم؟لأ إما تسعة عشرين أو تلاتين صح؟ ليش تبحططلي
+
+384
+00:32:22,450 --> 00:32:26,330
+أنت سبعة وعشرين؟ هذا زمان دوري، المفروض يكون شهرة
+
+385
+00:32:26,330 --> 00:32:30,270
+قدّم نحكي عنه، ليش هذا السبعة وعشرين؟ وكيف يصير
+
+386
+00:32:30,270 --> 00:32:35,230
+الشهر العربي إما تسعة وعشرين أو تلاتين؟ طيب، جالي
+
+387
+00:32:35,230 --> 00:32:38,350
+نبدأ في الأول، نخلص من الأرض حوالي الشمس، هذه سهلة
+
+388
+00:32:38,350 --> 00:32:41,890
+السنة الميلادية، أكم يوم؟
+
+389
+00:32:47,020 --> 00:32:51,420
+وربع مش كل اربع سنوات بتجينا سنة كبيرة ليه عشان
+
+390
+00:32:51,420 --> 00:32:57,320
+ربع ربع ربع تصير يوم تمام تلاتمية وخمسة وستين وربع
+
+391
+00:32:57,320 --> 00:33:04,200
+هاي السنة الميلادية تلاتمية وخمسة وستين وربع يوم
+
+392
+00:33:04,200 --> 00:33:09,460
+وهذا ايش هو هو الزمن الدوري لدوران الأرض حول الشمس
+
+393
+00:33:12,380 --> 00:33:16,600
+مش بيصير شهر اتنين تسعة عشرين اه؟ اه عشان يصير تلت
+
+394
+00:33:16,600 --> 00:33:21,720
+مية ستة وستين عشان تظبط معانا الأمور و يرجع زي ما
+
+395
+00:33:21,720 --> 00:33:25,460
+احنا طبعا مانفعش نقول كل سنة و ربع ولا و تلت لازم
+
+396
+00:33:25,460 --> 00:33:29,620
+يوم كامل فقالوا بسيطة اه البني ولدت تسعة و عشرين
+
+397
+00:33:29,620 --> 00:33:36,580
+اتنين كيف؟ بوفر ع أصحابه عيد الميلاد كل أربع سنوات
+
+398
+00:33:36,580 --> 00:33:43,100
+مش عيد ميلاد مرة تمام يلا يا بناتبدي التسارع بدي
+
+399
+00:33:43,100 --> 00:33:47,400
+التسارع هاي التسارع إذا إنت جبتلي أمجا بكون خلصت
+
+400
+00:33:47,400 --> 00:33:52,600
+ولا لأ لأنه آه بيعطاني إياها طيب الزمن الدولي
+
+401
+00:33:52,600 --> 00:33:56,900
+يعطاك إياه ولا لأ سنة ببدأ أحوّل السنة ل seconds
+
+402
+00:33:56,900 --> 00:34:04,200
+اه ما هو السمنة السنة كم يوم طوّجلنا 365.25 و
+
+403
+00:34:04,200 --> 00:34:11,700
+اليوم كم ساعة 24 و الساعة كم ساكن هاي نحولناهاواحد
+
+404
+00:34:11,700 --> 00:34:19,320
+اللي هو سنة عدد أيام السنة في عدد ساعات اليوم في
+
+405
+00:34:19,320 --> 00:34:25,920
+عدد ثواني الساعة هاي زمان الدوري قاللي عرفتي زمان
+
+406
+00:34:25,920 --> 00:34:29,580
+الدوري بتعرفي تجيبلي omega قلتله اه omega بتسوى 2π
+
+407
+00:34:29,580 --> 00:34:37,260
+على زمان الدوري قاللي هاي omega طلعوا omega بسوى 1
+
+408
+00:34:37,260 --> 00:34:43,380
+.9 فعشرة أساليب سبعةوالسرعة بتكون برضه بسيطة
+
+409
+00:34:43,380 --> 00:34:47,080
+خلّيني نتطلع على Omega هذه إيش الواحدة جالي radian
+
+410
+00:34:47,080 --> 00:34:52,180
+per second؟ لو جيت حكيت لواحد في الشارع من عامة
+
+411
+00:34:52,180 --> 00:34:56,160
+الناس ال radian بقرا فخشي إن كانت درجة بقدر أحس
+
+412
+00:34:56,160 --> 00:34:59,240
+فيها أكتر يعني لما تقوله خمس درجات أو عشرين درجة
+
+413
+00:34:59,240 --> 00:35:04,140
+بحسها جالي أحولليها بديش radian طيب هو كيف بدي أنا
+
+414
+00:35:04,140 --> 00:35:08,420
+أحول من radian ل second؟ جالي بسيطة هي ال πاي أكم
+
+415
+00:35:08,420 --> 00:35:15,050
+radianحاجة 180 درجة، مظبوط ولا لأ؟ تمام، لكن هي
+
+416
+00:35:15,050 --> 00:35:20,750
+بالنسبة ليه 180 درجة؟ طب الواحد ريادين أكم درجة؟
+
+417
+00:35:20,750 --> 00:35:26,290
+بقى أنا عرب، 180 عبارة ايه؟ قدش تطلع لـ57؟ و أين
+
+418
+00:35:26,290 --> 00:35:29,810
+الريادين بتسوي 57 و 13 درجة؟ إذن الريادين المضروبة
+
+419
+00:35:29,810 --> 00:35:33,810
+في 57 درجة و السكن بتحولها ليوم أشوف في اليوم إيش
+
+420
+00:35:33,810 --> 00:35:40,100
+بتتحرك الشمس قال لي هذا طلعت معايا تقريبا درجةأذن
+
+421
+00:35:40,100 --> 00:35:46,140
+الأرض كل يوم بتلف درجة حوالين الشمس هى كل يوم لما
+
+422
+00:35:46,140 --> 00:35:51,340
+نيجي 360 مصير جربت على السنة ولا لألأنه 360 جربت
+
+423
+00:35:51,340 --> 00:35:55,880
+على سنة هذا كلام منطقي طبعا إذا المعلومة طبعا هذا
+
+424
+00:35:55,880 --> 00:36:02,180
+مثال أغلبه ثقافي عشان نستمتع و نسمع فيه و لا نتخلص
+
+425
+00:36:02,180 --> 00:36:05,820
+من الامتحان لأن هذه الموضوع يا بنات في chapter 6
+
+426
+00:36:05,820 --> 00:36:09,900
+هنرجعله تفصيلا عنوان ال chapter circular motion
+
+427
+00:36:09,900 --> 00:36:13,640
+هنرجعله احنا هجيته نتعرف عليه و نقوله كيف حالك
+
+428
+00:36:14,360 --> 00:36:19,860
+ثقافة يعني متعة تمى اذا هلجيت الأرض بتلف كل يوم
+
+429
+00:36:19,860 --> 00:36:24,820
+درجة حول الشمس درجة تمى بدي التسارع انت خلينا نخلص
+
+430
+00:36:24,820 --> 00:36:27,680
+من الاخر انت ايش بدك بتقوله التسارع قللي ما هو
+
+431
+00:36:27,680 --> 00:36:30,420
+التسارع بتسوي أومجة تربيع في الأرض ولا لأ وهي
+
+432
+00:36:30,420 --> 00:36:36,030
+أومجة كالكورية ترجبتها رقم والسلامقاليل؟ اه قاليل
+
+433
+00:36:36,030 --> 00:36:38,970
+لما هو لازم يكون قاليل و لا انتوا بتشوفوا حالكم
+
+434
+00:36:38,970 --> 00:36:42,850
+بتدوخوا من كتر سرعة الأرض و بتنمشي فيكم مانحسش
+
+435
+00:36:42,850 --> 00:36:50,290
+سرعتها لأنها بطيئة طيب نجي للجمر حبيبنا جالي الجمر
+
+436
+00:36:50,290 --> 00:36:55,810
+انا قلتلك الزمن الدوري تبعه 27 و 13 يوم مظبوط او
+
+437
+00:36:55,810 --> 00:37:00,690
+لأ حوللي هذه المعلومة بالسكن بقوللي يوم 24 ساعة و
+
+438
+00:37:00,690 --> 00:37:06,300
+الساعة 1600 سكن جالي هذه الزمن الدوري يا حبيبيطيب
+
+439
+00:37:06,300 --> 00:37:10,080
+جيبلي Omega و قلتله اتنين Pi على زمن الدوري هذا هي
+
+440
+00:37:10,080 --> 00:37:13,820
+قاللي برضه Radian per second بدي انا اوصلها لعمة
+
+441
+00:37:13,820 --> 00:37:19,700
+الناس حوليها لدرجات باليوم دلي القمر بيلف تلت عشر
+
+442
+00:37:19,700 --> 00:37:23,520
+درجة كل يوم شوفوا الأرض بيلف درجة واحدة حوالي
+
+443
+00:37:23,520 --> 00:37:28,360
+الشمس القمر حوالي الأرض بيلف تلت عشر درجة عشان كده
+
+444
+00:37:28,360 --> 00:37:33,970
+كل شهر برجعتمام؟ برجع جالي طب بدي التسارع وقال
+
+445
+00:37:33,970 --> 00:37:38,970
+هالجي التسارع بحسبلكيا هالتسارع هالجي تليجي
+
+446
+00:37:38,970 --> 00:37:44,970
+معلومات ثقافية أكتر نجيم هذا ونرجعله احنا عشان
+
+447
+00:37:44,970 --> 00:37:51,250
+يبدأ الشهر العربي لازم ينولد الهلال بنسميه ولادة
+
+448
+00:37:51,250 --> 00:37:55,980
+الهلال سمعتوا في هذا المصطلح؟ تمامإيش معنى ولادة
+
+449
+00:37:55,980 --> 00:38:01,220
+الهلال؟ إنه لازم القمر يكون ما بين الأرض والشمس
+
+450
+00:38:01,220 --> 00:38:06,440
+على خط واحد يعني هي الشمس شايفينها؟ هي مركزها هي
+
+451
+00:38:06,440 --> 00:38:09,420
+مركز القمر وهي مركز الأرض لازم يكون في خط مستقيم
+
+452
+00:38:09,420 --> 00:38:16,420
+في هذه اللحظة بقول إن ولد الهلال إذا بدأ الشهر
+
+453
+00:38:16,420 --> 00:38:23,120
+فلكيا عشان يبدأ شرعيا في الحديث سوم لوريتهوفطر و
+
+454
+00:38:23,120 --> 00:38:26,920
+لا ورايتها، ذاكرينه؟ إذا لازم أشوف القمر طبعا في
+
+455
+00:38:26,920 --> 00:38:32,260
+هذه اللحظة القمر لا يراه لأن أشعة الشمس محجوبة
+
+456
+00:38:32,260 --> 00:38:37,000
+والأرض بتشوفش القمر تمام كيف بدي أشوفهم؟ هو القمر
+
+457
+00:38:37,000 --> 00:38:43,240
+بدي يلوف بدي يلوف هذه اللحظة لحظة اقتران أو ولادة
+
+458
+00:38:43,240 --> 00:38:47,760
+الهلال هي لحظة ثابتة عن جميع العالم ولا واحد
+
+459
+00:38:47,760 --> 00:38:52,860
+بيختلف فيهاربيعي الأول اللي احنا فيه كانت لحظة
+
+460
+00:38:52,860 --> 00:38:57,320
+ولادته موجودة بالساعة والدقيقة والثانية ومافيش
+
+461
+00:38:57,320 --> 00:39:03,000
+عليها خلاف ربيعي التاني بخش عن نت بقول .. بقول ليه
+
+462
+00:39:03,000 --> 00:39:07,820
+وقتيش بالظبط هيولدي الهلال هجيت بدينا ربيعي الأول
+
+463
+00:39:07,820 --> 00:39:12,880
+و بعد الشهر يمشي الجمر بدي يمشي الجمر بيمشي بيمشي
+
+464
+00:39:12,880 --> 00:39:18,230
+بيمشي وصل هناهجيت كمل دورة كاملة اكمل زاوية ماشية
+
+465
+00:39:18,230 --> 00:39:23,630
+360 درجة مش هي دورة كاملة جالي حلو جديش استحرق يوم
+
+466
+00:39:23,630 --> 00:39:27,370
+جالي سبعة و عشرين و تلت يوم اللي مكتوب عنكم سبعة و
+
+467
+00:39:27,370 --> 00:39:31,330
+عشرين و تلت يوم جالي طب هيا اكمل دورة كاملة ان
+
+468
+00:39:31,330 --> 00:39:35,290
+ولادي الهلال تبقى الشهر القادم بقوله لأليه؟ قال لي
+
+469
+00:39:35,290 --> 00:39:38,630
+لأنه مش عمص في المستوى، ليه؟ قال لي هو الأرض بتفكر
+
+470
+00:39:38,630 --> 00:39:41,410
+في السناك و أنت بتمشي يا جمر؟ هي الأرض ده ده
+
+471
+00:39:41,410 --> 00:39:46,210
+السناك و البداية كلوف، البداية كلوفأو كام يوم
+
+472
+00:39:46,210 --> 00:39:48,550
+الجمر قعد بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+473
+00:39:48,550 --> 00:39:48,630
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+474
+00:39:48,630 --> 00:39:49,090
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+475
+00:39:49,090 --> 00:39:49,790
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+476
+00:39:49,790 --> 00:39:53,470
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+477
+00:39:53,470 --> 00:39:58,210
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+478
+00:39:58,210 --> 00:40:06,510
+بـ بـ بـ بـ بـ بـ بـ بـ
+
+479
+00:40:06,510 --> 00:40:14,530
+بـ
+
+480
+00:40:14,710 --> 00:40:18,190
+أذن عشان كده سبعة وعشرين وشويه وكمان يومين وشويه
+
+481
+00:40:18,190 --> 00:40:22,830
+صاروا تسعة وعشرين وشويه تسعة وعشرين وشويه هي تسعة
+
+482
+00:40:22,830 --> 00:40:27,310
+وعشرين عشان
+
+483
+00:40:27,310 --> 00:40:30,850
+كده بيقول الشهر اما تسعة وعشرين او تلاتين ولازم
+
+484
+00:40:30,850 --> 00:40:34,960
+التلاتينات يكونوا اكتر من التسعة وعشريناتلأنه فيه
+
+485
+00:40:34,960 --> 00:40:40,700
+أكتر من الخمسة لو هذه 00 كان بحط رجل على رجل و
+
+486
+00:40:40,700 --> 00:40:45,860
+بقول ما حد يستطلق شهر رمضان تلاتين إذا شوال تسعة و
+
+487
+00:40:45,860 --> 00:40:48,980
+عشرين إذا نزل قعدة تلاتين إذا اللي ورا تسعة و
+
+488
+00:40:48,980 --> 00:40:53,560
+عشرين مظبطا لا تصير واحد واحد بس ماحسن الحظ إن هنا
+
+489
+00:40:53,560 --> 00:40:58,620
+فيه أرقام وبالتالي رمضان مرة بيكون تلاتين و مرة
+
+490
+00:40:58,620 --> 00:41:05,680
+بيكون تسعة و عشرين تمام؟ طبعاولا ممكن هدول لما
+
+491
+00:41:05,680 --> 00:41:10,920
+يخربطوا البني آدمين اللي بيفهموش هم بيخلوا واحد
+
+492
+00:41:10,920 --> 00:41:17,420
+تلاتين اما احنا شهرنا العربي لازم يكون اما تسعة و
+
+493
+00:41:17,420 --> 00:41:23,140
+عشرينأو تلاتين و لازم يكون عدد الشهور اللي تلاتين
+
+494
+00:41:23,140 --> 00:41:27,680
+أكثر من عدد الشهور التسعة و عشرين لأن هذه تسعة و
+
+495
+00:41:27,680 --> 00:41:31,960
+عشرين وأكتر من نص معناته أنت أقرب للتلاتين من
+
+496
+00:41:31,960 --> 00:41:35,360
+التسعة و عشرين فلازم عشان كده هذا الكلام اللي توي
+
+497
+00:41:35,360 --> 00:41:39,720
+حكيته بيقول لي note that in the period لما لف هذا
+
+498
+00:41:39,720 --> 00:41:46,260
+أكمل دورة كاملة الأرض دلت ثابتة ولا اتحركت لها
+
+499
+00:41:46,900 --> 00:41:51,120
+حوالي 27 درجة معناته يا جمر عشان تنولد من أول و
+
+500
+00:41:51,120 --> 00:41:55,680
+جديد مطلوب انك تمشي هذه المسافة الزاوية وهذه بدها
+
+501
+00:41:55,680 --> 00:42:00,880
+حوالي كمان يومين و شوية فبطلع الشهر الحقيقي اللي
+
+502
+00:42:00,880 --> 00:42:04,200
+بنتعامل معاه طبعا برضه معلومة ثقافية انتوا بتعرفوا
+
+503
+00:42:04,200 --> 00:42:08,340
+وقتش بتطلعوا عليه لان فأيه و جيت الدهر ولا المغرب
+
+504
+00:42:08,340 --> 00:42:16,900
+المغرب ليش احنا ليش يا بنات اخر يوم في شعبانمش
+
+505
+00:42:16,900 --> 00:42:21,020
+بنبدأ نصلي الترويح؟ ليش؟ بقوله لأنه لما أدني
+
+506
+00:42:21,020 --> 00:42:25,180
+المغرب بدأ رمضان لأنه شرعان يبدأ اليوم أداني
+
+507
+00:42:25,180 --> 00:42:29,360
+المغرب شرعان أخر يوم في رمضان بنصلي الترويح لأنه
+
+508
+00:42:29,360 --> 00:42:33,320
+لما جال الله أكبر وأفطلنا خلص رمضان وبالتالي
+
+509
+00:42:33,320 --> 00:42:37,160
+الترويح بعد العشاء خشت في اليوم ليش دي؟ يعني اليوم
+
+510
+00:42:37,160 --> 00:42:40,220
+شرعان اليوم الكنين بعد أداني المغرب يصير التلاتة
+
+511
+00:42:41,890 --> 00:42:47,830
+تمام؟ عشان كده هيك الشرع بنشتغل عليها و تطلع أقول
+
+512
+00:42:47,830 --> 00:42:51,770
+تقوصنا الدينية كيف بنعمل فيها، تمام؟ يعني مثلا
+
+513
+00:42:51,770 --> 00:42:54,790
+بتعرفوا أنتوا في عيد الأضحى فيه تكبيرات، احنا
+
+514
+00:42:54,790 --> 00:42:58,310
+بنكبر في كل الصلاوات و ماكنتش بتخلص بعد صلاة العصر
+
+515
+00:42:58,310 --> 00:43:01,310
+رابع يوم العيد، و المغرب ليش بنكبر؟ ليش بيقول خلص
+
+516
+00:43:01,310 --> 00:43:05,390
+العيد؟ لأن قد أن المغرب خلص العيد، خلصنا، خلصنا،
+
+517
+00:43:05,390 --> 00:43:11,440
+مافيش داعي اتكبر، تمام؟وبالتالي هذه المعلومات لازم
+
+518
+00:43:11,440 --> 00:43:14,840
+نكون عارفينها عشان كده بنقول كتالة بنقول لازم اللي
+
+519
+00:43:14,840 --> 00:43:17,420
+بديه يتطلع يكون أدين المغرب عشان نشوف اليوم بدأ
+
+520
+00:43:17,420 --> 00:43:21,440
+ولا مابدهاش طبعا المعلومة اللي لازم نفهمها هجيت
+
+521
+00:43:21,440 --> 00:43:26,380
+احنا واجتش بأدين المغرب اليوم عندنا ستة و نص جوله
+
+522
+00:43:26,380 --> 00:43:31,440
+ستة و نص لو اتخيلتوا مدينة زي الرباط وين وجع
+
+523
+00:43:31,440 --> 00:43:36,010
+الرباط؟في المغرب غرب جوركم على الستة و نص بيكون
+
+524
+00:43:36,010 --> 00:43:40,690
+المغرب قدر عندهم بيكون لسه تقريز الظهر اذا بقدر
+
+525
+00:43:40,690 --> 00:43:44,930
+المغرب بعد تلت ساعات اربع ساعات معناته لو انا شفت
+
+526
+00:43:44,930 --> 00:43:49,490
+الجمر معناته هو شايف الجمر قطعا اكتر مني ليش؟ لأن
+
+527
+00:43:49,490 --> 00:43:52,930
+هو كمان تقلت اربع ساعات الجمر بيكون عليه بيكون
+
+528
+00:43:52,930 --> 00:43:59,350
+ماشي وبالتالي لازم يشوفه لكنلو أنا قلت إيجي واحد
+
+529
+00:43:59,350 --> 00:44:04,650
+نفترض في طهران طهران وين وجعه؟ شرق جال أه في إيران
+
+530
+00:44:04,650 --> 00:44:08,390
+شرق يعني جال والله أنا ماشوفتش الجمر بقوله استنى
+
+531
+00:44:08,390 --> 00:44:11,990
+عليا أنا يمكن أشوفه ليش أنت لسه أنا المغرب تبقى
+
+532
+00:44:11,990 --> 00:44:14,590
+أنت قد مغربك أنا لسه بدي أربع ساعات لما يقدي
+
+533
+00:44:14,590 --> 00:44:18,330
+المغربي وبالتالي لما يقدي المغرب بيكون الجمر كبير
+
+534
+00:44:18,330 --> 00:44:22,830
+عندي وممكن أشوفه المعلومة اللي بدي أكون تعرفها إذا
+
+535
+00:44:22,830 --> 00:44:27,900
+واحد جانفي القاهرة انا ماشفتش الجمر وكان عالم
+
+536
+00:44:27,900 --> 00:44:33,280
+بمعنى صحيح ماحد يصدق واحد في دبي او واحد في تهران
+
+537
+00:44:33,280 --> 00:44:36,930
+يقول انا شفت الجمر ولا ممكنولا ممكن، إذا كان اللي
+
+538
+00:44:36,930 --> 00:44:41,070
+في القاهرة اللي هو غرب هذه المدن، ماشوفش القمر،
+
+539
+00:44:41,070 --> 00:44:45,870
+كيف أنت شفته؟ طب أنا كان كبير لما طلعت المغرب، انت
+
+540
+00:44:45,870 --> 00:44:50,070
+لسه قمرك صغير، كيف شفته؟ ماينفعش، لذا هذه
+
+541
+00:44:50,070 --> 00:44:53,870
+المعلومات اللي الشيخ الان حسموها أغلب الشيخ وخصوصا
+
+542
+00:44:53,870 --> 00:44:58,650
+القرضاوي قال إذا والعلماء قالوا القمر لم يولد،
+
+543
+00:44:58,650 --> 00:45:02,720
+ماحد يصدق واحد يقول شفته القمريقول بقى بكرا رمضان
+
+544
+00:45:02,720 --> 00:45:08,020
+ولا ممكن هذه خلاص معلومات يقينية لما القمر يقول لم
+
+545
+00:45:08,020 --> 00:45:12,560
+يولد بمعنى أخر صار ع خط واحد هي ولادة الجمر ما زال
+
+546
+00:45:12,560 --> 00:45:18,000
+هذه المعلومة اليقينية ماكنتش موجودة ساعة المغرب
+
+547
+00:45:18,000 --> 00:45:21,300
+نفترض ان احنا ستة و نص بقول انا والله هذا القمر
+
+548
+00:45:21,300 --> 00:45:25,620
+بيصير في هذا الشكل سبعة الاربع معناته عند المغرب
+
+549
+00:45:25,620 --> 00:45:29,890
+بلاقي جماربلا جيش أمر لأنه مش موجود في السماء أصلا
+
+550
+00:45:29,890 --> 00:45:33,010
+وبالتالي يجي واحد يقول طب أنا شفت بقولك شفتلك حاجة
+
+551
+00:45:33,010 --> 00:45:39,590
+تانية الله علمش اللي شفته يمكن شفت نجمة مرات
+
+552
+00:45:39,590 --> 00:45:43,770
+طبعا في خلاف فقه احنا ماعشنا نخش عنه انه توحيد
+
+553
+00:45:43,770 --> 00:45:47,450
+المطالع او انه تفرقة المطالع انه كل واحد كل واحد
+
+554
+00:45:47,450 --> 00:45:50,090
+له مطلع مختلف احنا ماعشنا نخش في الأمور الشرعية
+
+555
+00:45:50,090 --> 00:45:53,640
+انه في الأمور العلمية احكيالعلماء اللي بيختلفوا
+
+556
+00:45:53,640 --> 00:45:56,560
+عليا عشان نسوم رمضان، ان هذه ولادة القمر، هذا اللي
+
+557
+00:45:56,560 --> 00:45:59,180
+بيختلفوا عليا الرؤية؟ لأ، لأ، لأ، بيختلفوش على هذه
+
+558
+00:45:59,180 --> 00:46:02,400
+اللحظة، بيختلفوا على الرؤية، لأنهم بيقولوا بيكفيش
+
+559
+00:46:02,400 --> 00:46:05,860
+ولادة القمر لأن الحديث بيقول صوموا لرؤيته وافطروا
+
+560
+00:46:05,860 --> 00:46:09,860
+لرؤيته، والمشكلة عند الرؤية، فبصي يقول مين شاف
+
+561
+00:46:09,860 --> 00:46:14,560
+ومين ما شافش، وبصير الخلاف، طبعا أغلب البلدان حسمت
+
+562
+00:46:14,560 --> 00:46:20,930
+الأمر وما حد بيشوف، خلاص بيحسبوهاوانا كنت في تركيا
+
+563
+00:46:20,930 --> 00:46:25,190
+في ال 86 من ال 86 ان عمره ما حد في تركيا قال بدنا
+
+564
+00:46:25,190 --> 00:46:29,390
+نشوف الجمر وكتش رمضان بكرا وكتش العيد بكرا وكتش
+
+565
+00:46:29,390 --> 00:46:34,730
+العيد الأرحى معروف مخطوط من هجات لو تخشي على تقويم
+
+566
+00:46:34,730 --> 00:46:38,170
+خليني أقول وزارة الأوقات في تركيا كمان خمس سنوات
+
+567
+00:46:38,170 --> 00:46:43,010
+وكتش العيد معروفلا بدهم جمر ولا حاجة كيف؟ حسب
+
+568
+00:46:43,010 --> 00:46:47,130
+الحسابات هذه وهذه قطعية مش فيها خلاف وحسب قراءة
+
+569
+00:46:47,130 --> 00:46:53,150
+شرعية موجودة عندهم قراءة شرعية تمام انشوف
+
+570
+00:46:53,150 --> 00:46:56,510
+tangential
+
+571
+00:46:56,510 --> 00:47:04,090
+and radial acceleration هلجيت؟ اي vector اي vector
+
+572
+00:47:04,090 --> 00:47:10,030
+ممكن احلله الى مركبتين متعمدتينصينية وصادية صح طيب
+
+573
+00:47:10,030 --> 00:47:13,670
+هو مافيش اللي الصين والصاد متعمدات مش فيه القطبية
+
+574
+00:47:13,670 --> 00:47:18,290
+هلجتني القطبية فيها نص قطر ايش اللي دايما عمودي عن
+
+575
+00:47:18,290 --> 00:47:26,430
+نص القطر؟ المماسالمماس و لا لأ هدية المماس و نص
+
+576
+00:47:26,430 --> 00:47:30,570
+القطر بنفع تعتبرهم محاور اللي هي المحاور القطرية
+
+577
+00:47:30,570 --> 00:47:36,030
+لأن هم متعمدات ولا لأ إذا كل شغلتين متعمدتين هم
+
+578
+00:47:36,030 --> 00:47:41,440
+إحدافياتإذا الآن التصارع بدي أنا أحلله إلى
+
+579
+00:47:41,440 --> 00:47:45,620
+مُركّبتين متعاملتين واحدة بدي أسميها نُص قطرية
+
+580
+00:47:45,620 --> 00:47:51,640
+radial وواحدة tangential مماسية تمام يا بنات؟ حلو
+
+581
+00:47:51,640 --> 00:47:56,640
+النُص قطرية سميتها مركزية ولا لأ؟ قلتلك هذه بتيجي
+
+582
+00:47:56,640 --> 00:48:00,160
+من وين؟ من تغير ال direction تبع السرعة طب الآن
+
+583
+00:48:00,160 --> 00:48:04,580
+بدي أغير ال speed إذا إيه صار متغير في السرعة؟ ال
+
+584
+00:48:04,580 --> 00:48:11,470
+tintin غصم عنهمالـ Direction بطلّع تسرع مركزي طب و
+
+585
+00:48:11,470 --> 00:48:16,370
+ال magnitude بطلّع تسرع مماسي بطلّع تسرع مماسي إذا
+
+586
+00:48:16,370 --> 00:48:21,510
+بيقولّي if the speedالسرعة اللي تتغير من البرتقال
+
+587
+00:48:21,510 --> 00:48:28,750
+اللي تتغير من البرتقال
+
+588
+00:48:28,750 --> 00:48:31,470
+اللي تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+589
+00:48:31,470 --> 00:48:34,110
+تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+590
+00:48:34,110 --> 00:48:34,690
+تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+591
+00:48:34,690 --> 00:48:34,730
+تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+592
+00:48:34,730 --> 00:48:36,630
+تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+593
+00:48:36,630 --> 00:48:40,110
+تتغير من البرتقال اللي تتغير من البرتقال اللي تت
+
+594
+00:48:40,490 --> 00:48:44,670
+والتسارع المركزي بينتج عن تغير the direction of
+
+595
+00:48:44,670 --> 00:48:48,170
+the velocity دخلة المعلومة، هنسأل عليها، عشان كده
+
+596
+00:48:48,170 --> 00:48:51,430
+أنا بركز عليها، هنسأل عليها بالـQ إزاي؟ ده اللي
+
+597
+00:48:51,430 --> 00:48:54,930
+طبق الـtotal acceleration، مش هي المواكبتين جانب
+
+598
+00:48:54,930 --> 00:48:58,230
+بعيد، مش الصينية زايد الصادية، إذا المعنى تحتيك
+
+599
+00:48:58,230 --> 00:49:02,690
+تكتبها هيك النسق الطوية والمماسية، فبكتبها بدلالة
+
+600
+00:49:02,690 --> 00:49:07,450
+الـunit vectorsI و J أسمع عارفين هم ولا لأ؟ بنفع
+
+601
+00:49:07,450 --> 00:49:13,490
+أحط I و J و I ملزقة بال X و J ملزقة بال Y و لا لأ؟
+
+602
+00:49:13,490 --> 00:49:16,710
+طب هجت لا في X ولا في Y إذا بدنا نستحدث unit
+
+603
+00:49:16,710 --> 00:49:22,070
+vector الجيدة إيش هي؟ إذا المعناته R والفيتا إذا
+
+604
+00:49:22,070 --> 00:49:26,470
+المعناته هذه تكتب طبعا عادة بنرجحها إيه ال
+
+605
+00:49:26,470 --> 00:49:30,270
+centripetal باتجاه ال R يعني باتجاه نص القطر وال
+
+606
+00:49:30,270 --> 00:49:34,540
+tangential باتجاه الفيتاليه شرط السالب؟ قال لي أنا
+
+607
+00:49:34,540 --> 00:49:39,340
+باتجاهي المركز و الـR هيك رايح مش الـR بنرسمه من
+
+608
+00:49:39,340 --> 00:49:42,600
+المركز و رايحين إذا باتجاهي المركز عكس محط شرط
+
+609
+00:49:42,600 --> 00:49:49,640
+السالب صحيح؟ زي سالب I بالظبط قال لي نرجع قال لي
+
+610
+00:49:49,640 --> 00:49:54,560
+AC مش هي V تربيع على R؟ أه طيب ال team كيف تتوقعها
+
+611
+00:49:54,560 --> 00:49:58,000
+بالثانوية؟ قال لي هي مشتقة ال speed بالنسبة للزمن
+
+612
+00:49:58,000 --> 00:50:03,010
+طيب إذا ال speed ثابت اشتقها؟0 اذا لما يكون ال
+
+613
+00:50:03,010 --> 00:50:09,150
+speed constant فى تسرع مماثى لأ رزقنا للأولى انه
+
+614
+00:50:09,150 --> 00:50:15,070
+مافيش تغير فى ال speed اذا التسرع بس مركز اللى
+
+615
+00:50:15,070 --> 00:50:19,130
+سميتها uniform circular motion صحيح ولا لأ بنجف
+
+616
+00:50:19,130 --> 00:50:21,450
+هناك دى عفوة للعاوزة
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4_raw.json b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..b91278d851ff9058d163f8402859634e206bfcb4
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4_raw.json
@@ -0,0 +1 @@
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0.9801432291666666}, {"start": 1027.95, "end": 1028.11, "word": " ولا", "probability": 0.9404296875}, {"start": 1028.11, "end": 1028.45, "word": " لأ", "probability": 0.6839599609375}, {"start": 1028.45, "end": 1029.27, "word": " لأن", "probability": 0.680908203125}, {"start": 1029.27, "end": 1029.45, "word": " ال", "probability": 0.96923828125}, {"start": 1029.45, "end": 1029.83, "word": " velocity", "probability": 0.9111328125}, {"start": 1029.83, "end": 1030.31, "word": " عبارة", "probability": 0.993408203125}, {"start": 1030.31, "end": 1030.47, "word": " عن", "probability": 0.99755859375}, {"start": 1030.47, "end": 1030.91, "word": " direction", "probability": 0.8896484375}, {"start": 1030.91, "end": 1031.23, "word": " و", "probability": 0.9267578125}, {"start": 1031.23, "end": 1031.51, "word": " speed", "probability": 0.78076171875}], "temperature": 1.0}, {"id": 44, "seek": 104923, "start": 1032.17, "end": 1049.23, "text": "اتغير واحد منهم، إذا هي متغيرة، اتغير التانية من باب أولى، تمام، إذا في الحركة الدائرية في مجال يكون مافيش تسارع، ولا ممكن، ولا ممكن، بيصير فيه تناقض، كيف حركة دائرية مافيش تسارع؟", "tokens": [9307, 17082, 13546, 36764, 24401, 9154, 16095, 12399, 11933, 15730, 39896, 44650, 17082, 48923, 12399, 1975, 2655, 17082, 13546, 16712, 7649, 10632, 9154, 4724, 16758, 5551, 12610, 7578, 12399, 46811, 10943, 12399, 11933, 15730, 8978, 21542, 31747, 3660, 32748, 16373, 2288, 10632, 8978, 3714, 7435, 6027, 7251, 30544, 19446, 41185, 8592, 6055, 3794, 9640, 3615, 12399, 49429, 3714, 43020, 12399, 49429, 3714, 43020, 12399, 4724, 1829, 9381, 13546, 8978, 3224, 6055, 8315, 4587, 11242, 12399, 9122, 33911, 11331, 31747, 3660, 11778, 16373, 2288, 10632, 19446, 41185, 8592, 6055, 3794, 9640, 3615, 22807], "avg_logprob": -0.12987231310977732, "compression_ratio": 1.9404761904761905, "no_speech_prob": 1.2874603271484375e-05, "words": [{"start": 1032.17, "end": 1032.71, "word": "اتغير", "probability": 0.8268229166666666}, {"start": 1032.71, "end": 1033.09, "word": " واحد", "probability": 0.967041015625}, {"start": 1033.09, "end": 1033.89, "word": " منهم،", "probability": 0.8128255208333334}, {"start": 1033.89, "end": 1034.05, "word": " إذا", "probability": 0.621826171875}, {"start": 1034.05, "end": 1034.29, "word": " هي", "probability": 0.59619140625}, {"start": 1034.29, "end": 1035.27, "word": " متغيرة،", "probability": 0.904052734375}, {"start": 1035.27, "end": 1035.77, "word": " اتغير", "probability": 0.9241943359375}, {"start": 1035.77, "end": 1036.15, "word": " التانية", "probability": 0.626953125}, {"start": 1036.15, "end": 1036.29, "word": " من", "probability": 0.8349609375}, {"start": 1036.29, "end": 1036.49, "word": " باب", "probability": 0.938720703125}, {"start": 1036.49, "end": 1037.45, "word": " أولى،", "probability": 0.88720703125}, {"start": 1037.45, "end": 1038.33, "word": " تمام،", "probability": 0.8722330729166666}, {"start": 1038.33, "end": 1038.63, "word": " إذا", "probability": 0.93115234375}, {"start": 1038.63, "end": 1038.81, "word": " في", "probability": 0.94384765625}, {"start": 1038.81, "end": 1039.33, "word": " الحركة", "probability": 0.9534505208333334}, {"start": 1039.33, "end": 1040.33, "word": " الدائرية", "probability": 0.990234375}, {"start": 1040.33, "end": 1040.61, "word": " في", "probability": 0.80419921875}, {"start": 1040.61, "end": 1041.25, "word": " مجال", "probability": 0.9871419270833334}, {"start": 1041.25, "end": 1041.71, "word": " يكون", "probability": 0.97802734375}, {"start": 1041.71, "end": 1042.03, "word": " مافيش", "probability": 0.9444986979166666}, {"start": 1042.03, "end": 1043.11, "word": " تسارع،", "probability": 0.83193359375}, {"start": 1043.11, "end": 1043.69, "word": " ولا", "probability": 0.436767578125}, {"start": 1043.69, "end": 1044.85, "word": " ممكن،", "probability": 0.9290364583333334}, {"start": 1044.85, "end": 1045.05, "word": " ولا", "probability": 0.82177734375}, {"start": 1045.05, "end": 1045.67, "word": " ممكن،", "probability": 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" بيقوللي", "probability": 0.7821044921875}, {"start": 1057.69, "end": 1057.95, "word": " when", "probability": 0.73291015625}, {"start": 1057.95, "end": 1058.43, "word": " an", "probability": 0.892578125}, {"start": 1058.43, "end": 1059.21, "word": " object", "probability": 0.97021484375}, {"start": 1059.21, "end": 1059.97, "word": " أي", "probability": 0.740234375}, {"start": 1059.97, "end": 1060.41, "word": " جسم", "probability": 0.850341796875}, {"start": 1060.41, "end": 1061.53, "word": " moves", "probability": 0.76318359375}, {"start": 1061.53, "end": 1061.91, "word": " on", "probability": 0.9287109375}, {"start": 1061.91, "end": 1062.27, "word": " a", "probability": 0.9814453125}, {"start": 1062.27, "end": 1062.83, "word": " circular", "probability": 0.734375}, {"start": 1062.83, "end": 1063.51, "word": " path", "probability": 0.955078125}, {"start": 1063.51, "end": 1064.47, "word": " مصار", "probability": 0.8391927083333334}, {"start": 1064.47, "end": 1065.29, "word": " دائري", 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frequency جيد بس متعرف عليه برمز جيد Omega اسمه الـ Omega أديكم الرمز تبعه", "tokens": [1211, 28820, 38637, 7649, 10632, 30731, 12602, 16254, 995, 5296, 28820, 38637, 7649, 10632, 48812, 25513, 32239, 3224, 8978, 568, 4339, 20328, 5016, 1829, 5016, 22807, 1975, 15730, 20449, 8315, 47395, 4724, 1829, 39648, 5296, 1829, 3224, 570, 562, 8894, 28242, 11778, 13063, 3660, 6915, 568, 4339, 12602, 16254, 995, 5296, 20292, 3224, 13898, 11778, 47341, 3660, 46811, 10943, 264, 24413, 3073, 31439, 7893, 10874, 25708, 4724, 3794, 44650, 3615, 28480, 47356, 4724, 2288, 2304, 11622, 10874, 25708, 27645, 24525, 2304, 3224, 2423, 39184, 27645, 5551, 16254, 24793, 34892, 2304, 11622, 6055, 3555, 3615, 3224], "avg_logprob": -0.327636725269258, "compression_ratio": 1.4666666666666666, "no_speech_prob": 1.0132789611816406e-06, "words": [{"start": 1529.3, "end": 1529.86, "word": "لكل", "probability": 0.6483154296875}, {"start": 1529.86, "end": 1530.58, "word": " ثانية", "probability": 0.98681640625}, 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"end": 2075.24, "word": " طلعوا", "probability": 0.9044189453125}, {"start": 2075.24, "end": 2076.24, "word": " omega", "probability": 0.78173828125}, {"start": 2076.24, "end": 2077.04, "word": " بسوى", "probability": 0.72900390625}, {"start": 2077.04, "end": 2077.26, "word": " 1", "probability": 0.5478515625}, {"start": 2077.26, "end": 2077.88, "word": ".9", "probability": 0.98779296875}, {"start": 2077.88, "end": 2078.3, "word": " فعشرة", "probability": 0.60772705078125}, {"start": 2078.3, "end": 2078.86, "word": " أساليب", "probability": 0.638818359375}, {"start": 2078.86, "end": 2079.3, "word": " سبعة", "probability": 0.9298502604166666}], "temperature": 1.0}, {"id": 88, "seek": 210892, "start": 2080.96, "end": 2108.92, "text": "والسرعة بتكون برضه بسيطة خلّيني نتطلع على Omega هذه إيش الواحدة جالي radian per second؟ لو جيت حكيت لواحد في الشارع من عامة الناس ال radian بقرا فخشي إن كانت درجة بقدر أحس فيها أكتر يعني لما تقوله خمس درجات أو عشرين درجة بحسها جالي أحولليها بديش radian طيب هو كيف بدي أنا أحول من radian ل second؟ جالي بسيطة هي ال πاي أكم radian", "tokens": [2407, 6027, 3794, 2288, 27884, 39894, 30544, 4724, 43042, 3224, 4724, 3794, 1829, 9566, 3660, 16490, 1211, 11703, 9957, 1829, 8717, 2655, 9566, 1211, 3615, 15844, 27645, 29538, 11933, 1829, 8592, 2423, 14407, 24401, 3660, 10874, 6027, 1829, 2843, 952, 680, 1150, 22807, 45164, 10874, 36081, 11331, 4117, 36081, 5296, 14407, 24401, 8978, 25124, 9640, 3615, 9154, 6225, 10943, 3660, 2423, 8315, 3794, 2423, 2843, 952, 4724, 4587, 23557, 6156, 9778, 8592, 1829, 36145, 25961, 2655, 11778, 47341, 3660, 4724, 28543, 2288, 5551, 5016, 3794, 8978, 11296, 5551, 4117, 2655, 2288, 37495, 22653, 5296, 15042, 6055, 39648, 3224, 16490, 2304, 3794, 11778, 47341, 9307, 34051, 6225, 46309, 9957, 11778, 47341, 3660, 4724, 5016, 3794, 11296, 10874, 6027, 1829, 5551, 5016, 12610, 20292, 11296, 4724, 16254, 8592, 2843, 952, 23032, 1829, 3555, 31439, 9122, 33911, 4724, 16254, 41850, 5551, 5016, 12610, 9154, 2843, 952, 5296, 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صحيح ماحد يصدق واحد في دبي او واحد في تهران يقول انا شفت الجمر ولا ممكن", "tokens": [41185, 25062, 40294, 25720, 1975, 8315, 19446, 8592, 5172, 2655, 8592, 25724, 29973, 4032, 41361, 6225, 45340, 4724, 2304, 3615, 1863, 7578, 20328, 5016, 1829, 5016, 19446, 24401, 7251, 9381, 3215, 4587, 36764, 24401, 8978, 11778, 21292, 1975, 2407, 36764, 24401, 8978, 6055, 3224, 2288, 7649, 7251, 39648, 1975, 8315, 13412, 5172, 2655, 25724, 29973, 49429, 3714, 43020], "avg_logprob": -0.12380826069136798, "compression_ratio": 1.7394957983193278, "no_speech_prob": 5.304813385009766e-06, "words": [{"start": 2664.22, "end": 2664.4, "word": "في", "probability": 0.85546875}, {"start": 2664.4, "end": 2665.1, "word": " القاهرة", "probability": 0.9952799479166666}, {"start": 2665.1, "end": 2665.62, "word": " انا", "probability": 0.68212890625}, {"start": 2665.62, "end": 2666.1, "word": " ماشفتش", "probability": 0.796484375}, {"start": 2666.1, "end": 2666.54, "word": " الجمر", "probability": 0.924072265625}, 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"word": " ولا", "probability": 0.9462890625}, {"start": 3017.79, "end": 3018.65, "word": " لأ", "probability": 0.938720703125}, {"start": 3018.65, "end": 3019.13, "word": " بنجف", "probability": 0.7369791666666666}, {"start": 3019.13, "end": 3019.57, "word": " هناك", "probability": 0.54046630859375}, {"start": 3019.57, "end": 3020.65, "word": " دى", "probability": 0.467041015625}, {"start": 3020.65, "end": 3020.93, "word": " عفوة", "probability": 0.37286376953125}, {"start": 3020.93, "end": 3021.45, "word": " للعاوزة", "probability": 0.6283365885416666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3021.636, "duration_after_vad": 2934.2624999999884}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4_raw.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c7caf719d22bc11b961f3cbd6a4d6c01479c1063
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/okUXKQuChy4_raw.srt
@@ -0,0 +1,2472 @@
+1
+00:00:05,280 --> 00:00:09,540
+طبعا يا بنات خلينا نستكمل المثال أو نعيد المثال
+
+2
+00:00:09,540 --> 00:00:15,600
+حلقنا و بدينا نحله و قلنا إنه في عندى هدف بدي
+
+3
+00:00:15,600 --> 00:00:21,640
+أصيده و هان اللي بدي أصيده بدي ينشل هال gate بدي
+
+4
+00:00:21,640 --> 00:00:26,660
+أثبت إنه عشان يقدر يصيده لازم أول ما ينش يكون على
+
+5
+00:00:26,660 --> 00:00:31,820
+نفس الخط مع الهدف قبل ما ينزل مع الهدف الثابت
+
+6
+00:00:31,820 --> 00:00:37,730
+وبالتاليقلت إنه نفترض إنه بدي نصيبه بعض هنا إذا
+
+7
+00:00:37,730 --> 00:00:42,170
+قطعا بدي يكون موضعين زي بعض ولا لأ هذا هو trick
+
+8
+00:00:42,170 --> 00:00:47,230
+السؤال قال لي حلو أنا بأقذف أنا بدي أقذف قظيفة
+
+9
+00:00:47,230 --> 00:00:53,630
+عشان نصيب بأقذف بزاوية هذه الزاوية بعتبرها θيتاوفي
+
+10
+00:00:53,630 --> 00:00:57,630
+زاوية تابعة الخط لما رسمت ونشنت اللي بدي اعتبرها
+
+11
+00:00:57,630 --> 00:01:00,830
+Alpha هجيت انا بدي اثبت ان Theta و Alpha نفس زاوية
+
+12
+00:01:00,830 --> 00:01:05,750
+ولا لأ هذا هو اللي بدي اثبته واحد قلت في عندي
+
+13
+00:01:05,750 --> 00:01:10,250
+حركتين هذا عبارة عن ال target الهدف اللي بدي أصيبه
+
+14
+00:01:10,250 --> 00:01:17,220
+وهذا ال projectile اللي هياللي قدفتها تمام هيك؟
+
+15
+00:01:17,220 --> 00:01:23,140
+حلو قولت ال target بده ينزل سقوط حر قطعي بده ينزل
+
+16
+00:01:23,140 --> 00:01:27,080
+سقوط حر وبالتالي في السقوط الحر كان في عندي قانون
+
+17
+00:01:27,080 --> 00:01:32,500
+بيقول Y final مقص Y initial بتسوي VY initial في T
+
+18
+00:01:32,500 --> 00:01:37,700
+مقص نص GT تربيع ذاكرينه؟ قولت يبدأ يشتغل فيه طبعا
+
+19
+00:01:37,700 --> 00:01:42,310
+المحاور تبعتيأنا بدي أشتغل بناءً على هيك، إن هاي
+
+20
+00:01:42,310 --> 00:01:47,430
+المحاولة هو الدنياها، إذاً معناته هي الـOrigin،
+
+21
+00:01:47,430 --> 00:01:52,610
+وبالتالي، بداية أنا أسقطت سقوط، معناته السرعة
+
+22
+00:01:52,610 --> 00:01:56,490
+الإبتدائية تبعته بديش، هذا هو الهدف، إن أنا بدي
+
+23
+00:01:56,490 --> 00:02:00,090
+أسقط و هو بدي يقذف، هو بدي يقذف بسرعة إبتدائية
+
+24
+00:02:00,090 --> 00:02:03,630
+معينة، لكن أنا الهدف بدي أن أنزل و أنزل، معناته
+
+25
+00:02:03,630 --> 00:02:10,830
+هان، هذه Zero،تمام why final وين بده المصيد و بعيد
+
+26
+00:02:10,830 --> 00:02:15,570
+هنا why final بده اعتبره why تمام اذا why final هي
+
+27
+00:02:15,570 --> 00:02:22,310
+why طب وين كان بداية المشفوق اذا ناقص H تمام
+
+28
+00:02:22,310 --> 00:02:33,250
+بتساوي سفر ناقص نص جيل لتربية صحيح احكيه اللي بدك
+
+29
+00:02:33,250 --> 00:02:42,150
+هي تمامحلو من هنا اقدرت اقول انه H بدأنا نقول H
+
+30
+00:02:42,150 --> 00:02:50,570
+هنا وهذه H صارت Y زائد نص GT تربية خلاص قفلنا هذه
+
+31
+00:02:50,570 --> 00:02:57,320
+جيبناها العلاقة نشوف المخضوفةالمقظوفة قذفتها حسب
+
+32
+00:02:57,320 --> 00:03:01,380
+الرسمة بزاوية انت اعتبرتها θيتا صح ولا لأ اذا انا
+
+33
+00:03:01,380 --> 00:03:05,720
+في المقظوفات قلت اول حاجة بقول v initial x بتساوي
+
+34
+00:03:05,720 --> 00:03:11,180
+v initial cos θ و v initial y بتساوي v initial sin
+
+35
+00:03:11,180 --> 00:03:16,880
+θ بعملها لكل حركة المقظوفات بجسم معطياتي إلى سينية
+
+36
+00:03:16,880 --> 00:03:24,110
+وصادية تمقال لي في عندك قانون برضه هنا بيقول هذا
+
+37
+00:03:24,110 --> 00:03:28,550
+ال projectile Y final نقص Y initial بيسوي VY
+
+38
+00:03:28,550 --> 00:03:32,910
+initial في T minus half GT تربيع ولا لأ نفس الشغل
+
+39
+00:03:32,910 --> 00:03:38,430
+هذا القانون الصاضي قال لي الآن Y final و الله نفس
+
+40
+00:03:38,430 --> 00:03:42,790
+ال Y ماشي التانية نقلهم نفس ال Y؟ طب initial ال
+
+41
+00:03:42,790 --> 00:03:47,750
+projectile من وين بدأ؟من صفر إذا هذا بدأ من صفر
+
+42
+00:03:47,750 --> 00:03:53,490
+بتساوي .. قدّيش هذه هيها؟ the initial sine of
+
+43
+00:03:53,490 --> 00:03:59,910
+theta نقص half GT تربيع صحيك ولا لأ؟ اتطلع انتوا
+
+44
+00:03:59,910 --> 00:04:05,740
+هنا إيش عملتنا؟ هجيت هذه Y غير عن Y هذه؟ولا نفسه
+
+45
+00:04:05,740 --> 00:04:09,440
+لأنه عشان يصيدوا بعض لازم يكون اللي هو نفسه ال Y
+
+46
+00:04:09,440 --> 00:04:14,080
+إذا معناته بصح اللي هادي أجيبها و أحطها محل هادي
+
+47
+00:04:14,080 --> 00:04:16,000
+ولا لأ إذا بقوله
+
+48
+00:04:19,450 --> 00:04:24,610
+في هاد ال TV مظبوط كلامكم تمام إذا هاد ال Y جيبها
+
+49
+00:04:24,610 --> 00:04:32,450
+هنا قلتله إذا صار H بتثاوي طلعه V initial sine
+
+50
+00:04:32,450 --> 00:04:37,750
+theta في T هاد زائد و هاد ناقص بروحوا مع بعض قاللي
+
+51
+00:04:37,750 --> 00:04:41,510
+حلو طلعتلي H قاللي إنت إيش اللي بدك تثبته؟ بدي
+
+52
+00:04:41,510 --> 00:04:44,990
+قولله بدي أثبت إن Alpha و Theta إخوة نفس الزاوية
+
+53
+00:04:44,990 --> 00:04:48,890
+قلتله طلع ليه على الرسمةبتقدر تقولي من الرسمة أن
+
+54
+00:04:48,890 --> 00:04:55,810
+تاني الألفة هي عبارة عن مقابل ع ميوّر H على X صح
+
+55
+00:04:55,810 --> 00:05:01,170
+ولا لأ؟ H و الله جبتها ده اللي كيف بدك تجيب X؟
+
+56
+00:05:01,170 --> 00:05:03,610
+قلتله X لإن البروجيكت الموشي اللي فيه قانون بيقول
+
+57
+00:05:03,610 --> 00:05:09,550
+X final نغس X initial بتسوى V initial X في T
+
+58
+00:05:09,550 --> 00:05:14,110
+ذاكرينه؟هذه الـ projectile motion القانوني الوحيد
+
+59
+00:05:14,110 --> 00:05:19,130
+في الحلقة الصينية بيقول كله طاير X final هي X اللي
+
+60
+00:05:19,130 --> 00:05:25,250
+بتقول عنها و X initial صفر اذا X و V initial X وين
+
+61
+00:05:25,250 --> 00:05:33,110
+ها هي V initial cos θ T هاي Xجالي يلّا عوّط هاي H
+
+62
+00:05:33,110 --> 00:05:38,930
+و هاي X إذا هذه بتساوي ان عوّط V initial sin θ في
+
+63
+00:05:38,930 --> 00:05:44,090
+T على V initial cos θ في T V initial مع V initial
+
+64
+00:05:44,090 --> 00:05:49,090
+راحة sin θ على cos θ تان الثيتا تان الألفة بتساوي
+
+65
+00:05:49,090 --> 00:05:53,690
+تان الثيتا إذا الثيتا هي نفس الألفة و المطلوب
+
+66
+00:05:53,690 --> 00:06:00,680
+إثباته كمان يا بنات؟هذا المثال خلصنا هانا عملتها
+
+67
+00:06:00,680 --> 00:06:06,500
+زي ما أنا كتبتها حطيت ال target على اعتبار انه في
+
+68
+00:06:06,500 --> 00:06:10,700
+falling حطيتها على المجموعة هذا هذا الحل عساس انه
+
+69
+00:06:10,700 --> 00:06:14,120
+لو مخوض عينكم في الورق و ال projector اللي هي
+
+70
+00:06:14,120 --> 00:06:20,660
+القذيفة اللي قذفتها حطيت قوامينها و بعد كده قلتبعد
+
+71
+00:06:20,660 --> 00:06:24,620
+ما حطيتها وجيبت H و X وقالت it is not from the
+
+72
+00:06:24,620 --> 00:06:27,480
+projectile that for the projectile to hit the
+
+73
+00:06:27,480 --> 00:06:30,920
+target they must have the same position لازم
+
+74
+00:06:30,920 --> 00:06:36,100
+يضربوا بعض في نفس المكان وبالتالي جيبت Y وجيبت H
+
+75
+00:06:36,100 --> 00:06:41,740
+وجيبت X ومنها قلت اذا θ هي نفس ال alpha تمام؟ وحل
+
+76
+00:06:41,740 --> 00:06:46,760
+الكتاب بين ايديكم مختلف شوية مش قضية حد خلصناه؟
+
+77
+00:06:46,760 --> 00:06:49,960
+شوف هالسؤال
+
+78
+00:06:52,820 --> 00:06:59,380
+جلي متزلج بتعرفوها رياضة التزلج بروحوا بنط و نطة و
+
+79
+00:06:59,380 --> 00:07:02,340
+بعدين في الأخر نازلين على التلج ولا مش نازلين
+
+80
+00:07:02,340 --> 00:07:07,490
+نازلين مين ننزله؟الجاذبية إذا هي projectile motion
+
+81
+00:07:07,490 --> 00:07:12,090
+لأن اللي بتحكم فيهم هي الجاذبية الأرضية و هي
+
+82
+00:07:12,090 --> 00:07:17,310
+تعريفه projectile motion جالي a sky jumper بيقفز
+
+83
+00:07:17,310 --> 00:07:26,610
+قافظ التلج leaves the sky track المسار تبع التلج
+
+84
+00:07:26,610 --> 00:07:30,810
+track مسار هو لما يفلكي المسار بس ما تشوفي الهواء
+
+85
+00:07:32,330 --> 00:07:35,470
+بقى عبث و بيروح في الهو و بعدين بنزل اذا فار
+
+86
+00:07:35,470 --> 00:07:40,890
+project الموشي leavesThe sky track moving
+
+87
+00:07:40,890 --> 00:07:47,010
+horizontally قال لي أول ما طرع أسار في الهوى طلع
+
+88
+00:07:47,010 --> 00:07:53,950
+بسرعة أفقية فقط يعني V Initial Y جديش سفر قال لي
+
+89
+00:07:53,950 --> 00:07:58,030
+هذه حركة مغظوفات وفي حركة المغظوفات احنا متعودين
+
+90
+00:07:58,030 --> 00:08:03,790
+ان نجسم الحركة لسنية وصادرية ولا لأ حلو هاي بدنا
+
+91
+00:08:03,790 --> 00:08:07,790
+نجسم هاي بدنا نقول X motion
+
+92
+00:08:11,550 --> 00:08:17,950
+Why مش الحركة الصينية والصاضية تم نجي على السؤال
+
+93
+00:08:17,950 --> 00:08:22,970
+كل حاجة معطية بتشوفها صيني ولا صاضي ولي لا هي هيك
+
+94
+00:08:22,970 --> 00:08:27,330
+ولا هي هيك بدي أحللها مش هيك اتفاقناها حلو جالي
+
+95
+00:08:27,330 --> 00:08:33,430
+قُدِفَت بسرعة أفوخية معناته V Y Initial Gradiation
+
+96
+00:08:33,430 --> 00:08:41,660
+سفرلأنه مافيش صرعة ابتدائية صادية هو قاللي صينية
+
+97
+00:08:41,660 --> 00:08:46,900
+فقط كيف عرفتي انه صينية من كلمة horizontally صحيح؟
+
+98
+00:08:46,900 --> 00:08:53,520
+V X initial قاللي و الله خمسة و عشرين هاي أول معطف
+
+99
+00:08:53,520 --> 00:09:01,250
+بتفجيني هيك؟ حلو قاللي رسمةأشون يا جلّي هذا الرصم
+
+100
+00:09:01,250 --> 00:09:03,990
+من معطيات السؤال ولا لأ؟ يا جلّي اتطلع ال origin
+
+101
+00:09:03,990 --> 00:09:07,950
+أنوة اللي مضيكيها هنا إذا هو بدأ من هنا من نقطة ال
+
+102
+00:09:07,950 --> 00:09:13,090
+origin يعني x initial قداش و y initial سفر إذا
+
+103
+00:09:13,090 --> 00:09:19,570
+بقوله x initial ها x initial سفر و y initial سفر
+
+104
+00:09:20,860 --> 00:09:24,980
+أيش بدك؟ بقولي where does اه The landing inclined
+
+105
+00:09:24,980 --> 00:09:29,320
+below her falls off with a slope of 35 degree
+
+106
+00:09:29,320 --> 00:09:34,860
+قاللي المسار اللي بتسجط عليه مش عدل بيميل بزاوي 35
+
+107
+00:09:34,860 --> 00:09:41,080
+درجة شايفين الرسمة؟إذا هو أو هي لما طارت بدى تنزل
+
+108
+00:09:41,080 --> 00:09:45,900
+على التلج والمصار هاد ميل جديه الزاوية ميلانه؟ قال
+
+109
+00:09:45,900 --> 00:09:51,740
+لي 35 درجة قال لي هيها 35 طب احنا بمعلومات المدرسة
+
+110
+00:09:51,740 --> 00:09:55,480
+بنقدر نقول هادي الزاوية هي نفسها هادي بالتبادل ولا
+
+111
+00:09:55,480 --> 00:10:01,500
+لأ؟ إذا هادي الزاوية كدهش؟ 35 وين ودها تنزل؟ قال
+
+112
+00:10:01,500 --> 00:10:02,920
+لي نفترض ان بتنزل هادي
+
+113
+00:10:11,160 --> 00:10:17,140
+بتقدر تقول إيه إذا هذه الزاوية في تاني الفاي sorry
+
+114
+00:10:17,140 --> 00:10:20,760
+سايني الفاي خلينا نقول واحدة واحدة كوسايني الفاي
+
+115
+00:10:20,760 --> 00:10:27,960
+اللي هي 35 بتساوي مجاور أواطر المجاور X ولا لأ إذا
+
+116
+00:10:27,960 --> 00:10:38,020
+X على Dcos φ بتساوي y على d طبعا بنيجي هجيت للموضع
+
+117
+00:10:38,020 --> 00:10:46,600
+معناته بقدر أجوبكم هنا x final بتساوي d cos ف؟ صح
+
+118
+00:10:46,600 --> 00:10:53,860
+ولا لأ طب ال y بس دي رباكم تحت ال origin تحت ال
+
+119
+00:10:53,860 --> 00:10:57,640
+origin بال minus إذا معناته بقوله هنا y final
+
+120
+00:10:57,640 --> 00:11:06,750
+بساوي سالب d sin فاتفجن أيه يا بنات؟ خلص ايش بده؟
+
+121
+00:11:06,750 --> 00:11:11,490
+جالي بدي دي جالي يلّا نشوف نخبص في القوانين اللي
+
+122
+00:11:11,490 --> 00:11:15,950
+عندنا الحركة السنية هي اللي هي قانون واحدة X final
+
+123
+00:11:15,950 --> 00:11:19,910
+نقص X initial بتساوي V initial X في T صح ولا لأ؟
+
+124
+00:11:19,910 --> 00:11:25,570
+اكتبوا قولتله ها X final نقص X initial بتساوي V
+
+125
+00:11:25,570 --> 00:11:31,790
+initial X في T مش غيرهنجي معاول جدّيش X فاين هاي
+
+126
+00:11:31,790 --> 00:11:39,210
+دي وهاي قصاني الفاين جدّيش هذي؟ Zero جدّيش هذي؟
+
+127
+00:11:39,210 --> 00:11:44,870
+خمسة وعشرين T هاي اللي قدرتها عليه قولوا يا خلينا
+
+128
+00:11:44,870 --> 00:11:47,050
+نجيب الزمن ما هو الزمن اللي بقدر أشحته من هو
+
+129
+00:11:47,050 --> 00:11:51,930
+المكان مظبوط ولا سيني وصاضي خلينا نجهزه T بتسوي D
+
+130
+00:11:51,930 --> 00:11:56,590
+قصين هذي الفاين خمسة وتلاتين ولا لأ على خمسة
+
+131
+00:11:56,590 --> 00:12:01,260
+وعشرين هذي جهزتهوشوف الحركة الصادرية خلصنا من
+
+132
+00:12:01,260 --> 00:12:05,200
+الصينية اللي قدرنا نعمله فيه عملناه نجيلها وقال
+
+133
+00:12:05,200 --> 00:12:10,560
+والله في قانون بيقول y final ناقص y initial سواء v
+
+134
+00:12:10,560 --> 00:12:17,300
+initial او y initial t ناقص half gt تربيه ذاكرينه؟
+
+135
+00:12:17,300 --> 00:12:24,370
+ذي الله نعوضجدّيش y final؟ سالب دي sign ال five
+
+136
+00:12:24,370 --> 00:12:30,530
+إذا سالب دي sign الخمسة و تلاتين جدّيش y initial؟
+
+137
+00:12:30,530 --> 00:12:38,290
+سفر بتساوي جدّيش دي y initial؟ سفر إذا بتساوي سالب
+
+138
+00:12:38,290 --> 00:12:46,290
+نص جي إيش أدي؟T تربية بينفعش حتى منها مش هي T نفس
+
+139
+00:12:46,290 --> 00:12:51,010
+السنية وسادية واحد اذا بدل ما تحط اللي T اعوض يا
+
+140
+00:12:51,010 --> 00:12:58,690
+عم اعوضنا دي كوسايم الخمسة وتلاتين على خمسة وعشرين
+
+141
+00:12:58,690 --> 00:13:05,230
+كل تربية مظبوذك ولا لأ طلعوا على المعادلة ايش
+
+142
+00:13:05,230 --> 00:13:11,580
+المجهول الوحيد طلعنا ديخلص السؤال نيجي نتطلع بقول
+
+143
+00:13:11,580 --> 00:13:17,060
+السالب مع السالب روحه صح ها دي دي تربيع و هنا في
+
+144
+00:13:17,060 --> 00:13:27,220
+دي اذا ها دي بتصير sin 35 بساوي نص g cos تربيع 35
+
+145
+00:13:27,220 --> 00:13:38,350
+في دي في دي على 625 اللي هو 25 تربيعجالي يلّا و
+
+146
+00:13:38,350 --> 00:13:42,990
+قولتله إذا دي اللي بتدور عليها بتثوي هذه نص و هذه
+
+147
+00:13:42,990 --> 00:13:46,350
+ستمية و خمسة و عشرين يعني تدورها في اتنين ستمية و
+
+148
+00:13:46,350 --> 00:13:49,630
+ستمية ألف و متين و خمسة و عشرين و خمسة و عشرين إذا
+
+149
+00:13:49,630 --> 00:13:55,290
+ألف و متين و خمسين إذا ألف و متين و خمسين في sin
+
+150
+00:13:55,290 --> 00:14:02,730
+الخمسة و تلاتين على جي في cosine تربيع الخمسة و
+
+151
+00:14:02,730 --> 00:14:07,030
+تلاتين يلّا ال calculator طلعتها مية و تسعةصح ولا
+
+152
+00:14:07,030 --> 00:14:12,190
+لا؟ وإذا طلعنا دي يي بقدر أجيب X final و Y final
+
+153
+00:14:12,190 --> 00:14:20,310
+خلاص هاي السؤال أي السفسار سهل العملية تمام يا
+
+154
+00:14:20,310 --> 00:14:25,130
+بنات؟ هي حركة المغضوفات حركة المغضوفات حركة مهمة
+
+155
+00:14:25,130 --> 00:14:30,040
+وبتنط في كتير امتحانات كأسئلةإيش .. كيف نشتغل
+
+156
+00:14:30,040 --> 00:14:32,760
+عليها؟ إيش الستراتيجية؟ بقوله أول حاجة بدي أجسمها
+
+157
+00:14:32,760 --> 00:14:36,520
+حركتين صينية و صادية بروح بتطلع على المعطيات
+
+158
+00:14:36,520 --> 00:14:40,000
+المعطل الصيني بحطه تحت الصيني و الصادي بحطه تحت
+
+159
+00:14:40,000 --> 00:14:44,240
+الصادي اللي لا هو صيني ولا هو صادي بدي أجسمه أحلله
+
+160
+00:14:44,240 --> 00:14:47,640
+إلى مركبة صينية و مركبة صادية و بعدين بدي أشتغل
+
+161
+00:14:47,640 --> 00:14:51,420
+إيش بدك؟ بدي مسافة صينية بروح أقارن الصينية بدي
+
+162
+00:14:51,420 --> 00:14:55,390
+مسافة صادية بروح أقارن الصادية بدي زمان انتحارروح
+
+163
+00:14:55,390 --> 00:14:58,310
+صيني أو روح صادي صح ولا لأ؟ و بنشتغل على هذه
+
+164
+00:14:58,310 --> 00:15:06,610
+الأساس تمه اذا أول حاجة جيبني X final و Y final من
+
+165
+00:15:06,610 --> 00:15:10,710
+القانون اللي بنعرفه و بعدين ده اللي في عندي X
+
+166
+00:15:10,710 --> 00:15:14,210
+final ناقص X initial اللي هي سفر بيسوي X initial
+
+167
+00:15:14,210 --> 00:15:20,430
+في T طلعليهاأعوض و منها بقدر أجيب T و استخدم قانون
+
+168
+00:15:20,430 --> 00:15:25,250
+ال Y بنفس الكيفية على اعتبار ان VY initial صفر
+
+169
+00:15:25,250 --> 00:15:32,450
+طلحها قال لي Substituting عوض من T هالها اللي
+
+170
+00:15:32,450 --> 00:15:37,090
+عملناه قال لي طلعت عندك المعادلة الحلوة هايها و
+
+171
+00:15:37,090 --> 00:15:41,210
+طلعت منها D طلعت 109 وبناء عليها جبت ال position
+
+172
+00:15:41,210 --> 00:15:52,160
+تبع الالرياضية لما نزلت على الأرض تمى أنواننا
+
+173
+00:15:52,160 --> 00:15:58,120
+التالي هو نوع من أنواع الحركة المستوية ويسمى
+
+174
+00:15:58,120 --> 00:16:04,160
+circular من circle مظبوط ولا لأ حركة دائرية كل جسم
+
+175
+00:16:04,160 --> 00:16:08,260
+بدور بقول عنه بتحرك حركة دائرية بدور تمى
+
+176
+00:16:10,360 --> 00:16:14,380
+في الشوارع يعني فيه دوارات بتعرف الدوار؟ السيارة
+
+177
+00:16:14,380 --> 00:16:17,160
+لما تخش الدوار على طول بقول صارت حركتها حركة
+
+178
+00:16:17,160 --> 00:16:21,860
+دائرية لأنها بدأت لف تمه هاجيت يا بنات في الحركة
+
+179
+00:16:21,860 --> 00:16:26,960
+الدائرية تصورولي معاه هيك في مجال واحد يتحرك حركة
+
+180
+00:16:26,960 --> 00:16:35,320
+دائرية ويخل اتجاه صرعته ثابت اتجاه صرعته هو إيش
+
+181
+00:16:35,320 --> 00:16:39,650
+لازم يسوي مش هو لازم يميل؟ لازم يظل يميلولّا لو
+
+182
+00:16:39,650 --> 00:16:44,330
+دلّه اتجاه صرعته ثابت بطلت الحركة دائرية فانا بمشي
+
+183
+00:16:44,330 --> 00:16:49,810
+خط مصطقين تمام إذا في الحركة الدائرية اتجاه الصرعة
+
+184
+00:16:49,810 --> 00:16:54,790
+دائما متغير ولا لأ؟طب حلو انشوف ايش تعريف الـ
+
+185
+00:16:54,790 --> 00:16:59,890
+acceleration معدل تغير سرعة بالنسبالي الزمن اتغيرت
+
+186
+00:16:59,890 --> 00:17:03,850
+السرعة اذا في acceleration طب في حركة دائرية مسموح
+
+187
+00:17:03,850 --> 00:17:07,470
+لل velocity تظلها ثابتة اقل ال direction تبعها
+
+188
+00:17:07,470 --> 00:17:11,230
+متغير ولا لأ لأن ال velocity عبارة عن direction و
+
+189
+00:17:11,230 --> 00:17:16,150
+speedاتغير واحد منهم، إذا هي متغيرة، اتغير التانية
+
+190
+00:17:16,150 --> 00:17:21,250
+من باب أولى، تمام، إذا في الحركة الدائرية في مجال
+
+191
+00:17:21,250 --> 00:17:26,610
+يكون مافيش تسارع، ولا ممكن، ولا ممكن، بيصير فيه
+
+192
+00:17:26,610 --> 00:17:31,210
+تناقض، كيف حركة دائرية مافيش تسارع؟طبعا؟ إذا
+
+193
+00:17:31,210 --> 00:17:35,090
+معناته إيش بيقوللي طب وقت إيش بتسميها uniform و
+
+194
+00:17:35,090 --> 00:17:39,210
+وقت إيش بتسميها non uniform بيقوللي when an object
+
+195
+00:17:39,210 --> 00:17:46,150
+أي جسم moves on a circular path مصار دائري with
+
+196
+00:17:46,150 --> 00:17:52,650
+constant speed بقدر يقول constant velocity؟بالصحيح
+
+197
+00:17:52,650 --> 00:17:56,250
+لأنه بيبقى في تناقض بالكلام بجهود لأن كيف circular
+
+198
+00:17:56,250 --> 00:18:00,150
+بيحظر في constant velocity أما constant speed مسمح
+
+199
+00:18:00,150 --> 00:18:04,050
+لك بيبقى الاشي يتغير ال direction إذا كانت ال
+
+200
+00:18:04,050 --> 00:18:08,910
+speed constant بيقول هذه حركة دائرية بس منطلمة طيب
+
+201
+00:18:08,910 --> 00:18:11,770
+وإذا ال speed مش constant بتبطى ال uniform it's a
+
+202
+00:18:11,770 --> 00:18:16,810
+non uniform circular motion if the speed is
+
+203
+00:18:16,810 --> 00:18:19,750
+constant the object is said to be in a uniform
+
+204
+00:18:19,750 --> 00:18:23,820
+circular motion طيبهذه حركة دائرية مش عادي دائرة
+
+205
+00:18:23,820 --> 00:18:29,660
+وهذا الجسم بنخليه يلف في
+
+206
+00:18:29,660 --> 00:18:33,220
+نقطة من النقاط لو بدي أرسم المماثل هي السرعة
+
+207
+00:18:33,220 --> 00:18:39,040
+اتجاهها زي جابلها ولا ممكن ولا ممكن معناته كيف
+
+208
+00:18:39,040 --> 00:18:43,520
+اتجاه السرعات بقوله اتجاه السرعات هي هيك و هيك و
+
+209
+00:18:43,520 --> 00:18:48,780
+هيك و هيك صح؟ في سهم من الأسهم الأربعة اتجاهه زي
+
+210
+00:18:48,780 --> 00:18:58,070
+أخوإذن دائما اتجاه سرعة ماله متغير تمام؟ حلو بقول
+
+211
+00:18:58,070 --> 00:19:02,010
+لي as the velocity is always tangent to the path
+
+212
+00:19:02,010 --> 00:19:05,510
+flowed طبعا دائما السرعة لازم يكون مماس انتوا
+
+213
+00:19:05,510 --> 00:19:10,330
+عارفين ان السرعة مشتقة X؟ومش تقّمعها من المماس؟
+
+214
+00:19:10,330 --> 00:19:15,050
+إذا المماس تمام وهي واضحة يعني إن واحد ماشي صرعته
+
+215
+00:19:15,050 --> 00:19:19,250
+معاه وبالتالي هو بلف صوت و بتلف معاه بقول بما إن
+
+216
+00:19:19,250 --> 00:19:24,290
+الصوعة دايما tangent مماس للمسار اللي فيه شغال
+
+217
+00:19:24,290 --> 00:19:27,730
+عليه the direction of the velocity in uniform
+
+218
+00:19:27,730 --> 00:19:32,670
+circular motion always changing دائما متغيرة إيش
+
+219
+00:19:32,670 --> 00:19:37,020
+اللي خلّها متغيرة؟ ال direction صح؟لأن انت بتغير
+
+220
+00:19:37,020 --> 00:19:39,820
+ال direction قاعدة إذا انت فاهمة ان السرعة مالها
+
+221
+00:19:39,820 --> 00:19:46,520
+متغيرة حلو اتغيرت السرعة ايش اتولد تسارق صح مازال
+
+222
+00:19:46,520 --> 00:19:51,160
+اتغيرت السرعة صار في عندك تسارق بقول لي although
+
+223
+00:19:51,160 --> 00:19:56,320
+although ايش معناته برغم من انه the speed is
+
+224
+00:19:56,320 --> 00:20:01,550
+constantلسبيت constant يجي واحد يقول لك ال speed
+
+225
+00:20:01,550 --> 00:20:05,630
+constant ال acceleration يساوي سفير لأ لأن ال
+
+226
+00:20:05,630 --> 00:20:10,990
+acceleration بتتبعش ال speed بتتبع velocity بيقول
+
+227
+00:20:10,990 --> 00:20:15,350
+although the speed is constantWe have an
+
+228
+00:20:15,350 --> 00:20:19,950
+acceleration. من وين إجت؟ It's due to the change
+
+229
+00:20:19,950 --> 00:20:23,050
+of the direction of the velocity.إذن، في عندي
+
+230
+00:20:23,050 --> 00:20:27,690
+تسارع بينتج فقط من تغير الـdirection تبع
+
+231
+00:20:27,690 --> 00:20:33,170
+الـvelocity.طب هذا إيش صفاته؟ قاللي هذا إله اشتقاق
+
+232
+00:20:33,170 --> 00:20:37,190
+مش مطموض بإنه في هذا المستوى.لو اشتقيت هذا التسارع
+
+233
+00:20:37,190 --> 00:20:39,970
+اللي جاي من تغير الـdirection، حيكون اتجاهه باتجاه
+
+234
+00:20:39,970 --> 00:20:44,580
+المركز.اتجاه التسارع كيف؟ باتجاه المركزي بيقول
+
+235
+00:20:44,580 --> 00:20:49,040
+this acceleration is directed اتجاهها towards the
+
+236
+00:20:49,040 --> 00:20:52,780
+center طب واحد باتجاه ال center ايش هسميه؟ قالوا
+
+237
+00:20:52,780 --> 00:20:57,100
+سموه مركزي عشان ما حد يخربطيه ليش مركزي؟ لأن
+
+238
+00:20:57,100 --> 00:21:01,540
+اتجاهه باتجاه مين؟ المركز تمام؟ طبعا اتفقنا انه
+
+239
+00:21:01,540 --> 00:21:05,180
+إثبات رياضي بس لسه شوية مهل عليكم عشان نديكم
+
+240
+00:21:05,180 --> 00:21:09,120
+إثباته في سنة تانية بصيروا تقدروا تعملوله إثبات
+
+241
+00:21:09,120 --> 00:21:13,650
+تفصيلي تمامcentripetal acceleration يعني تسارع
+
+242
+00:21:13,650 --> 00:21:19,550
+مركزي and is given by طب كيف مقداره قالوا برضه هذه
+
+243
+00:21:19,550 --> 00:21:23,050
+الإثبات البياضي بيطلعلك المقدار بيساوي V تربيع على
+
+244
+00:21:23,050 --> 00:21:26,230
+R ذاكرين لما خدنا ال dimensions وقلنا لكم هذا
+
+245
+00:21:26,230 --> 00:21:31,810
+التسارع المركزي إثبات
+
+246
+00:21:31,810 --> 00:21:36,880
+الهندسيمش الرياضي الإثبات الهندس اللي أخدتيه صحيح
+
+247
+00:21:36,880 --> 00:21:40,080
+بعرف اللي هو عشان كده لأ أنا جاي بهدا و لأ أنا جاي
+
+248
+00:21:40,080 --> 00:21:43,460
+بهدا اللي أخدتيه في المدرسة سهل وبالتالي كبرتوا
+
+249
+00:21:43,460 --> 00:21:45,920
+عليه و اللي أخدت .. اللي بتاخدوه رياضي لسه أنتوا
+
+250
+00:21:45,920 --> 00:21:52,140
+بدري عليكم الإثبات الرياضي حلو A C C يعني
+
+251
+00:21:52,140 --> 00:21:56,680
+centripetal صح ولا لأ طيب احنا أخدنا رموز كتيرة A
+
+252
+00:21:56,680 --> 00:22:03,860
+X إيش يعنيسينية طب و why صادية طب لو كتبتلك هيك
+
+253
+00:22:03,860 --> 00:22:12,640
+ايش بتتوقع هذه R ذاكرين الاحداثيات القطبية كان
+
+254
+00:22:12,640 --> 00:22:18,280
+فيها R و θ R يعني نص خطر عمركم سمعتوا نص خطر بومرش
+
+255
+00:22:18,280 --> 00:22:22,320
+في المركز اذا المراد اللي ما اقول مركزي بيكتبوها R
+
+256
+00:22:23,130 --> 00:22:27,630
+مش نفس الشيء او ولا في نص خطر بمرش في المركز اذا
+
+257
+00:22:27,630 --> 00:22:31,670
+المرات هنكتبها R و المرات هنكتبها C واحدة ولا لأ؟
+
+258
+00:22:31,670 --> 00:22:35,070
+واحدة نفس العملية بدأ ما اكتب X وY بدأ اكتب R
+
+259
+00:22:35,070 --> 00:22:39,290
+وقعدنا هنكتب كمان فيتا اللي انتوا عارفينها كما
+
+260
+00:22:39,290 --> 00:22:44,920
+شايفين الأشهر الخضاء الخضراء الخضاءهدوله اتجاه
+
+261
+00:22:44,920 --> 00:22:48,420
+التسارع كلهم باتجاه المركز ولا لا؟ لكن مرة صيني و
+
+262
+00:22:48,420 --> 00:22:53,420
+مرة شاضي شايفينها؟ تتغير تمام حسب النقطة المهم
+
+263
+00:22:53,420 --> 00:23:00,080
+تكون باتجاه المركز احسن شويه لسه بدل علينا هذا
+
+264
+00:23:00,080 --> 00:23:06,080
+بدنا نيوتن اه لسه نيوتن مش في طريق اللي وراه تمام؟
+
+265
+00:23:06,080 --> 00:23:11,260
+حلو بس مهل واحدة واحدة بنمشي دادة دادة هذا نيوتن
+
+266
+00:23:11,260 --> 00:23:15,570
+هيك بقولو لسه عن نيوتن ما جيناهوش و أنا قلت ما هو
+
+267
+00:23:15,570 --> 00:23:20,450
+المظبوط بس أنا قلت هيك حكيتها بس هو اصلا مش انا
+
+268
+00:23:20,450 --> 00:23:23,830
+اللي قلتها نيوتن اللي جات عفوا بتساوي ام ايه صحيح
+
+269
+00:23:23,830 --> 00:23:30,890
+تمام تمام ده اللي ما زال في حركة دائريةوالدائرة
+
+270
+00:23:30,890 --> 00:23:35,590
+بتدلها تدلها تلف ولا لأ؟ في تكرار ما زال في تكرار
+
+271
+00:23:35,590 --> 00:23:37,810
+في المادة اللي أخدنا منها كمها المصطلح بدي نعيده
+
+272
+00:23:37,810 --> 00:23:43,230
+احنا وياكم عارفينها في تردد و زمن دوري سمعتوا
+
+273
+00:23:43,230 --> 00:23:47,470
+فيهم؟ و هدول مرتبطين بالحركة الدائرية والحركة
+
+274
+00:23:47,470 --> 00:23:52,310
+المتكررة بنسميها تمام؟ قال ليش تعرفي الزمن الدوري؟
+
+275
+00:23:53,290 --> 00:23:58,230
+هو عبارة عن زمن الدورة الواحدة مشاكل اتفجنا تمام
+
+276
+00:23:58,230 --> 00:24:02,730
+هاي الزمن الدوري then the period اللي هو الزمن
+
+277
+00:24:02,730 --> 00:24:06,630
+الدوري يعني اللي رمزه capital T is defined as the
+
+278
+00:24:06,630 --> 00:24:09,990
+time needed هو الزمن اللازم for the particle to
+
+279
+00:24:09,990 --> 00:24:14,110
+complete one revolution revolution دورة من يقول
+
+280
+00:24:14,110 --> 00:24:20,700
+يجديش مسافة الدورة؟2XR 2XR هذي الزاوية تبعته لكن
+
+281
+00:24:20,700 --> 00:24:25,280
+المسافة محيط مظموش محيط قال لي في اي بي تويتر قولي
+
+282
+00:24:25,280 --> 00:24:29,540
+الزمن الدورة بساوي مسافة الدورة على السرعة ولا لأ
+
+283
+00:24:29,540 --> 00:24:36,420
+هذا هيمسافة الدورة اللي هو المحيط أسرة طيب إيش
+
+284
+00:24:36,420 --> 00:24:40,280
+مرتبط بالزمن الدوري معكوس الزمن الدوري التردد
+
+285
+00:24:40,280 --> 00:24:44,760
+التردد قالوا ال frequency the reciprocal يعني
+
+286
+00:24:44,760 --> 00:24:48,380
+معكوس reciprocal يعني واحد على X هذا مسميه
+
+287
+00:24:48,380 --> 00:24:51,460
+reciprocal the reciprocal of the period is called
+
+288
+00:24:51,460 --> 00:24:54,620
+the frequency which is defined as the number of
+
+289
+00:24:54,620 --> 00:24:58,660
+revolution in one secondحاجات لما نقول وحدة التردد
+
+290
+00:24:58,660 --> 00:25:04,640
+في المدرسة كذا دورة أو كذا دورة في الثانية مش
+
+291
+00:25:04,640 --> 00:25:09,040
+هيكون نكتب او years كذا دورة في الثانية والدورة
+
+292
+00:25:09,040 --> 00:25:12,200
+احنا عارفينها طب انا بديش دورة بدي وحدة جديدة
+
+293
+00:25:12,200 --> 00:25:19,900
+Radian هو الدورة أكم Radian الدورة أكم Radianمش
+
+294
+00:25:19,900 --> 00:25:24,720
+تقول تلت مية و ستين درجة تلت مية و ستين اتنين باى
+
+295
+00:25:24,720 --> 00:25:32,360
+اذا عشان يتحول من دورةلكل ثانية إلى رديا لكل ثانية
+
+296
+00:25:32,360 --> 00:25:37,100
+ضرب ليه في 2π صحيح؟ اذا معناته بيقول ليه because
+
+297
+00:25:37,100 --> 00:25:42,080
+when revolution كل دورة equals 2π رديا لليه 360
+
+298
+00:25:42,080 --> 00:25:47,060
+درجة تمام the angular speed هو frequency جيد بس
+
+299
+00:25:47,060 --> 00:25:50,540
+متعرف عليه برمز جيد Omega اسمه الـ Omega أديكم
+
+300
+00:25:50,540 --> 00:25:56,160
+الرمز تبعهسمعتوا فيها Omega هذه؟ Small Omega بس هو
+
+301
+00:25:56,160 --> 00:25:58,980
+اتنين بقى في ال frequency ليه ضورتوا في اتنين بقى؟
+
+302
+00:25:58,980 --> 00:26:02,920
+عشان احوّن من دورة لكل ثانية إلى radian لكل ثانية
+
+303
+00:26:02,920 --> 00:26:05,600
+طب و ال frequency مش مجردة بقى بالزمن واحد على
+
+304
+00:26:05,600 --> 00:26:07,740
+اتين هاد يكونها المعلومات تحت المجلة بس أنا بس
+
+305
+00:26:07,740 --> 00:26:13,620
+بتذكر حالنا فيها تمى قاللي حلو انت ايش جبتلي حسب
+
+306
+00:26:13,620 --> 00:26:17,520
+هذا القانون Omega بسوة V على R و توي قلتلي هادي
+
+307
+00:26:17,520 --> 00:26:22,950
+اللي هي ACبتساوي V تربيع على R ولا لأ؟ حطولي بديل
+
+308
+00:26:22,950 --> 00:26:27,530
+V Omega في R مايه دي بتصير Omega تربيع R تربيع على
+
+309
+00:26:27,530 --> 00:26:31,810
+R بتصير Omega تربيع في R الشيء Omega ده اللي
+
+310
+00:26:31,810 --> 00:26:35,290
+بيسميها مرات سرعة زاوية عشان نميز بينها و بين ال
+
+311
+00:26:35,290 --> 00:26:38,650
+frequency العادى لكن لما نكبر بنقول عنها frequency
+
+312
+00:26:38,650 --> 00:26:43,290
+برضه هي frequency هي تردد زاوية تمام عشان نميزه عن
+
+313
+00:26:43,290 --> 00:26:44,170
+ال frequency العادى
+
+314
+00:26:47,340 --> 00:26:52,580
+إذن هي الكتابة اللي كتبناها حلو قالوا إيش في أمثلة
+
+315
+00:26:52,580 --> 00:26:58,560
+ربانية في حركات دائرية احنا كنا السيارة في الضوار
+
+316
+00:26:58,560 --> 00:27:04,040
+لكن قبل السيارة ربنا خلق الأرض تدور حول الشمس
+
+317
+00:27:04,040 --> 00:27:09,120
+والجمر تدور حول الأرض والإلكترون تدور حول النواة
+
+318
+00:27:09,120 --> 00:27:14,860
+صح ولا هذي حركات ربانية وعندكم علم إن علم الفلك من
+
+319
+00:27:14,860 --> 00:27:19,390
+أقدم العلومصحيح؟ شوفوا من وقتاش من أيام سيدنا
+
+320
+00:27:19,390 --> 00:27:23,010
+إبراهيم .. ذاكرين الجدال اللي كان بينه و بين ربه و
+
+321
+00:27:23,010 --> 00:27:26,170
+حاجة إبراهيم ربها كل ما شاف الجمر و شاف الشمس
+
+322
+00:27:26,170 --> 00:27:31,050
+الإنسان بطبيعته دائما بحب يصطلع الكون اللي حواليه
+
+323
+00:27:31,050 --> 00:27:36,010
+يعني بصحى الواحد بلاجئه انه طلعت الشمسعودت صارت
+
+324
+00:27:36,010 --> 00:27:40,270
+شوب، بعدين عوّلت بردت، بعدين غابت الشمس، صح ولا؟
+
+325
+00:27:40,270 --> 00:27:44,470
+فالإنسان قاعد يقعد يفكر، و بعدين هذا جمر مرة بتصير
+
+326
+00:27:44,470 --> 00:27:49,210
+بضوء في الليل و مرة بتطفي، اذا هذا العلم من زمان
+
+327
+00:27:49,210 --> 00:27:55,510
+الإنسان بدور عليه، و الآن أصبح شبههيقيني عشان كده
+
+328
+00:27:55,510 --> 00:28:00,010
+جوالاتنا معانا صح ولا لأ و بنفتح الجزيرة من وين
+
+329
+00:28:00,010 --> 00:28:03,710
+بتبث الجزيرة؟ من الدوحة و بنفتح العربية بتبث من
+
+330
+00:28:03,710 --> 00:28:07,990
+دبي و بنفتح و بنفتح كل هذا من وين إجا؟ قالي والله
+
+331
+00:28:07,990 --> 00:28:11,530
+لا والله أقمار الصناعية مش موجودة لا معانا جوالات
+
+332
+00:28:11,530 --> 00:28:16,250
+ولا بنعرف نتفرج على أي محطة تمام؟ اذا كل هذه
+
+333
+00:28:16,250 --> 00:28:22,390
+التكنولوجيا مبنية على علم جديد اسمه علم الفلكتمام
+
+334
+00:28:22,390 --> 00:28:27,010
+وصار يقيني مرات بتسمعوا انه بيصير عندنا كسوف او
+
+335
+00:28:27,010 --> 00:28:32,070
+خصوف و بيصير فيه اعلانات و كل الناس بتصدق و
+
+336
+00:28:32,070 --> 00:28:35,670
+الحكومة بتصدق و بتعمل احتياطاتها ولا لا بيقولك
+
+337
+00:28:35,670 --> 00:28:39,130
+الكسوف بدي يبدأ الساعة اتنين اتين و عشر دقايق و
+
+338
+00:28:39,130 --> 00:28:42,670
+خمسة و عشرين ثانية تصوروا ليش؟ اللي اتطلع ليه قعدت
+
+339
+00:28:42,670 --> 00:28:47,670
+متولا صدقهصح؟ إذن الحسابات دقيقة بيقولّك هذا بترجع
+
+340
+00:28:47,670 --> 00:28:51,130
+وقالي ربع الساعة و اتخلص وبعد ما عنصر جات بعد ربع
+
+341
+00:28:51,130 --> 00:28:56,350
+الساعة ولا كأنه صار إيش إذا صار عندنا من المعلومات
+
+342
+00:28:56,350 --> 00:29:03,500
+العلمية اللي اتصل إلى درجة اليقينهي نيجي قال لي من
+
+343
+00:29:03,500 --> 00:29:07,480
+ضمن .. طبعا احنا بنعرف في آية بتقول الشمس والقمر
+
+344
+00:29:07,480 --> 00:29:11,300
+بحسبها الها حساباته ولا مالاش حسابات؟ الها حساباته
+
+345
+00:29:11,300 --> 00:29:16,340
+وهي الإنسان توصل لحساباتها بيقول the earth الأرض
+
+346
+00:29:16,340 --> 00:29:22,260
+revolves بتدور around the sun حول الشمس in an
+
+347
+00:29:22,260 --> 00:29:26,800
+orbit بيقول يفترض إنه دائرة هو طبعا بيداوي بيكون
+
+348
+00:29:26,800 --> 00:29:32,130
+لكن أنا بتعتبره دائرة تقريبانص قطر الدوران اللي هي
+
+349
+00:29:32,130 --> 00:29:35,670
+المسافة بين مركز الأرض إلى مركز الشمس one point
+
+350
+00:29:35,670 --> 00:29:40,590
+five ten to power eleven متر يعني حوالي مية وخمسين
+
+351
+00:29:40,590 --> 00:29:46,870
+مليون كيلومتر اتخيل انت عادي تمه .. روح طلعلك رحلة
+
+352
+00:29:46,870 --> 00:29:51,070
+من هال الشمس وكتينشوف وكتينفك اتصال تمه .. and
+
+353
+00:29:51,070 --> 00:29:56,700
+complete one revolutionبكمل دورة كاملة كل سنة،
+
+354
+00:29:56,700 --> 00:30:00,300
+معلومة بنعرفها ولا لا؟ ماشي احنا شهر يناير، واحد
+
+355
+00:30:00,300 --> 00:30:03,760
+يناير، بعد سنة، نصير واحد يناير، معناه ان رجعت
+
+356
+00:30:03,760 --> 00:30:09,780
+الأرض عن نفس النقطة اللي كانت من الشمس، اذا كل سنة
+
+357
+00:30:09,780 --> 00:30:14,580
+الأرض بتكمل دورة واحدة كإذا هذا زمان الدوري ولا لا
+
+358
+00:30:14,580 --> 00:30:18,160
+تبع الأرض؟مش هي تعريف الزمن الدوري؟ الزمن الدوري
+
+359
+00:30:18,160 --> 00:30:21,540
+هو الزمن اللازم عشان اكمل دورة كاملة في هذه الحالة
+
+360
+00:30:21,540 --> 00:30:26,940
+القمع الارض بتكون لفت 360 درجة ولا لا؟ 360 درجة
+
+361
+00:30:26,940 --> 00:30:32,980
+لفت تمام؟ جالي ايش بدك؟ جالي بدي .. اه الارض
+
+362
+00:30:32,980 --> 00:30:38,320
+بتتخلق حركة دائرية بنفع مايكون لها تسارع إلا يكون
+
+363
+00:30:38,320 --> 00:30:42,000
+لها تسارع بقول اوجده بقول اوجده what is the
+
+364
+00:30:42,000 --> 00:30:44,930
+centripetal acceleration of the earth؟المثال اللي
+
+365
+00:30:44,930 --> 00:30:49,010
+ورا أو المطبوب التاني قاللي فلتك من الأرض نشوف كيف
+
+366
+00:30:49,010 --> 00:30:52,490
+يصير رمضان ويصير عيد ويصير حج ويصير بداية أشهر
+
+367
+00:30:52,490 --> 00:30:56,470
+وبتجاتلوا المسلمين هذا صام وهذا ماصامش، مظبوط ولا
+
+368
+00:30:56,470 --> 00:31:02,130
+لأ؟ نشوف كيف احنا بنبدأ أشهرنا العربية؟ قالوا حسب
+
+369
+00:31:02,130 --> 00:31:06,070
+الجمر، صح؟ طب الجمر إيش بتحرك؟ قاللي والله حركة
+
+370
+00:31:06,070 --> 00:31:10,990
+معروفة وربنا خلقهاFind the acceleration of the
+
+371
+00:31:10,990 --> 00:31:15,890
+moon اه لأن الـ moon بلوف حوالي الأرض تمام بقولي
+
+372
+00:31:15,890 --> 00:31:18,210
+the moon towards the earth if the moon revolves
+
+373
+00:31:18,210 --> 00:31:22,670
+بلوف about the earth in an orbit برضه في مدار of
+
+374
+00:31:22,670 --> 00:31:25,550
+average radius نسقطه أظن هذه متر مش كيلومتر
+
+375
+00:31:25,550 --> 00:31:29,960
+بالخاطر اه هنا محطوطة كده لمكان مش مشكلةand mix
+
+376
+00:31:29,960 --> 00:31:35,100
+وبيعمل دورة كاملة تشوفوا الأرض بتعمل كل سنة دورة
+
+377
+00:31:35,100 --> 00:31:41,660
+الجمر بيعمل كل شهر دورة كل شهر تطلع الشهر ايه كم
+
+378
+00:31:41,660 --> 00:31:47,900
+يوم حاطه عمركم ما اسمعتوا في شهر عربي 27 يوم ولا
+
+379
+00:31:47,900 --> 00:31:56,100
+28 عربي عربي ثم 28 يوم
+
+380
+00:32:00,410 --> 00:32:07,110
+انت بتعرفش ما يسمى أشهر عربية؟ محرم
+
+381
+00:32:07,110 --> 00:32:11,930
+و سفر و جماد و ربيع و رمضان و شوال هاي الأشهر
+
+382
+00:32:11,930 --> 00:32:16,090
+العربية خليني أسألك و اسأليه أمك و أبوك عمكم سبت و
+
+383
+00:32:16,090 --> 00:32:22,450
+28 يوم؟لأ إما تسعة عشرين أو تلاتين صح؟ ليش تبحططلي
+
+384
+00:32:22,450 --> 00:32:26,330
+أنت سبعة وعشرين؟ هذا زمان دوري، المفروض يكون شهرة
+
+385
+00:32:26,330 --> 00:32:30,270
+قدّم نحكي عنه، ليش هذا السبعة وعشرين؟ وكيف يصير
+
+386
+00:32:30,270 --> 00:32:35,230
+الشهر العربي إما تسعة وعشرين أو تلاتين؟ طيب، جالي
+
+387
+00:32:35,230 --> 00:32:38,350
+نبدأ في الأول، نخلص من الأرض حوالي الشمس، هذه سهلة
+
+388
+00:32:38,350 --> 00:32:41,890
+السنة الميلادية، أكم يوم؟
+
+389
+00:32:47,020 --> 00:32:51,420
+وربع مش كل اربع سنوات بتجينا سنة كبيرة ليه عشان
+
+390
+00:32:51,420 --> 00:32:57,320
+ربع ربع ربع تصير يوم تمام تلاتمية وخمسة وستين وربع
+
+391
+00:32:57,320 --> 00:33:04,200
+هاي السنة الميلادية تلاتمية وخمسة وستين وربع يوم
+
+392
+00:33:04,200 --> 00:33:09,460
+وهذا ايش هو هو الزمن الدوري لدوران الأرض حول الشمس
+
+393
+00:33:12,380 --> 00:33:16,600
+مش بيصير شهر اتنين تسعة عشرين اه؟ اه عشان يصير تلت
+
+394
+00:33:16,600 --> 00:33:21,720
+مية ستة وستين عشان تظبط معانا الأمور و يرجع زي ما
+
+395
+00:33:21,720 --> 00:33:25,460
+احنا طبعا مانفعش نقول كل سنة و ربع ولا و تلت لازم
+
+396
+00:33:25,460 --> 00:33:29,620
+يوم كامل فقالوا بسيطة اه البني ولدت تسعة و عشرين
+
+397
+00:33:29,620 --> 00:33:36,580
+اتنين كيف؟ بوفر ع أصحابه عيد الميلاد كل أربع سنوات
+
+398
+00:33:36,580 --> 00:33:43,100
+مش عيد ميلاد مرة تمام يلا يا بناتبدي التسارع بدي
+
+399
+00:33:43,100 --> 00:33:47,400
+التسارع هاي التسارع إذا إنت جبتلي أمجا بكون خلصت
+
+400
+00:33:47,400 --> 00:33:52,600
+ولا لأ لأنه آه بيعطاني إياها طيب الزمن الدولي
+
+401
+00:33:52,600 --> 00:33:56,900
+يعطاك إياه ولا لأ سنة ببدأ أحوّل السنة ل seconds
+
+402
+00:33:56,900 --> 00:34:04,200
+اه ما هو السمنة السنة كم يوم طوّجلنا 365.25 و
+
+403
+00:34:04,200 --> 00:34:11,700
+اليوم كم ساعة 24 و الساعة كم ساكن هاي نحولناهاواحد
+
+404
+00:34:11,700 --> 00:34:19,320
+اللي هو سنة عدد أيام السنة في عدد ساعات اليوم في
+
+405
+00:34:19,320 --> 00:34:25,920
+عدد ثواني الساعة هاي زمان الدوري قاللي عرفتي زمان
+
+406
+00:34:25,920 --> 00:34:29,580
+الدوري بتعرفي تجيبلي omega قلتله اه omega بتسوى 2π
+
+407
+00:34:29,580 --> 00:34:37,260
+على زمان الدوري قاللي هاي omega طلعوا omega بسوى 1
+
+408
+00:34:37,260 --> 00:34:43,380
+.9 فعشرة أساليب سبعةوالسرعة بتكون برضه بسيطة
+
+409
+00:34:43,380 --> 00:34:47,080
+خلّيني نتطلع على Omega هذه إيش الواحدة جالي radian
+
+410
+00:34:47,080 --> 00:34:52,180
+per second؟ لو جيت حكيت لواحد في الشارع من عامة
+
+411
+00:34:52,180 --> 00:34:56,160
+الناس ال radian بقرا فخشي إن كانت درجة بقدر أحس
+
+412
+00:34:56,160 --> 00:34:59,240
+فيها أكتر يعني لما تقوله خمس درجات أو عشرين درجة
+
+413
+00:34:59,240 --> 00:35:04,140
+بحسها جالي أحولليها بديش radian طيب هو كيف بدي أنا
+
+414
+00:35:04,140 --> 00:35:08,420
+أحول من radian ل second؟ جالي بسيطة هي ال πاي أكم
+
+415
+00:35:08,420 --> 00:35:15,050
+radianحاجة 180 درجة، مظبوط ولا لأ؟ تمام، لكن هي
+
+416
+00:35:15,050 --> 00:35:20,750
+بالنسبة ليه 180 درجة؟ طب الواحد ريادين أكم درجة؟
+
+417
+00:35:20,750 --> 00:35:26,290
+بقى أنا عرب، 180 عبارة ايه؟ قدش تطلع لـ57؟ و أين
+
+418
+00:35:26,290 --> 00:35:29,810
+الريادين بتسوي 57 و 13 درجة؟ إذن الريادين المضروبة
+
+419
+00:35:29,810 --> 00:35:33,810
+في 57 درجة و السكن بتحولها ليوم أشوف في اليوم إيش
+
+420
+00:35:33,810 --> 00:35:40,100
+بتتحرك الشمس قال لي هذا طلعت معايا تقريبا درجةأذن
+
+421
+00:35:40,100 --> 00:35:46,140
+الأرض كل يوم بتلف درجة حوالين الشمس هى كل يوم لما
+
+422
+00:35:46,140 --> 00:35:51,340
+نيجي 360 مصير جربت على السنة ولا لألأنه 360 جربت
+
+423
+00:35:51,340 --> 00:35:55,880
+على سنة هذا كلام منطقي طبعا إذا المعلومة طبعا هذا
+
+424
+00:35:55,880 --> 00:36:02,180
+مثال أغلبه ثقافي عشان نستمتع و نسمع فيه و لا نتخلص
+
+425
+00:36:02,180 --> 00:36:05,820
+من الامتحان لأن هذه الموضوع يا بنات في chapter 6
+
+426
+00:36:05,820 --> 00:36:09,900
+هنرجعله تفصيلا عنوان ال chapter circular motion
+
+427
+00:36:09,900 --> 00:36:13,640
+هنرجعله احنا هجيته نتعرف عليه و نقوله كيف حالك
+
+428
+00:36:14,360 --> 00:36:19,860
+ثقافة يعني متعة تمى اذا هلجيت الأرض بتلف كل يوم
+
+429
+00:36:19,860 --> 00:36:24,820
+درجة حول الشمس درجة تمى بدي التسارع انت خلينا نخلص
+
+430
+00:36:24,820 --> 00:36:27,680
+من الاخر انت ايش بدك بتقوله التسارع قللي ما هو
+
+431
+00:36:27,680 --> 00:36:30,420
+التسارع بتسوي أومجة تربيع في الأرض ولا لأ وهي
+
+432
+00:36:30,420 --> 00:36:36,030
+أومجة كالكورية ترجبتها رقم والسلامقاليل؟ اه قاليل
+
+433
+00:36:36,030 --> 00:36:38,970
+لما هو لازم يكون قاليل و لا انتوا بتشوفوا حالكم
+
+434
+00:36:38,970 --> 00:36:42,850
+بتدوخوا من كتر سرعة الأرض و بتنمشي فيكم مانحسش
+
+435
+00:36:42,850 --> 00:36:50,290
+سرعتها لأنها بطيئة طيب نجي للجمر حبيبنا جالي الجمر
+
+436
+00:36:50,290 --> 00:36:55,810
+انا قلتلك الزمن الدوري تبعه 27 و 13 يوم مظبوط او
+
+437
+00:36:55,810 --> 00:37:00,690
+لأ حوللي هذه المعلومة بالسكن بقوللي يوم 24 ساعة و
+
+438
+00:37:00,690 --> 00:37:06,300
+الساعة 1600 سكن جالي هذه الزمن الدوري يا حبيبيطيب
+
+439
+00:37:06,300 --> 00:37:10,080
+جيبلي Omega و قلتله اتنين Pi على زمن الدوري هذا هي
+
+440
+00:37:10,080 --> 00:37:13,820
+قاللي برضه Radian per second بدي انا اوصلها لعمة
+
+441
+00:37:13,820 --> 00:37:19,700
+الناس حوليها لدرجات باليوم دلي القمر بيلف تلت عشر
+
+442
+00:37:19,700 --> 00:37:23,520
+درجة كل يوم شوفوا الأرض بيلف درجة واحدة حوالي
+
+443
+00:37:23,520 --> 00:37:28,360
+الشمس القمر حوالي الأرض بيلف تلت عشر درجة عشان كده
+
+444
+00:37:28,360 --> 00:37:33,970
+كل شهر برجعتمام؟ برجع جالي طب بدي التسارع وقال
+
+445
+00:37:33,970 --> 00:37:38,970
+هالجي التسارع بحسبلكيا هالتسارع هالجي تليجي
+
+446
+00:37:38,970 --> 00:37:44,970
+معلومات ثقافية أكتر نجيم هذا ونرجعله احنا عشان
+
+447
+00:37:44,970 --> 00:37:51,250
+يبدأ الشهر العربي لازم ينولد الهلال بنسميه ولادة
+
+448
+00:37:51,250 --> 00:37:55,980
+الهلال سمعتوا في هذا المصطلح؟ تمامإيش معنى ولادة
+
+449
+00:37:55,980 --> 00:38:01,220
+الهلال؟ إنه لازم القمر يكون ما بين الأرض والشمس
+
+450
+00:38:01,220 --> 00:38:06,440
+على خط واحد يعني هي الشمس شايفينها؟ هي مركزها هي
+
+451
+00:38:06,440 --> 00:38:09,420
+مركز القمر وهي مركز الأرض لازم يكون في خط مستقيم
+
+452
+00:38:09,420 --> 00:38:16,420
+في هذه اللحظة بقول إن ولد الهلال إذا بدأ الشهر
+
+453
+00:38:16,420 --> 00:38:23,120
+فلكيا عشان يبدأ شرعيا في الحديث سوم لوريتهوفطر و
+
+454
+00:38:23,120 --> 00:38:26,920
+لا ورايتها، ذاكرينه؟ إذا لازم أشوف القمر طبعا في
+
+455
+00:38:26,920 --> 00:38:32,260
+هذه اللحظة القمر لا يراه لأن أشعة الشمس محجوبة
+
+456
+00:38:32,260 --> 00:38:37,000
+والأرض بتشوفش القمر تمام كيف بدي أشوفهم؟ هو القمر
+
+457
+00:38:37,000 --> 00:38:43,240
+بدي يلوف بدي يلوف هذه اللحظة لحظة اقتران أو ولادة
+
+458
+00:38:43,240 --> 00:38:47,760
+الهلال هي لحظة ثابتة عن جميع العالم ولا واحد
+
+459
+00:38:47,760 --> 00:38:52,860
+بيختلف فيهاربيعي الأول اللي احنا فيه كانت لحظة
+
+460
+00:38:52,860 --> 00:38:57,320
+ولادته موجودة بالساعة والدقيقة والثانية ومافيش
+
+461
+00:38:57,320 --> 00:39:03,000
+عليها خلاف ربيعي التاني بخش عن نت بقول .. بقول ليه
+
+462
+00:39:03,000 --> 00:39:07,820
+وقتيش بالظبط هيولدي الهلال هجيت بدينا ربيعي الأول
+
+463
+00:39:07,820 --> 00:39:12,880
+و بعد الشهر يمشي الجمر بدي يمشي الجمر بيمشي بيمشي
+
+464
+00:39:12,880 --> 00:39:18,230
+بيمشي وصل هناهجيت كمل دورة كاملة اكمل زاوية ماشية
+
+465
+00:39:18,230 --> 00:39:23,630
+360 درجة مش هي دورة كاملة جالي حلو جديش استحرق يوم
+
+466
+00:39:23,630 --> 00:39:27,370
+جالي سبعة و عشرين و تلت يوم اللي مكتوب عنكم سبعة و
+
+467
+00:39:27,370 --> 00:39:31,330
+عشرين و تلت يوم جالي طب هيا اكمل دورة كاملة ان
+
+468
+00:39:31,330 --> 00:39:35,290
+ولادي الهلال تبقى الشهر القادم بقوله لأليه؟ قال لي
+
+469
+00:39:35,290 --> 00:39:38,630
+لأنه مش عمص في المستوى، ليه؟ قال لي هو الأرض بتفكر
+
+470
+00:39:38,630 --> 00:39:41,410
+في السناك و أنت بتمشي يا جمر؟ هي الأرض ده ده
+
+471
+00:39:41,410 --> 00:39:46,210
+السناك و البداية كلوف، البداية كلوفأو كام يوم
+
+472
+00:39:46,210 --> 00:39:48,550
+الجمر قعد بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+473
+00:39:48,550 --> 00:39:48,630
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+474
+00:39:48,630 --> 00:39:49,090
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+475
+00:39:49,090 --> 00:39:49,790
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+476
+00:39:49,790 --> 00:39:53,470
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+477
+00:39:53,470 --> 00:39:58,210
+بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ بـ
+
+478
+00:39:58,210 --> 00:40:06,510
+بـ بـ بـ بـ بـ بـ بـ بـ
+
+479
+00:40:06,510 --> 00:40:14,530
+بـ
+
+480
+00:40:14,710 --> 00:40:18,190
+أذن عشان كده سبعة وعشرين وشويه وكمان يومين وشويه
+
+481
+00:40:18,190 --> 00:40:22,830
+صاروا تسعة وعشرين وشويه تسعة وعشرين وشويه هي تسعة
+
+482
+00:40:22,830 --> 00:40:27,310
+وعشرين عشان
+
+483
+00:40:27,310 --> 00:40:30,850
+كده بيقول الشهر اما تسعة وعشرين او تلاتين ولازم
+
+484
+00:40:30,850 --> 00:40:34,960
+التلاتينات يكونوا اكتر من التسعة وعشريناتلأنه فيه
+
+485
+00:40:34,960 --> 00:40:40,700
+أكتر من الخمسة لو هذه 00 كان بحط رجل على رجل و
+
+486
+00:40:40,700 --> 00:40:45,860
+بقول ما حد يستطلق شهر رمضان تلاتين إذا شوال تسعة و
+
+487
+00:40:45,860 --> 00:40:48,980
+عشرين إذا نزل قعدة تلاتين إذا اللي ورا تسعة و
+
+488
+00:40:48,980 --> 00:40:53,560
+عشرين مظبطا لا تصير واحد واحد بس ماحسن الحظ إن هنا
+
+489
+00:40:53,560 --> 00:40:58,620
+فيه أرقام وبالتالي رمضان مرة بيكون تلاتين و مرة
+
+490
+00:40:58,620 --> 00:41:05,680
+بيكون تسعة و عشرين تمام؟ طبعاولا ممكن هدول لما
+
+491
+00:41:05,680 --> 00:41:10,920
+يخربطوا البني آدمين اللي بيفهموش هم بيخلوا واحد
+
+492
+00:41:10,920 --> 00:41:17,420
+تلاتين اما احنا شهرنا العربي لازم يكون اما تسعة و
+
+493
+00:41:17,420 --> 00:41:23,140
+عشرينأو تلاتين و لازم يكون عدد الشهور اللي تلاتين
+
+494
+00:41:23,140 --> 00:41:27,680
+أكثر من عدد الشهور التسعة و عشرين لأن هذه تسعة و
+
+495
+00:41:27,680 --> 00:41:31,960
+عشرين وأكتر من نص معناته أنت أقرب للتلاتين من
+
+496
+00:41:31,960 --> 00:41:35,360
+التسعة و عشرين فلازم عشان كده هذا الكلام اللي توي
+
+497
+00:41:35,360 --> 00:41:39,720
+حكيته بيقول لي note that in the period لما لف هذا
+
+498
+00:41:39,720 --> 00:41:46,260
+أكمل دورة كاملة الأرض دلت ثابتة ولا اتحركت لها
+
+499
+00:41:46,900 --> 00:41:51,120
+حوالي 27 درجة معناته يا جمر عشان تنولد من أول و
+
+500
+00:41:51,120 --> 00:41:55,680
+جديد مطلوب انك تمشي هذه المسافة الزاوية وهذه بدها
+
+501
+00:41:55,680 --> 00:42:00,880
+حوالي كمان يومين و شوية فبطلع الشهر الحقيقي اللي
+
+502
+00:42:00,880 --> 00:42:04,200
+بنتعامل معاه طبعا برضه معلومة ثقافية انتوا بتعرفوا
+
+503
+00:42:04,200 --> 00:42:08,340
+وقتش بتطلعوا عليه لان فأيه و جيت الدهر ولا المغرب
+
+504
+00:42:08,340 --> 00:42:16,900
+المغرب ليش احنا ليش يا بنات اخر يوم في شعبانمش
+
+505
+00:42:16,900 --> 00:42:21,020
+بنبدأ نصلي الترويح؟ ليش؟ بقوله لأنه لما أدني
+
+506
+00:42:21,020 --> 00:42:25,180
+المغرب بدأ رمضان لأنه شرعان يبدأ اليوم أداني
+
+507
+00:42:25,180 --> 00:42:29,360
+المغرب شرعان أخر يوم في رمضان بنصلي الترويح لأنه
+
+508
+00:42:29,360 --> 00:42:33,320
+لما جال الله أكبر وأفطلنا خلص رمضان وبالتالي
+
+509
+00:42:33,320 --> 00:42:37,160
+الترويح بعد العشاء خشت في اليوم ليش دي؟ يعني اليوم
+
+510
+00:42:37,160 --> 00:42:40,220
+شرعان اليوم الكنين بعد أداني المغرب يصير التلاتة
+
+511
+00:42:41,890 --> 00:42:47,830
+تمام؟ عشان كده هيك الشرع بنشتغل عليها و تطلع أقول
+
+512
+00:42:47,830 --> 00:42:51,770
+تقوصنا الدينية كيف بنعمل فيها، تمام؟ يعني مثلا
+
+513
+00:42:51,770 --> 00:42:54,790
+بتعرفوا أنتوا في عيد الأضحى فيه تكبيرات، احنا
+
+514
+00:42:54,790 --> 00:42:58,310
+بنكبر في كل الصلاوات و ماكنتش بتخلص بعد صلاة العصر
+
+515
+00:42:58,310 --> 00:43:01,310
+رابع يوم العيد، و المغرب ليش بنكبر؟ ليش بيقول خلص
+
+516
+00:43:01,310 --> 00:43:05,390
+العيد؟ لأن قد أن المغرب خلص العيد، خلصنا، خلصنا،
+
+517
+00:43:05,390 --> 00:43:11,440
+مافيش داعي اتكبر، تمام؟وبالتالي هذه المعلومات لازم
+
+518
+00:43:11,440 --> 00:43:14,840
+نكون عارفينها عشان كده بنقول كتالة بنقول لازم اللي
+
+519
+00:43:14,840 --> 00:43:17,420
+بديه يتطلع يكون أدين المغرب عشان نشوف اليوم بدأ
+
+520
+00:43:17,420 --> 00:43:21,440
+ولا مابدهاش طبعا المعلومة اللي لازم نفهمها هجيت
+
+521
+00:43:21,440 --> 00:43:26,380
+احنا واجتش بأدين المغرب اليوم عندنا ستة و نص جوله
+
+522
+00:43:26,380 --> 00:43:31,440
+ستة و نص لو اتخيلتوا مدينة زي الرباط وين وجع
+
+523
+00:43:31,440 --> 00:43:36,010
+الرباط؟في المغرب غرب جوركم على الستة و نص بيكون
+
+524
+00:43:36,010 --> 00:43:40,690
+المغرب قدر عندهم بيكون لسه تقريز الظهر اذا بقدر
+
+525
+00:43:40,690 --> 00:43:44,930
+المغرب بعد تلت ساعات اربع ساعات معناته لو انا شفت
+
+526
+00:43:44,930 --> 00:43:49,490
+الجمر معناته هو شايف الجمر قطعا اكتر مني ليش؟ لأن
+
+527
+00:43:49,490 --> 00:43:52,930
+هو كمان تقلت اربع ساعات الجمر بيكون عليه بيكون
+
+528
+00:43:52,930 --> 00:43:59,350
+ماشي وبالتالي لازم يشوفه لكنلو أنا قلت إيجي واحد
+
+529
+00:43:59,350 --> 00:44:04,650
+نفترض في طهران طهران وين وجعه؟ شرق جال أه في إيران
+
+530
+00:44:04,650 --> 00:44:08,390
+شرق يعني جال والله أنا ماشوفتش الجمر بقوله استنى
+
+531
+00:44:08,390 --> 00:44:11,990
+عليا أنا يمكن أشوفه ليش أنت لسه أنا المغرب تبقى
+
+532
+00:44:11,990 --> 00:44:14,590
+أنت قد مغربك أنا لسه بدي أربع ساعات لما يقدي
+
+533
+00:44:14,590 --> 00:44:18,330
+المغربي وبالتالي لما يقدي المغرب بيكون الجمر كبير
+
+534
+00:44:18,330 --> 00:44:22,830
+عندي وممكن أشوفه المعلومة اللي بدي أكون تعرفها إذا
+
+535
+00:44:22,830 --> 00:44:27,900
+واحد جانفي القاهرة انا ماشفتش الجمر وكان عالم
+
+536
+00:44:27,900 --> 00:44:33,280
+بمعنى صحيح ماحد يصدق واحد في دبي او واحد في تهران
+
+537
+00:44:33,280 --> 00:44:36,930
+يقول انا شفت الجمر ولا ممكنولا ممكن، إذا كان اللي
+
+538
+00:44:36,930 --> 00:44:41,070
+في القاهرة اللي هو غرب هذه المدن، ماشوفش القمر،
+
+539
+00:44:41,070 --> 00:44:45,870
+كيف أنت شفته؟ طب أنا كان كبير لما طلعت المغرب، انت
+
+540
+00:44:45,870 --> 00:44:50,070
+لسه قمرك صغير، كيف شفته؟ ماينفعش، لذا هذه
+
+541
+00:44:50,070 --> 00:44:53,870
+المعلومات اللي الشيخ الان حسموها أغلب الشيخ وخصوصا
+
+542
+00:44:53,870 --> 00:44:58,650
+القرضاوي قال إذا والعلماء قالوا القمر لم يولد،
+
+543
+00:44:58,650 --> 00:45:02,720
+ماحد يصدق واحد يقول شفته القمريقول بقى بكرا رمضان
+
+544
+00:45:02,720 --> 00:45:08,020
+ولا ممكن هذه خلاص معلومات يقينية لما القمر يقول لم
+
+545
+00:45:08,020 --> 00:45:12,560
+يولد بمعنى أخر صار ع خط واحد هي ولادة الجمر ما زال
+
+546
+00:45:12,560 --> 00:45:18,000
+هذه المعلومة اليقينية ماكنتش موجودة ساعة المغرب
+
+547
+00:45:18,000 --> 00:45:21,300
+نفترض ان احنا ستة و نص بقول انا والله هذا القمر
+
+548
+00:45:21,300 --> 00:45:25,620
+بيصير في هذا الشكل سبعة الاربع معناته عند المغرب
+
+549
+00:45:25,620 --> 00:45:29,890
+بلاقي جماربلا جيش أمر لأنه مش موجود في السماء أصلا
+
+550
+00:45:29,890 --> 00:45:33,010
+وبالتالي يجي واحد يقول طب أنا شفت بقولك شفتلك حاجة
+
+551
+00:45:33,010 --> 00:45:39,590
+تانية الله علمش اللي شفته يمكن شفت نجمة مرات
+
+552
+00:45:39,590 --> 00:45:43,770
+طبعا في خلاف فقه احنا ماعشنا نخش عنه انه توحيد
+
+553
+00:45:43,770 --> 00:45:47,450
+المطالع او انه تفرقة المطالع انه كل واحد كل واحد
+
+554
+00:45:47,450 --> 00:45:50,090
+له مطلع مختلف احنا ماعشنا نخش في الأمور الشرعية
+
+555
+00:45:50,090 --> 00:45:53,640
+انه في الأمور العلمية احكيالعلماء اللي بيختلفوا
+
+556
+00:45:53,640 --> 00:45:56,560
+عليا عشان نسوم رمضان، ان هذه ولادة القمر، هذا اللي
+
+557
+00:45:56,560 --> 00:45:59,180
+بيختلفوا عليا الرؤية؟ لأ، لأ، لأ، بيختلفوش على هذه
+
+558
+00:45:59,180 --> 00:46:02,400
+اللحظة، بيختلفوا على الرؤية، لأنهم بيقولوا بيكفيش
+
+559
+00:46:02,400 --> 00:46:05,860
+ولادة القمر لأن الحديث بيقول صوموا لرؤيته وافطروا
+
+560
+00:46:05,860 --> 00:46:09,860
+لرؤيته، والمشكلة عند الرؤية، فبصي يقول مين شاف
+
+561
+00:46:09,860 --> 00:46:14,560
+ومين ما شافش، وبصير الخلاف، طبعا أغلب البلدان حسمت
+
+562
+00:46:14,560 --> 00:46:20,930
+الأمر وما حد بيشوف، خلاص بيحسبوهاوانا كنت في تركيا
+
+563
+00:46:20,930 --> 00:46:25,190
+في ال 86 من ال 86 ان عمره ما حد في تركيا قال بدنا
+
+564
+00:46:25,190 --> 00:46:29,390
+نشوف الجمر وكتش رمضان بكرا وكتش العيد بكرا وكتش
+
+565
+00:46:29,390 --> 00:46:34,730
+العيد الأرحى معروف مخطوط من هجات لو تخشي على تقويم
+
+566
+00:46:34,730 --> 00:46:38,170
+خليني أقول وزارة الأوقات في تركيا كمان خمس سنوات
+
+567
+00:46:38,170 --> 00:46:43,010
+وكتش العيد معروفلا بدهم جمر ولا حاجة كيف؟ حسب
+
+568
+00:46:43,010 --> 00:46:47,130
+الحسابات هذه وهذه قطعية مش فيها خلاف وحسب قراءة
+
+569
+00:46:47,130 --> 00:46:53,150
+شرعية موجودة عندهم قراءة شرعية تمام انشوف
+
+570
+00:46:53,150 --> 00:46:56,510
+tangential
+
+571
+00:46:56,510 --> 00:47:04,090
+and radial acceleration هلجيت؟ اي vector اي vector
+
+572
+00:47:04,090 --> 00:47:10,030
+ممكن احلله الى مركبتين متعمدتينصينية وصادية صح طيب
+
+573
+00:47:10,030 --> 00:47:13,670
+هو مافيش اللي الصين والصاد متعمدات مش فيه القطبية
+
+574
+00:47:13,670 --> 00:47:18,290
+هلجتني القطبية فيها نص قطر ايش اللي دايما عمودي عن
+
+575
+00:47:18,290 --> 00:47:26,430
+نص القطر؟ المماسالمماس و لا لأ هدية المماس و نص
+
+576
+00:47:26,430 --> 00:47:30,570
+القطر بنفع تعتبرهم محاور اللي هي المحاور القطرية
+
+577
+00:47:30,570 --> 00:47:36,030
+لأن هم متعمدات ولا لأ إذا كل شغلتين متعمدتين هم
+
+578
+00:47:36,030 --> 00:47:41,440
+إحدافياتإذا الآن التصارع بدي أنا أحلله إلى
+
+579
+00:47:41,440 --> 00:47:45,620
+مُركّبتين متعاملتين واحدة بدي أسميها نُص قطرية
+
+580
+00:47:45,620 --> 00:47:51,640
+radial وواحدة tangential مماسية تمام يا بنات؟ حلو
+
+581
+00:47:51,640 --> 00:47:56,640
+النُص قطرية سميتها مركزية ولا لأ؟ قلتلك هذه بتيجي
+
+582
+00:47:56,640 --> 00:48:00,160
+من وين؟ من تغير ال direction تبع السرعة طب الآن
+
+583
+00:48:00,160 --> 00:48:04,580
+بدي أغير ال speed إذا إيه صار متغير في السرعة؟ ال
+
+584
+00:48:04,580 --> 00:48:11,470
+tintin غصم عنهمالـ Direction بطلّع تسرع مركزي طب و
+
+585
+00:48:11,470 --> 00:48:16,370
+ال magnitude بطلّع تسرع مماسي بطلّع تسرع مماسي إذا
+
+586
+00:48:16,370 --> 00:48:21,510
+بيقولّي if the speedالسرعة اللي تتغير من البرتقال
+
+587
+00:48:21,510 --> 00:48:28,750
+اللي تتغير من البرتقال
+
+588
+00:48:28,750 --> 00:48:31,470
+اللي تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+589
+00:48:31,470 --> 00:48:34,110
+تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+590
+00:48:34,110 --> 00:48:34,690
+تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+591
+00:48:34,690 --> 00:48:34,690
+تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+592
+00:48:34,690 --> 00:48:34,690
+تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+593
+00:48:34,690 --> 00:48:34,730
+تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+594
+00:48:34,730 --> 00:48:36,630
+تتغير من البرتقال اللي تتغير من البرتقال اللي
+
+595
+00:48:36,630 --> 00:48:40,110
+تتغير من البرتقال اللي تتغير من البرتقال اللي تت
+
+596
+00:48:40,490 --> 00:48:44,670
+والتسارع المركزي بينتج عن تغير the direction of
+
+597
+00:48:44,670 --> 00:48:48,170
+the velocity دخلة المعلومة، هنسأل عليها، عشان كده
+
+598
+00:48:48,170 --> 00:48:51,430
+أنا بركز عليها، هنسأل عليها بالـQ إزاي؟ ده اللي
+
+599
+00:48:51,430 --> 00:48:54,930
+طبق الـtotal acceleration، مش هي المواكبتين جانب
+
+600
+00:48:54,930 --> 00:48:58,230
+بعيد، مش الصينية زايد الصادية، إذا المعنى تحتيك
+
+601
+00:48:58,230 --> 00:49:02,690
+تكتبها هيك النسق الطوية والمماسية، فبكتبها بدلالة
+
+602
+00:49:02,690 --> 00:49:07,450
+الـunit vectorsI و J أسمع عارفين هم ولا لأ؟ بنفع
+
+603
+00:49:07,450 --> 00:49:13,490
+أحط I و J و I ملزقة بال X و J ملزقة بال Y و لا لأ؟
+
+604
+00:49:13,490 --> 00:49:16,710
+طب هجت لا في X ولا في Y إذا بدنا نستحدث unit
+
+605
+00:49:16,710 --> 00:49:22,070
+vector الجيدة إيش هي؟ إذا المعناته R والفيتا إذا
+
+606
+00:49:22,070 --> 00:49:26,470
+المعناته هذه تكتب طبعا عادة بنرجحها إيه ال
+
+607
+00:49:26,470 --> 00:49:30,270
+centripetal باتجاه ال R يعني باتجاه نص القطر وال
+
+608
+00:49:30,270 --> 00:49:34,540
+tangential باتجاه الفيتاليه شرط السالب؟ قال لي أنا
+
+609
+00:49:34,540 --> 00:49:39,340
+باتجاهي المركز و الـR هيك رايح مش الـR بنرسمه من
+
+610
+00:49:39,340 --> 00:49:42,600
+المركز و رايحين إذا باتجاهي المركز عكس محط شرط
+
+611
+00:49:42,600 --> 00:49:49,640
+السالب صحيح؟ زي سالب I بالظبط قال لي نرجع قال لي
+
+612
+00:49:49,640 --> 00:49:54,560
+AC مش هي V تربيع على R؟ أه طيب ال team كيف تتوقعها
+
+613
+00:49:54,560 --> 00:49:58,000
+بالثانوية؟ قال لي هي مشتقة ال speed بالنسبة للزمن
+
+614
+00:49:58,000 --> 00:50:03,010
+طيب إذا ال speed ثابت اشتقها؟0 اذا لما يكون ال
+
+615
+00:50:03,010 --> 00:50:09,150
+speed constant فى تسرع مماثى لأ رزقنا للأولى انه
+
+616
+00:50:09,150 --> 00:50:15,070
+مافيش تغير فى ال speed اذا التسرع بس مركز اللى
+
+617
+00:50:15,070 --> 00:50:19,130
+سميتها uniform circular motion صحيح ولا لأ بنجف
+
+618
+00:50:19,130 --> 00:50:21,450
+هناك دى عفوة للعاوزة
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/tTmo29ZCZv4.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/tTmo29ZCZv4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a231865ebe788f430b2e13b14a8a987c6da9d276
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/tTmo29ZCZv4.srt
@@ -0,0 +1,1877 @@
+1
+00:00:05,240 --> 00:00:09,160
+تمام، نسمي باسم الله، ونكمل اليوم، بنخلص هذا ال
+
+2
+00:00:09,160 --> 00:00:12,660
+chapter، المقدمة على أساس إن شاء الله يوم التاني
+
+3
+00:00:12,660 --> 00:00:17,120
+نبدأ بداية جدية، احنا حكينا في المحاضرة الماضية
+
+4
+00:00:17,120 --> 00:00:23,180
+المهم، نقول هل يَأخذنا، إنّه اتعلمنا إنّه في عندي كم
+
+5
+00:00:23,180 --> 00:00:29,130
+نظام للوحدات، ثلاث أنظمة، النظام الأشهر هو الـ SI
+
+6
+00:00:29,130 --> 00:00:33,950
+system، اللي له اسم ثاني، MKS system، اللي بيستخدم ال
+
+7
+00:00:33,950 --> 00:00:37,750
+meter للـ length، و الـ kilogram للـ masses، و الـ
+
+8
+00:00:37,750 --> 00:00:42,270
+seconds للـ times، النظام الثاني، الجاوزي، و النظام
+
+9
+00:00:42,270 --> 00:00:45,330
+الأقل شهرة هو الـ British، تمام.
+
+10
+00:00:47,620 --> 00:00:52,540
+هذه المواضيع الآن، هناخدها شبه أنتو بتعرفوها، بس
+
+11
+00:00:52,540 --> 00:00:55,480
+بدنا نمر عليها مرور الكرام، موجودة في الكتاب، وبدنا
+
+12
+00:00:55,480 --> 00:00:58,340
+نمشي عليها، لأن كده مش كتير مهمة، لأن أنتو بتعرفوها
+
+13
+00:00:58,340 --> 00:01:04,660
+يعني أديكم مثال، عندكم مسافتين، وفي الآخر تتعاملوا
+
+14
+00:01:04,660 --> 00:01:10,440
+معاهم في مسألة ما، واحدة جسمكم إياها بالميل، وواحدة
+
+15
+00:01:10,440 --> 00:01:13,980
+جسمكم إياها بالمتر، مثلاً خمسة ميل زائد ثلاثة متر، ينفع
+
+16
+00:01:13,980 --> 00:01:18,410
+نجمعهم، ثمانية؟ ما ينفعش، لازم نحول واحد للتاني، صح
+
+17
+00:01:18,410 --> 00:01:23,810
+ولا لأ؟ إذن عنواننا الآن، Conversion، تحويل، of
+
+18
+00:01:23,810 --> 00:01:27,830
+units، تحويل الوحدات، تمام هيك؟ هذا هو النوع
+
+19
+00:01:27,830 --> 00:01:30,950
+الهام، أعرفه من أول، من زمان، إنه ما ينفعش تحويل
+
+20
+00:01:30,950 --> 00:01:35,070
+متر وسنتيمتر وتجمعهم، أو كيلوغرام وطُنّ وتجمعهم، صح
+
+21
+00:01:35,070 --> 00:01:41,670
+ولا لأ؟ إذن، إيش بيقول لي؟ بيقول لي، if different unit
+
+22
+00:01:41,670 --> 00:01:45,290
+systems، احنا متفقين، إذا في كلمة إنجليزية مش عارفين
+
+23
+00:01:45,290 --> 00:01:48,390
+هأقول لكم معناها، بس سهل عليكم، بعد ما تروحوا و
+
+24
+00:01:48,390 --> 00:01:52,270
+تدوروا عليها، بس أنا أظن إن الكلمة أغلبها مرت عليكم
+
+25
+00:01:52,270 --> 00:01:56,250
+تمام، if different unit systems are used، إذا
+
+26
+00:01:56,250 --> 00:02:01,100
+استخدمت أكثر من unit system، تمام؟ in a physical
+
+27
+00:02:01,100 --> 00:02:05,840
+equation، one system should be chosen، اختاروا واحد زي
+
+28
+00:02:05,840 --> 00:02:11,720
+ما بنقول، اِختاروا نظاماً واحداً، one system should be
+
+29
+00:02:11,720 --> 00:02:16,560
+chosen، and all the quantities، كل الكميات بعد كده
+
+30
+00:02:16,560 --> 00:02:21,300
+must be converted، من convert to conversion، التحويل
+
+31
+00:02:21,300 --> 00:02:25,220
+must be converted، لازم يتحولوا، to that chosen
+
+32
+00:02:25,220 --> 00:02:28,460
+system، للنظام اللي إخترته، إخترت الـ SI system،
+
+33
+00:02:28,460 --> 00:02:32,520
+كل الكميات اللي حواليك بيكون على هذا النظام ده،
+
+34
+00:02:32,520 --> 00:02:37,160
+من غير ما تجمع، ولا تطرح، ولا تضرب، مش سطر SI system، و
+
+35
+00:02:37,160 --> 00:02:41,920
+سطر اللي وراه جاوزي، يعني، تمام هيك؟ طب، تبقى اتحولوا، و
+
+36
+00:02:41,920 --> 00:02:45,360
+الله، علمونا من زمان، وبنحول... إيش هالشغلة؟ بس مش
+
+37
+00:02:45,360 --> 00:02:49,260
+من اللي اتعلمناها، يعني مثلاً لو عندك اثنين كيلومتر، و
+
+38
+00:02:49,260 --> 00:02:52,920
+بدك تعملها متر، إيش بتسوّي هنا؟ مش بتضربوا في ألف؟
+
+39
+00:02:52,920 --> 00:02:58,860
+وخلصنا، لكن، تلعبوا كيف بيعملوها هم، بشغلة حلوة،
+
+40
+00:02:58,860 --> 00:03:05,100
+بيقول لي، for example، ها ينطينا مثال، جالي مسطرة
+
+41
+00:03:05,100 --> 00:03:08,240
+إلها طرف بقياس centimeter، وطرف ثاني بقياس الـ inch
+
+42
+00:03:09,120 --> 00:03:13,020
+بتعرفوا هذه الشغلة؟ جست مسافة المسطرة... تحت الـ
+
+43
+00:03:13,020 --> 00:03:17,980
+centimeter خربانة عندي، حَفِّتها جست بالـ inch عندي،
+
+44
+00:03:17,980 --> 00:03:23,860
+مسافة مقدارها خمسة عشر inch، جستها، تمام؟ بدي أقولي
+
+45
+00:03:23,860 --> 00:03:28,920
+كم centimeter، هلّجيت الـ inch، كم centimeter، مش
+
+46
+00:03:28,920 --> 00:03:32,260
+حافظها، إن شاء الله بحفظها، أكتب على جوجل، بديكم إياها
+
+47
+00:03:32,260 --> 00:03:35,100
+تمام؟ واحد بيقول، هو في امتحان، في جوجل بيقول، احنا
+
+48
+00:03:35,100 --> 00:03:39,840
+الـ google تبعك مش مشكلة، بديكم إياها، طبعاً؟ بيقول لي،
+
+49
+00:03:39,840 --> 00:03:45,400
+عندك خمسة عشر انش، حول لي إياها، we want، we wish to
+
+50
+00:03:45,400 --> 00:03:49,860
+convert، بنحول الخمسة عشر انش، into centimeters، لـ
+
+51
+00:03:49,860 --> 00:03:53,420
+centimeters، المعلومة اللي بدي أديكم إياها، معطى أنه
+
+52
+00:03:53,420 --> 00:03:57,100
+يا عمّ، الواحد انش عبارة عن 2.54
+
+53
+00:03:57,100 --> 00:04:01,280
+centimeter، تمام هيك؟ حلو، جاه كيف بتعمل التحويل؟
+
+54
+00:04:01,280 --> 00:04:06,180
+جاه شغلة سهلة جداً، اتعلمنا من زمان، إنّه لما نضرب أي
+
+55
+00:04:06,180 --> 00:04:11,200
+شغلة بواحد، أو نقسم على واحد، بيصير إيش؟ يعني بظلّ لك
+
+56
+00:04:11,200 --> 00:04:14,960
+تضربي بواحد، صح ولا لأ؟ وبيضلّ لك، تقسمي على واحد، جاه
+
+57
+00:04:14,960 --> 00:04:18,140
+هذا النظام اللي ببدأ استخدمه كيف؟ ده اللي أنت شوف
+
+58
+00:04:18,140 --> 00:04:24,440
+تعيش، معطيني واحد inch بتساوي 2.54 cm، بتدي الواحد
+
+59
+00:04:24,440 --> 00:04:30,450
+هذا، عشان أعمله، أقول أعيش، أقسم على الـ inch، صح هيك؟
+
+60
+00:04:30,450 --> 00:04:35,250
+قال لي هاه، أنت أديتني هذه المعلومة، قلت له بقدر أقول
+
+61
+00:04:35,250 --> 00:04:41,470
+الواحد بيساوي 2.54 cm على الـ inch، أطلع فوق، بدي أسوي
+
+62
+00:04:41,470 --> 00:04:44,710
+هالـ gate،  هذا الواحد، بدي أضربه هنا، بيصح لي ولا
+
+63
+00:04:44,710 --> 00:04:48,810
+بيصح لي؟ بيصح لي، للواحد، طب، لما أضرب، بيصير الـ
+
+64
+00:04:48,810 --> 00:04:51,570
+inch هذا مع الـ inch هذا بيصير، ولا لأ؟ إيش بيضلّ
+
+65
+00:04:51,570 --> 00:04:58,490
+الوحدة؟ هي اتحولت، هي اتحولت، يلا نعمل، Since
+
+66
+00:04:58,490 --> 00:05:02,890
+multiplying any quantity، بيقول بما أنه ضرب أي كمية
+
+67
+00:05:02,890 --> 00:05:07,130
+multiply، معناتها ضرب، تمام، و product معناتها برضه
+
+68
+00:05:07,130 --> 00:05:12,310
+ضرب، multiplying any quantity by one، ضرب أي رقم
+
+69
+00:05:12,310 --> 00:05:16,410
+بواحد، leaves it unchanged، بيخليها زي ما هي، وهذه
+
+70
+00:05:16,410 --> 00:05:20,620
+معلومة نعرفها كلنا، we can write، قال لي، هذه
+
+71
+00:05:20,620 --> 00:05:24,540
+الخمسة عشر اللي بدك تحوّلها، ضربتها في واحد، أمي كنا
+
+72
+00:05:24,540 --> 00:05:27,540
+بنقول، صح؟ قال لي، طب، مش هي الواحد، قلت له هاي الواحد
+
+73
+00:05:27,540 --> 00:05:33,000
+أنا أديتكم إياها، عوضت محل الواحد، ضربت انش مع انش، طار
+
+74
+00:05:33,000 --> 00:05:37,660
+وأنا ما رتّبت بالكالكوليتور، ضربت هذه في هذه، إيش ضلّ؟
+
+75
+00:05:37,660 --> 00:05:42,360
+أنا حولت لكم إياها، فالخمسة عشر انش طلعت حوالي ثمانية
+
+76
+00:05:42,360 --> 00:05:46,890
+وثلاثين فاصلة واحد centimeter، تمام يا بنات؟ سهل أظنّ
+
+77
+00:05:46,890 --> 00:05:50,490
+واحد يقول، طب، أنا كنت متعود أحول بالطريقة اللي كنت
+
+78
+00:05:50,490 --> 00:05:54,170
+متعلّمها في المدارس، تظلّ زي ما أنت، مش جاية يعني، بس
+
+79
+00:05:54,170 --> 00:06:01,230
+احنا نتعلم كيف يعملوها، نشوف الأمثلة، جالي، في أمريكا
+
+80
+00:06:01,230 --> 00:06:05,130
+بيستخدموا النظام البريطاني كتير، خصوصاً في الشوارع،
+
+81
+00:06:05,130 --> 00:06:07,950
+المسافات، يعني هم بيقولوا والله، المسافة بين نيويورك
+
+82
+00:06:07,950 --> 00:06:12,030
+وواشنطن كذا ميل، مش كذا كيلومتر، هيك بتعودوا عليهم،
+
+83
+00:06:12,030 --> 00:06:14,650
+هيك اللي اعتمدوا، بنفس العملية، في بريطانيا،
+
+84
+00:06:14,650 --> 00:06:18,980
+بيستخدموا هذا النظام، بيقول لي، أنت بتعرفي في الشوارع،
+
+85
+00:06:18,980 --> 00:06:23,800
+فيه جارمة، فيه إشارات ضوئية، وإشارات مرور، صح ولا لأ؟
+
+86
+00:06:23,800 --> 00:06:27,160
+اللي أحمر، واللي أزرق، واللي مش عارف إيش، لما تمشي
+
+87
+00:06:27,160 --> 00:06:30,920
+على شارع الرشيد، بيكون مكتوب لك السرعة القصوى، نفترض
+
+88
+00:06:30,920 --> 00:06:35,640
+ثمانين كيلومتر في الساعة، مظبوط ولا لأ؟ ليش؟ على أساس
+
+89
+00:06:35,640 --> 00:06:40,500
+إنك لو مشيت تسعين، وخلفك الشرطي، ما اتجهتش، السبب، لإنه
+
+90
+00:06:40,500 --> 00:06:45,480
+جاي لك، ممنوع تنطّ الثمانين، هنا بيقول لي، أن
+
+91
+00:06:45,480 --> 00:06:48,960
+Interstate Highway، Highway، كلمة عربية، بنعرفها، كنا
+
+92
+00:06:48,960 --> 00:06:54,100
+صح؟ ولا طريق سريع، Interstate، بين الولايات، يعني بين
+
+93
+00:06:54,100 --> 00:06:57,640
+ولاية أوهايو، وولاية كاليفورنيا، أنتو عارفين
+
+94
+00:06:57,640 --> 00:07:01,080
+أمريكا عبارة عن عدة ولايات، مظبوط ولا لأ؟ فبيقى في
+
+95
+00:07:01,080 --> 00:07:06,060
+طرق كبيرة، واسعة، وسريعة، بين الولايات، جاه، الشرطة
+
+96
+00:07:06,060 --> 00:07:11,740
+حاطة جارمة، ممنوع تتجاوز خمسة وسبعين ميل، per hour،
+
+97
+00:07:11,740 --> 00:07:18,080
+هيك الجارمة، السائق قاعد بيسوق، نفترض، في جوا السيارة
+
+98
+00:07:18,080 --> 00:07:23,740
+معالمة، عنده ثمانية وثلاثين متر، per second، هَلّجيت الميل بأول
+
+99
+00:07:23,740 --> 00:07:28,340
+نظام بريطاني، و الـ ثمانية وثلاثين متر per second، نظامي الأساسي،
+
+100
+00:07:28,340 --> 00:07:34,180
+صح؟ بدي أعرف، الشرطة بيصح لها تخالفني ولا لأ؟ بدي أشوف
+
+101
+00:07:34,180 --> 00:07:38,240
+سرعتي اللي هي ثمانية وثلاثين متر per second، أكثر من الـ 75 ولا
+
+102
+00:07:38,240 --> 00:07:43,100
+أقل؟ فهمتوا عليّ كيف؟ طب، قول لي، is، بسأل، is a
+
+103
+00:07:43,100 --> 00:07:48,340
+driver، الـ driver يعني سائق، exceeding، تجاوز،
+
+104
+00:07:49,280 --> 00:07:53,680
+exceeding the speed limit، حد السرعة القصوى اللي
+
+105
+00:07:53,680 --> 00:07:58,500
+أنا حاطّة كشرطة، اللي هو 75 ميل per hour، إيش بدك
+
+106
+00:07:58,500 --> 00:08:02,820
+تسوي؟ قال لي، هذا الرقم حول لي إياه لـ per hour، وشوف
+
+107
+00:08:02,820 --> 00:08:06,800
+لي إياه، أكثر من 75 ولا أقل؟ مظبوط هيك ولا لأ؟ إيش بدك
+
+108
+00:08:06,800 --> 00:08:10,740
+تحول؟ قال لي، هذه والله معقدة ومركبة، فيها ميل وفيها
+
+109
+00:08:10,740 --> 00:08:13,300
+hour، احكي، 1609
+
+110
+00:08:20,480 --> 00:08:24,980
+الأولى، كم سنتيمتر؟ الأولى، كم سنتيمتر؟ ثلاثين وثلاث
+
+111
+00:08:24,980 --> 00:08:29,540
+مية؟ هذا اللي بدنا نسويه، طيب، هلّجيت الميل كم
+
+112
+00:08:29,540 --> 00:08:32,980
+متر؟ واحد يقولك، طب، أنا مش حافظها، برضه بنرجع بنقول،
+
+113
+00:08:32,980 --> 00:08:36,020
+احنا بنديكم إياها، ما تفرّجش، لو مش حافظينها، يعني مش
+
+114
+00:08:36,020 --> 00:08:40,220
+مطلوب منكم تحفظوا كل شيء، أما نقول مثلاً، الله، عيب،
+
+115
+00:08:40,220 --> 00:08:43,460
+نديكم الساعة، كم دقيقة، ولا لأ؟ ولا... ولا... ولا
+
+116
+00:08:43,460 --> 00:08:46,560
+واحد يقول، لا، بدي أدّي... نديكم إياها، بس في شغلات
+
+117
+00:08:46,560 --> 00:08:50,660
+الواحد يكون عارفها، من ساعة ما اتولد، مظبوط ولا لأ؟
+
+118
+00:08:50,660 --> 00:08:55,750
+تمام، بيقول لي، واحد ميل، أنا أعطيتكم إياها، واحد متر
+
+119
+00:08:55,750 --> 00:08:59,770
+بيساوي واحد على 1609 ميل، أو العكس، واحد
+
+120
+00:08:59,770 --> 00:09:03,370
+متر بيساوي 1609 متر، تمام، جالي، بدي
+
+121
+00:09:03,370 --> 00:09:06,390
+الواحد، مش أنت قلت لي، اضربي في واحد أو اقسمي على واحد،
+
+122
+00:09:06,390 --> 00:09:10,830
+بيصح اللي تمام، بدي الواحد، قلت له، الواحد اقسمي على
+
+123
+00:09:10,830 --> 00:09:16,540
+متر، تمام؟ حلو، قال لي، طيب، و الـ second كم hour، تقول
+
+124
+00:09:16,540 --> 00:09:20,660
+واحد على 3600، إذا برضه عندك واحد
+
+125
+00:09:20,660 --> 00:09:25,520
+second بتساوي واحد على 3600 hour، أمين،
+
+126
+00:09:25,520 --> 00:09:31,050
+طب، بدي الواحد، اقسم على second، اقسم لي، نيجي لهذه
+
+127
+00:09:31,050 --> 00:09:33,990
+الكمية، جالي، think، بيه، الـ meter في الـ bus to
+
+128
+00:09:33,990 --> 00:09:38,350
+second، في المقام ده، كده أنت لما تيجي تعمل، تمام؟
+
+129
+00:09:38,350 --> 00:09:43,530
+إذا أول حاجة بدك تضربي هذه الواحد في الـ bus، وتقسمي
+
+130
+00:09:43,530 --> 00:09:47,410
+على الواحد هذا، فهمتوا عليّ كيف؟ عشان إن كل واحد
+
+131
+00:09:47,410 --> 00:09:52,390
+حسب وحدته، جالي هذه ثمانية وثلاثين meter per
+
+132
+00:09:52,390 --> 00:09:56,170
+second، الثمانية والثلاثين بدي أضربها في الواحد هذا،
+
+133
+00:09:56,170 --> 00:10:00,950
+بيصح لك، ضربت في الواحد، اقسم على الواحد هذا، طب، إيش
+
+134
+00:10:00,950 --> 00:10:05,550
+قسمت؟ عشان استكنت في المقام، قسمت، طيب، واحنا في
+
+135
+00:10:05,550 --> 00:10:10,830
+القسمة، بنفع نحولها لضرب؟ ساعتها بنقلب، وبنقلب، عليكم يا
+
+136
+00:10:10,830 --> 00:10:15,570
+وردة، ما تشتركي، هي إن أنا أعمل اللي تعرفه، هي عملته
+
+137
+00:10:15,570 --> 00:10:21,210
+هذه القسمة، ضربت، صارت ضرب، مقام صار بسط، مقام صارت
+
+138
+00:10:21,210 --> 00:10:25,130
+بسط، وبسط، صارت بسط، طبعاً، عشان صار معايا مثل ما
+
+139
+00:10:25,130 --> 00:10:29,030
+عملت، ضاع ولا ما ضاع؟ تمام، واستكن بعض، واستكن بعض، ولا لأ؟
+
+140
+00:10:29,030 --> 00:10:34,010
+يلا بالـ calculator، طلعت خمسة وثمانين ميل بالـ hour،
+
+141
+00:10:34,010 --> 00:10:39,250
+تجاوز كتير، معناته بده مخالفة، الله، مجد الكون،
+
+142
+00:10:39,250 --> 00:10:44,630
+صحيح ولا لأ؟ طبعاً، أنا فهمت الآن التحويل، هي نحول تلك،
+
+143
+00:10:44,630 --> 00:10:54,310
+سهلة، تمام هيك؟ حلو، احكوا، عيد؟ عيد، هلّجيت أنت لما
+
+144
+00:10:54,310 --> 00:10:57,370
+تيجي تحولي سرعة عامة، إيش بتسوّي؟ مش أنت بتعرفي
+
+145
+00:10:57,370 --> 00:11:00,650
+الشغل اللي بدك تحوليه، نفترض، بدك تحولي أنت عندك، إيش
+
+146
+00:11:00,650 --> 00:11:05,330
+بدك تحوليه؟ ثمانية وثلاثين متر per second، صح؟ أنا بدي أحول الـ
+
+147
+00:11:05,330 --> 00:11:11,550
+ثمانية وثلاثين متر per second، هاي ثمانية وثلاثين متر per second، إيش بيبقى
+
+148
+00:11:11,550 --> 00:11:15,750
+تسوي؟ المتر بيبقى ميل، مش لو بيبقى، تحوليه لميل،
+
+149
+00:11:15,750 --> 00:11:21,370
+بيبقى أقوله المتر، كم؟ قال لي، اه، واحد على 1609، طبعاً...
+
+150
+00:11:21,370 --> 00:11:24,290
+واحد على... بدي أضرب فيه، واحد على 1609،
+
+151
+00:11:24,290 --> 00:11:27,430
+هو يكون إن أنا أعمل هيك، اه، واحد على 1609،
+
+152
+00:11:27,430 --> 00:11:35,510
+عشان قلت لكم، أنا ما بغشّشكم إياها، بتكونوا حفظتها طبعاً،
+
+153
+00:11:35,510 --> 00:11:40,090
+انتبهوا لي، أنا بأحكي بالعربي، قلت، أنا ما بغشّشكم إياها حتى،
+
+154
+00:11:40,090 --> 00:11:47,010
+أقول جوجل، أنا بأصحّح معاكم، طبعاً، احكي، اه، الـ second كم
+
+155
+00:11:47,010 --> 00:11:52,970
+hour؟ عايزة تبقي بس، عشان الـ second تحت، بقوله، هيدا بيصير،
+
+156
+00:11:52,970 --> 00:11:58,650
+واحد على 3600، خلصنا، خلصنا، من حلينا المشكلة،
+
+157
+00:11:58,650 --> 00:12:13,990
+ولا لأ؟ أنا هي عملتها بالبلدي، دي، احكي، إيه، للميل، أنتِ
+
+158
+00:12:13,990 --> 00:12:18,920
+بتحولي من متر لميل، ولا من ميل لمتر؟ اه، بده يكبر ولا
+
+159
+00:12:18,920 --> 00:12:25,840
+بده يصغر؟ أنتِ مش بتحولي من ميل لمتر، من متر لميل،
+
+160
+00:12:25,840 --> 00:12:30,160
+أنتِ
+
+161
+00:12:30,160 --> 00:12:36,320
+هيك فكرتي؟ لا، الميل أكبر من كيلومتر، هو أكثر من كيلو،
+
+162
+00:12:36,3
+
+223
+00:17:19,200 --> 00:17:23,000
+بحطّليش digits يعني مثلاً أنتو بتطلعوا على الميزان
+
+224
+00:17:23,000 --> 00:17:28,180
+قديش وزنكم؟ ثلاثة وثمانين، تمام؟ ذهبت... أنا
+
+225
+00:17:28,180 --> 00:17:33,840
+عشان المعلّق عند الشباب 62، تمام؟ ما ينفعش واحد يقول لي
+
+226
+00:17:33,840 --> 00:17:38,600
+والله، تتفلزف 62 و 35% من الـ graph، أنا جبت 35%
+
+227
+00:17:39,230 --> 00:17:43,790
+الميزان الدقيق، ههه، لأ، دا قبل 62 صح ولا لأ؟ إذا لو
+
+228
+00:17:43,790 --> 00:17:48,390
+لقيت أنتو زوجتوا معناته أخلّتوا بالأمانة العلمية ولا لأ؟
+
+229
+00:17:48,390 --> 00:17:51,090
+تكون أخلت بالأمانة العلمية، عشان كده يبدأ إنك تكتب صح
+
+230
+00:17:51,090 --> 00:17:56,470
+عشان أنا أفهم اللي بدّي أقرأه، إيش هو الجهاز اللي جسّد
+
+231
+00:17:56,470 --> 00:18:01,660
+فيه، يعني مثلاً ساعة... في السباقات يا بنات، في ساعة
+
+232
+00:18:01,660 --> 00:18:06,580
+بتجسّ جزء من مئة من الـ second، الجهاز بيكون هيك، أمّا
+
+233
+00:18:06,580 --> 00:18:11,500
+والله بسعْتي أنا وأقول والله هذا استغرقت المسافة
+
+234
+00:18:11,500 --> 00:18:14,760
+عشر ثواني وخمسة وثلاثين في المئة من الثانية
+
+235
+00:18:14,760 --> 00:18:20,020
+مستحيل! من وين جبتها هذه؟ اللي بيقول عنها الأمانة
+
+236
+00:18:20,020 --> 00:18:24,580
+العلمية، فإيش القواعد؟ تمام، هاي بيقول لي for example
+
+237
+00:18:25,730 --> 00:18:29,330
+مثلاً اللي بتعرفوا أداة رقمية، when you measure a
+
+238
+00:18:29,330 --> 00:18:33,810
+distance... دي بتجسّ مسافة by a meter stick، اللي هي
+
+239
+00:18:33,810 --> 00:18:37,150
+المصطلح تماماً، your measurement should be written
+
+240
+00:18:37,150 --> 00:18:43,710
+as 2.3 cm، أنتَ أول ما أقرأ هيك بقول تمام، بقول هذا
+
+241
+00:18:43,710 --> 00:18:48,630
+أكيد صح وهذا أكيد صح وهذا أنا شاكّك فيه، إيش يعني
+
+242
+00:18:48,630 --> 00:18:51,730
+شاكّك فيه، بقول هذا ممكن يزيد واحد أو ينقص واحد، لأنه
+
+243
+00:18:51,730 --> 00:18:55,270
+أنتَ لما تيجي تجسّ، لو طلعت من الجانب بزيت، طلعت من
+
+244
+00:18:55,270 --> 00:19:00,210
+الجانب هينا بجلّ، صح؟ إذا أنتَ عشان تكون بندق فيه
+
+245
+00:19:00,210 --> 00:19:02,930
+إلهام، عيار، وكيف تقرأ، والله علمك، يكون أنتَ محول
+
+246
+00:19:02,930 --> 00:19:07,610
+مظبوط أو لا، بالتالي لكن المحول ما خبطش في هذا، مخبط
+
+247
+00:19:07,610 --> 00:19:11,630
+في هذا، فبيصير القاعدة اللي صارت تقول لي هذا وهذا
+
+248
+00:19:11,630 --> 00:19:17,300
+أكيد، وهذا تقديري، هذا تقديري، يمكن يزيد شوية ينقص شوية
+
+249
+00:19:17,300 --> 00:19:21,140
+إذا بيقول لي this means that، هذا بيعني لما تكتب لي
+
+250
+00:19:21,140 --> 00:19:27,700
+هذا، أنّه the measurement is accurate، صحيح، بس في عدم
+
+251
+00:19:27,700 --> 00:19:34,180
+يقين، uncertainty، certain يقين، عكسه في عدم يقين
+
+252
+00:19:34,180 --> 00:19:39,700
+مقداره إمّا بيزيد أو بينقص 0.1، يعني هذا بيصير إمّا 0.2
+
+253
+00:19:39,700 --> 00:19:45,250
+أو 0.4، تمام؟ حلو، بيقول لي طب أنتَ في الجهة هذه إيش...
+
+254
+00:19:45,250 --> 00:19:48,470
+ده هو في الـ significant figures، بقول آه هذا الرقم
+
+255
+00:19:48,470 --> 00:19:55,110
+بنسمّيه كم رقم له مهمّ، بقول له ثلاثة، إذا هذا له ثلاثة
+
+256
+00:19:55,110 --> 00:19:59,870
+significant figures، ثلاثة significant figures، The
+
+257
+00:19:59,870 --> 00:20:05,410
+number of significant figures، أو الأرقام المعنوية
+
+258
+00:20:05,410 --> 00:20:09,530
+ذات القيمة in a measurement can be defined as the
+
+259
+00:20:09,530 --> 00:20:14,030
+number of digits، digits يعني رقم، that are
+
+260
+00:20:14,030 --> 00:20:18,050
+measured with certainty، الأرقام اللي أنتَ متأكد
+
+261
+00:20:18,050 --> 00:20:22,100
+منهم، واحد واثنين، صح ولا لأ؟ هدول أنا متأكد منهم
+
+262
+00:20:22,100 --> 00:20:27,560
+plus، إيش يعني plus؟ زائد، أضيف لهم plus the last
+
+263
+00:20:27,560 --> 00:20:31,940
+digit which is an estimate، اللي هي تقريبية، إذا
+
+264
+00:20:31,940 --> 00:20:34,360
+المعنى هذا أكمل significant figure، بقول واحد
+
+265
+00:20:34,360 --> 00:20:38,180
+اثنين، ثلاثة، إذا هذا له ثلاثة significant figures
+
+266
+00:20:38,180 --> 00:20:43,370
+تمام، بيقول لي الـ 12.3 ميجارومنت، 12.3 ميجارومنت، 12
+
+267
+00:20:43,370 --> 00:20:43,870
+.3 ميجارومنت، 12.3 ميجارومنت، 12.3 ميجارومنت، 12.3
+
+268
+00:20:43,870 --> 00:20:47,710
+ميجارومنت، 12.3 ميجارومنت، 12.3 ميجارومنت، 12.3
+
+269
+00:20:47,710 --> 00:20:52,810
+ميجارومنت، 12.3 ميجارومنت، 12.3 ميجارومنت، 12.3
+
+270
+00:20:52,810 --> 00:20:52,870
+ميجارومنت، 12.3 ميجارومنت، 12.3 ميجارومنت، 12.3
+
+271
+00:20:52,870 --> 00:20:54,010
+ميجارومنت، 12.3 ميجارومنت، 12.3 ميجارومنت، 12.3
+
+272
+00:20:54,010 --> 00:20:54,050
+ميجارومنت، 12.3 ميجارومنت، 12.3 ميجارومنت، 12.3
+
+273
+00:20:54,050 --> 00:20:54,070
+ميجارومنت، 12.3 ميجارومنت، 12.3 ميجارومنت، 12.3
+
+274
+00:20:54,070 --> 00:20:59,930
+ميجارومنت، 12... لأ، لابس يد واحد، لابس واحد، فهذه شغلات
+
+275
+00:20:59,930 --> 00:21:04,790
+معروفة، طيب، بيقول لي طب أنا كم بدي أتعلم أعرف أن هذا
+
+276
+00:21:04,790 --> 00:21:07,930
+الرقم كم significant figures؟ قال لي فيه الها قواعد
+
+277
+00:21:07,930 --> 00:21:11,970
+to determine the number of significant figures for
+
+278
+00:21:11,970 --> 00:21:15,090
+a measure means، أي رقم قدامك تقول لي كم significant
+
+279
+00:21:15,090 --> 00:21:19,590
+figure، على طول بدّي أتعلم، we use the following
+
+280
+00:21:19,590 --> 00:21:25,980
+rules، القواعد التالية، واحد سهلة، بيقول لكل الأرقام
+
+281
+00:21:25,980 --> 00:21:31,520
+اللي مش صفر، عدّهم، أداك رقم ما زال مش صفر، عدهم، إذا
+
+282
+00:21:31,520 --> 00:21:35,960
+non-zero digits، اللي مش صفر، non-zero digits are
+
+283
+00:21:35,960 --> 00:21:39,280
+always significant، عدّهم significant، طيب، إيش
+
+284
+00:21:39,280 --> 00:21:43,960
+زيهم؟ قال لي 14، فيهم أصفار؟ كم واحد؟ two
+
+285
+00:21:43,960 --> 00:21:48,560
+significant figures، has two significant figures،
+
+286
+00:21:48,560 --> 00:21:52,940
+واحد، ثلاثة، ستة، فيها أصفار؟ أكمل واحد، إذًا ثلاثة
+
+287
+00:21:52,940 --> 00:21:57,560
+significant figures، نحكي عربي صح؟ سهلة ههه، فيه
+
+288
+00:21:57,560 --> 00:22:01,480
+zeros، مشكلتهم مشكلة، بيقول الـ zeros إذا كانوا
+
+289
+00:22:01,480 --> 00:22:06,680
+محصورين بين أرقام عدّهم، محصورين يعني إيش؟ الصفر ما
+
+290
+00:22:06,680 --> 00:22:11,900
+بينهم، إذًا zeros between non-zero digits are
+
+291
+00:22:11,900 --> 00:22:17,560
+significant، عدّهم، زي 4 0 3 6، وين الـ 0
+
+292
+00:22:17,560 --> 00:22:21,900
+محطوطه؟ مش عايمة، وعاملّة فيه القام محصور، إذا عدّه
+
+293
+00:22:21,900 --> 00:22:28,080
+عدّ أربعة، أربعة، تمام، has four significant figures
+
+294
+00:22:28,080 --> 00:22:31,720
+one point zero six، فلتوا من هذه الـ point اللي هي
+
+295
+00:22:31,720 --> 00:22:35,720
+الفاصلة، منجزعة، والصفر بين واحد وستة ولا لا؟ عدّوا
+
+296
+00:22:35,720 --> 00:22:40,460
+كم واحد؟ إذًا ثلاثة significant figures، إذا خلّصنا
+
+297
+00:22:40,460 --> 00:22:44,860
+اللي من الصفر كلّه وبدّك تعدّه، صح؟ الصفر له قواعد، إذا
+
+298
+00:22:44,860 --> 00:22:50,060
+الصفر محصور عدّه، تمام، هيك احنا بنحكي بالبلدي هينا، إذا
+
+299
+00:22:50,060 --> 00:22:51,640
+الصفر محصور عدّه
+
+300
+00:22:54,370 --> 00:22:57,070
+بيقول لي Zero is placed to the left، في مثل عربي
+
+301
+00:22:57,070 --> 00:23:02,370
+بيقول لو جالت لكم أمّكم أو سيدكم إن فلان صفر على شمال
+
+302
+00:23:02,370 --> 00:23:08,130
+إيش بيفهموا منه؟ يعني ما لهوش قيمة، ما لهوش أهمية، نفس
+
+303
+00:23:08,130 --> 00:23:13,710
+القاعدة، طبقوها، إذا الصفر على شمال ينسوه، نفس القاعدة؟
+
+304
+00:23:13,710 --> 00:23:18,750
+ماشي، يعني ما لهوش قيمة يعني؟ الله يردّه، صح؟ بغضّ
+
+305
+00:23:18,750 --> 00:23:22,950
+النظر، بقول zeros placed to the left of non-zero
+
+306
+00:23:22,950 --> 00:23:28,610
+digits are not significant، إنسى، ههه، تشوفوا هينا
+
+307
+00:23:28,610 --> 00:23:33,090
+في إشارة، اللي هي فاصلة، بغضّ النظر، قال لي ها، هدول
+
+308
+00:23:33,090 --> 00:23:37,190
+الأصفار، على شمال ولا لأ؟ is an atom significant؟
+
+309
+00:23:37,190 --> 00:23:43,690
+واحد، الأصفار ما عدّناهمش، سهل، أظنّ إنّ في حد ما سمعوش فيه
+
+310
+00:23:43,690 --> 00:23:48,910
+المثل، صفر على شمال، وهاد بينضلّ متذاكرين، وصفر على
+
+311
+00:23:48,910 --> 00:23:54,230
+شمال بدّي إياه، لأ، خلاص يُهمل، سهل، هاد كاين studio 6 و
+
+312
+00:23:54,230 --> 00:24:02,710
+بيعرفوا علم، تمام، حلو، أحكي non-zero، أحكي
+
+313
+00:24:06,660 --> 00:24:09,580
+أنتَ فاكّروش كثير في الامتحان، هادي مدّ يو مش في
+
+314
+00:24:09,580 --> 00:24:15,160
+الامتحان، رسّيك، فقعفة هادي، أنتَ بيقول لك كيف نكتبها،
+
+315
+00:24:15,160 --> 00:24:17,940
+يعني أنا مركّز، لأن أنتو هتخشوا، يعني أمكرا
+
+316
+00:24:17,940 --> 00:24:21,740
+هتخشوا في الرسم، مش هتجسّوا، هتخشوا في المعمل،
+
+317
+00:24:21,740 --> 00:24:25,040
+هتجسّوا، فهادي بيديها عشان كيف تتعاملوا مع الأرقام
+
+318
+00:24:25,790 --> 00:24:30,670
+تمام؟ فاتّكي مني الحفظ، ما تحفظيش شيء، تمام، بيقول الـ
+
+319
+00:24:30,670 --> 00:24:35,030
+zeros at the end of a number and to the right of a
+
+320
+00:24:35,030 --> 00:24:39,250
+decimal are significant، نجي على اليمين، قال لي إذا
+
+321
+00:24:39,250 --> 00:24:44,490
+لجيت إشارة عشرية، اللي هي فاصلة، عدّ الأصفار اللي على اليمين
+
+322
+00:24:44,490 --> 00:24:48,010
+هو مش اللي على اليسار، اللي على اليسار خلّصنا منها، صفر على
+
+323
+00:24:48,010 --> 00:24:51,370
+يسار اللي خلّصنا منه، لجيت، نجي لليمين، قال لي اليمين
+
+324
+00:24:51,370 --> 00:24:57,780
+بدّك تعدّه، إذا كان فيه فاصلة عشرية، تمام؟ إذًا بيقول لي
+
+325
+00:24:57,780 --> 00:25:02,340
+زي إيش؟ جاب لي 16، هذه على مين؟ ومش على مين؟ وهذه
+
+326
+00:25:02,340 --> 00:25:06,840
+النقطة فاصلة، إذًا نعدّها كم واحدة دول؟ ثلاثة، أيوة
+
+327
+00:25:06,840 --> 00:25:12,660
+شايفينهم؟ أربعة، برافو عليكم، تمام؟ أربعة، طيب نيجي
+
+328
+00:25:12,660 --> 00:25:20,140
+نقول بالـ calculator، تمام؟ أنا هدول الشمّة 200 ولا
+
+329
+00:25:20,140 --> 00:25:27,120
+مش 200؟ 200، حلو، طيب وهذه؟ 2، 2 زي بعيط؟ فأنا قشّطان
+
+330
+00:25:27,120 --> 00:25:31,620
+لكن آجي أقول كم significant figure هينا؟ واحد و
+
+331
+00:25:31,620 --> 00:25:37,100
+أيضاً واحد، طب كيف؟ إيش معنى واحد؟ هذه اثنين، لما
+
+332
+00:25:37,100 --> 00:25:41,340
+تدينيها واحد، معناه هذا مش يقيني، معناه أنا الرقم
+
+333
+00:25:41,340 --> 00:25:45,860
+تبعي إمّا واحد أو ثلاثة، صح؟ هينا بقول له معناه الرقم
+
+334
+00:25:45,860 --> 00:25:49,400
+إمّا مئة أو ثلاثمئة، طب أنا ما جَسّتش هيك، القراءة تبعتي
+
+335
+00:25:49,400 --> 00:25:55,600
+مش هيك، القراءة تبعتي أكثر دقّة، إذا اكتب ليها هيك، إذا
+
+336
+00:25:55,600 --> 00:25:58,680
+أنا كم significant في قياسي؟ ثلاثة! صار إيش
+
+337
+00:25:58,680 --> 00:26:02,280
+بتقولي أنتَ لما تكتبه هيك؟ بقول لك هذه إمّا 201 أو
+
+338
+00:26:02,280 --> 00:26:09,900
+199، على وين أنا شاكّك في الأخير بس، لكن بدون هذه أنا
+
+339
+00:26:09,900 --> 00:26:15,520
+شاكّك في هذه، شاكّك في هذه، إذا بيقول لي هينا هذه بعد ما
+
+340
+00:26:15,520 --> 00:26:21,200
+خلصناهن، خلّصنا من هذه، هينا zeros at the end of a
+
+341
+00:26:21,200 --> 00:26:26,760
+number without a decimal، بدون فاصلة عشرية، are not
+
+342
+00:26:26,760 --> 00:26:30,380
+significant، is not significant، ما زالت ما حطّتش إشارة
+
+343
+00:26:30,380 --> 00:26:36,340
+فاصلة عشرية، اللي حتى على اليمين ما تعدّوش، آه... آه...
+
+344
+00:26:36,340 --> 00:26:38,820
+إذا أنتَ... أنتَ اللي بيبقى يكتب... أنا بدّي أفهم
+
+345
+00:26:38,820 --> 00:26:43,080
+بناءً على كتابتك... أنتَ بتقول لي والله إنّ أنا شاكّك
+
+346
+00:26:43,080 --> 00:26:45,760
+في الاثنين، وأكتبه هيك... أنتَ بتقول لي لأ، أنا هادي
+
+347
+00:26:45,760 --> 00:26:47,940
+متأكد منها، وهادي متأكد منها... هادي شاكة فيها...
+
+348
+00:26:47,940 --> 00:26:52,020
+بيبقى يكتب لي هيك عشان أفهم عليك... ساعتها هادي
+
+349
+00:26:52,020 --> 00:26:55,000
+بقول عنها three significant figures، لكن هيك بقولها
+
+350
+00:26:55,000 --> 00:26:59,830
+كم واحد؟ واحد، إذًا Zeroes، Zero at the end of a
+
+351
+00:26:59,830 --> 00:27:03,630
+number without a decimal point، دون فاصلة عشرية، is
+
+352
+00:27:03,630 --> 00:27:09,470
+not significant، ما تعدّهاش، Thus، جيت 4200
+
+353
+00:27:09,470 --> 00:27:13,370
+وحطّيت فاصلة، جيت أربعة، Has four significant
+
+354
+00:27:13,370 --> 00:27:19,610
+figures، why؟ 4200 بدون فاصلة، ليش؟ من وين
+
+355
+00:27:19,610 --> 00:27:24,190
+سؤالنا على الـ... إيش اللي نحفظه؟ سهلين، مظبوط؟
+
+356
+00:27:24,190 --> 00:27:31,460
+سهلين، 4200 في فاصلة عشرية؟ إذا ما تعدّيش الأصفار
+
+357
+00:27:31,460 --> 00:27:38,360
+أكملوها، حد هينا في فاصلة عشرية عدّهم، تصيروا أربعة
+
+358
+00:27:38,360 --> 00:27:46,060
+شوفتوا إيه؟ حلو، جاب لي، طيب أنتو علمتوني اللي هي
+
+359
+00:27:46,060 --> 00:27:51,450
+الرموز العلمية، لمنجور، سرعة الضوء، ثلاثة بون ثمانية
+
+360
+00:27:51,450 --> 00:27:55,090
+في عشرة أس ثمانية، مظبوط ولا لأ؟ ثلاثة بون ثمانية
+
+361
+00:27:55,090 --> 00:27:58,190
+في عشرة أس ثمانية، أنا ثلاثة وثمانية وتحطّ جنبهم سبعة
+
+362
+00:27:58,190 --> 00:28:01,470
+أصفار ولا لأ؟ قال لي هادي ثلاثة بون ثمانية بنسمّيها
+
+363
+00:28:01,470 --> 00:28:05,610
+إيش؟ بنسمّيها رمز علمي، ده ريحنا أكتر، قال لي في
+
+364
+00:28:05,610 --> 00:28:11,390
+الرموز العلمية كلّ إيش بدّك تعدّه؟ كلّ الأصفار، تمام؟ إذا
+
+365
+00:28:11,390 --> 00:28:15,610
+بيقول لي all digits in a number in a scientific
+
+366
+00:28:15,610 --> 00:28:18,610
+notation، scientific notation، اللي هي في عشرة أسّ
+
+367
+00:28:18,610 --> 00:28:24,530
+تمام؟ are significant، for example 4.2 في عشرة أسّ
+
+368
+00:28:24,530 --> 00:28:30,250
+ثلاثة، طب هتطلعوا يا بنات، جيت 4.2 في عشرة أسّ ثلاثة
+
+369
+00:28:30,250 --> 00:28:37,450
+و 4.20 في عشرة أسّ ثلاثة، و 4.200 في عشرة أسّ ثلاثة
+
+370
+00:28:38,490 --> 00:28:44,290
+كالكيليتر في فرق بين هدول؟ ولا شيء، ولا شيء، في فرق
+
+371
+00:28:44,290 --> 00:28:52,030
+كالكيليتر رقم نفسه، تلعب... أنتَ مش م... مش مأمنة
+
+372
+00:28:52,030 --> 00:28:56,850
+اتّصنّي شوية، هجيب الهادي في الكالكيليتر كيف تتحوّل؟
+
+373
+00:28:56,850 --> 00:29:02,490
+مظبوط؟
+
+374
+00:29:02,490 --> 00:29:06,210
+نيجي لهادي، نيجي لهادي
+
+375
+00:29:08,470 --> 00:29:13,470
+في حد اختلف؟ لأ، طب قول لي ليش، إيش كتابتها؟ بقول له حلو
+
+376
+00:29:13,470 --> 00:29:16,530
+هامّ أنتَ إيش بتقول؟ بقول لي هادي أنا مش متأكد منه
+
+377
+00:29:16,530 --> 00:29:21,510
+صح؟ معناته هادي إمّا أربعة آلاف وثلاثمئة أو أربعة
+
+378
+00:29:21,510 --> 00:29:25,970
+آلاف ومئة، هامّ بتقول لي أنتَ هادي أنا مش متأكد منه
+
+379
+00:29:25,970 --> 00:29:30,850
+إذا إمّا أربعة آلاف واثنين وعشرة أو أربعة آلاف و
+
+380
+00:29:30,850 --> 00:29:36,050
+مية وتسعين، صحيح؟ هينا قال أنتَ هذا بس اللي مش متأكد
+
+381
+00:29:36,050 --> 00:29:45,630
+منه، إذا إمّا 4201 أو 4199، لكن كرقم حسابي كل واحد بس
+
+382
+00:29:45,630 --> 00:29:54,750
+بفرج، أنتَ تقول لي كيف جَسّت، تمام؟ حلو، هذا يعرف للشوة الـ
+
+383
+00:29:5
+
+445
+00:35:32,120 --> 00:35:37,860
+أحط أحد عشر وأنا غير مفهومة بدي أستخدم الـ scientific
+
+446
+00:35:37,860 --> 00:35:41,240
+notation لما أحط الـ scientific notation طلعت كتبتها
+
+447
+00:35:41,240 --> 00:35:44,140
+one point one في عشرين، اثنين، أكمل واحدة دول
+
+448
+00:35:50,350 --> 00:35:56,070
+ثلاثة هذه خمسة وأطلع، ولا أقل من خمسة، إذا أقل من
+
+449
+00:35:56,070 --> 00:36:00,630
+خمسة الله لا يردها بأضيعها، طب إذا أكثر من خمسة
+
+450
+00:36:00,630 --> 00:36:06,210
+بخليها اثنين، يعني لو هذه خمسة أو ستة أو ثمانية
+
+451
+00:36:06,210 --> 00:36:12,250
+بخلي one point two طبعاً احكوا معايا، معايا احكوا
+
+452
+00:36:12,250 --> 00:36:16,630
+معايا، مش قلنا عشان تسألوا، وناخد حسنات، دكتور احكي
+
+453
+00:36:16,630 --> 00:36:21,950
+أنها هي مئة وثلاث عشرة، مئة وثلاث عشرة وشوية طبعاً أنا
+
+454
+00:36:21,950 --> 00:36:24,690
+بأخذ أول شيء، أول رقم، المئة طبعاً من الثلاث عشرة اللي
+
+455
+00:36:24,690 --> 00:36:30,270
+بشوف وضعها، وأقربها بالضبط، طبعاً غيرها احكي
+
+456
+00:36:30,270 --> 00:36:33,850
+الأرقام اللي بعد الفاصلة وغيرها من حسد
+
+457
+00:36:35,980 --> 00:36:42,440
+حسب كم significant figures، هجيت له هذا أنا أنا أنا
+
+458
+00:36:42,440 --> 00:36:42,700
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+459
+00:36:42,700 --> 00:36:45,140
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+460
+00:36:45,140 --> 00:36:45,260
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+461
+00:36:45,260 --> 00:36:46,880
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+462
+00:36:46,880 --> 00:36:48,520
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+463
+00:36:48,520 --> 00:36:48,620
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+464
+00:36:48,620 --> 00:36:53,120
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+465
+00:36:53,120 --> 00:36:58,370
+أنا، أنا، أنا، أنا، أبزود اللي جابله، أنا
+
+466
+00:36:58,370 --> 00:37:02,070
+ما بديش إيه في كل الحالات، لأنه لو قعدت بعملي خلال، بصير
+
+467
+00:37:02,070 --> 00:37:05,890
+ثلاثة significant figures، ما ينفعش أخليه، إما بأخذ
+
+468
+00:37:05,890 --> 00:37:11,310
+منه نفسه وبزود اللي جابله، أو الله لا يرده، تمام؟
+
+469
+00:37:11,310 --> 00:37:15,670
+هاي اللي بيقول لي، ما ينفعش تكتب 113، لأنه بيصير
+
+470
+00:37:15,670 --> 00:37:22,830
+ثلاثة، ولا 113.1، بيصيروا أربعة، but as reported
+
+471
+00:37:22,830 --> 00:37:29,500
+before، يجب تكتبوا هيك، اثنين، تمام؟ خلصنا من
+
+472
+00:37:29,500 --> 00:37:34,740
+الضرب والقسمة بتروح تعدلي الـ significant figures
+
+473
+00:37:34,740 --> 00:37:39,040
+جوابك لازم يكون بعدد أقل واحد، طب وبالجمع والطرح
+
+474
+00:37:39,040 --> 00:37:40,900
+قال لي ليه؟ ما لك أي دعوة بالـ significant figures
+
+475
+00:37:40,900 --> 00:37:44,520
+بقول له إيش إلي دعوة؟ قال لي إليك دعوة بالفاصلة
+
+476
+00:37:44,520 --> 00:37:49,480
+العشرية، شوف لي موضع الفاصلة العشرية، بعد الفاصلة
+
+477
+00:37:49,480 --> 00:37:57,070
+كم رقم عندك، جوابك بدي يكون نفس العملية، عند أقل عدد
+
+478
+00:37:57,070 --> 00:38:01,690
+بعد الفاصلة العشرية، يعني when numbers are added or
+
+479
+00:38:01,690 --> 00:38:06,510
+subtracted، added يعني جمعت، subtracted طرحت وطرحت
+
+480
+00:38:06,510 --> 00:38:10,450
+واتجمع، عملية حسابية واحدة، حلو، بيقول لي the number
+
+481
+00:38:10,450 --> 00:38:14,910
+of decimal places، decimal places موضع الإشارة
+
+482
+00:38:14,910 --> 00:38:20,580
+الفاصلة العشرية، decimal places مكان الفاصلة، تمام، in
+
+483
+00:38:20,580 --> 00:38:23,940
+the result should equal the smallest number of
+
+484
+00:38:23,940 --> 00:38:27,760
+decimal places of any term in the added or
+
+485
+00:38:27,760 --> 00:38:33,240
+subtracted numbers، حسب الأصغر، يعني هذول هما إيش بين
+
+486
+00:38:33,240 --> 00:38:38,320
+هما دول زائد ولا مش زائد؟ زائد، بقول الأول بعد الفصل
+
+487
+00:38:38,320 --> 00:38:42,380
+العشرية كم رقم فيه، والثاني، الجواب لازم يكون واحد
+
+488
+00:38:42,380 --> 00:38:47,650
+لازم يكون واحد، اللي هو الأقل، هجيت نيجي نجمع
+
+489
+00:38:47,650 --> 00:38:50,830
+بالجمع العادي يا بنات، احنا كنا في الـ.. لما
+
+490
+00:38:50,830 --> 00:38:53,250
+علمونا في البستان كيف نجمع ولا ما علموناش في
+
+491
+00:38:53,250 --> 00:38:57,310
+البستان، لسه هنجمع، أظن خليني أشوف مئة وخمسة وأربعين
+
+492
+00:38:57,310 --> 00:39:01,990
+point
+
+493
+00:39:01,990 --> 00:39:06,070
+five، ستة point ثمانية أربعة، مش كانوا يقولوا لي نحط
+
+494
+00:39:06,070 --> 00:39:12,750
+صفر هنا عشان نعرف نجمع، يلا صفر وأربعة خمسة، ولا
+
+495
+00:39:12,750 --> 00:39:20,820
+نحط إيش؟  صفر هنا، خمسة وثمانية ثلاثة، وستة وستة، صحيح بقول
+
+496
+00:39:20,820 --> 00:39:23,220
+هذا الجواب، هيك طلع الـ calculator، بقول لهم ممنوع
+
+497
+00:39:23,220 --> 00:39:27,280
+تكتبوا هيك، ليش؟ لأنه كم واحدة هذول؟ اثنتين، وهذه
+
+498
+00:39:27,280 --> 00:39:31,260
+واحدة.. هذي واحدة.. ما ينفعش تتحط واحدة، لأنه أقل
+
+499
+00:39:31,260 --> 00:39:38,010
+واحد فيهم واحد، طيب نيجي لهنا، هذه لا أريد أن أحصل
+
+500
+00:39:38,010 --> 00:39:41,470
+عليها، لأ بجيبها، والله لا يردها، وإذا كانت خمسة أو
+
+501
+00:39:41,470 --> 00:39:45,350
+فوق، هذه عليك تخليها أربعة، تمام هيك؟ عليك تخليها
+
+502
+00:39:45,350 --> 00:39:51,770
+أربعة، فبقول لي هذه هنا كتبناها هي point ثلاثة
+
+503
+00:39:51,770 --> 00:39:56,450
+بتخليها إيش هيك ولا بتخليها هيك؟ تمام هيك؟ حلو، قال
+
+504
+00:39:56,450 --> 00:40:00,330
+لي خليني آخذ مثالين ثانين، هجيت نرجع للـ significant
+
+505
+00:40:00,330 --> 00:40:05,450
+figures، كم significant figures هنا؟ واحدة، برة عليكم
+
+506
+00:40:05,450 --> 00:40:10,680
+هناك significant figures، خمسة، لما جيت أطلع قلت واحد
+
+507
+00:40:10,680 --> 00:40:13,080
+اثنين ثلاثة، بدي أجمع، ما لي أي دعوة في الـ
+
+508
+00:40:13,080 --> 00:40:16,240
+significant figures، أربعة أربعة، إذا أخليهم جمعتهم
+
+509
+00:40:16,240 --> 00:40:21,140
+يطلع أربعة، أنا ما بدي أربعة، قالوا واحد اثنين ثلاثة
+
+510
+00:40:21,140 --> 00:40:25,860
+واحد اثنين ثلاثة، تمام، واحد اثنين ثلاثة، عادي ما فيش
+
+511
+00:40:25,860 --> 00:40:31,120
+إشكالية، بغض النظر عن الـ significant figures، تمام
+
+512
+00:40:31,120 --> 00:40:39,530
+عادي، اللي حكيناه، نشوف اللي هو المثال، المساحة جالي
+
+513
+00:40:39,530 --> 00:40:49,600
+جستلك الطول، جاي 12.71 متر، أربعة حلو، والعرض جاي 3
+
+514
+00:40:49,600 --> 00:40:55,120
+.46 متر، ثلاثة، إيش بدّك تعمل؟ قال لي بدي المساحة، مساحة
+
+515
+00:40:55,120 --> 00:40:58,940
+أضرب ولا أجمع؟ أضرب، ما زال أضرب، ما لي دعوة في الـ
+
+516
+00:40:58,940 --> 00:41:02,000
+significant figures، هذا أربعة وهذا ثلاثة، شو لازم
+
+517
+00:41:02,000 --> 00:41:05,720
+الجوّاب يكون؟ لازم يكون ثلاثة، قال لي يلا بالـ
+
+518
+00:41:05,720 --> 00:41:11,350
+calculator، ضربت، طلعت إجابة هيك، هذا جواب الـ
+
+519
+00:41:11,350 --> 00:41:14,830
+calculator، بينفع اكتبه زي الـ calculator؟ بقول له لأ
+
+520
+00:41:14,830 --> 00:41:20,050
+بقول له أنت بتقول لي لازم نكون ثلاثة، بقول له هذا  همعند
+
+521
+00:41:20,050 --> 00:41:23,530
+هنا بدي أوقف، انتبهي هنا بدي أوقف، بقول إيش جنبه
+
+522
+00:41:23,530 --> 00:41:28,790
+سبعة، هذا بدي يكبر، بدي يصير عشرة، عشرة يعني صفر وهذا
+
+523
+00:41:28,790 --> 00:41:31,890
+بدي يصير أربعة، أربعة وأربعين، أكتب أربعة وأربعين
+
+524
+00:41:31,890 --> 00:41:35,690
+ما ينفعش اثنين، بيصيروا لازم يكون أربعة وأربعين فاصلة
+
+525
+00:41:35,690 --> 00:41:44,660
+صفر عشان يصيروا ثلاثة، صح؟ مع أنه، احكي، أرجعي 145.6
+
+526
+00:41:44,660 --> 00:41:47,920
+قلت إنه بعد الفاصلة خمسة، وبعد الفاصلة أربعة
+
+527
+00:41:47,920 --> 00:41:51,560
+ثمانية، يعني ليش ما عدّلت إنه أربعة أو ثلاثة، أربعة
+
+528
+00:41:51,560 --> 00:41:56,420
+ثمانية؟ إن هي وين؟ هنا، اه اه هنا، هجيت احنا جمعناهم
+
+529
+00:41:56,420 --> 00:42:01,600
+هذول، نضبط ولا لأ؟ هي 152.34، أنا إيش قاعد هنا؟ بيجمع
+
+530
+00:42:01,600 --> 00:42:06,300
+وفي الجمع بيقول لي لازم الجواب يكون بعد الفاصلة
+
+531
+00:42:06,300 --> 00:42:11,450
+العشرية أقل واحد من الاثنين، وقلت له هنا واحد وهنا
+
+532
+00:42:11,450 --> 00:42:14,950
+اثنين، لازم الجواب يكون واحد، فلازم يكون واحد بعد
+
+533
+00:42:14,950 --> 00:42:18,390
+الإشارة، أنا لما جمعتهم طلع هذا، أنا بقول له هذه
+
+534
+00:42:18,390 --> 00:42:22,090
+عشان هي أربعة، بألغيها، لو كانت خمسة وفوق بصير هذه
+
+535
+00:42:22,090 --> 00:42:27,950
+أربعة، تمام هيك؟ حلو، جاي هيك، طلعت، قلت له إذا هذه
+
+536
+00:42:27,950 --> 00:42:33,270
+عشان تطلع بالضبط ثلاثة لازم تكتبها أربعة وأربعين
+
+537
+00:42:33,270 --> 00:42:42,920
+نقطة صفر، هيك بتطلع، هاتي هو من فهمك إيش ورانا بس
+
+538
+00:42:42,920 --> 00:42:47,480
+بتجرّبي ولا لأ؟ بس مرات بتقولوا واحد حرام
+
+539
+00:42:47,480 --> 00:42:49,780
+الكالكوليتر بتاعتك بتكتب، اكتب زي ما كتبت
+
+540
+00:42:49,780 --> 00:42:54,460
+الكالكوليتر، مفروض لأ، احنا ممكن نعدّل عليها، بس احكي
+
+541
+00:42:54,460 --> 00:42:58,100
+يا بنتي طبعاً، هلأ ثلاثة وأربعين point سبعة وتسعون
+
+542
+00:42:58,100 --> 00:43:01,200
+اه طبعاً، قربنا على العشرة، ثلاثة، أربعة وأربعين، حلو
+
+543
+00:43:01,200 --> 00:43:06,510
+هشوزا الستة والستين، وين الستة والستين؟ احنا نظرنا نجي
+
+544
+00:43:06,510 --> 00:43:10,150
+وراهم، لما يوصلوا جهنم، ونشيل فيهم، أنا ببطل، أنا إيش
+
+545
+00:43:10,150 --> 00:43:13,810
+بدي ألغي؟ بدي ألغي السبعة، صح؟ لأنه عندي التسعة
+
+546
+00:43:13,810 --> 00:43:18,410
+بدي أخلص السبعة، بينفع ألغيها بدون ما آخذ تأثيرها
+
+547
+00:43:18,410 --> 00:43:22,190
+لأنه أكبر من الخمسة، طيب هي بتأثر على مين؟ على اللي
+
+548
+00:43:22,190 --> 00:43:26,270
+جاب لها، التسعة، إيش بدي يصير؟ خلص، هجيت الست والستين، نشيل
+
+549
+00:43:26,270 --> 00:43:29,550
+فيها، طب ما اللي جاب لها أكلتها، اسمها السبعة
+
+550
+00:43:34,290 --> 00:43:39,210
+لأ، سنة، في فرق الجمع والطرح غير عن الضرب والقسمة، في
+
+551
+00:43:39,210 --> 00:43:42,330
+الضرب والقسمة، الأقل في الـ significant figures، في
+
+552
+00:43:42,330 --> 00:43:46,650
+الجمع والطرح، الأقل في موضع الفاصلة العشرية، فهمت
+
+553
+00:43:46,650 --> 00:43:51,890
+عليها؟ هذا الفرق، تمام، وبرضه ما ينفعش نكتب أربعة
+
+554
+00:43:51,890 --> 00:43:58,630
+وأربعين، لأن أربعة وأربعين بيصير اثنين، تمام، حلو، نعمل
+
+555
+00:43:58,630 --> 00:44:04,600
+quiz، شوف كنا نحكي عربي ولا صيني، يعجب عليكي ثاني، تمام
+
+556
+00:44:04,600 --> 00:44:07,600
+بقول لي how many significant figures are in the
+
+557
+00:44:07,600 --> 00:44:16,340
+number 0003، احكيه، هطلع أخوك، الخيارات تبعتنا واحد
+
+558
+00:44:16,340 --> 00:44:24,060
+ولا مش واحد، سهل سهل، صفر، عشمان، bravo عليكم، حلو
+
+559
+00:44:24,060 --> 00:44:34,260
+بقول لي أنا بدي أضرب، بدي أضرب ثاني، بدي أضرب 2.34
+
+560
+00:44:34,260 --> 00:44:38,500
+ثلاثة significant figures في 2.0، ثلاثة significant
+
+561
+00:44:38,500 --> 00:44:42,900
+figures، الإجابة إيش لازم تكون؟ اثنين، bravo، بس أشوف
+
+562
+00:44:42,900 --> 00:44:50,520
+الخيارات وأرجع إليك، تمام؟ هذه الخيارات تبعتنا 4
+
+563
+00:44:50,520 --> 00:44:58,960
+.6 ولا 4.7؟ هذا الـ calculator يا بنات، ليش؟
+
+564
+00:44:59,980 --> 00:45:07,480
+لأنه ثمانية، هذا هي، مش صناعة صاروخ، سهل العملية وين
+
+565
+00:45:07,480 --> 00:45:13,460
+هالبتقول أنا الأخير اثنين شوية، لذا هذا، تمام، the
+
+566
+00:45:13,460 --> 00:45:16,500
+results of the arithmetic operation، هنا بدي أجمع
+
+567
+00:45:16,500 --> 00:45:23,500
+أجمع، إيش بتطلع؟ موضع الفاصلة، بقول واحد اثنين ثلاثة
+
+568
+00:45:23,500 --> 00:45:27,280
+هنا لازم الجواب يكون واحد، لازم الجواب يكون واحد
+
+569
+00:45:27,280 --> 00:45:28,940
+طلع عليا عشان تجاوبي
+
+570
+00:45:34,100 --> 00:45:40,440
+دالباكم هيك، الكالكوليتر خمسة عشرة
+
+571
+00:45:40,440 --> 00:45:48,460
+point تسعة، قربنا، احكي في الـ.. في الجبل، تقربي اه
+
+572
+00:45:48,460 --> 00:45:51,780
+الـ.. بيطلع اثنين، عندك عدد كله ولا بعد الفاصلة
+
+573
+00:45:51,780 --> 00:45:55,040
+بعد الضرب بيطلع عندك اثنين، اثنين significant
+
+574
+00:45:55,040 --> 00:45:58,100
+figures، significant figures، اه significant figures
+
+575
+00:45:58,100 --> 00:46:02,340
+كله مش أي ما ندعو في الفاصلة العشرية، في الضرب، في الـ
+
+576
+00:46:02,340 --> 00:46:07,000
+significant figures، تمام؟ دكتور، عيد لي الأخير ثاني
+
+577
+00:46:07,000 --> 00:46:15,350
+عيد لي الأخير ثاني، أشرح لي؟ زائد، في الزائد بهمني موضع
+
+578
+00:46:15,350 --> 00:46:20,450
+الفاصلة العشرية، صحيح؟ هي اللي بهمني، إيش وراها؟
+
+579
+00:46:20,450 --> 00:46:24,770
+بقول له هادي واحد اثنين ثلاثة، وهادي واحد، الجواب
+
+580
+00:46:24,770 --> 00:46:29,070
+لازم يكون لأصغر كم؟ إذا لازم جوابك يكون بعد
+
+581
+00:46:29,070 --> 00:46:33,990
+الفاصلة في واحد بس، لما أجيت أنا جمعت طلع هذا
+
+582
+00:46:33,990 --> 00:46:38,580
+الرقم، بقول له هذول ثلاثة، بدي واحد، بدك تبقى على
+
+583
+00:46:38,580 --> 00:46:43,520
+هذه، طب هذي أخليها ثمانية ولا أخليها تسعة؟ ليش؟ لأنه
+
+584
+00:46:43,520 --> 00:46:54,940
+جنبها أكثر من خمسة، أيصفّ صفر، احكي، إيه؟ مش
+
+585
+00:46:54,940 --> 00:47:02,820
+بالجمع والضرب، الجمع محمد والضرب عزيزة، بيختلفوا
+
+586
+00:47:02,820 --> 00:47:07,190
+عاد، تمام؟ ما تقولش جمع وضرب، هذه عملية غير عن هذه
+
+587
+00:47:07,190 --> 00:47:14,710
+في الجمع والطرح، الإجراء بنأخذ موضع الفاصلة العشرية
+
+588
+00:47:14,710 --> 00:47:19,430
+في الضرب، إيش الإجراء؟ القسمة، بتأخذ فيه significant
+
+589
+00:47:19,430 --> 00:47:24,530
+figures، تمام هيك؟ خلصنا الـ chapter، تمام يا بنات؟
+
+590
+00:47:24,530 --> 00:47:30,770
+إذا هذول الأسئلة قبل السبت ما نكون حلوة، طيب حاضر
+
+591
+00:47:30,770 --> 00:47:33,130
+يعطيكم العافية، نشوفكم السبت إن شاء الله
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/tTmo29ZCZv4_raw.json b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/tTmo29ZCZv4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a9b3e1cb49898ca8c7bf48f6547e082d50e2baf9
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/tTmo29ZCZv4_raw.json
@@ -0,0 +1 @@
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{"start": 1100.02, "end": 1100.56, "word": " العلمية", "probability": 0.9947916666666666}, {"start": 1100.56, "end": 1101.06, "word": " فإيه", "probability": 0.941162109375}, {"start": 1101.06, "end": 1102.1, "word": " القواعد", "probability": 0.9505208333333334}, {"start": 1102.1, "end": 1103.24, "word": " تمام", "probability": 0.8466796875}, {"start": 1103.24, "end": 1103.7, "word": " هاي", "probability": 0.652099609375}, {"start": 1103.7, "end": 1103.9, "word": " بيقول", "probability": 0.9285481770833334}, {"start": 1103.9, "end": 1104.0, "word": " لي", "probability": 0.491455078125}, {"start": 1104.0, "end": 1104.14, "word": " for", "probability": 0.94921875}, {"start": 1104.14, "end": 1104.58, "word": " example", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 49, "seek": 113097, "start": 1105.73, "end": 1130.97, "text": "مثلًا اللي تعرفوا دراب ترقمية when you measure a distance .. دي جيس مسافة by a meter stick اللي هي المصطلح تمامًا your measurement should be written 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"end": 1137.43, "word": " إذا", "probability": 0.813232421875}, {"start": 1137.43, "end": 1137.63, "word": " انت", "probability": 0.54736328125}, {"start": 1137.63, "end": 1137.95, "word": " عشان", "probability": 0.98046875}, {"start": 1137.95, "end": 1138.71, "word": " تكون", "probability": 0.95458984375}, {"start": 1138.71, "end": 1139.93, "word": " بندق", "probability": 0.483642578125}, {"start": 1139.93, "end": 1140.21, "word": " فيه", "probability": 0.69482421875}, {"start": 1140.21, "end": 1140.43, "word": " إلهام", "probability": 0.8748372395833334}, {"start": 1140.43, "end": 1140.75, "word": " عيار", "probability": 0.7996419270833334}, {"start": 1140.75, "end": 1140.97, "word": " وكيف", "probability": 0.8935546875}, {"start": 1140.97, "end": 1141.35, "word": " تقرأ", "probability": 0.90576171875}, {"start": 1141.35, "end": 1141.47, "word": " و", "probability": 0.28955078125}, {"start": 1141.47, "end": 1141.67, "word": " الله", "probability": 0.86328125}, {"start": 1141.67, "end": 1142.03, "word": " علمك", "probability": 0.5436197916666666}, {"start": 1142.03, "end": 1142.33, "word": " يكون", "probability": 0.799560546875}, {"start": 1142.33, "end": 1142.55, "word": " أنت", "probability": 0.7127685546875}, {"start": 1142.55, "end": 1142.93, "word": " أحول", "probability": 0.8963216145833334}, {"start": 1142.93, "end": 1144.21, "word": " مظبوط", "probability": 0.716748046875}, {"start": 1144.21, "end": 1144.39, "word": " او", "probability": 0.54254150390625}, {"start": 1144.39, "end": 1144.83, "word": " لا،", "probability": 0.6060791015625}, {"start": 1144.83, "end": 1145.45, "word": " بالتالي", "probability": 0.84588623046875}, {"start": 1145.45, "end": 1145.89, "word": " لكن", "probability": 0.5}, {"start": 1145.89, "end": 1146.41, "word": " الأحول", "probability": 0.9591471354166666}, {"start": 1146.41, "end": 1146.93, "word": " مخبطش", "probability": 0.732763671875}, {"start": 1146.93, "end": 1147.07, "word": " في", "probability": 0.96044921875}, {"start": 1147.07, "end": 1147.33, "word": " هذا،", "probability": 0.733154296875}, {"start": 1147.33, "end": 1147.61, "word": " مخبط", "probability": 0.9840087890625}, {"start": 1147.61, "end": 1147.73, "word": " في", "probability": 0.9921875}, {"start": 1147.73, "end": 1147.99, "word": " هذا", "probability": 0.98388671875}, {"start": 1147.99, "end": 1149.03, "word": " فبصير", "probability": 0.7845458984375}, {"start": 1149.03, "end": 1149.59, "word": " القاعدة", "probability": 0.982666015625}, {"start": 1149.59, "end": 1149.71, "word": " اللي", "probability": 0.980712890625}, {"start": 1149.71, "end": 1150.21, "word": " صارت", "probability": 0.9871419270833334}, {"start": 1150.21, "end": 1150.91, "word": " تقولي", "probability": 0.57470703125}, {"start": 1150.91, "end": 1151.17, "word": " هذا", "probability": 0.74755859375}, {"start": 1151.17, "end": 1151.37, "word": " و", "probability": 0.54345703125}, {"start": 1151.37, "end": 1151.63, "word": " هذا", "probability": 0.94482421875}, {"start": 1151.63, "end": 1152.25, "word": " أكيد", "probability": 0.9724934895833334}], "temperature": 1.0}, {"id": 51, "seek": 118140, "start": 1152.7, "end": 1181.4, "text": "و هذا تقديري هذا تقديري يمكن زادي شوية خس شوية اذا بيقولي this means that هذا بيعني لما تكتبلي هذا انه the measurement is accurate صحيح بس في عدم يقين uncertainty certain يقين عن عكسه في عدم يقين مقداره اما بزيد او بقل 0.1 يعني هذا بصير اما 0.2 او 0.4", "tokens": [2407, 23758, 6055, 28543, 13546, 1829, 23758, 6055, 28543, 13546, 1829, 7251, 43020, 30767, 18513, 1829, 13412, 2407, 10632, 16490, 3794, 13412, 2407, 10632, 1975, 15730, 4724, 1829, 39648, 1829, 341, 1355, 300, 23758, 4724, 40228, 22653, 5296, 15042, 6055, 4117, 2655, 3555, 20292, 23758, 16472, 3224, 264, 13160, 307, 8559, 20328, 5016, 1829, 5016, 4724, 3794, 8978, 6225, 40448, 7251, 4587, 9957, 15697, 1629, 7251, 4587, 9957, 18871, 6225, 4117, 3794, 3224, 8978, 6225, 40448, 7251, 4587, 9957, 3714, 28543, 9640, 3224, 1975, 15042, 4724, 11622, 25708, 1975, 2407, 4724, 4587, 1211, 1958, 13, 16, 37495, 22653, 23758, 4724, 9381, 13546, 1975, 15042, 1958, 13, 17, 1975, 2407, 1958, 13, 19], "avg_logprob": -0.18418142225890033, "compression_ratio": 1.7321428571428572, "no_speech_prob": 1.3709068298339844e-06, "words": [{"start": 1152.7, "end": 1152.92, "word": "و", "probability": 0.9375}, {"start": 1152.92, "end": 1153.36, "word": " هذا", "probability": 0.484375}, {"start": 1153.36, "end": 1154.38, "word": " تقديري", "probability": 0.8990478515625}, {"start": 1154.38, "end": 1155.28, "word": " هذا", "probability": 0.28466796875}, {"start": 1155.28, "end": 1155.78, "word": " تقديري", "probability": 0.970703125}, {"start": 1155.78, "end": 1155.96, "word": " يمكن", "probability": 0.6500244140625}, {"start": 1155.96, "end": 1156.32, "word": " زادي", "probability": 0.5623372395833334}, {"start": 1156.32, "end": 1156.6, "word": " شوية", "probability": 0.8836263020833334}, {"start": 1156.6, "end": 1156.84, "word": " خس", "probability": 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0.772216796875}, {"start": 1162.66, "end": 1163.12, "word": " the", "probability": 0.705078125}, {"start": 1163.12, "end": 1163.62, "word": " measurement", "probability": 0.79248046875}, {"start": 1163.62, "end": 1164.14, "word": " is", "probability": 0.97119140625}, {"start": 1164.14, "end": 1164.96, "word": " accurate", "probability": 0.86962890625}, {"start": 1164.96, "end": 1166.2, "word": " صحيح", "probability": 0.98583984375}, {"start": 1166.2, "end": 1166.74, "word": " بس", "probability": 0.97265625}, {"start": 1166.74, "end": 1167.22, "word": " في", "probability": 0.87158203125}, {"start": 1167.22, "end": 1167.7, "word": " عدم", "probability": 0.906982421875}, {"start": 1167.7, "end": 1168.28, "word": " يقين", "probability": 0.9358723958333334}, {"start": 1168.28, "end": 1169.52, "word": " uncertainty", "probability": 0.76171875}, {"start": 1169.52, "end": 1170.66, "word": " certain", "probability": 0.90625}, {"start": 1170.66, "end": 1171.38, "word": " يقين", "probability": 0.9659830729166666}, {"start": 1171.38, "end": 1172.08, "word": " عن", "probability": 0.1165771484375}, {"start": 1172.08, "end": 1172.7, "word": " عكسه", "probability": 0.986328125}, {"start": 1172.7, "end": 1173.24, "word": " في", "probability": 0.90478515625}, {"start": 1173.24, "end": 1173.68, "word": " عدم", "probability": 0.980224609375}, {"start": 1173.68, "end": 1174.18, "word": " يقين", "probability": 0.9889322916666666}, {"start": 1174.18, "end": 1175.06, "word": " مقداره", "probability": 0.9552001953125}, {"start": 1175.06, "end": 1175.5, "word": " اما", "probability": 0.842041015625}, {"start": 1175.5, "end": 1176.08, "word": " بزيد", "probability": 0.9596354166666666}, {"start": 1176.08, "end": 1176.36, "word": " او", "probability": 0.969482421875}, {"start": 1176.36, "end": 1176.72, "word": " بقل", "probability": 0.71533203125}, {"start": 1176.72, "end": 1176.96, "word": " 0", "probability": 0.5078125}, {"start": 1176.96, "end": 1177.56, "word": ".1", "probability": 0.99365234375}, {"start": 1177.56, "end": 1178.34, "word": " يعني", "probability": 0.934326171875}, {"start": 1178.34, "end": 1178.56, "word": " هذا", "probability": 0.401123046875}, {"start": 1178.56, "end": 1178.88, "word": " بصير", "probability": 0.8523763020833334}, {"start": 1178.88, "end": 1179.08, "word": " اما", "probability": 0.901611328125}, {"start": 1179.08, "end": 1179.28, "word": " 0", "probability": 0.93408203125}, {"start": 1179.28, "end": 1179.7, "word": ".2", "probability": 0.993896484375}, {"start": 1179.7, "end": 1180.44, "word": " او", "probability": 0.95263671875}, {"start": 1180.44, "end": 1180.58, "word": " 0", "probability": 0.984375}, {"start": 1180.58, "end": 1181.4, "word": ".4", "probability": 0.99658203125}], "temperature": 1.0}, {"id": 52, "seek": 119833, "start": 1181.99, "end": 1198.33, "text": "تمام؟ حلو بيقولي طب انت في الجثة هذه ايش .. ده هو في ال significant figures بقول اه هذا الرقم بنسميه اكم رقم له مهم بقوله تلاتة اذا هذا له تلاتة significant figures تلاتة significant figures", "tokens": [39237, 10943, 22807, 11331, 1211, 2407, 4724, 1829, 39648, 1829, 23032, 3555, 16472, 2655, 8978, 25724, 12984, 3660, 29538, 1975, 1829, 8592, 4386, 11778, 3224, 31439, 8978, 2423, 4776, 9624, 4724, 39648, 1975, 3224, 23758, 34892, 4587, 2304, 44945, 38251, 1829, 3224, 1975, 24793, 12602, 4587, 2304, 46740, 3714, 16095, 4724, 39648, 3224, 6055, 1211, 9307, 3660, 1975, 15730, 23758, 46740, 6055, 1211, 9307, 3660, 4776, 9624, 6055, 1211, 9307, 3660, 4776, 9624], "avg_logprob": -0.2696368247270584, "compression_ratio": 1.7730061349693251, "no_speech_prob": 1.6093254089355469e-06, "words": [{"start": 1181.99, "end": 1182.77, "word": "تمام؟", "probability": 0.8251953125}, {"start": 1182.77, "end": 1183.23, "word": " حلو", "probability": 0.9597981770833334}, {"start": 1183.23, "end": 1183.83, "word": " بيقولي", "probability": 0.6319580078125}, {"start": 1183.83, "end": 1183.97, "word": " طب", "probability": 0.873779296875}, {"start": 1183.97, "end": 1184.15, "word": " انت", "probability": 0.85205078125}, {"start": 1184.15, "end": 1184.25, "word": " في", "probability": 0.8818359375}, {"start": 1184.25, "end": 1184.63, "word": " الجثة", "probability": 0.6278483072916666}, {"start": 1184.63, "end": 1184.87, "word": " هذه", "probability": 0.432861328125}, {"start": 1184.87, "end": 1185.07, "word": " ايش", "probability": 0.8142903645833334}, {"start": 1185.07, "end": 1185.25, "word": " ..", "probability": 0.19140625}, {"start": 1185.25, "end": 1185.59, "word": " ده", "probability": 0.682861328125}, {"start": 1185.59, "end": 1185.73, "word": " هو", "probability": 0.39453125}, {"start": 1185.73, "end": 1185.87, "word": " في", "probability": 0.6943359375}, {"start": 1185.87, "end": 1185.87, "word": " ال", "probability": 0.85791015625}, {"start": 1185.87, "end": 1186.19, "word": " significant", "probability": 0.3740234375}, {"start": 1186.19, "end": 1186.71, "word": " figures", "probability": 0.9150390625}, {"start": 1186.71, "end": 1187.27, "word": " بقول", "probability": 0.544189453125}, {"start": 1187.27, "end": 1187.49, "word": " اه", "probability": 0.7998046875}, {"start": 1187.49, "end": 1187.71, "word": " هذا", "probability": 0.75927734375}, {"start": 1187.71, "end": 1188.47, "word": " الرقم", "probability": 0.9777018229166666}, {"start": 1188.47, "end": 1190.31, "word": " بنسميه", "probability": 0.79742431640625}, {"start": 1190.31, "end": 1190.53, "word": " اكم", "probability": 0.7159423828125}, {"start": 1190.53, "end": 1191.05, "word": " رقم", "probability": 0.99609375}, {"start": 1191.05, "end": 1191.29, "word": " له", "probability": 0.2449951171875}, {"start": 1191.29, "end": 1191.79, "word": " مهم", "probability": 0.97314453125}, {"start": 1191.79, "end": 1192.45, "word": " بقوله", "probability": 0.92822265625}, {"start": 1192.45, "end": 1193.25, "word": " تلاتة", "probability": 0.9237060546875}, {"start": 1193.25, "end": 1194.03, "word": " اذا", "probability": 0.72509765625}, {"start": 1194.03, "end": 1194.43, "word": " هذا", "probability": 0.7890625}, {"start": 1194.43, "end": 1194.65, "word": " له", "probability": 0.72314453125}, {"start": 1194.65, "end": 1195.11, "word": " تلاتة", "probability": 0.9708251953125}, {"start": 1195.11, "end": 1195.55, "word": " significant", "probability": 0.77587890625}, {"start": 1195.55, "end": 1196.29, "word": " figures", "probability": 0.9228515625}, {"start": 1196.29, "end": 1197.35, "word": " تلاتة", "probability": 0.96728515625}, {"start": 1197.35, "end": 1197.71, "word": " significant", "probability": 0.80908203125}, {"start": 1197.71, "end": 1198.33, "word": " figures", "probability": 0.9130859375}], "temperature": 1.0}, {"id": 53, "seek": 122055, "start": 1199.41, "end": 1220.55, "text": "The number of significant figures أو الأرقام المعنوية ذات القيمة in a measurement can be defined as the number of digits، digits يعني رقم، that are measured with certainty، الأرقام اللي أنت متأكد منهم، واحد واتنين، صح ولا لأ؟", "tokens": [2278, 1230, 295, 4776, 9624, 34051, 16247, 2288, 4587, 10943, 9673, 3615, 1863, 2407, 10632, 29910, 9307, 25062, 32640, 3660, 294, 257, 13160, 393, 312, 7642, 382, 264, 1230, 295, 27011, 12399, 27011, 37495, 22653, 12602, 4587, 2304, 12399, 300, 366, 12690, 365, 27022, 12399, 16247, 2288, 4587, 10943, 13672, 1829, 14739, 2655, 44650, 10721, 4117, 3215, 9154, 16095, 12399, 36764, 24401, 4032, 9307, 1863, 9957, 12399, 20328, 5016, 49429, 5296, 10721, 22807], "avg_logprob": -0.23986486124025808, "compression_ratio": 1.4829268292682927, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1199.41, "end": 1199.87, "word": "The", "probability": 0.0343017578125}, {"start": 1199.87, "end": 1200.33, "word": " number", "probability": 0.89892578125}, {"start": 1200.33, "end": 1200.63, "word": " of", "probability": 0.9794921875}, {"start": 1200.63, "end": 1201.21, "word": " significant", "probability": 0.7841796875}, {"start": 1201.21, "end": 1203.71, "word": " figures", "probability": 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{"start": 1264.49, "end": 1264.61, "word": " ان", "probability": 0.82421875}, {"start": 1264.61, "end": 1264.79, "word": " هذا", "probability": 0.80078125}, {"start": 1264.79, "end": 1265.15, "word": " الرقم", "probability": 0.97509765625}, {"start": 1265.15, "end": 1265.41, "word": " اكم", "probability": 0.724609375}, {"start": 1265.41, "end": 1265.81, "word": " significant", "probability": 0.62744140625}, {"start": 1265.81, "end": 1266.43, "word": " figures", "probability": 0.8427734375}, {"start": 1266.43, "end": 1267.03, "word": " قاللي", "probability": 0.642333984375}, {"start": 1267.03, "end": 1267.13, "word": " في", "probability": 0.79833984375}, {"start": 1267.13, "end": 1267.39, "word": " الها", "probability": 0.398590087890625}, {"start": 1267.39, "end": 1267.93, "word": " قواعد", "probability": 0.9562174479166666}, {"start": 1267.93, "end": 1268.79, "word": " to", "probability": 0.3984375}, {"start": 1268.79, "end": 1269.31, "word": " determine", "probability": 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0.9842529296875}, {"start": 1273.79, "end": 1274.43, "word": " تقولي", "probability": 0.876953125}, {"start": 1274.43, "end": 1274.63, "word": " اكم", "probability": 0.9677734375}, {"start": 1274.63, "end": 1275.09, "word": " significant", "probability": 0.84912109375}, {"start": 1275.09, "end": 1275.63, "word": " figure", "probability": 0.8779296875}, {"start": 1275.63, "end": 1276.03, "word": " على", "probability": 0.697265625}, {"start": 1276.03, "end": 1276.23, "word": " طول", "probability": 0.981689453125}, {"start": 1276.23, "end": 1276.63, "word": " بده", "probability": 0.660888671875}, {"start": 1276.63, "end": 1277.39, "word": " اتعلم", "probability": 0.9649658203125}, {"start": 1277.39, "end": 1278.61, "word": " we", "probability": 0.79296875}, {"start": 1278.61, "end": 1278.99, "word": " use", "probability": 0.8662109375}, {"start": 1278.99, "end": 1279.17, "word": " the", "probability": 0.93017578125}, {"start": 1279.17, "end": 1279.59, "word": " following", "probability": 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4587, 2304, 19446, 30767, 6027, 37893, 8608, 5172, 2288, 6225, 3215, 3224, 12399, 1975, 15730, 2107, 12, 32226, 27011, 13672, 1829, 37893, 4018, 12399, 2107, 12, 32226, 27011, 366, 1009, 4776, 12399, 6055, 22488, 16095, 4776, 23032, 1829, 3555, 12399, 1975, 1829, 3224, 30767, 1829, 16095, 22807, 50239, 20292, 3499, 12399, 8978, 16095, 8608, 5172, 9640, 22807, 5551, 24793, 36764, 24401, 12399, 732, 4776, 9624, 575, 732, 4776, 9624, 12399, 36764, 24401, 12399, 6055, 1211, 9307, 3660, 12399, 8608, 2655, 3660, 12399, 8978, 11296, 8608, 5172, 9640, 22807], "avg_logprob": -0.3122234639868272, "compression_ratio": 1.8177777777777777, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1284.52, "end": 1284.88, "word": "بقول", "probability": 0.420654296875}, {"start": 1284.88, "end": 1285.26, "word": " لكل", "probability": 0.5450439453125}, {"start": 1285.26, "end": 1285.98, "word": " الأرقام", "probability": 0.967529296875}, {"start": 1285.98, "end": 1286.16, "word": " اللي", "probability": 0.8388671875}, {"start": 1286.16, "end": 1286.34, "word": " مش", "probability": 0.92529296875}, {"start": 1286.34, "end": 1286.64, "word": " سفر", "probability": 0.8302408854166666}, {"start": 1286.64, "end": 1287.66, "word": " عدهم،", "probability": 0.622650146484375}, {"start": 1287.66, "end": 1288.16, "word": " ادّاك", "probability": 0.691064453125}, {"start": 1288.16, "end": 1288.66, "word": " رقم", "probability": 0.9873046875}, {"start": 1288.66, "end": 1289.06, "word": " ما", "probability": 0.515625}, {"start": 1289.06, "end": 1289.26, "word": " زال", "probability": 0.953125}, {"start": 1289.26, "end": 1289.44, "word": " مش", "probability": 0.96728515625}, {"start": 1289.44, "end": 1289.8, "word": " سفر", "probability": 0.9954427083333334}, {"start": 1289.8, "end": 1291.3, "word": " عده،", "probability": 0.77191162109375}, {"start": 1291.3, "end": 1291.52, "word": " اذا", "probability": 0.708251953125}, {"start": 1291.52, "end": 1292.3, "word": " non", "probability": 0.343994140625}, {"start": 1292.3, "end": 1292.9, "word": "-zero", "probability": 0.6875}, {"start": 1292.9, "end": 1293.4, "word": " digits", "probability": 0.767578125}, {"start": 1293.4, "end": 1293.74, "word": " اللي", "probability": 0.8857421875}, {"start": 1293.74, "end": 1293.92, "word": " مش", "probability": 0.98828125}, {"start": 1293.92, "end": 1294.42, "word": " zero،", "probability": 0.4608154296875}, {"start": 1294.42, "end": 1294.64, "word": " non", "probability": 0.59716796875}, {"start": 1294.64, "end": 1295.36, "word": "-zero", "probability": 0.796630859375}, {"start": 1295.36, "end": 1295.76, "word": " digits", "probability": 0.8623046875}, {"start": 1295.76, "end": 1295.96, "word": " are", "probability": 0.83740234375}, {"start": 1295.96, "end": 1296.3, "word": " always", "probability": 0.88720703125}, {"start": 1296.3, "end": 1296.94, "word": " significant،", "probability": 0.750244140625}, {"start": 1296.94, "end": 1297.34, "word": " تعدهم", "probability": 0.6839192708333334}, {"start": 1297.34, "end": 1297.76, "word": " significant", "probability": 0.58056640625}, {"start": 1297.76, "end": 1299.16, "word": " طيب،", "probability": 0.79345703125}, {"start": 1299.16, "end": 1299.28, "word": " ايه", "probability": 0.8177083333333334}, {"start": 1299.28, "end": 1299.66, "word": " زيهم؟", "probability": 0.779052734375}, {"start": 1299.66, "end": 1299.9, "word": " قاللي", "probability": 0.526123046875}, {"start": 1299.9, "end": 1300.52, "word": " 14،", "probability": 0.65234375}, {"start": 1300.52, "end": 1300.76, "word": " فيهم", "probability": 0.942626953125}, {"start": 1300.76, "end": 1301.8, "word": " سفار؟", "probability": 0.9000244140625}, {"start": 1301.8, "end": 1302.22, "word": " أكم", "probability": 0.50115966796875}, {"start": 1302.22, "end": 1303.46, "word": " واحد،", "probability": 0.7233072916666666}, {"start": 1303.46, "end": 1303.96, "word": " two", "probability": 0.5302734375}, {"start": 1303.96, "end": 1304.68, "word": " significant", "probability": 0.794921875}, {"start": 1304.68, "end": 1305.2, "word": " figures", "probability": 0.92041015625}, {"start": 1305.2, "end": 1306.4, "word": " has", "probability": 0.1348876953125}, {"start": 1306.4, "end": 1306.62, "word": " two", "probability": 0.943359375}, {"start": 1306.62, "end": 1307.14, "word": " significant", "probability": 0.8623046875}, {"start": 1307.14, "end": 1308.56, "word": " figures،", "probability": 0.6649169921875}, {"start": 1308.56, "end": 1308.94, "word": " واحد،", "probability": 0.8986002604166666}, {"start": 1308.94, "end": 1309.22, "word": " تلاتة،", "probability": 0.8322265625}, {"start": 1309.22, "end": 1309.5, "word": " ستة،", "probability": 0.9549560546875}, {"start": 1309.5, "end": 1309.7, "word": " فيها", "probability": 0.9873046875}, {"start": 1309.7, "end": 1310.22, "word": " سفار؟", "probability": 0.91455078125}], "temperature": 1.0}, {"id": 58, "seek": 133240, "start": 1310.9, "end": 1332.4, "text": "أكمل واحد إذاً تلاتة significant figures نحكي عربي صح؟ سهلة هجت فيه zeros مشكلتهم مشكلة بيقول ال zeros إذا كانوا محضونين من أرقام عدهم محضونين يعني إيش السفر ما بينهم إذاً zeros between non-zero digits are significant", "tokens": [10721, 24793, 1211, 36764, 24401, 11933, 15730, 14111, 6055, 1211, 9307, 3660, 4776, 9624, 8717, 5016, 4117, 1829, 6225, 2288, 21292, 20328, 5016, 22807, 8608, 3224, 1211, 3660, 8032, 7435, 2655, 8978, 3224, 35193, 37893, 28820, 2655, 16095, 37893, 28820, 3660, 4724, 1829, 39648, 2423, 35193, 11933, 15730, 25961, 14407, 3714, 5016, 11242, 11536, 9957, 9154, 5551, 2288, 4587, 10943, 6225, 3215, 16095, 3714, 5016, 11242, 11536, 9957, 37495, 22653, 11933, 1829, 8592, 21136, 5172, 2288, 19446, 49374, 16095, 11933, 15730, 14111, 35193, 1296, 2107, 12, 32226, 27011, 366, 4776], "avg_logprob": -0.22372939101942294, "compression_ratio": 1.5277777777777777, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 1310.9, "end": 1311.3, "word": "أكمل", "probability": 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"word": " zeros", "probability": 0.7119140625}, {"start": 1317.92, "end": 1318.46, "word": " مشكلتهم", "probability": 0.95263671875}, {"start": 1318.46, "end": 1319.24, "word": " مشكلة", "probability": 0.984375}, {"start": 1319.24, "end": 1320.16, "word": " بيقول", "probability": 0.9396158854166666}, {"start": 1320.16, "end": 1320.38, "word": " ال", "probability": 0.58642578125}, {"start": 1320.38, "end": 1320.88, "word": " zeros", "probability": 0.87353515625}, {"start": 1320.88, "end": 1321.16, "word": " إذا", "probability": 0.975341796875}, {"start": 1321.16, "end": 1321.48, "word": " كانوا", "probability": 0.989501953125}, {"start": 1321.48, "end": 1322.3, "word": " محضونين", "probability": 0.928125}, {"start": 1322.3, "end": 1323.08, "word": " من", "probability": 0.99267578125}, {"start": 1323.08, "end": 1323.74, "word": " أرقام", "probability": 0.9931640625}, {"start": 1323.74, "end": 1324.36, "word": " عدهم", "probability": 0.7902018229166666}, {"start": 1324.36, "end": 1325.38, "word": " محضونين", "probability": 0.95361328125}, {"start": 1325.38, "end": 1325.6, "word": " يعني", "probability": 0.97119140625}, {"start": 1325.6, "end": 1325.76, "word": " إيش", "probability": 0.8567708333333334}, {"start": 1325.76, "end": 1326.54, "word": " السفر", "probability": 0.69384765625}, {"start": 1326.54, "end": 1326.68, "word": " ما", "probability": 0.79052734375}, {"start": 1326.68, "end": 1327.26, "word": " بينهم", "probability": 0.9853515625}, {"start": 1327.26, "end": 1328.46, "word": " إذاً", "probability": 0.82373046875}, {"start": 1328.46, "end": 1329.12, "word": " zeros", "probability": 0.88427734375}, {"start": 1329.12, "end": 1329.76, "word": " between", "probability": 0.91552734375}, {"start": 1329.76, "end": 1330.38, "word": " non", "probability": 0.7412109375}, {"start": 1330.38, "end": 1331.16, "word": "-zero", "probability": 0.705078125}, {"start": 1331.16, "end": 1331.56, "word": " digits", "probability": 0.97265625}, {"start": 1331.56, "end": 1331.9, "word": " are", "probability": 0.91064453125}, {"start": 1331.9, "end": 1332.4, "word": " significant", "probability": 0.85498046875}], "temperature": 1.0}, {"id": 59, "seek": 134392, "start": 1333.5, "end": 1343.92, "text": "تهملهمش ادهم زي 4 0 3 6 و اين الـ 0 محطوله مش عيمينه و عشماله فيه القام محضون اذا عده عد اربعة", "tokens": [2655, 16095, 1211, 16095, 8592, 1975, 3215, 16095, 30767, 1829, 1017, 1958, 805, 1386, 4032, 1975, 9957, 2423, 39184, 1958, 3714, 5016, 9566, 12610, 3224, 37893, 6225, 32640, 9957, 3224, 4032, 6225, 8592, 2304, 6027, 3224, 8978, 3224, 25062, 10943, 3714, 5016, 11242, 11536, 1975, 15730, 6225, 3215, 3224, 6225, 3215, 1975, 25513, 27884], "avg_logprob": -0.3673295487057079, "compression_ratio": 1.4504504504504505, "no_speech_prob": 2.562999725341797e-06, "words": [{"start": 1333.5, "end": 1334.22, "word": "تهملهمش", "probability": 0.71318359375}, {"start": 1334.22, "end": 1334.72, "word": " ادهم", "probability": 0.6707763671875}, {"start": 1334.72, "end": 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2001.92, "end": 2003.1, "word": " العرض،", "probability": 0.9235026041666666}, {"start": 2003.1, "end": 2003.74, "word": " جوابك", "probability": 0.985595703125}, {"start": 2003.74, "end": 2004.08, "word": " لازم", "probability": 0.9820963541666666}, {"start": 2004.08, "end": 2004.76, "word": " يكون", "probability": 0.9931640625}, {"start": 2004.76, "end": 2005.26, "word": " جد", "probability": 0.7342529296875}, {"start": 2005.26, "end": 2005.72, "word": " أقل", "probability": 0.9656575520833334}, {"start": 2005.72, "end": 2006.38, "word": " واحد،", "probability": 0.79150390625}, {"start": 2006.38, "end": 2006.58, "word": " عشان", "probability": 0.9807942708333334}, {"start": 2006.58, "end": 2006.86, "word": " تكون", "probability": 0.984130859375}, {"start": 2006.86, "end": 2007.18, "word": " أكثر", "probability": 0.8972981770833334}, {"start": 2007.18, "end": 2007.56, "word": " دقة", "probability": 0.960693359375}, {"start": 2007.56, "end": 2008.02, "word": " و", "probability": 0.974609375}, {"start": 2008.02, "end": 2008.34, "word": " علمي", "probability": 0.818359375}, {"start": 2008.34, "end": 2008.76, "word": " أكتر", "probability": 0.982177734375}], "temperature": 1.0}, {"id": 86, "seek": 201813, "start": 2009.61, "end": 2018.13, "text": "تمام عشان تكون يقينى اذا بيقول ليه when multiplying or dividing اما تضرب او بتجسم والجسم ماهي ضرب", "tokens": [39237, 10943, 6225, 8592, 7649, 6055, 30544, 7251, 4587, 9957, 7578, 1975, 15730, 4724, 1829, 39648, 32239, 3224, 562, 30955, 420, 26764, 1975, 15042, 6055, 11242, 25513, 1975, 2407, 39894, 7435, 38251, 16070, 7435, 38251, 19446, 3224, 1829, 48812, 25513], "avg_logprob": -0.28830031069313605, "compression_ratio": 1.2258064516129032, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2009.61, "end": 2009.99, "word": "تمام", "probability": 0.59515380859375}, {"start": 2009.99, "end": 2010.25, "word": " عشان", "probability": 0.806640625}, {"start": 2010.25, "end": 2010.49, "word": " تكون", "probability": 0.9443359375}, {"start": 2010.49, "end": 2011.15, "word": " يقينى", "probability": 0.71270751953125}, {"start": 2011.15, "end": 2011.67, "word": " اذا", "probability": 0.59381103515625}, {"start": 2011.67, "end": 2012.05, "word": " بيقول", "probability": 0.9357096354166666}, {"start": 2012.05, "end": 2012.49, "word": " ليه", "probability": 0.675048828125}, {"start": 2012.49, "end": 2012.81, "word": " when", "probability": 0.455322265625}, {"start": 2012.81, "end": 2013.59, "word": " multiplying", "probability": 0.919921875}, {"start": 2013.59, "end": 2014.05, "word": " or", "probability": 0.798828125}, {"start": 2014.05, "end": 2014.73, "word": " dividing", "probability": 0.91357421875}, {"start": 2014.73, "end": 2015.67, "word": " اما", "probability": 0.7685546875}, {"start": 2015.67, "end": 2016.13, "word": " تضرب", "probability": 0.8655598958333334}, {"start": 2016.13, "end": 2016.45, "word": " او", "probability": 0.937744140625}, {"start": 2016.45, "end": 2017.09, "word": " بتجسم", "probability": 0.91845703125}, {"start": 2017.09, "end": 2017.53, "word": " والجسم", "probability": 0.7391357421875}, {"start": 2017.53, "end": 2017.79, "word": " ماهي", "probability": 0.7513020833333334}, {"start": 2017.79, "end": 2018.13, "word": " ضرب", "probability": 0.9873046875}], "temperature": 1.0}, {"id": 87, "seek": 204510, "start": 2019.04, "end": 2045.1, "text": "When multiplying or dividing several quantities عدة كميات زي ما قلنا طول و عرض The number of significant figure in the final answer is the same as the number of significant figures in the quantity having the smallest number الأقل The smallest number of significant figures ان ترجم بالبلدي عندي كميتين طول و عرض", "tokens": [11645, 30955, 420, 26764, 2940, 22927, 6225, 41891, 9122, 2304, 1829, 9307, 30767, 1829, 19446, 12174, 1211, 8315, 23032, 12610, 4032, 6225, 43042, 440, 1230, 295, 4776, 2573, 294, 264, 2572, 1867, 307, 264, 912, 382, 264, 1230, 295, 4776, 9624, 294, 264, 11275, 1419, 264, 16998, 1230, 16247, 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2025.32, "word": " زي", "probability": 0.684814453125}, {"start": 2025.32, "end": 2025.4, "word": " ما", "probability": 0.94091796875}, {"start": 2025.4, "end": 2025.64, "word": " قلنا", "probability": 0.8408203125}, {"start": 2025.64, "end": 2025.88, "word": " طول", "probability": 0.9794921875}, {"start": 2025.88, "end": 2025.98, "word": " و", "probability": 0.9521484375}, {"start": 2025.98, "end": 2026.28, "word": " عرض", "probability": 0.870361328125}, {"start": 2026.28, "end": 2027.22, "word": " The", "probability": 0.59326171875}, {"start": 2027.22, "end": 2027.66, "word": " number", "probability": 0.947265625}, {"start": 2027.66, "end": 2027.94, "word": " of", "probability": 0.9814453125}, {"start": 2027.94, "end": 2028.72, "word": " significant", "probability": 0.80078125}, {"start": 2028.72, "end": 2029.12, "word": " figure", "probability": 0.5244140625}, {"start": 2029.12, "end": 2029.4, "word": " in", "probability": 0.92822265625}, {"start": 2029.4, "end": 2029.6, "word": " the", "probability": 0.92919921875}, {"start": 2029.6, "end": 2030.02, "word": " final", "probability": 0.94873046875}, {"start": 2030.02, "end": 2030.74, "word": " answer", "probability": 0.96923828125}, {"start": 2030.74, "end": 2031.44, "word": " is", "probability": 0.70361328125}, {"start": 2031.44, "end": 2031.66, "word": " the", "probability": 0.9306640625}, {"start": 2031.66, "end": 2031.96, "word": " same", "probability": 0.9091796875}, {"start": 2031.96, "end": 2032.16, "word": " as", "probability": 0.951171875}, {"start": 2032.16, "end": 2032.34, "word": " the", "probability": 0.873046875}, {"start": 2032.34, "end": 2032.7, "word": " number", "probability": 0.94921875}, {"start": 2032.7, "end": 2032.96, "word": " of", "probability": 0.9755859375}, {"start": 2032.96, "end": 2033.66, "word": " significant", "probability": 0.8232421875}, {"start": 2033.66, "end": 2034.22, "word": " figures", "probability": 0.81103515625}, {"start": 2034.22, "end": 2034.8, "word": " in", 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significant", "probability": 0.86474609375}, {"start": 2040.78, "end": 2041.32, "word": " figures", "probability": 0.869140625}, {"start": 2041.32, "end": 2041.7, "word": " ان", "probability": 0.63330078125}, {"start": 2041.7, "end": 2042.1, "word": " ترجم", "probability": 0.74658203125}, {"start": 2042.1, "end": 2042.62, "word": " بالبلدي", "probability": 0.663330078125}, {"start": 2042.62, "end": 2043.58, "word": " عندي", "probability": 0.7164306640625}, {"start": 2043.58, "end": 2044.54, "word": " كميتين", "probability": 0.9837646484375}, {"start": 2044.54, "end": 2044.76, "word": " طول", "probability": 0.982666015625}, {"start": 2044.76, "end": 2044.86, "word": " و", "probability": 0.99072265625}, {"start": 2044.86, "end": 2045.1, "word": " عرض", "probability": 0.9833984375}], "temperature": 1.0}, {"id": 88, "seek": 207069, "start": 2045.86, "end": 2070.7, "text": "الطول تلاتية significant figures العرض two significant figures الإجابة ايش بيكون؟ اتنين لازم تكون اتنين وكيف بتخليها اتنين؟ ال calculator طلعتلي خمسة ولا ستة بيبقى تخليهم اتنين و بالتقريب تمام هد ندي مثال جالي for example جالي فيه disk تعرف ال disk؟", "tokens": [6027, 9566, 12610, 6055, 1211, 9307, 10632, 4776, 9624, 18863, 43042, 732, 4776, 9624, 33688, 7435, 16758, 3660, 1975, 1829, 8592, 4724, 1829, 30544, 22807, 1975, 2655, 1863, 9957, 5296, 31377, 2304, 6055, 30544, 1975, 2655, 1863, 9957, 4032, 4117, 33911, 39894, 9778, 20292, 11296, 1975, 2655, 1863, 9957, 22807, 2423, 24993, 23032, 1211, 34268, 20292, 16490, 2304, 3794, 3660, 49429, 8608, 2655, 3660, 4724, 1829, 3555, 4587, 7578, 6055, 9778, 20292, 16095, 1975, 2655, 1863, 9957, 4032, 20666, 2655, 4587, 16572, 3555, 46811, 10943, 8032, 3215, 8717, 16254, 50113, 6027, 10874, 6027, 1829, 337, 1365, 10874, 6027, 1829, 8978, 3224, 12355, 37279, 28480, 2423, 12355, 22807], "avg_logprob": -0.24999999392915656, "compression_ratio": 1.703056768558952, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2045.86, "end": 2046.54, "word": 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2.34 تلاتة significant figures في 2.0 تلاتة significant figures الإيجابي إيش لازم تكون؟ 2 براو بس أشوف الخيارات و برجع إليك تمام؟ هاي الخيارات تبعتنا 4.6 ولا 4.7؟ هاي ال calculator يا بنات ليش؟", "tokens": [3555, 16254, 5551, 11242, 25513, 568, 13, 12249, 6055, 1211, 9307, 3660, 4776, 9624, 8978, 568, 13, 15, 6055, 1211, 9307, 3660, 4776, 9624, 33688, 1829, 7435, 16758, 1829, 11933, 1829, 8592, 5296, 31377, 2304, 6055, 30544, 22807, 568, 4724, 23557, 2407, 4724, 3794, 5551, 8592, 38688, 33962, 1829, 9640, 9307, 4032, 4724, 47341, 3615, 11933, 20292, 4117, 46811, 10943, 22807, 8032, 47302, 33962, 1829, 9640, 9307, 6055, 3555, 34268, 8315, 1017, 13, 21, 49429, 1017, 13, 22, 22807, 8032, 47302, 2423, 24993, 35186, 4724, 8315, 2655, 32239, 8592, 22807], "avg_logprob": -0.26648350796856723, "compression_ratio": 1.6010362694300517, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2671.9, "end": 2672.26, "word": "بدي", "probability": 0.659423828125}, {"start": 2672.26, "end": 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figures significant figures اه significant figures كله مش اي ما ندعو في الفاصلة عشرية في الضرب في ال significant figures", "tokens": [3215, 6027, 3555, 995, 24793, 39896, 4117, 6027, 4117, 12610, 36081, 2288, 16490, 2304, 14851, 3615, 8592, 935, 6055, 3794, 27884, 12174, 25513, 8315, 1975, 5016, 4117, 1829, 8978, 2423, 4386, 8978, 25724, 36150, 1975, 2655, 4587, 2288, 21292, 1975, 3224, 2423, 4386, 4724, 1829, 9566, 1211, 3615, 1975, 2655, 1863, 9957, 43242, 4117, 6225, 3215, 3215, 28242, 3224, 4032, 20193, 39182, 27188, 33546, 37977, 39182, 6024, 114, 25513, 4724, 1829, 9566, 1211, 3615, 43242, 4117, 1975, 2655, 1863, 9957, 1975, 2655, 1863, 9957, 4776, 9624, 4776, 9624, 1975, 3224, 4776, 9624, 28242, 3224, 37893, 1975, 1829, 19446, 8717, 3215, 3615, 2407, 8978, 27188, 33546, 37977, 6225, 46309, 10632, 8978, 6024, 114, 25513, 8978, 2423, 4776, 9624], "avg_logprob": -0.3535487280558732, "compression_ratio": 2.0934579439252334, "no_speech_prob": 3.5762786865234375e-07, "words": 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"word": " جريبه؟", "probability": 0.90703125}, {"start": 2837.05, "end": 2837.77, "word": " الجسمة", "probability": 0.9456380208333334}, {"start": 2837.77, "end": 2838.77, "word": " بتاخد", "probability": 0.8759765625}, {"start": 2838.77, "end": 2838.95, "word": " فيه", "probability": 0.7294921875}, {"start": 2838.95, "end": 2839.43, "word": " significant", "probability": 0.39794921875}, {"start": 2839.43, "end": 2840.11, "word": " figures", "probability": 0.92236328125}, {"start": 2840.11, "end": 2841.07, "word": " تمام", "probability": 0.948974609375}, {"start": 2841.07, "end": 2841.69, "word": " هيك؟", "probability": 0.8680013020833334}, {"start": 2841.69, "end": 2842.23, "word": " خلصنا", "probability": 0.9163818359375}, {"start": 2842.23, "end": 2842.49, "word": " ال", "probability": 0.7578125}, {"start": 2842.49, "end": 2842.79, "word": " chapter", "probability": 0.94189453125}, {"start": 2842.79, "end": 2843.81, "word": " تمام", "probability": 0.973876953125}, {"start": 2843.81, "end": 2843.89, "word": " يا", "probability": 0.986328125}, {"start": 2843.89, "end": 2844.53, "word": " بنات؟", "probability": 0.90673828125}, {"start": 2844.53, "end": 2844.67, "word": " اذا", "probability": 0.753173828125}, {"start": 2844.67, "end": 2845.01, "word": " هدول", "probability": 0.89697265625}, {"start": 2845.01, "end": 2845.69, "word": " الأسئلة", "probability": 0.9656982421875}, {"start": 2845.69, "end": 2846.69, "word": " قبل", "probability": 0.971435546875}, {"start": 2846.69, "end": 2847.23, "word": " السبت", "probability": 0.9142252604166666}, {"start": 2847.23, "end": 2847.79, "word": " مابنكون", "probability": 0.488250732421875}, {"start": 2847.79, "end": 2848.89, "word": " حلوه", "probability": 0.7425537109375}, {"start": 2848.89, "end": 2850.15, "word": " طيب", "probability": 0.7766927083333334}, {"start": 2850.15, "end": 2850.77, "word": " حاضر", "probability": 0.90380859375}, {"start": 2850.77, "end": 2851.55, "word": " يعطيكوا", "probability": 0.8275390625}, {"start": 2851.55, "end": 2852.01, "word": " العافية", "probability": 0.9635416666666666}, {"start": 2852.01, "end": 2852.41, "word": " نشوفكم", "probability": 0.8914794921875}, {"start": 2852.41, "end": 2852.71, "word": " السبت", "probability": 0.9788411458333334}, {"start": 2852.71, "end": 2852.85, "word": " ان", "probability": 0.705078125}, {"start": 2852.85, "end": 2853.11, "word": " شاء", "probability": 0.904052734375}, {"start": 2853.11, "end": 2853.13, "word": " الله", "probability": 0.96630859375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2853.50025, "duration_after_vad": 2763.206874999987}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/tTmo29ZCZv4_raw.srt b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/tTmo29ZCZv4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b791580425066c4781830b8bb183a95ccec8f5a0
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/tTmo29ZCZv4_raw.srt
@@ -0,0 +1,2368 @@
+1
+00:00:05,240 --> 00:00:09,160
+تمام نسمي باسم الله و نكمل اليوم بنخلص هذا ال
+
+2
+00:00:09,160 --> 00:00:12,660
+chapter المقدمة على اساس ان شاء الله يوم التاني
+
+3
+00:00:12,660 --> 00:00:17,120
+نبدأ بداية الجدية احنا حكينا في المحاضرة الماضية
+
+4
+00:00:17,120 --> 00:00:23,180
+المهم نقول هل ياخدنا انه اتعلمنا انه في عندي اكم
+
+5
+00:00:23,180 --> 00:00:29,130
+نظام للوحدات تلت أنظمة النظام الاشهرهو الـ SI
+
+6
+00:00:29,130 --> 00:00:33,950
+system اللي له اسم تاني MKSystem اللي بيستخدم ال
+
+7
+00:00:33,950 --> 00:00:37,750
+meter لل length و ال kilogram لل masses و ال
+
+8
+00:00:37,750 --> 00:00:42,270
+seconds ل ال times النظام التاني الجاوزيا والنظام
+
+9
+00:00:42,270 --> 00:00:45,330
+الأقل شهرا هو ال British تمام
+
+10
+00:00:47,620 --> 00:00:52,540
+هذه المواضيع الآن هناخدها شبه انتوا بتعرفوها بس
+
+11
+00:00:52,540 --> 00:00:55,480
+بدنا نمر عليها مرور الكرام موجودة في الكتاب و بدنا
+
+12
+00:00:55,480 --> 00:00:58,340
+نمشي عليها لأن كده مش كتير مهمة لإن انتوا بتعرفوها
+
+13
+00:00:58,340 --> 00:01:04,660
+يعني أديكم مثال عنكم مسافتين وفي الآخر تتعاملوا
+
+14
+00:01:04,660 --> 00:01:10,440
+معاهم في مسألة ما واحدة جسمكم إياها بالميل وواحدة
+
+15
+00:01:10,440 --> 00:01:13,980
+جسمكم إياها بالمتر مثلا خمسة ميل زي تلاتة متر منفع
+
+16
+00:01:13,980 --> 00:01:18,410
+أجمحهم تمانية؟بنفعش، لازم نحوّل واحد للتاني، صح
+
+17
+00:01:18,410 --> 00:01:23,810
+ولا لأ؟ إذا عنواننا الآن Conversion تحويل of
+
+18
+00:01:23,810 --> 00:01:27,830
+units، تحويل الوحدات، تمام هيك؟ هذا هو النوع
+
+19
+00:01:27,830 --> 00:01:30,950
+الحملي أعرفه من أول، من زمان، إنه بنفعش تحويل جلي
+
+20
+00:01:30,950 --> 00:01:35,070
+متر وصنتيمتر وتجمعهم أو كيلو جرام وطن وتجمعهم، صح
+
+21
+00:01:35,070 --> 00:01:41,670
+ولا لأ؟ إذا إيش بيقوللي؟بقول لي if different unit
+
+22
+00:01:41,670 --> 00:01:45,290
+systems احنا متفقين إذا في كلمة انجليزية مش عارفين
+
+23
+00:01:45,290 --> 00:01:48,390
+هقولي ليش معناها بس سهل عليكم بعد ما تروحوا و
+
+24
+00:01:48,390 --> 00:01:52,270
+تدوروا عليها بس أنا أظن إن الكلمة أغلبها مرت عليكم
+
+25
+00:01:52,270 --> 00:01:56,250
+تمام if different unit systems are used إذا
+
+26
+00:01:56,250 --> 00:02:01,100
+استخدمت أكثر من unit systemتمام؟ in a physical
+
+27
+00:02:01,100 --> 00:02:05,840
+equation one system should be chosen اختلق واحد زي
+
+28
+00:02:05,840 --> 00:02:11,720
+ما بنقول ارسلك ع بر اختلق نظامone system should be
+
+29
+00:02:11,720 --> 00:02:16,560
+chosen and all the quantities كل الكميات بعد كده
+
+30
+00:02:16,560 --> 00:02:21,300
+must be converted من convert to conversion التحويل
+
+31
+00:02:21,300 --> 00:02:25,220
+must be converted لازم يتحولهم to that choosing
+
+32
+00:02:25,220 --> 00:02:28,460
+system للsystem اللي اختارته اختارت ال S.I system
+
+33
+00:02:28,460 --> 00:02:32,520
+كل الكميات اللي حواليك بيكون على هذا ال system ده
+
+34
+00:02:32,520 --> 00:02:37,160
+من لا تجمع ولا تطرح ولا تضرب مش سطر S.I system و
+
+35
+00:02:37,160 --> 00:02:41,920
+سطر اللي ورا جاوز يعنيتمام هيك؟ طب تبقى اتحوّل و
+
+36
+00:02:41,920 --> 00:02:45,360
+الله علمونا من زمان و بنحوّل .. إيش هالشغلة؟ بس مش
+
+37
+00:02:45,360 --> 00:02:49,260
+من اللي اتعلمها يعني مثلا لو عندك اتنين كيلو متر و
+
+38
+00:02:49,260 --> 00:02:52,920
+بدك تعملها متر، إيش بتسويه هنا؟ مش تقدروا في الف؟
+
+39
+00:02:52,920 --> 00:02:58,860
+وخلصنا، لكن تلعبوا كيف بيعملوها هم بشغلة حلوة،
+
+40
+00:02:58,860 --> 00:03:05,100
+بقولي for example، ها يندي مثال، جالي جثة المصطرعة
+
+41
+00:03:05,100 --> 00:03:08,240
+إلها طرف بجثب centimeter و طرف تاني بجثب الinch
+
+42
+00:03:09,120 --> 00:03:13,020
+بتعرفوا هذه الشغلاء؟ جست مسافة المسا .. تحت ال
+
+43
+00:03:13,020 --> 00:03:17,980
+centimeter خربانة عندي حفتها جست بال inch عندي
+
+44
+00:03:17,980 --> 00:03:23,860
+مسافة مقدارها خمس عشر inch جستها تمام؟ بديك تقولي
+
+45
+00:03:23,860 --> 00:03:28,920
+أكم centimeter هلجيت ال inch أكم centimeter مش
+
+46
+00:03:28,920 --> 00:03:32,260
+حافظه ان شاء الله بحفظته اكتب على جوجل بديكي إياها
+
+47
+00:03:32,260 --> 00:03:35,100
+تمام؟ واحد بيقول هو في امتحان في جوجل بيقول احنا
+
+48
+00:03:35,100 --> 00:03:39,840
+ال google تبعك مش مشكلة بديكي إياهاطبعا؟ بقوللي
+
+49
+00:03:39,840 --> 00:03:45,400
+عندك خمس عشر انش حوللي ياها we wantها we wish to
+
+50
+00:03:45,400 --> 00:03:49,860
+convert بنا نحول الخمس عشر انش into centimeters لأ
+
+51
+00:03:49,860 --> 00:03:53,420
+centimeters المعلومة اللي بدي أديكي ياها معطى أنه
+
+52
+00:03:53,420 --> 00:03:57,100
+يا عم الواحد انش عبارة عن اتنين point fifty four
+
+53
+00:03:57,100 --> 00:04:01,280
+centimeterتمام هيك؟ حلو جاله كيف بتعمل التحويل؟
+
+54
+00:04:01,280 --> 00:04:06,180
+جاله شغله سهل جدا اتعلمنا من زمان انه لما نضرب اي
+
+55
+00:04:06,180 --> 00:04:11,200
+شغلة بواحد او نجسم ع واحد بصيرش ايه؟ يعني بصحيلك
+
+56
+00:04:11,200 --> 00:04:14,960
+تضرفي واحد صح ولا لأ؟ و بصح حدك اتجسم ع واحد جاله
+
+57
+00:04:14,960 --> 00:04:18,140
+هذا النظام اللي بدأ استخدمه كيف؟ ده اللي انت شوف
+
+58
+00:04:18,140 --> 00:04:24,440
+تعيش معطيني واحد inch بتساوي 2.44 cm بتدي الواحد
+
+59
+00:04:24,440 --> 00:04:30,450
+هذاعشان اعمله عايش اجسم؟ جسم ع ال inch صحيك تمام؟
+
+60
+00:04:30,450 --> 00:04:35,250
+قاللي هاه انت اديتني هذه المعلومة قولتله بقدر اقول
+
+61
+00:04:35,250 --> 00:04:41,470
+الواحد بيساوي 2.44 cm ع ال inch اتطلعوش بدي اسوي
+
+62
+00:04:41,470 --> 00:04:44,710
+هال gate هد الواحد بدي اضربه هنا بصحليه ولا
+
+63
+00:04:44,710 --> 00:04:48,810
+بصحليش؟ بصحليه للواحد طب لما اضرب طلعش بيصير ال
+
+64
+00:04:48,810 --> 00:04:51,570
+inch هدا مع ال inch هدا بيصير ولا لأ؟ ايش بيظل
+
+65
+00:04:51,570 --> 00:04:58,490
+الوحدة؟ هي اتحولت هي اتحولت يالا نعملSince
+
+66
+00:04:58,490 --> 00:05:02,890
+multiplying any quantity بيقول بما انه ضرب أي كمية
+
+67
+00:05:02,890 --> 00:05:07,130
+multiply معناتها ضرب تمام و product معناتها برضه
+
+68
+00:05:07,130 --> 00:05:12,310
+ضرب multiplying any quantity by one ضرب أي رقم
+
+69
+00:05:12,310 --> 00:05:16,410
+بواحد leaves it unchanged بيخليها زي ما هي وهذه
+
+70
+00:05:16,410 --> 00:05:20,620
+معلومة نعرفها كلناwe can write قال لي هذه
+
+71
+00:05:20,620 --> 00:05:24,540
+الخمستاشر اللي بدك تحوّلها ضربتها في واحد امي كنا
+
+72
+00:05:24,540 --> 00:05:27,540
+بنقول صح قال لي طب مش هي الواحد قلت له هاي الواحد
+
+73
+00:05:27,540 --> 00:05:33,000
+انا ادتك اياها عوض محل الواحد ضربت انش مع انش طار
+
+74
+00:05:33,000 --> 00:05:37,660
+وانا ماترش بالكالكولاتر ضربت هذه في هذه ايش ضال؟
+
+75
+00:05:37,660 --> 00:05:42,360
+انا حولتلك اياها فالخمستاشر انش طلعت حوالي تمانية
+
+76
+00:05:42,360 --> 00:05:46,890
+وتلاتين point one centimeter تمام يا بنات؟سهل أظن
+
+77
+00:05:46,890 --> 00:05:50,490
+واحد يقول طب أنا كنت متعود أحول بالطريقة اللي كنت
+
+78
+00:05:50,490 --> 00:05:54,170
+متعلمها في المدارس تظل زي ما انت مش جاضية يعني بس
+
+79
+00:05:54,170 --> 00:06:01,230
+احنا نتعلم كيف يعملوها نشوف المثالجالي في أمريكا
+
+80
+00:06:01,230 --> 00:06:05,130
+بيستخدموا النظام البريطاني كتير خصوصا في الشوارع
+
+81
+00:06:05,130 --> 00:06:07,950
+المسافات يعني هم بيقولوا والله المسافة بين نيويورك
+
+82
+00:06:07,950 --> 00:06:12,030
+وواشنطن كذا ميل مش كذا كيلومتر هيك بتعودين عليهم
+
+83
+00:06:12,030 --> 00:06:14,650
+هيك اللي اعتمدوا بنفس العملية في بريطانيا
+
+84
+00:06:14,650 --> 00:06:18,980
+بيستخدموا هذا النظامبيقوللي انت بتعرفه في الشوارع
+
+85
+00:06:18,980 --> 00:06:23,800
+فيه جرمالة فيه إشارات ضوئية وإشارات مرور صح ولا لأ
+
+86
+00:06:23,800 --> 00:06:27,160
+اللي أحمر و اللي أزرق و اللي مش عارف إيش لما تمشي
+
+87
+00:06:27,160 --> 00:06:30,920
+على شارع الرشيد بيكون مكتبلك السرعة القصوى نفطرت
+
+88
+00:06:30,920 --> 00:06:35,640
+80 كيلومتر في الساعة مظلوط ولا لا؟ ليش؟ على أساس
+
+89
+00:06:35,640 --> 00:06:40,500
+إنك لو مشيت 90 وخلفك الشرطي ماتجهتش السبسب لإنه
+
+90
+00:06:40,500 --> 00:06:45,480
+جايليك ممنوع تنط التمانين هنا بيقولليأُنأم
+
+91
+00:06:45,480 --> 00:06:48,960
+Interstate Highway Highway كلمة عربية بنعرفها كنا
+
+92
+00:06:48,960 --> 00:06:54,100
+صح ولا طريق سريع Interstate بين الولايات يعني بين
+
+93
+00:06:54,100 --> 00:06:57,640
+ولاية أوهايو وولاية نفطرالكاليفورنيا أنتوا عارفين
+
+94
+00:06:57,640 --> 00:07:01,080
+أمريكا عبارة عن عدة ولايات مظبوط ولا لا فبقى في
+
+95
+00:07:01,080 --> 00:07:06,060
+طرق كبيرة واسعة وسريعة بين الولايات جال الشرطة
+
+96
+00:07:06,060 --> 00:07:11,740
+حاطة جارمة ممنوعة تتجاوز خمسة وسبعين ميل per hour
+
+97
+00:07:11,740 --> 00:07:18,080
+هيك الجارمةالسواك قاعد بسوق نفترض في جوا السيارة
+
+98
+00:07:18,080 --> 00:07:23,740
+إمعالمة عنده 38 متر per second هجيت الميل بأول
+
+99
+00:07:23,740 --> 00:07:28,340
+نظام بريطانيوالـ 38 متر per second نظامي الأسئي
+
+100
+00:07:28,340 --> 00:07:34,180
+صح؟ بدي أعرف الشرطة بصحله يخلفني ولا لأ؟ بدي أشوف
+
+101
+00:07:34,180 --> 00:07:38,240
+سرعتي اللي هي 38 متر per second أكتر من الـ 75 ولا
+
+102
+00:07:38,240 --> 00:07:43,100
+أقل؟ فهمتوا عليا كيف؟ طب وقوللي is بسأل is a
+
+103
+00:07:43,100 --> 00:07:48,340
+driver ال driver يعني سواك السائق exceeding اتجاوز
+
+104
+00:07:49,280 --> 00:07:53,680
+exceeding the speed limit حد السرعة القصوى اللي
+
+105
+00:07:53,680 --> 00:07:58,500
+انا حاطه كشرطة اللي هو 75 ميل per hour ايش بدك
+
+106
+00:07:58,500 --> 00:08:02,820
+تسوي؟ قاللي هذا الرقم حول ليه ل 100 per hour وشوف
+
+107
+00:08:02,820 --> 00:08:06,800
+ليه أكتر من 75 ولا أجل؟ مظبوط هيك ولا لأ؟ ايه بدك
+
+108
+00:08:06,800 --> 00:08:10,740
+تحول؟ قاللي هذه والله معقدة ومركبة فيها ميل وفيها
+
+109
+00:08:10,740 --> 00:08:13,300
+hour احكي 1609
+
+110
+00:08:20,480 --> 00:08:24,980
+الأولى كام ساكنت؟ الأولى كام ساكنت؟ تلتنا و تلت
+
+111
+00:08:24,980 --> 00:08:29,540
+مية؟ هذا اللي بدنا نسويه طيب هلجيت ال meal أكم
+
+112
+00:08:29,540 --> 00:08:32,980
+متر؟ وحد يقولك طب أنا مش حافظه برضه بنرجع بنقول
+
+113
+00:08:32,980 --> 00:08:36,020
+احنا نديكوا مية ماتفرجش لو مش حافظينه يعني مش
+
+114
+00:08:36,020 --> 00:08:40,220
+مطلوب منكم ينطبصهم كل شيءأما نقول مثلا الله عيب
+
+115
+00:08:40,220 --> 00:08:43,460
+نديكم الساعة أكمل دقيقة ولا لا ولا .. ولا .. ولا
+
+116
+00:08:43,460 --> 00:08:46,560
+واحد يقول لا بدي أديه .. نديكي إياها بس في شغلات
+
+117
+00:08:46,560 --> 00:08:50,660
+الواحد يكون عارفها من ساعة من ولد مظبوط ولا لأ
+
+118
+00:08:50,660 --> 00:08:55,750
+تمام بيقولي واحد ميل أنا أعطيتكي إياهاواحد متر
+
+119
+00:08:55,750 --> 00:08:59,770
+بيساوي واحد على الف ستمية وتسعة ميل او العكس واحد
+
+120
+00:08:59,770 --> 00:09:03,370
+متر بيساوي الف ستمية وتسعة متر تمام جالي بدي
+
+121
+00:09:03,370 --> 00:09:06,390
+الواحد مش انت قلتلي اضرف في واحد او اجسم على واحد
+
+122
+00:09:06,390 --> 00:09:10,830
+بصحي اللي تمام بدي الواحد قلتله الواحد اجسم على
+
+123
+00:09:10,830 --> 00:09:16,540
+مترتمام؟ حلو قال لي طيب و ال second اكم hour تقول
+
+124
+00:09:16,540 --> 00:09:20,660
+واحد على تلت تلاف و ستمية اذا برضه عندك واحد
+
+125
+00:09:20,660 --> 00:09:25,520
+second بتساوي واحد على تلت تلاف و ستمية hour امين
+
+126
+00:09:25,520 --> 00:09:31,050
+طب بدي الواحد جسم ع second جسمجالي نيجي لهذه
+
+127
+00:09:31,050 --> 00:09:33,990
+المقدار جالي think بيه ال meter في ال bus to
+
+128
+00:09:33,990 --> 00:09:38,350
+second في المقاهة ده كده انت لما تيجي تعمل تمام؟
+
+129
+00:09:38,350 --> 00:09:43,530
+اذا اول حاجة بدك تضرب هذه الواحد في ال bus و تجسم
+
+130
+00:09:43,530 --> 00:09:47,410
+على الواحد هذا فهمتوا عليا كيف؟ عشان ان كل واحد
+
+131
+00:09:47,410 --> 00:09:52,390
+حسب وحدته جالي هذه تمانية و تلاتين meter per
+
+132
+00:09:52,390 --> 00:09:56,170
+second التمانية و تلاتين بدي اضربها في الواحد هذا
+
+133
+00:09:56,170 --> 00:10:00,950
+بصح لك ضربت في الواحدجسم على الواحد هذا طب إيش
+
+134
+00:10:00,950 --> 00:10:05,550
+جسمت؟ عشان استكنت في المقام جسمت طيب و احنا في
+
+135
+00:10:05,550 --> 00:10:10,830
+الجسمة بنفع نحولها لضرب؟ ساعتها بنجر براواليكم يا
+
+136
+00:10:10,830 --> 00:10:15,570
+وردي ماشتركوا هي ان انا اعمل اللي تعرفينه هي عملته
+
+137
+00:10:15,570 --> 00:10:21,210
+هذه الجسمة ضربت صارت ضرب مقام صارت بست مقام صارت
+
+138
+00:10:21,210 --> 00:10:25,130
+بست و بست صارت مقام طبعا عشان صار معايا مثل ما
+
+139
+00:10:25,130 --> 00:10:29,030
+عملت ضاع ولا مضاعاشتمام و سكن بع سكن بعض ولا لأ؟
+
+140
+00:10:29,030 --> 00:10:34,010
+يلا بال calculator طلعت خمس و تمانين ميت بال hour
+
+141
+00:10:34,010 --> 00:10:39,250
+اتجاوز كتير معناته بده مخالفة الله لم جدش الكون
+
+142
+00:10:39,250 --> 00:10:44,630
+صحيح ولا لأ طبعا أنا بهمن الآن التحويل هي نحور تلك
+
+143
+00:10:44,630 --> 00:10:54,310
+سهلة تمام هيك؟ حلو احكوا عيد؟ عيدهلجيت انت لما
+
+144
+00:10:54,310 --> 00:10:57,370
+تيجي تحولي بسرعة عامة، ايش بتسوي؟ مش انت بتعرف
+
+145
+00:10:57,370 --> 00:11:00,650
+الشغل اللي بيك تحوليها، نفترض بيدحول انت عندك ايش
+
+146
+00:11:00,650 --> 00:11:05,330
+بيك تحوليه؟ 38 متر per second، صح؟ انا بيدحول الـ
+
+147
+00:11:05,330 --> 00:11:11,550
+38 متر per second، هاي 38 متر per second ايش بيبقى
+
+148
+00:11:11,550 --> 00:11:15,750
+تسوي؟ المتر بيبقى ميل، مش لو بيبقى تحوليها لميل،
+
+149
+00:11:15,750 --> 00:11:21,370
+بيبقى أقوله المتر أكمل، قاللي اه 1 على 1609طبعا ..
+
+150
+00:11:21,370 --> 00:11:24,290
+واحد على .. بدي اضغط فيه واحد على الف ستمية وتسعة
+
+151
+00:11:24,290 --> 00:11:27,430
+هو يكون ان انا اعمل هيك اه واحد على الف ستمية
+
+152
+00:11:27,430 --> 00:11:35,510
+وتسعة عشان قلتلك انا بغشتش كياها بتكونش حفظها طبعا
+
+153
+00:11:35,510 --> 00:11:40,090
+انتبهولي انا بحكي بالعربي قولت انا بغشتش كياها حتى
+
+154
+00:11:40,090 --> 00:11:47,010
+قولت جوجل انا بصين معاكي طبعا احكي اه السكن ات اكم
+
+155
+00:11:47,010 --> 00:11:52,970
+hourعايزة بقيت بس عشان السكن تحت بقوله هدى بيصير
+
+156
+00:11:52,970 --> 00:11:58,650
+واحد على تلت تلاف سكنية خلصنا خلصنا من حلت المشكلة
+
+157
+00:11:58,650 --> 00:12:13,990
+ولا لا انا هي عملتها بالبلد دى احكى ايه للميل انت
+
+158
+00:12:13,990 --> 00:12:18,920
+بتحول من متى لميل ولا من مين لمتىأه بده يكبر ولا
+
+159
+00:12:18,920 --> 00:12:25,840
+بده يصغر؟ انت مش بتحوليش من ميل لمتر، من متر لمير
+
+160
+00:12:25,840 --> 00:12:30,160
+انت
+
+161
+00:12:30,160 --> 00:12:36,320
+هيك فكرت؟ لا الميل أكبر من كيلومتر هو أكتر من كيلو
+
+162
+00:12:36,320 --> 00:12:41,440
+نص كيلو ستمية لما يقولك المسافة مائة ميل يعني
+
+163
+00:12:41,440 --> 00:12:48,000
+حوالي مائة وستين كيلومتر فهمتوا عليها كيف؟تمى ..
+
+164
+00:12:48,000 --> 00:12:52,140
+okay بنات .. تمى .. و زي ما اتفقنا هذه ثقافة يعنى
+
+165
+00:12:52,140 --> 00:12:54,380
+.. كنا .. لإنه عارفين هي محلاب ويبقى عارف اللي حول
+
+166
+00:12:54,380 --> 00:12:59,180
+.. أول مرة تحولوا عمركم .. نحول طب عمرنا .. بس هيك
+
+167
+00:12:59,180 --> 00:13:05,430
+يعني طريقة ..بالظبط هذه الطريقة مرتبة لكن في الآخر
+
+168
+00:13:05,430 --> 00:13:08,690
+لو عملتيها بلد عمليها مش مشكلة في الآخر احنا بدنا
+
+169
+00:13:08,690 --> 00:13:12,030
+نأكل عنب لإيش نقاتل الناطور في النهاية ما بدناش
+
+170
+00:13:12,030 --> 00:13:16,550
+اشوه العنب مابديش واحد يجمع خمسة متر زي تلاتة ميل
+
+171
+00:13:16,550 --> 00:13:21,550
+ويقول لي تمانيها هاي اللي بديش ايه هاجد كيف تعملها
+
+172
+00:13:21,550 --> 00:13:26,030
+انتحار اعملها صح المهم وكل الطرق تؤدي إلى روما وده
+
+173
+00:13:26,030 --> 00:13:28,690
+طريق واحدة اتفقنا يا بنات؟ حلو
+
+174
+00:13:31,470 --> 00:13:35,030
+الحاجب بيقول الـ Driver is indeed exceeding the
+
+175
+00:13:35,030 --> 00:13:40,550
+speed قطعا تجاوز الحد تبع السرعة and he should
+
+176
+00:13:40,550 --> 00:13:44,050
+slow down و لازم يوطي .. ماقالش اتخالف الحمد لله
+
+177
+00:13:44,050 --> 00:13:50,430
+تمام؟ قال لازم يوطي سرعته تمام أخر حاجة في مواضيع
+
+178
+00:13:50,430 --> 00:13:55,360
+هذا ال chapter significant figuresطبعا في مصطلح
+
+179
+00:13:55,360 --> 00:13:58,840
+تعامل علماء تي بيركزوا عليه بيقولوا في حاجة اسمها
+
+180
+00:13:58,840 --> 00:14:02,660
+امانة علمية امانة علمية ايش يعني امانة علمية
+
+181
+00:14:02,660 --> 00:14:09,180
+ماتزيفش اي معلومة ولا تزيف اي نتيجة طلعت عندك في
+
+182
+00:14:09,180 --> 00:14:12,520
+المختبر يعني انا دي اعمل مثل بقى اضربه كمان شوية
+
+183
+00:14:12,520 --> 00:14:17,300
+في مختبر فيزيا الف هيطلب منك اجيسي تثارع الجاذبية
+
+184
+00:14:17,300 --> 00:14:22,950
+الأرضية جديش9.8 واحد بقى مالك تجربة طلعت معاها
+
+185
+00:14:22,950 --> 00:14:26,130
+عشرة ندت على صاحبيتها اللي هناك ماكنتش طلعت عندك
+
+186
+00:14:26,130 --> 00:14:30,630
+قلت 9.8 قلت يا وردي هذا هتاخد عشرة من عشرة وانا
+
+187
+00:14:30,630 --> 00:14:33,810
+هاخد خمسة من عشرة بس أنا زيب في النتائج اللي عندها
+
+188
+00:14:33,810 --> 00:14:37,790
+اتفبرت فيها عشان تطلع 9.8 منقول أخلك بالأمان
+
+189
+00:14:37,790 --> 00:14:42,420
+العلمية لأنه هي جاسة شغلة وكتبت شغلةمظبط ولا لأ؟
+
+190
+00:14:42,420 --> 00:14:46,140
+هذه بيسموها أمانة علمية من كتر أهمية الأمانة
+
+191
+00:14:46,140 --> 00:14:50,900
+العلمية العلماء عملوا قواعد عشان انت تكون صادق مع
+
+192
+00:14:50,900 --> 00:14:54,840
+حالك وصادق مع الرقم اللي بدك تكتبه انت بدك تكتب
+
+193
+00:14:54,840 --> 00:14:59,580
+رقم بدك تفهم وانا افهم اللي بقرأ الرقم انت ايش
+
+194
+00:14:59,580 --> 00:15:07,320
+اللي عملته بنفع الواحد يكتب رقم اكثر دقة من الجهاز
+
+195
+00:15:07,320 --> 00:15:11,880
+اللي جاسبالفعل، انت مين اللي داك الرقم؟ مش الجهاز؟
+
+196
+00:15:11,880 --> 00:15:17,560
+طب كيف؟ بتكتبلي أكتر دقة منه؟ هذا مثلوا بالـ
+
+197
+00:15:17,560 --> 00:15:22,540
+Significant Figures أو الأرقام ذات المعنىتمام؟ هاي
+
+198
+00:15:22,540 --> 00:15:23,980
+معناه الـ Significance في الجامعة. انا مش ممكن
+
+199
+00:15:23,980 --> 00:15:28,520
+اكتب ليه. In science، في كل العلوم، أي إن كان نوع
+
+200
+00:15:28,520 --> 00:15:33,160
+العلوم، بيقولي أنا ميجار منتي. كلنا، بغض النظر عن
+
+201
+00:15:33,160 --> 00:15:37,440
+تخصصاتنا، اذا كان معمرية ولا مدنية ولا ميكانيكية
+
+202
+00:15:37,440 --> 00:15:42,960
+ولا حاجة، كلنا هنجيس. وكنا بدنا نستخدم القياسات.
+
+203
+00:15:43,300 --> 00:15:48,550
+ولازم نتعلم كيف اكتب قياسي.بدي أتعلم عشان اللي
+
+204
+00:15:48,550 --> 00:15:53,830
+يقرأ بيقولي أو يفهم عليّ أنا كيف جسد تمام؟ بيقولي
+
+205
+00:15:53,830 --> 00:15:57,210
+any .. any measurement should not be more accurate
+
+206
+00:15:57,210 --> 00:16:01,870
+ممنوع تكون أكثر دقة more accurate .. accurate يعني
+
+207
+00:16:01,870 --> 00:16:07,470
+دقيق أو صحيحmore accurate than what is allowed by
+
+208
+00:16:07,470 --> 00:16:12,550
+the equipment أكثر دقة من المسموح إليك بواسطة
+
+209
+00:16:12,550 --> 00:16:16,990
+الآلة اللي بتجيس تمام؟ used to measure that
+
+210
+00:16:16,990 --> 00:16:23,050
+quantity ندّي مثال صارخ بتعرفوا المساطر؟ بيتجوزوا
+
+211
+00:16:23,050 --> 00:16:29,470
+مسافة إيش أصغر تدريج في المسارات؟من ليه؟ تمام انت
+
+212
+00:16:29,470 --> 00:16:36,530
+جفت و لجيت المسافة مقدرها 5.2 cm بقول صحيح لكن لو
+
+213
+00:16:36,530 --> 00:16:40,350
+اجا واحد يتفلسف و بقوله في نفس المصطر جسلي و كتبلي
+
+214
+00:16:40,350 --> 00:16:44,910
+هنا سبعة بقوله كذاب كيف جبت السبعة هذه؟ من وين جبت
+
+215
+00:16:44,910 --> 00:16:48,790
+السبعة؟ اصلا التنين انا بود اشكك فيها لسه عملي
+
+216
+00:16:48,790 --> 00:16:54,170
+تكون تلاتةمظهرة لأ وممكن تكون واحد اذا هان انت
+
+217
+00:16:54,170 --> 00:16:59,150
+بطلت امين علميا لان هذا الرقم اكثر دقة من المصطرة
+
+218
+00:17:00,160 --> 00:17:03,860
+واحنا بنقول بما يكون الرقم أكتر دقة من الآلة اللي
+
+219
+00:17:03,860 --> 00:17:07,300
+بتجيس .. بتستخدمها في القياس يعني مثلا زي نفطار
+
+220
+00:17:07,300 --> 00:17:10,700
+الميزان طبعا انتوا بتعرفوا الميزان العادى وفيه
+
+221
+00:17:10,700 --> 00:17:15,120
+ميزان دهب الميزان الدهب بجيس جزء milligram لكن
+
+222
+00:17:15,120 --> 00:17:19,200
+اللي بدي أجيس .. أوزن بندورة ولا أوزن حالي ولا ..
+
+223
+00:17:19,200 --> 00:17:23,000
+بحطليش digits يعني مثلا إنتوا بتطفعوا على الميزان
+
+224
+00:17:23,000 --> 00:17:28,180
+قدش وزنكم تلتة تمانين نفطارينتمام؟ ذهبت .. انا
+
+225
+00:17:28,180 --> 00:17:33,840
+عشان المعلق عند الشباب 62 تمام؟ ماينفعش واحد تقولي
+
+226
+00:17:33,840 --> 00:17:38,600
+و الله تتفلزف 62 و 35% من ال graph انا جبت 35%
+
+227
+00:17:39,230 --> 00:17:43,790
+الميزان الدكياها لأ دا قبل 62 صح ولا لأ؟ إذا لو
+
+228
+00:17:43,790 --> 00:17:48,390
+قيت انت زوجت معناته أخلت بالأمان العلمية ولا لأ؟
+
+229
+00:17:48,390 --> 00:17:51,090
+تكون أخلت بالأمان العلمية عشان كده يبدأك تكتب صح
+
+230
+00:17:51,090 --> 00:17:56,470
+عشان أنا أفهم اللي بدي أقرأ إيش هو الجهاز اللي جسد
+
+231
+00:17:56,470 --> 00:18:01,660
+فيه يعني مثلا ساعتنافي الصباقات يا بنات في ساعة
+
+232
+00:18:01,660 --> 00:18:06,580
+بتجيس جزء من مية من ال second الجهاز بيكون هيك أما
+
+233
+00:18:06,580 --> 00:18:11,500
+والله بسعتي أنا و أقول والله هذا استغرقت المسافة
+
+234
+00:18:11,500 --> 00:18:14,760
+عشر ثواني و خمسة و تلاتين في المية من الثانية
+
+235
+00:18:14,760 --> 00:18:20,020
+مستحيل من وين جبتها هذه اللي بيقول عنها الأمانة
+
+236
+00:18:20,020 --> 00:18:24,580
+العلمية فإيه القواعد تمام هاي بيقول لي for example
+
+237
+00:18:25,730 --> 00:18:29,330
+مثلًا اللي تعرفوا دراب ترقمية when you measure a
+
+238
+00:18:29,330 --> 00:18:33,810
+distance .. دي جيس مسافة by a meter stick اللي هي
+
+239
+00:18:33,810 --> 00:18:37,150
+المصطلح تمامًا your measurement should be written
+
+240
+00:18:37,150 --> 00:18:43,710
+as 2.3 cm أنت أول ما أقرأ هيك بقول تمام بقول هذا
+
+241
+00:18:43,710 --> 00:18:48,630
+أكيد صح و هذا أكيد صح و هذا أنا شاكك فيه إيش يعني
+
+242
+00:18:48,630 --> 00:18:51,730
+شاكك فيه بقول هذا ممكن يزيد واحد أو يجيل واحدلأنه
+
+243
+00:18:51,730 --> 00:18:55,270
+إنت لما تيجي تجييز لو طلعت من الجانب بزيت طلعت من
+
+244
+00:18:55,270 --> 00:19:00,210
+الجانب هنا بجل صح؟ إذا انت عشان تكون بندق فيه
+
+245
+00:19:00,210 --> 00:19:02,930
+إلهام عيار وكيف تقرأ و الله علمك يكون أنت أحول
+
+246
+00:19:02,930 --> 00:19:07,610
+مظبوط او لا، بالتالي لكن الأحول مخبطش في هذا، مخبط
+
+247
+00:19:07,610 --> 00:19:11,630
+في هذا فبصير القاعدة اللي صارت تقولي هذا و هذا
+
+248
+00:19:11,630 --> 00:19:17,300
+أكيدو هذا تقديري هذا تقديري يمكن زادي شوية خس شوية
+
+249
+00:19:17,300 --> 00:19:21,140
+اذا بيقولي this means that هذا بيعني لما تكتبلي
+
+250
+00:19:21,140 --> 00:19:27,700
+هذا انه the measurement is accurate صحيح بس في عدم
+
+251
+00:19:27,700 --> 00:19:34,180
+يقين uncertainty certain يقين عن عكسه في عدم يقين
+
+252
+00:19:34,180 --> 00:19:39,700
+مقداره اما بزيد او بقل 0.1 يعني هذا بصير اما 0.2
+
+253
+00:19:39,700 --> 00:19:45,250
+او 0.4تمام؟ حلو بيقولي طب انت في الجثة هذه ايش ..
+
+254
+00:19:45,250 --> 00:19:48,470
+ده هو في ال significant figures بقول اه هذا الرقم
+
+255
+00:19:48,470 --> 00:19:55,110
+بنسميه اكم رقم له مهم بقوله تلاتة اذا هذا له تلاتة
+
+256
+00:19:55,110 --> 00:19:59,870
+significant figures تلاتة significant figuresThe
+
+257
+00:19:59,870 --> 00:20:05,410
+number of significant figures أو الأرقام المعنوية
+
+258
+00:20:05,410 --> 00:20:09,530
+ذات القيمة in a measurement can be defined as the
+
+259
+00:20:09,530 --> 00:20:14,030
+number of digits، digits يعني رقم، that are
+
+260
+00:20:14,030 --> 00:20:18,050
+measured with certainty، الأرقام اللي أنت متأكد
+
+261
+00:20:18,050 --> 00:20:22,100
+منهم، واحد واتنين، صح ولا لأ؟هدول أنا متأكد منهم
+
+262
+00:20:22,100 --> 00:20:27,560
+plus ايش يعني plus زائد اضيفلهم plus the last
+
+263
+00:20:27,560 --> 00:20:31,940
+digit which is an estimate اللي هي تقريبية اذا
+
+264
+00:20:31,940 --> 00:20:34,360
+المعناته هذا اكمل significant figure بقول واحد
+
+265
+00:20:34,360 --> 00:20:38,180
+اتنين تلاتة اذا هذا له تلاتة significant figures
+
+266
+00:20:38,180 --> 00:20:43,370
+تمامبيقول لي الـ 12.3 ميجارومنت 12.3 ميجارومنت 12
+
+267
+00:20:43,370 --> 00:20:43,870
+.3 ميجارومنت 12.3 ميجارومنت 12.3 ميجارومنت 12.3
+
+268
+00:20:43,870 --> 00:20:47,710
+ميجارومنت 12.3 ميجارومنت 12.3 ميجارومنت 12.3
+
+269
+00:20:47,710 --> 00:20:52,810
+ميجارومنت 12.3 ميجارومنت 12.3 ميجارومنت 12.3
+
+270
+00:20:52,810 --> 00:20:52,870
+ميجارومنت 12.3 ميجارومنت 12.3 ميجارومنت 12.3
+
+271
+00:20:52,870 --> 00:20:54,010
+ميجارومنت 12.3 ميجارومنت 12.3 ميجارومنت 12.3
+
+272
+00:20:54,010 --> 00:20:54,050
+ميجارومنت 12.3 ميجارومنت 12.3 ميجارومنت 12.3
+
+273
+00:20:54,050 --> 00:20:54,070
+ميجارومنت 12.3 ميجارومنت 12.3 ميجارومنت 12.3
+
+274
+00:20:54,070 --> 00:20:59,930
+ميجارومنت 12.لأ لابس يد واحد لابس واحد فهذه شغلات
+
+275
+00:20:59,930 --> 00:21:04,790
+معروفة طيب بقولي طب انا كام بده اتعلم اعرف ان هذا
+
+276
+00:21:04,790 --> 00:21:07,930
+الرقم اكم significant figures قاللي في الها قواعد
+
+277
+00:21:07,930 --> 00:21:11,970
+to determine the number of significant figures for
+
+278
+00:21:11,970 --> 00:21:15,090
+a measure means اي رقم قدامك تقولي اكم significant
+
+279
+00:21:15,090 --> 00:21:19,590
+figure على طول بده اتعلم we use the following
+
+280
+00:21:19,590 --> 00:21:25,980
+rules القواعد التالية واحد السهلةبقول لكل الأرقام
+
+281
+00:21:25,980 --> 00:21:31,520
+اللي مش سفر عدهم، ادّاك رقم ما زال مش سفر عده، اذا
+
+282
+00:21:31,520 --> 00:21:35,960
+non-zero digits اللي مش zero، non-zero digits are
+
+283
+00:21:35,960 --> 00:21:39,280
+always significant، تعدهم significant طيب، ايه
+
+284
+00:21:39,280 --> 00:21:43,960
+زيهم؟ قاللي 14، فيهم سفار؟ أكم واحد، two
+
+285
+00:21:43,960 --> 00:21:48,560
+significant figures has two significant figures،
+
+286
+00:21:48,560 --> 00:21:52,940
+واحد، تلاتة، ستة، فيها سفار؟أكمل واحد إذاً تلاتة
+
+287
+00:21:52,940 --> 00:21:57,560
+significant figures نحكي عربي صح؟ سهلة هجت فيه
+
+288
+00:21:57,560 --> 00:22:01,480
+zeros مشكلتهم مشكلة بيقول ال zeros إذا كانوا
+
+289
+00:22:01,480 --> 00:22:06,680
+محضونين من أرقام عدهم محضونين يعني إيش السفر ما
+
+290
+00:22:06,680 --> 00:22:11,900
+بينهم إذاً zeros between non-zero digits are
+
+291
+00:22:11,900 --> 00:22:17,560
+significantتهملهمش ادهم زي 4 0 3 6 و اين الـ 0
+
+292
+00:22:17,560 --> 00:22:21,900
+محطوله مش عيمينه و عشماله فيه القام محضون اذا عده
+
+293
+00:22:21,900 --> 00:22:28,080
+عد اربعةأربعة تمام has four significant figures
+
+294
+00:22:28,080 --> 00:22:31,720
+one point zero six فلتوا من هذه ال point اللي هي
+
+295
+00:22:31,720 --> 00:22:35,720
+الفاصلة منجزعة و السفر بين واحد و ستة ولا لا عدوا
+
+296
+00:22:35,720 --> 00:22:40,460
+اكم واحد اذا تلاتة significant figures اذا خلصنا
+
+297
+00:22:40,460 --> 00:22:44,860
+اللي من السفر كله و بدك تعده صح السفر له قواعد اذا
+
+298
+00:22:44,860 --> 00:22:50,060
+السفر محضون عده تمام هيك احنا بنحكي بالبلد هنا اذا
+
+299
+00:22:50,060 --> 00:22:51,640
+السفر محضون عده
+
+300
+00:22:54,370 --> 00:22:57,070
+بقول لي Zero is placed to the left في مثل عربي
+
+301
+00:22:57,070 --> 00:23:02,370
+بيقول لو جالتكم امكم او سيدكم ان فلان سفر ع شمال
+
+302
+00:23:02,370 --> 00:23:08,130
+ايش بيفهموا منه يعني مالوش قيمة مالوش اهمية نفس
+
+303
+00:23:08,130 --> 00:23:13,710
+القاعدة طبقوها اذا السفر ع شمال ينسوهنفس القاعدة؟
+
+304
+00:23:13,710 --> 00:23:18,750
+ماشي يعني مالوش قيمة يعني؟ الله يرده، صح؟ بغض
+
+305
+00:23:18,750 --> 00:23:22,950
+النظر، بقول zeros placed to the left of non-zero
+
+306
+00:23:22,950 --> 00:23:28,610
+digits are not significant إنسان، هال، تشوفوا هنا
+
+307
+00:23:28,610 --> 00:23:33,090
+في إشارة، اللي هي فاصلة، بغض النظر، قاللي ها، هدول
+
+308
+00:23:33,090 --> 00:23:37,190
+الأصفار، عشمال ولا لأ؟ is an atom significant؟
+
+309
+00:23:37,190 --> 00:23:43,690
+واحد، الأصفر ما عدتهمشسهل أظنني في حد ماسمعوش فيه
+
+310
+00:23:43,690 --> 00:23:48,910
+المثال سفر ع شمال وهد بينضلنا متذاكرين و سفر ع
+
+311
+00:23:48,910 --> 00:23:54,230
+شمال بدياه لأ خلاص يهمل سهل هد كاين studio 6 و
+
+312
+00:23:54,230 --> 00:24:02,710
+بيعرفوا علم تمام حلو أحكي non-zero أحكي
+
+313
+00:24:06,660 --> 00:24:09,580
+انت فاكروش كتير في الامتحان، هادي ميديو مش في
+
+314
+00:24:09,580 --> 00:24:15,160
+الامتحان، رسيك، فقعفة هادي، انت بقولك كيف نكتبها،
+
+315
+00:24:15,160 --> 00:24:17,940
+يعني انا مركزي، لأن انتوا هتخشوا، يعني امكرا
+
+316
+00:24:17,940 --> 00:24:21,740
+هتخشوا في المرسم، مش هتجيسوا، هتخشوا في المعمل،
+
+317
+00:24:21,740 --> 00:24:25,040
+هتجيسوا، فهادي بيديها عشان كيف تتعاملوا مع الأرقام
+
+318
+00:24:25,790 --> 00:24:30,670
+تمام؟ فاتيكي مني الحفظ ماتحفظيش إشي تمام بيقول الـ
+
+319
+00:24:30,670 --> 00:24:35,030
+zeros at the end of a number and to the right of a
+
+320
+00:24:35,030 --> 00:24:39,250
+decimal are significant نجي عاليمين قال لي إذا
+
+321
+00:24:39,250 --> 00:24:44,490
+لجيت إشارة عشرية ليه فاصلة عدي الأصفر اللي عاليمين
+
+322
+00:24:44,490 --> 00:24:48,010
+هو مش اللي ع اليسار اللي ع اليسار خلصنا منها سفر ع
+
+323
+00:24:48,010 --> 00:24:51,370
+أسماع اللي خلصنا منه لجيت نجي لليمين قال لي اليمين
+
+324
+00:24:51,370 --> 00:24:57,780
+بدك تعده إذا كان فيه فاصلة عشريةتمام؟ إذن بيقولي
+
+325
+00:24:57,780 --> 00:25:02,340
+زي إيش؟ جلي 16 هدي علي مين و مش علي مين؟ و هذه
+
+326
+00:25:02,340 --> 00:25:06,840
+النقطة فاصلة إذا نعدها كم واحدة دول؟ تلاتة أيوة
+
+327
+00:25:06,840 --> 00:25:12,660
+شايفينهم؟ أربعة براوا عليكم تمام؟ أربعة طيب نيجي
+
+328
+00:25:12,660 --> 00:25:20,140
+نقول بال calculator تمام؟ أنا هدول الشمّة 200 ولا
+
+329
+00:25:20,140 --> 00:25:27,120
+مش 200؟ 200 حلو طيب و هذه؟ 2 2 زي بعيط؟فأنا قشطان
+
+330
+00:25:27,120 --> 00:25:31,620
+لكن اجي اقول اكم significant figure هنا واحد و
+
+331
+00:25:31,620 --> 00:25:37,100
+ايضا واحد طب كيف؟ ايش معناه واحد؟ هذه اتنين لما
+
+332
+00:25:37,100 --> 00:25:41,340
+تدينيها واحد معناه هذا مش يقيني معناه انا الرقم
+
+333
+00:25:41,340 --> 00:25:45,860
+تبعي اما واحد او تلاتة صح؟ هنا بقوله معناه الرقم
+
+334
+00:25:45,860 --> 00:25:49,400
+اما مية او تلاتمية طب انا مجستش هيك القالة تبعتي
+
+335
+00:25:49,400 --> 00:25:55,600
+مش هيك القالة تبعتي اكثر دقة اذا اكتبليها هيكأذا
+
+336
+00:25:55,600 --> 00:25:58,680
+أنا كام significant في Garçar؟ تلاتة! صار إيش
+
+337
+00:25:58,680 --> 00:26:02,280
+بتقولي إنت لما تكتبها هيك؟ بقولك هذه إما 201 أو
+
+338
+00:26:02,280 --> 00:26:09,900
+199 على وين أنا شككت في الأخير بس لكن بدون هذه أنا
+
+339
+00:26:09,900 --> 00:26:15,520
+شككت في هذه شككت في هذه إذا بيقولي هنا هذه بعد ما
+
+340
+00:26:15,520 --> 00:26:21,200
+خلصتهن خلصنا من هذه هنا zeros at the end of a
+
+341
+00:26:21,200 --> 00:26:26,760
+number without a decimal بدون فاصلة عشرية are not
+
+342
+00:26:26,760 --> 00:26:30,380
+significant is not significant ما زال محطتش إشارة
+
+343
+00:26:30,380 --> 00:26:36,340
+فاصلة عشرية اللي حتى على اليمين ماتعدوشأه .. اه ..
+
+344
+00:26:36,340 --> 00:26:38,820
+اذا انت .. انت اللي بيبقى تكتب .. انا بدي أفهم
+
+345
+00:26:38,820 --> 00:26:43,080
+بناء على كتابتك .. انت بتقوللي والله ان انا شاكك
+
+346
+00:26:43,080 --> 00:26:45,760
+في التنين و اكتبها هيك .. انت بتقوللي لأ انا هادي
+
+347
+00:26:45,760 --> 00:26:47,940
+متأكد منها و هادي متأكد منها .. هادي شاكت فيها ..
+
+348
+00:26:47,940 --> 00:26:52,020
+بيبقى تكتبلي هيك عشان أفهم عليك .. ساعتها هادي
+
+349
+00:26:52,020 --> 00:26:55,000
+بقول عنها three significant figures لكن هيك بقولها
+
+350
+00:26:55,000 --> 00:26:59,830
+كم واحد؟ واحدأذن Zeroes Zero at the end of a
+
+351
+00:26:59,830 --> 00:27:03,630
+number without a decimal point دون فاصلة عشرية is
+
+352
+00:27:03,630 --> 00:27:09,470
+not significant تعدهاش، تعدهمش Thus، هجيت 4200
+
+353
+00:27:09,470 --> 00:27:13,370
+وحطت فاصلة، هجت أربعة Has four significant
+
+354
+00:27:13,370 --> 00:27:19,610
+figures، why؟ 4200 بدون فاصلة، لين؟ من اتوى
+
+355
+00:27:19,610 --> 00:27:24,190
+سؤالتنا على ال .. إيش اللي نحفظه؟ سهلين، مظبوط؟
+
+356
+00:27:24,190 --> 00:27:31,460
+سهلين4200 في فاصلة عشرية؟ إذا ما تعديش الأصفار
+
+357
+00:27:31,460 --> 00:27:38,360
+أكملواها حد هنا في فاصلة عشرية عديهم تصيروا أربعة
+
+358
+00:27:38,360 --> 00:27:46,060
+شوفتي إيه؟ حلو جالي طيب أنتوا علمتونا اللي هي
+
+359
+00:27:46,060 --> 00:27:51,450
+الرموز العلمية لمنجور سرعت الضوءتلاتة بون تمانية
+
+360
+00:27:51,450 --> 00:27:55,090
+فعشرة أس تمانية مظبوط ولا لأ تلاتة بون تمانية
+
+361
+00:27:55,090 --> 00:27:58,190
+فعشرة أس تمانية انا تلاتة تمانية وتحط جنبهم سبع
+
+362
+00:27:58,190 --> 00:28:01,470
+أسفار ولا لأ قاللي هادي تلاتة بون تمانية بنسميها
+
+363
+00:28:01,470 --> 00:28:05,610
+إيش؟ بنسميها رمز علمي ده ريحنا أكتر قاللي في
+
+364
+00:28:05,610 --> 00:28:11,390
+الرموز العلمية كل إيش بدك تعده كل الأسفارتمام؟ إذا
+
+365
+00:28:11,390 --> 00:28:15,610
+بيقوللي all digits in a number in a scientific
+
+366
+00:28:15,610 --> 00:28:18,610
+notation scientific notation اللي هي في عشر أقص
+
+367
+00:28:18,610 --> 00:28:24,530
+تمام؟ are significant for example 4.2 في عشر أقص
+
+368
+00:28:24,530 --> 00:28:30,250
+تلاتة طب هتطلعوا يا بنات هجيت 4.2 في عشر أقص تلاتة
+
+369
+00:28:30,250 --> 00:28:37,450
+و 4.20 في عشر أقص تلاتة و 4.200 في عشر أقص تلاتة
+
+370
+00:28:38,490 --> 00:28:44,290
+ككالكوليتر في فرد بين هدول؟ ولا شي ولا شي في فرد
+
+371
+00:28:44,290 --> 00:28:52,030
+ككالكوليتر رقم نفسه تلعب .. انت مش م .. مش مأمنة
+
+372
+00:28:52,030 --> 00:28:56,850
+اتسنى شوية هجي الهادي في الكالكوليتر كيف تتحول؟
+
+373
+00:28:56,850 --> 00:29:02,490
+مظبوط؟
+
+374
+00:29:02,490 --> 00:29:06,210
+نجيليهادي نجيليهادي
+
+375
+00:29:08,470 --> 00:29:13,470
+في حد اختلف؟ لأ طب قوليش ليه إيش كتابات؟ بقوله حلو
+
+376
+00:29:13,470 --> 00:29:16,530
+هام انت إيش بتقولي؟ بقولي هادي أنا مش متأكد منه
+
+377
+00:29:16,530 --> 00:29:21,510
+صح؟ معناته هادي أما أربعة آلاف و تلاتمية أو أربعة
+
+378
+00:29:21,510 --> 00:29:25,970
+آلاف و مية هام بتقولي أنت هادي أنا مش متأكد منه
+
+379
+00:29:25,970 --> 00:29:30,850
+إذا إما أربعة آلاف و متين و عشرة أو أربعة آلاف و
+
+380
+00:29:30,850 --> 00:29:36,050
+مية و تسعينصحيح؟ هنا قال انت هذا بس اللي مش متأكد
+
+381
+00:29:36,050 --> 00:29:45,630
+منه اذا اما 4201 او 4199 لكن كرقم حسابي كل واحد بس
+
+382
+00:29:45,630 --> 00:29:54,750
+بفرج انت تقولي كيف جثت تمام؟ حلو هذا يعرف للشوة ال
+
+383
+00:29:54,750 --> 00:29:59,320
+scientific notation يعني يا بنات هي هذااكتبوا ليها
+
+384
+00:29:59,320 --> 00:30:06,920
+بدلالة الرمز العلمي كيف بنا نكتبه احكي .. احكي ..
+
+385
+00:30:06,920 --> 00:30:10,880
+بنفعش تقولي 15 طب عشان معرفة اللي هي لازم الرقم
+
+386
+00:30:10,880 --> 00:30:16,220
+يكون بين 1 و 9 اذا 1.5 طبعا انت لما تيجي تقولي و
+
+387
+00:30:16,220 --> 00:30:23,280
+الله كتكون تفهم عليا 15 في 10 أقصى 2 لكن كرمز علمي
+
+388
+00:30:23,280 --> 00:30:28,110
+مش صحيح انت تكتب 1.5 في 10 أقصى 3لازم الرقم يكون
+
+389
+00:30:28,110 --> 00:30:37,350
+أقل من عشرة تمام؟ وبالتالي هذا كيف بكتبه؟ إذن هي
+
+390
+00:30:37,350 --> 00:30:41,250
+تعريف الرمز العلمي a number between one and ten
+
+391
+00:30:41,250 --> 00:30:44,250
+عشان كده مايفعلش تقولي خمس دقايق one and ten
+
+392
+00:30:44,250 --> 00:30:49,950
+multiplied by مضروف في عشرة raised to some
+
+393
+00:30:49,950 --> 00:30:54,010
+exponent exponent يعني أُس عشرة و بتحط فوق العشرة
+
+394
+00:30:54,010 --> 00:31:03,910
+أُسThe quantity 4200 كيف بيك تكتبها؟ 4.2×10² أقصد
+
+395
+00:31:03,910 --> 00:31:07,690
+2 لازم يكون أقل من 9 أو أقل من 10
+
+396
+00:31:10,590 --> 00:31:14,470
+ما هو هى اللى جاله طول وقلت انه انا لو كتبت 4
+
+397
+00:31:14,470 --> 00:31:20,170
+.2×10∙3 معناته فيه زائد او ناقص مية 4100 او 4300
+
+398
+00:31:20,170 --> 00:31:26,330
+لكن لو كتبت هيك بس هذا اللى شاكك فيه plus or minus
+
+399
+00:31:26,330 --> 00:31:36,530
+واحد طيب امننا اعهدنا ربنا نكون امناء في القياسات
+
+400
+00:31:36,530 --> 00:31:41,660
+وفي العلم كتبتانت مهندس بدي اشوف الشجرة جديش
+
+401
+00:31:41,660 --> 00:31:46,880
+مساحتها مش مهم جدا او غرفة عشان اجيس احكي بنتى
+
+402
+00:31:46,880 --> 00:31:54,680
+احكي يا بنتى اه
+
+403
+00:31:54,680 --> 00:31:58,720
+بنعده كيف
+
+404
+00:31:58,720 --> 00:32:03,440
+يعني كيف كيف كيف يعني هاي خمسة و هاي صفر صفر بحط
+
+405
+00:32:03,440 --> 00:32:09,780
+هنا تلاتة اهمحضونين هدول مش محضونين كله بتعديهم
+
+406
+00:32:09,780 --> 00:32:15,500
+سفره
+
+407
+00:32:15,500 --> 00:32:21,260
+ع الشمال ستة جالت عنها وين
+
+408
+00:32:21,260 --> 00:32:28,860
+هنا هنا اه
+
+409
+00:32:28,860 --> 00:32:35,380
+هيك انهضل انهضل مانهضلش
+
+410
+00:32:36,740 --> 00:32:42,540
+فاصلة بتحضنش فاصلة غلبانة بتدفّيش بدّيك رقم يحضن
+
+411
+00:32:42,540 --> 00:32:51,640
+تمام يا بنتي؟ غيرها تمام قال لي جسد صح و كتبتلك صح
+
+412
+00:32:51,640 --> 00:32:59,280
+طوله عرض بدّي المساحة لما تديني طوله عرض ايش هسوي
+
+413
+00:32:59,280 --> 00:33:04,340
+طول فعبدادرب صح؟ قال لي طيب انت الآن ال calculator
+
+414
+00:33:04,340 --> 00:33:08,460
+هتطلعلك رقممثبتولة لأ بالـCalculator؟ دربت؟ طلع
+
+415
+00:33:08,460 --> 00:33:12,820
+عندي رقم، بدك تكتبه صح. كيف أعمله؟ جالي حلو،
+
+416
+00:33:12,820 --> 00:33:17,740
+اتطلعلي على إنت إيش و كيف طولك و كيف عرضك، أديليها
+
+417
+00:33:17,740 --> 00:33:21,240
+كم significant figure في الطول و كم significant
+
+418
+00:33:21,240 --> 00:33:26,580
+figure في العرض، جوابك لازم يكون جد أقل واحد، عشان
+
+419
+00:33:26,580 --> 00:33:31,670
+تكون أكثر دقة و علمي أكترتمام عشان تكون يقينى اذا
+
+420
+00:33:31,670 --> 00:33:36,450
+بيقول ليه when multiplying or dividing اما تضرب او
+
+421
+00:33:36,450 --> 00:33:41,060
+بتجسم والجسم ماهي ضربWhen multiplying or dividing
+
+422
+00:33:41,060 --> 00:33:46,280
+several quantities عدة كميات زي ما قلنا طول و عرض
+
+423
+00:33:46,280 --> 00:33:50,020
+The number of significant figure in the final
+
+424
+00:33:50,020 --> 00:33:53,660
+answer is the same as the number of significant
+
+425
+00:33:53,660 --> 00:33:57,380
+figures in the quantity having the smallest number
+
+426
+00:33:57,380 --> 00:34:01,320
+الأقل The smallest number of significant figures
+
+427
+00:34:01,320 --> 00:34:07,080
+ان ترجم بالبلدي عندي كميتين طول و عرضالطول تلاتية
+
+428
+00:34:07,080 --> 00:34:10,680
+significant figures العرض two significant figures
+
+429
+00:34:10,680 --> 00:34:16,040
+الإجابة ايش بيكون؟ اتنين لازم تكون اتنين وكيف
+
+430
+00:34:16,040 --> 00:34:20,480
+بتخليها اتنين؟ ال calculator طلعتلي خمسة ولا ستة
+
+431
+00:34:20,480 --> 00:34:25,840
+بيبقى تخليهم اتنين و بالتقريب تمام هد ندي مثال
+
+432
+00:34:25,840 --> 00:34:31,660
+جالي for example جالي فيه disk تعرف ال disk؟دائرة
+
+433
+00:34:31,660 --> 00:34:36,120
+تعرف القانون ما هي ساعة الدائرة باي ار تربيع ال
+
+434
+00:34:36,120 --> 00:34:40,520
+باي انا بجيسها و لا معروفة باي معروفة اي شركة جيسه
+
+435
+00:34:40,520 --> 00:34:44,660
+ار جيسلي ار جالك والله جستلك ار ستة point zero
+
+436
+00:34:44,660 --> 00:34:49,680
+centimeter ستة point zero وانت تحت ال zero تسوي
+
+437
+00:34:49,680 --> 00:34:54,080
+سؤالنا محضوب هنا بس ايش في point بس على اليمين هذا
+
+438
+00:34:54,080 --> 00:35:00,040
+صح هذا في point يزن بده عدهأزن أكم significant
+
+439
+00:35:00,040 --> 00:35:04,760
+figure؟ اتنين الجواب ايش لازم يطلع؟ اتنين بفعل
+
+440
+00:35:04,760 --> 00:35:09,960
+يطلع أربعة؟ لأ يلا يا calculator باي بحط باي في ال
+
+441
+00:35:09,960 --> 00:35:16,580
+calculator و ستة تربية ضربت طلعي جواب هيو طلعيش
+
+442
+00:35:16,580 --> 00:35:21,780
+طلعي جواب؟تمام شكرا واحتين انتلتة اربعة خمسة ستة
+
+443
+00:35:21,780 --> 00:35:26,480
+تمام هي هذا الموضوع فعدته واحتين انتلتة اربعة خمسة
+
+444
+00:35:26,480 --> 00:35:32,120
+ستة مفهوم يكون ستة؟ لأ لازم اتنين طب لازم اتنين
+
+445
+00:35:32,120 --> 00:35:37,860
+احط احداش وانا غير مفهوش بدي اتسخدم ال scientific
+
+446
+00:35:37,860 --> 00:35:41,240
+notation لما احط ال scientific notation طلعت كتبته
+
+447
+00:35:41,240 --> 00:35:44,140
+one point one في عشر رقص اتنين اكمل واحدة دول
+
+448
+00:35:50,350 --> 00:35:56,070
+تلاتة هادى خمسة واطلع و لا أقل من خمسة إذا أقل من
+
+449
+00:35:56,070 --> 00:36:00,630
+خمسة الله لا يردها بضيعها طب إذا أكتر من خمسة
+
+450
+00:36:00,630 --> 00:36:06,210
+بخليها اتنين يعني لو هذه خمسة أو ستة أو تمانية
+
+451
+00:36:06,210 --> 00:36:12,250
+بخلي one point twoطبعا احكوا معايا معايا احكوا
+
+452
+00:36:12,250 --> 00:36:16,630
+معايا مش قلنا عشان تسأله و ناخد حسنات دكتور احكي
+
+453
+00:36:16,630 --> 00:36:21,950
+انها هي مية و تلتاش مية و تلتاش و شوية طبعا انا
+
+454
+00:36:21,950 --> 00:36:24,690
+باخد اول اشي اول رقم المية طبعا من التلتاش اللي
+
+455
+00:36:24,690 --> 00:36:30,270
+بشوف وضع عليها و بقربها بالظبط طبعا غيرها احكي
+
+456
+00:36:30,270 --> 00:36:33,850
+الأرقام اللي بعد الفضل و غير الدرمن حسد
+
+457
+00:36:35,980 --> 00:36:42,440
+حسب اكم significant figures هجيتله هذا انا انا انا
+
+458
+00:36:42,440 --> 00:36:42,700
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+459
+00:36:42,700 --> 00:36:45,140
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+460
+00:36:45,140 --> 00:36:45,260
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+461
+00:36:45,260 --> 00:36:46,880
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+462
+00:36:46,880 --> 00:36:48,520
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+463
+00:36:48,520 --> 00:36:48,620
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+464
+00:36:48,620 --> 00:36:53,120
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+465
+00:36:53,120 --> 00:36:53,120
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+466
+00:36:53,120 --> 00:36:58,370
+انا انا انا انا انا انا انا ابزود اللي جابله، أنا
+
+467
+00:36:58,370 --> 00:37:02,070
+مابديش إيه في كل حوات لإنه لو قعد بعملي خلال، بصير
+
+468
+00:37:02,070 --> 00:37:05,890
+تلاتة significant figures، مانفعش أخليه، إما باخد
+
+469
+00:37:05,890 --> 00:37:11,310
+منه نفسه و بزود اللي جابله، أو الله لرده، تمام؟
+
+470
+00:37:11,310 --> 00:37:15,670
+هاي اللي بيقوللي، مانفعش تكتب 113، لإنه بيصير
+
+471
+00:37:15,670 --> 00:37:22,830
+تلاتة، ولا 113.1، بيصيروا أربعة، but as reported
+
+472
+00:37:22,830 --> 00:37:29,500
+before، بيجب تكتبوا هيك، اتنين، تمام؟خلصنا من
+
+473
+00:37:29,500 --> 00:37:34,740
+الضرب والجسمة بتروح تعدّلي ال significant figures
+
+474
+00:37:34,740 --> 00:37:39,040
+جوابك لازم يكون بعدد أقل واحد طب و جامع و اتطرح
+
+475
+00:37:39,040 --> 00:37:40,900
+قال لي ليه مالكاي دعوة بال significant figures
+
+476
+00:37:40,900 --> 00:37:44,520
+هفقلي إيش إلي دعوة قال لي إليك دعوة بالفاصلة
+
+477
+00:37:44,520 --> 00:37:49,480
+العشرية شوف ليه موضع الفاصلة العشرية بعد الفاصلة
+
+478
+00:37:49,480 --> 00:37:57,070
+أكم رقم عندك جوابك بدي يكوننفس العملية عند أقل عدد
+
+479
+00:37:57,070 --> 00:38:01,690
+بعد الفاصلة العشرية يعني when numbers are added or
+
+480
+00:38:01,690 --> 00:38:06,510
+subtracted ادد يعني جمعت subtracted طريحات واتطرح
+
+481
+00:38:06,510 --> 00:38:10,450
+واتجمع عملية حسابية واحدة حلو بيقول لي the number
+
+482
+00:38:10,450 --> 00:38:14,910
+of decimal places decimal places موضع الإشارة
+
+483
+00:38:14,910 --> 00:38:20,580
+الفاصلة العشرية decimal places مكان الفاصلةتمام in
+
+484
+00:38:20,580 --> 00:38:23,940
+the result should equal the smallest number of
+
+485
+00:38:23,940 --> 00:38:27,760
+decimal places of any term in the added or
+
+486
+00:38:27,760 --> 00:38:33,240
+subtracted numbers حسب الأصغر يعني هد هما إيش بين
+
+487
+00:38:33,240 --> 00:38:38,320
+هما دول زائد ولا مش زائد زائد بقول الأول بعد الفصل
+
+488
+00:38:38,320 --> 00:38:42,380
+العشرية كم رقم فيه والتاني الجواب لازم يكون واحد
+
+489
+00:38:42,380 --> 00:38:47,650
+لازم يكون واحداللي هو الأقل هجيت نيجي نجمع
+
+490
+00:38:47,650 --> 00:38:50,830
+بالجامعي البلدي يا بنات احنا كنا في ال .. لما
+
+491
+00:38:50,830 --> 00:38:53,250
+علمونا في البستان كيف نجمع ولّا ما علموناش في
+
+492
+00:38:53,250 --> 00:38:57,310
+البستان لسه هنجمع اظن خلّيني نشوف مية و خمسة و
+
+493
+00:38:57,310 --> 00:39:01,990
+أربعين point
+
+494
+00:39:01,990 --> 00:39:06,070
+five ستة point تمانية أربعة مش كانوا يقولوني نحط
+
+495
+00:39:06,070 --> 00:39:12,750
+صفر هنا عشان نعرف نجمع يلّا صفر و أربعة خمسة ولا
+
+496
+00:39:12,750 --> 00:39:20,820
+نحط عياصبي هناخمسة و تمانية ستة و ستة صحيح بقول
+
+497
+00:39:20,820 --> 00:39:23,220
+هاي الجواب هيك طلع ال calculator بقولهم ممنوع
+
+498
+00:39:23,220 --> 00:39:27,280
+تكتبوا هيك ليش؟ لأنه كم واحدة هدوة تمتين وهذه
+
+499
+00:39:27,280 --> 00:39:31,260
+واحدة .. هذي واحدة .. منفعش تتحلي واحدة لأنه أقل
+
+500
+00:39:31,260 --> 00:39:38,010
+واحد فيهم واحد طيب نيجي لهناهذه لا أريد أن أحصل
+
+501
+00:39:38,010 --> 00:39:41,470
+عليها لأ بجيبها و الله لا يردها وإذا كانت خمسة أو
+
+502
+00:39:41,470 --> 00:39:45,350
+فوق هذه عليك تخليها أربعة تمام هك؟ عليك تخليها
+
+503
+00:39:45,350 --> 00:39:51,770
+أربعة فبقوللي هذه هنا كتبناها هي point تلاتة
+
+504
+00:39:51,770 --> 00:39:56,450
+بتخليها إيش هيك و لا بتخليها هيك تمام هك؟ حلو قال
+
+505
+00:39:56,450 --> 00:40:00,330
+لي خليني أخد مثالين تانين هجيت نرجع لل significant
+
+506
+00:40:00,330 --> 00:40:05,450
+figures أكم significant figures هنا واحد بره عليكم
+
+507
+00:40:05,450 --> 00:40:10,680
+هناكـ Significant Figures خمسة لما جيت تطلع تقولت
+
+508
+00:40:10,680 --> 00:40:13,080
+واحد تانين تلاتة بدي أجمع ماليش دعوة في الـ
+
+509
+00:40:13,080 --> 00:40:16,240
+Significant Figures اربع اربع اذا اخليهم جمعتهم
+
+510
+00:40:16,240 --> 00:40:21,140
+تطلع راهين انا مابدي اتراح قالوا واحد تانين تلاتة
+
+511
+00:40:21,140 --> 00:40:25,860
+واحد تانين تلاتة تمام واحد تانين تلاتة عادى مافيش
+
+512
+00:40:25,860 --> 00:40:31,120
+إشكالية بغض النظر عن الـ Significant Figures تمام
+
+513
+00:40:31,120 --> 00:40:39,530
+عادى اللي حكيناها نشوف اللي هو المثالالمساحة جالي
+
+514
+00:40:39,530 --> 00:40:49,600
+جستلك الطول لجيته 12.71 متر أربع حلووالعرض جسده 3
+
+515
+00:40:49,600 --> 00:40:55,120
+.46 متر تلاتة ايش بدات؟ قال لي بدي المساحة مساحة
+
+516
+00:40:55,120 --> 00:40:58,940
+اضرب ولا اجمع؟ اضرب مازال اضرب الي دعوة في ال
+
+517
+00:40:58,940 --> 00:41:02,000
+significant figures هذا أربعة و هذا تلاتة شو لازم
+
+518
+00:41:02,000 --> 00:41:05,720
+الجوا بيكون؟ لازم يكون تلاتة قال لي يلا بال
+
+519
+00:41:05,720 --> 00:41:11,350
+calculator اضرب ضربت طلع إجابة هيكهذا يجاوب ال
+
+520
+00:41:11,350 --> 00:41:14,830
+calculator بينفع اكتبه زي ال calculator؟ بقوله لأ
+
+521
+00:41:14,830 --> 00:41:20,050
+بقوله انت بتقولي لازم نكون تلاتة بقوله هذا همعند
+
+522
+00:41:20,050 --> 00:41:23,530
+هنا بدي اوقف انتبهي هنا بدي اوقف بقول ايش جنبه
+
+523
+00:41:23,530 --> 00:41:28,790
+سبعة هذا بدي يكبر بدي يصير عشرة عشرة يعني سفر وهذا
+
+524
+00:41:28,790 --> 00:41:31,890
+بدي يصير اربعة اربعة واربعين اكتب اربعة واربعين
+
+525
+00:41:31,890 --> 00:41:35,690
+بنفعش اتنين بيصيروا لازم يكون اربعة واربعين فاصلة
+
+526
+00:41:35,690 --> 00:41:44,660
+سفر عشان يصيروا تلاتة صح؟ مع انه احكيأرجعى 145.6
+
+527
+00:41:44,660 --> 00:41:47,920
+قولت انه بعد الفاصلة خمسة وبعد الفاصلة اربعة
+
+528
+00:41:47,920 --> 00:41:51,560
+تمانية يعني ليش ما عدت انه اربعة او تلاتة اربعة
+
+529
+00:41:51,560 --> 00:41:56,420
+تمانية ان هي وين هنا اه اه هنا هجيت احنا جمعناهم
+
+530
+00:41:56,420 --> 00:42:01,600
+هيهم نظبط ولا لأ هي 152.34 انا ايش قاعد هنا بيجمع
+
+531
+00:42:01,600 --> 00:42:06,300
+وفي الجامع بيقولي لازم يجواب يكون بعد الفاصلة
+
+532
+00:42:06,300 --> 00:42:11,450
+العشريةأقل واحد من الاتنين و قلت له هنا واحد و هنا
+
+533
+00:42:11,450 --> 00:42:14,950
+اتنين لازم الجواب يكون واحد فلازم يكون واحد بعد
+
+534
+00:42:14,950 --> 00:42:18,390
+الاشارة انا لما جمعتهم طلعت انتي انا بقوله هذه
+
+535
+00:42:18,390 --> 00:42:22,090
+عشان هاربعة بلغيها لو كانت خمسة و فوق بصير هذه
+
+536
+00:42:22,090 --> 00:42:27,950
+اربعة تمام هيك؟ حلو جالي هيك طلعت قلت له اذا هذه
+
+537
+00:42:27,950 --> 00:42:33,270
+عشان تطلع بالظبط تلاتة لازم تكتبها اربعة و اربعين
+
+538
+00:42:33,270 --> 00:42:42,920
+نقطة سفرهك بتطلع هاتي هو من فهمك إيش ورانا بس
+
+539
+00:42:42,920 --> 00:42:47,480
+بتجربى ولا لأ بس مرات بتقولوا واحد حرام
+
+540
+00:42:47,480 --> 00:42:49,780
+الكالكوليتر بتاعة بتكتب اكتب زي ما كتبت
+
+541
+00:42:49,780 --> 00:42:54,460
+الكالكوليتر مفروض لأ احنا ممكن نعدل عليها بس احكي
+
+542
+00:42:54,460 --> 00:42:58,100
+يا بنتى طبعا هلأ تلاتة و أربعين point سبعة و تسعين
+
+543
+00:42:58,100 --> 00:43:01,200
+اه طبعا قربنا على العشرة ثالثة أربع و أربعين حلو
+
+544
+00:43:01,200 --> 00:43:06,510
+هشوزا الستة و ستين وين الستة وستينأحنا نظرنا نجي
+
+545
+00:43:06,510 --> 00:43:10,150
+وراهم لما يصلوا جهنم و نشيل فيهم أنا ببطلع أنا إيش
+
+546
+00:43:10,150 --> 00:43:13,810
+بدي ألغي؟ بدي ألغي السابعة، صح؟ لأن عندي التسعة
+
+547
+00:43:13,810 --> 00:43:18,410
+بدي أخلص السابعة بينفع ألغيها بدون ما أخد تأثيرها
+
+548
+00:43:18,410 --> 00:43:22,190
+لأنه أكبر من الخمسة طيب هي بتتأثر عن مين؟ عن اللي
+
+549
+00:43:22,190 --> 00:43:26,270
+جابلها التسعة إيش بدي أصير؟ خلص هجي الست وستي نشيل
+
+550
+00:43:26,270 --> 00:43:29,550
+فيها طب ما اللي جابلها أكلتها اسمهم السابعة
+
+551
+00:43:34,290 --> 00:43:39,210
+لأ سنة في فرق الجمع والطرح غير عن الضرب والجسمة في
+
+552
+00:43:39,210 --> 00:43:42,330
+الضرب والجسمة الأقل في ال significant figures في
+
+553
+00:43:42,330 --> 00:43:46,650
+الجمع والطرح الأقل في موضع الفاصلة العشرية فهمت
+
+554
+00:43:46,650 --> 00:43:51,890
+عليها؟ هاي الفرق تمام وبرضه مانفعش نكتب اربع
+
+555
+00:43:51,890 --> 00:43:58,630
+واربعين لان اربع واربعين بيصير اتنين تمام حلو نعمل
+
+556
+00:43:58,630 --> 00:44:04,600
+quiz شوف كنا نحكي عربي ولا صينيعجب عليكي ثاني تمام
+
+557
+00:44:04,600 --> 00:44:07,600
+بقولي how many significant figures are in the
+
+558
+00:44:07,600 --> 00:44:16,340
+number 0003 احكيه هطلع أخوك الخيارات تبعتنا واحد
+
+559
+00:44:16,340 --> 00:44:24,060
+ولا مش واحد سهل سهل سفر عشمان bravo عليكم حلو
+
+560
+00:44:24,060 --> 00:44:34,260
+بقولي أنا بدي أضرب بدي أضرب ثانيبدي أضرب 2.34
+
+561
+00:44:34,260 --> 00:44:38,500
+تلاتة significant figures في 2.0 تلاتة significant
+
+562
+00:44:38,500 --> 00:44:42,900
+figures الإيجابي إيش لازم تكون؟ 2 براو بس أشوف
+
+563
+00:44:42,900 --> 00:44:50,520
+الخيارات و برجع إليك تمام؟ هاي الخيارات تبعتنا 4
+
+564
+00:44:50,520 --> 00:44:58,960
+.6 ولا 4.7؟ هاي ال calculator يا بنات ليش؟
+
+565
+00:44:59,980 --> 00:45:07,480
+لأنه تمانية هذا هي مش صناعة صاروخ سهل العملية وين
+
+566
+00:45:07,480 --> 00:45:13,460
+هال بتقول أنا الأخير اتنى شوية لذا هادي تمام the
+
+567
+00:45:13,460 --> 00:45:16,500
+results of the arithmetic operation هنا بدي اجمع
+
+568
+00:45:16,500 --> 00:45:23,500
+اجمع ايش بتطلع موضع الفاصلة بقول واحد تانين تلاتة
+
+569
+00:45:23,500 --> 00:45:27,280
+هنا لازم الجواب يكون واحد لازم الجواب يكون واحد
+
+570
+00:45:27,280 --> 00:45:28,940
+طلع عليا عشان تجاوبي
+
+571
+00:45:34,100 --> 00:45:40,440
+دالباكم هيكالكوليتر خمستعش
+
+572
+00:45:40,440 --> 00:45:48,460
+point تسعة قربنا احكي في ال .. في الجبل اتقربي اه
+
+573
+00:45:48,460 --> 00:45:51,780
+ال .. بيطلع اتنين عندك عدد كله و لا بعد الفاصلة
+
+574
+00:45:51,780 --> 00:45:55,040
+بعد الضرب بيطلع عندك اتنين اتنين significant
+
+575
+00:45:55,040 --> 00:45:58,100
+figures significant figures اه significant figures
+
+576
+00:45:58,100 --> 00:46:02,340
+كله مش اي ما ندعو في الفاصلة عشرية في الضرب في ال
+
+577
+00:46:02,340 --> 00:46:07,000
+significant figuresتمام؟ دكتور عيدى الأخير تانى
+
+578
+00:46:07,000 --> 00:46:15,350
+عيدى الأخير تانى اشهادى؟زائد في الزائد بهمني موضع
+
+579
+00:46:15,350 --> 00:46:20,450
+الفاصلة العشرية صحيح؟ هي اللي بهمني ايش وراها؟
+
+580
+00:46:20,450 --> 00:46:24,770
+بقول له ها دي واحد تنين تلاتة وها دي واحد الجواب
+
+581
+00:46:24,770 --> 00:46:29,070
+لازم يكون لأصغر اكم؟ اذا لازم جوابك يكون بعد
+
+582
+00:46:29,070 --> 00:46:33,990
+الفاصلة في واحد بس لما اجيت انا جمعت طلع هذا
+
+583
+00:46:33,990 --> 00:46:38,580
+الرقامبقول له هدول ثلاثة، بدي واحد، بدك تبقى على
+
+584
+00:46:38,580 --> 00:46:43,520
+هذه طب هدى خليها تمانية ولا خليها تسعة؟ ليش؟ لأنه
+
+585
+00:46:43,520 --> 00:46:54,940
+جنبها أكتر من خمسة أيصف صراخة، احكي ايه؟ مش
+
+586
+00:46:54,940 --> 00:47:02,820
+بالجامع والضرب، الجامع محمد والضرب، عزيزة، بيجربوش
+
+587
+00:47:02,820 --> 00:47:07,190
+ربعادتمام؟ ماتقولش جمع و ضرب هذه عملية غير عن هذه
+
+588
+00:47:07,190 --> 00:47:14,710
+في الجمع و الطرح اجرائب ناخد موضع الفاصلة العشرية
+
+589
+00:47:14,710 --> 00:47:19,430
+فالضرب ايش جريبه؟ الجسمة بتاخد فيه significant
+
+590
+00:47:19,430 --> 00:47:24,530
+figures تمام هيك؟ خلصنا ال chapter تمام يا بنات؟
+
+591
+00:47:24,530 --> 00:47:30,770
+اذا هدول الأسئلة قبل السبت مابنكون حلوه طيب حاضر
+
+592
+00:47:30,770 --> 00:47:33,130
+يعطيكوا العافية نشوفكم السبت ان شاء الله
+
diff --git a/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/wm95gY8dbmo_raw.json b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/wm95gY8dbmo_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..09eabd04b5e07ed2aaeefa604ba617edd653e9c2
--- /dev/null
+++ b/PL9fwy3NUQKwb6OQhcTn5SkdK0XkcfDNyC/wm95gY8dbmo_raw.json
@@ -0,0 +1 @@
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عنكم كتير بدل ال meter بدي اختار ال centimeter طب هو ال meter كام centimeter؟", "tokens": [3615, 8592, 7649, 16472, 2655, 13672, 1829, 44713, 9778, 40448, 47395, 4032, 7649, 2655, 13672, 1829, 5551, 9381, 43500, 47356, 1975, 15730, 8978, 18871, 16254, 2423, 5959, 21948, 1185, 23032, 1829, 3555, 35186, 5959, 21948, 1975, 1829, 8592, 4724, 36081, 14851, 9778, 40448, 22807, 50239, 1975, 8315, 3714, 16758, 16254, 8592, 1975, 17082, 46152, 24793, 9122, 2655, 13546, 3714, 16758, 16254, 8592, 1975, 8592, 1829, 9566, 18871, 24793, 9122, 2655, 13546, 47525, 1211, 2423, 9255, 4724, 16254, 1975, 46456, 9640, 2423, 31914, 23032, 3555, 31439, 2423, 9255, 9122, 10943, 31914, 22807], "avg_logprob": -0.2890624993521234, "compression_ratio": 1.7938144329896908, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 1490.16, "end": 1490.52, "word": "عشان", "probability": 0.8927408854166666}, {"start": 1490.52, "end": 1490.68, "word": " انت", "probability": 0.75830078125}, {"start": 1490.68, "end": 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"word": " كتير", "probability": 0.89697265625}, {"start": 3130.04, "end": 3130.6, "word": " طلبة", "probability": 0.9462890625}, {"start": 3130.6, "end": 3131.5, "word": " بيجوني", "probability": 0.91787109375}, {"start": 3131.5, "end": 3132.2, "word": " مبرمجين", "probability": 0.95478515625}, {"start": 3132.2, "end": 3132.34, "word": " مش", "probability": 0.88720703125}, {"start": 3132.34, "end": 3132.6, "word": " عارفين", "probability": 0.8870849609375}, {"start": 3132.6, "end": 3132.84, "word": " كيف", "probability": 0.958740234375}, {"start": 3132.84, "end": 3133.24, "word": " برمجوا", "probability": 0.83896484375}, {"start": 3133.24, "end": 3133.66, "word": " حالهم", "probability": 0.9806315104166666}, {"start": 3133.66, "end": 3134.1, "word": " ان", "probability": 0.26513671875}, {"start": 3134.1, "end": 3134.34, "word": " كل", "probability": 0.87890625}, {"start": 3134.34, "end": 3134.64, "word": " ثابت", "probability": 0.9905598958333334}, {"start": 3134.64, "end": 3134.9, 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0.9913736979166666}, {"start": 3140.81, "end": 3141.19, "word": " بكتب", "probability": 0.884521484375}, {"start": 3141.19, "end": 3141.43, "word": " له", "probability": 0.484375}, {"start": 3141.43, "end": 3141.93, "word": " has", "probability": 0.80322265625}, {"start": 3141.93, "end": 3142.15, "word": " no", "probability": 0.93310546875}, {"start": 3142.15, "end": 3142.59, "word": " units", "probability": 0.93359375}, {"start": 3142.59, "end": 3142.95, "word": " بقولك", "probability": 0.5359700520833334}, {"start": 3142.95, "end": 3143.07, "word": " ايه", "probability": 0.6692708333333334}, {"start": 3143.07, "end": 3143.29, "word": " الشهادة", "probability": 0.6024576822916666}, {"start": 3143.29, "end": 3143.69, "word": " حلوة", "probability": 0.9718017578125}, {"start": 3143.69, "end": 3146.03, "word": " لأ", "probability": 0.71240234375}, {"start": 3146.03, "end": 3146.73, "word": " الثوابت", "probability": 0.847265625}, {"start": 3146.73, "end": 3146.95, "word": " ممكن", 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3154.59, "word": " والجاذبية", "probability": 0.866455078125}, {"start": 3154.59, "end": 3155.31, "word": " الأرضية", "probability": 0.87890625}, {"start": 3155.31, "end": 3155.95, "word": " اذا", "probability": 0.7939453125}, {"start": 3155.95, "end": 3156.81, "word": " نفعكين", "probability": 0.4187255859375}, {"start": 3156.81, "end": 3157.27, "word": " برمجين", "probability": 0.9080078125}, {"start": 3157.27, "end": 3157.65, "word": " والله", "probability": 0.633544921875}, {"start": 3157.65, "end": 3158.21, "word": " علمونا", "probability": 0.8504638671875}, {"start": 3158.21, "end": 3158.63, "word": " الثابت", "probability": 0.85430908203125}, {"start": 3158.63, "end": 3158.93, "word": " مالوش", "probability": 0.9033203125}, {"start": 3158.93, "end": 3159.47, "word": " وحدات", "probability": 0.9833984375}, {"start": 3159.47, "end": 3159.65, "word": " مين", "probability": 0.564208984375}, {"start": 3159.65, "end": 3160.03, "word": " يقول", "probability": 0.96826171875}, {"start": 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0.56707763671875}, {"start": 3172.18, "end": 3173.08, "word": " بيه", "probability": 0.5948893229166666}, {"start": 3173.08, "end": 3173.64, "word": " اه", "probability": 0.7225341796875}, {"start": 3173.64, "end": 3176.94, "word": " طبعا", "probability": 0.827880859375}, {"start": 3176.94, "end": 3177.6, "word": " بس", "probability": 0.85693359375}, {"start": 3177.6, "end": 3177.96, "word": " عشان", "probability": 0.97119140625}, {"start": 3177.96, "end": 3178.28, "word": " تكون", "probability": 0.9853515625}, {"start": 3178.28, "end": 3178.38, "word": " ال", "probability": 0.49609375}, {"start": 3178.38, "end": 3178.56, "word": " total", "probability": 0.74462890625}, {"start": 3178.56, "end": 3178.9, "word": " أقل", "probability": 0.5316569010416666}, {"start": 3178.9, "end": 3179.16, "word": " لازم", "probability": 0.9737955729166666}, {"start": 3179.16, "end": 3180.12, "word": " تكون", "probability": 0.6688232421875}, {"start": 3180.12, "end": 3181.2, "word": " بالظبط", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qbYlBzRs10_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qbYlBzRs10_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2e77b3904180d8fd23d9d6d409d629d4574400f7
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/-qbYlBzRs10_raw.srt
@@ -0,0 +1,1092 @@
+1
+00:00:21,530 --> 00:00:25,710
+بسم الله الرحمن الرحيم لازلنا في موضوع الـ
+
+2
+00:00:25,710 --> 00:00:29,410
+Integral domain اللي ابتدأناه قبل ذلك و اليوم
+
+3
+00:00:29,410 --> 00:00:33,930
+بنكمل على نفس الموضوع وصلنا المرة اللي فاتت إلى
+
+4
+00:00:33,930 --> 00:00:38,130
+النظرية اللي أمامنا اللي بنصفها كما يلي every
+
+5
+00:00:38,130 --> 00:00:44,070
+finite integral domain is a field يعني احنا بتكون
+
+6
+00:00:44,070 --> 00:00:48,930
+عندنا Integral domain وهذا ال Integral domain عدد
+
+7
+00:00:48,930 --> 00:00:55,520
+العناصر محدودإن حدث ذلك يبقى هذا الكلام يكون فيه
+
+8
+00:00:55,520 --> 00:00:59,900
+لأ طب الفرق بين ال integral و ال domain ال
+
+9
+00:00:59,900 --> 00:01:04,640
+integral domain و ال field شغلة واحدة كل واحد ميزه
+
+10
+00:01:04,640 --> 00:01:09,660
+ب ثلاث شغلات تنتين مشتركة فيما بينهما و هي
+
+11
+00:01:09,660 --> 00:01:14,280
+communicative ring with unity و الشغلة التالتة ان
+
+12
+00:01:14,280 --> 00:01:18,480
+ال integral domain مافيش فيه zero divisors لكن ال
+
+13
+00:01:18,480 --> 00:01:25,050
+fieldكل عنصر غير صفري يكون له معكوش يبقى every non
+
+14
+00:01:25,050 --> 00:01:29,950
+zero element is a unit أو has a multiplicative
+
+15
+00:01:29,950 --> 00:01:35,890
+inverse نعم كويس بنجي نفرض صحيك هذا اي كلام يبقى
+
+16
+00:01:35,890 --> 00:01:44,230
+بداجي اقول let L R تساوي و اي واحد و اتنى و لغاية
+
+17
+00:01:44,230 --> 00:01:57,320
+A N D Afinite field finite integral domain
+
+18
+00:01:57,320 --> 00:02:01,560
+with
+
+19
+00:02:01,560 --> 00:02:12,300
+ال a i لا تسوى a g for i لا تسوى g
+
+20
+00:02:18,860 --> 00:02:23,200
+يبدو ان افترض الارة اللي عناصر و اي واحد و اي
+
+21
+00:02:23,200 --> 00:02:28,060
+اتنين و اي ان finite integral domain يبدو هذا
+
+22
+00:02:28,060 --> 00:02:34,220
+integral domain عدد العناصر محدود و يساوي n من
+
+23
+00:02:34,220 --> 00:02:40,140
+العناصر تمام و ليش واحد فيهم زي التاني كان بإمكاني
+
+24
+00:02:40,140 --> 00:02:45,840
+أصيخة و أقول are with distinct elements يبقى عناصر
+
+25
+00:02:45,840 --> 00:02:51,540
+منفصلة عن بعضها تماما ولا عنصريساوي الثاني لأن لا
+
+26
+00:02:51,540 --> 00:02:57,420
+فرض R هي العلاصر ولا عنصر فيهم يساوي الثاني لكل I
+
+27
+00:02:57,420 --> 00:03:06,240
+لا تساوي G بتحاول أثبت أن هذه is a field طيب الآن
+
+28
+00:03:06,240 --> 00:03:18,020
+ال R is ال R is commutative ring
+
+29
+00:03:19,630 --> 00:03:26,750
+with unity واحد
+
+30
+00:03:26,750 --> 00:03:37,370
+مثل يبقى one three افترض ان ال unity اعتبرنا هو
+
+31
+00:03:37,370 --> 00:03:44,410
+الواحد ايش ضايل علينا نثبر ان كل عنصر من هذا غير
+
+32
+00:03:44,410 --> 00:03:50,700
+صفر يكون united يبقى فتاليا اقول افترضإن الـ A
+
+33
+00:03:50,700 --> 00:04:01,420
+موجود في الـ ring R بحيث أن الـ A لا يقل لـ 0 يبقى
+
+34
+00:04:01,420 --> 00:04:06,960
+الـ A عنصر غير صفري موجود في الـ R يبقى الـ A هذا
+
+35
+00:04:06,960 --> 00:04:12,620
+قد يكون الـ A1 وقد يكون الـ A2 وقد يكون الـ A3 وقد
+
+36
+00:04:12,620 --> 00:04:19,210
+وقد يكون الـ A N يبقى أي عنصر من هذه العناصرالان
+
+37
+00:04:19,210 --> 00:04:28,790
+ده set اللي هي A في R ايش يعني؟ يعني بدي اضرب ال
+
+38
+00:04:28,790 --> 00:04:33,350
+element غير الصفري في ال set R يعني بدي اضربه في
+
+39
+00:04:33,350 --> 00:04:38,210
+كل عناصر من عناصر ال ring اللي عندنا يبقى بده يصير
+
+40
+00:04:38,210 --> 00:04:45,910
+A A1 و A A2 ونظل ماشينا غير A A N
+
+41
+00:04:49,960 --> 00:04:55,340
+طيب الست هذه صار فيها عناصر جديدة ممكن يتنين
+
+42
+00:04:55,340 --> 00:05:00,880
+يساويوا بعض؟ لأ لأ ربما لأ لأ ممكن يحصل ممكن يحصل
+
+43
+00:05:00,880 --> 00:05:06,720
+لكن انا ها ها بدي اثبت ان ولا واحد فيهم بدي يساوي
+
+44
+00:05:06,720 --> 00:05:11,400
+التاني يعني هدول كذلك are destined ولا واحد زي
+
+45
+00:05:11,400 --> 00:05:17,380
+التاني خالص نهائي يبقى باجي بقوله the set ar هاي
+
+46
+00:05:17,380 --> 00:05:26,680
+العناصر هذهhas distinct elements
+
+47
+00:05:26,680 --> 00:05:32,760
+because
+
+48
+00:05:32,760 --> 00:05:37,240
+أنا
+
+49
+00:05:37,240 --> 00:05:43,900
+أدعي الآن أن هذه العناصر ولا واحد زي التاني طبعاً
+
+50
+00:05:43,900 --> 00:05:48,400
+بدنا نشوف هل الادعاء هذا اللي أنا بقوله صحيهوالله
+
+51
+00:05:48,400 --> 00:05:59,300
+غير صحيح because if مثلا ال a في ال ai بده ساوي ال
+
+52
+00:05:59,300 --> 00:06:10,120
+a في ال aj والi لا تساوي الجي افترض ان اتنين منهم
+
+53
+00:06:10,120 --> 00:06:15,620
+كان متساويين مين مايكون i ومين مايكون j بس من
+
+54
+00:06:15,620 --> 00:06:21,750
+همالهم مايتساووشافترضت ان اثنين متساوين لمين لل I
+
+55
+00:06:21,750 --> 00:06:27,250
+لا يساوي ال J. بتشوف هذا الفرض لوين بده يوصلني.
+
+56
+00:06:27,890 --> 00:06:32,670
+إذا وصلني إلى نتيجة صحيحة بيكون كلامي هذا باطل.
+
+57
+00:06:33,050 --> 00:06:39,650
+وإذا وصلني إلى نتيجة خاطئة بصير كلامي هذا بصير هذا
+
+58
+00:06:39,650 --> 00:06:44,070
+كلامي صحيح. لأن هدول دسن ولا واحد زي التاني. الا
+
+59
+00:06:44,070 --> 00:06:48,800
+افترضت ان اثنين سوا بعض.على عكس ما نجيه الفوق بدي
+
+60
+00:06:48,800 --> 00:06:55,420
+أشوف هذا وين بدي أوصيك يبقى ذنب بقدر أقول ال a في
+
+61
+00:06:55,420 --> 00:07:02,420
+ال a i نقص ال a في ال a j بده ساوي زير باستخدام ال
+
+62
+00:07:02,420 --> 00:07:09,000
+distributive law بقدر أقول هذا الكلام a في ال a i
+
+63
+00:07:09,000 --> 00:07:15,120
+نقص ال a j بده ساوي مين؟ بده ساوي زيره هذا أيش
+
+64
+00:07:15,120 --> 00:07:23,970
+معناه؟هذا معناه ان ال a بده يساوي zero او ال ai
+
+65
+00:07:23,970 --> 00:07:30,970
+ناقص ال aj بده يساوي zero لكن انا فارغ ان ال a لن
+
+66
+00:07:30,970 --> 00:07:38,250
+يساوي zero يبقى هنا بعدين بقوله since بما ان ال a
+
+67
+00:07:38,250 --> 00:07:49,210
+لا يساوي zero we have ان ال aiالـ AI ناقص ال AJ هو
+
+68
+00:07:49,210 --> 00:07:56,230
+اللي بده يسوى Z هذا إيش معناه؟ معناه إن ال AI بده
+
+69
+00:07:56,230 --> 00:08:03,030
+يسوى مين؟ AJ على عكس الكلام أحنا فرضينه من الأساس
+
+70
+00:08:03,030 --> 00:08:12,150
+يبقى هذا this is contradiction هذا تناقض
+
+71
+00:08:15,900 --> 00:08:20,680
+يناقض مين؟ يناقض العبارة اللي قلناها هذه ان ال AI
+
+72
+00:08:20,680 --> 00:08:26,200
+لا يسوى ال AJ فلعلنا ال AI يسوى AJ، إذا هذا كلام
+
+73
+00:08:26,200 --> 00:08:32,240
+خطأ، من أين أجا الخطأ؟ من الفرض الخطأ اللي أنا
+
+74
+00:08:32,240 --> 00:08:37,440
+فرضته، يبقى فعلا هذول are distinct ولا واحد زي
+
+75
+00:08:37,440 --> 00:08:43,820
+التاني، يبقى هنا ال A
+
+76
+00:08:55,140 --> 00:09:02,320
+الـ A في الـ A1 والـ A في الـ A2 والـ A في الـ AN
+
+77
+00:09:02,320 --> 00:09:12,640
+are distinct يبقى ولا واحد فيهم زي التاني تمامطيب
+
+78
+00:09:12,640 --> 00:09:18,220
+كويس يبقى أخدنا معلومة أن هذه العناصر منفصلة عن
+
+79
+00:09:18,220 --> 00:09:25,220
+بعضها تماما مافيش تساوي بين أي عنصرية السؤال هو طب
+
+80
+00:09:25,220 --> 00:09:30,220
+هي ال R closed under multiplication ولا لا؟ لأن
+
+81
+00:09:30,220 --> 00:09:34,100
+عملية الطرق is a binary operational يبقى ال A في
+
+82
+00:09:34,100 --> 00:09:40,240
+ال A وعناصر موجود where؟ في ال ring A و ال A في ال
+
+83
+00:09:40,240 --> 00:09:40,780
+A2
+
+84
+00:09:47,270 --> 00:09:58,410
+يبقى بالي بقوله since بما ان ال R is closed under
+
+85
+00:09:58,410 --> 00:10:01,490
+multiplication
+
+86
+00:10:13,450 --> 00:10:20,470
+إن الار العناصر هذه كلها اي اي اي اي اي اي اي اي
+
+87
+00:10:20,470 --> 00:10:23,290
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+88
+00:10:23,290 --> 00:10:24,210
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+89
+00:10:24,210 --> 00:10:26,490
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+90
+00:10:26,490 --> 00:10:26,670
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+91
+00:10:26,670 --> 00:10:33,630
+اي اي اي اي
+
+92
+00:10:33,630 --> 00:10:33,630
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+93
+00:10:33,630 --> 00:10:41,990
+اي اي اي اي اي اي اي اي اي
+
+94
+00:10:41,990 --> 00:10:48,300
+ابدأ مع نصر رنج احنا هنا قلنا ال R integral domain
+
+95
+00:10:48,300 --> 00:10:52,280
+ال integral domain يحتاج ولا ال unity ولا لا يبقى
+
+96
+00:10:52,280 --> 00:10:57,980
+معناته واحد فيهم بده يساوي ال unity صح ولا لا يبقى
+
+97
+00:10:57,980 --> 00:11:08,040
+ماجي بقوله نعم الواحد موجود في R because ال R is
+
+98
+00:11:08,040 --> 00:11:10,440
+an integral
+
+99
+00:11:13,890 --> 00:11:19,630
+domain يبقى الواحد لازم يساوي طبعا اللي هو ال
+
+100
+00:11:19,630 --> 00:11:25,430
+unity الواحد هذا لازم يساوي واحد من هذه العناصر
+
+101
+00:11:25,430 --> 00:11:32,250
+يبقى هذا بدي يعطيك ان ال a في ال a كمثلا بدي أساوي
+
+102
+00:11:32,250 --> 00:11:40,470
+اللي هي ال unity one إيش تفسيرك لهذا الكلام؟ان ال
+
+103
+00:11:40,470 --> 00:11:46,930
+a is a unit صح لان ماخد ال a بسويش ال zero صح يبقى
+
+104
+00:11:46,930 --> 00:11:59,250
+this means that هذا يعني ان ال a is a unit يبقى
+
+105
+00:11:59,250 --> 00:12:07,250
+every non zero element is a unit يبقى هنا سا every
+
+106
+00:12:08,610 --> 00:12:18,790
+non-zero element element
+
+107
+00:12:18,790 --> 00:12:28,430
+of R is a unit therefore
+
+108
+00:12:28,430 --> 00:12:32,950
+ولهذا
+
+109
+00:12:32,950 --> 00:12:37,710
+الـ R is a field
+
+110
+00:12:48,980 --> 00:12:57,280
+السؤال بدعمل العكس هل ال field integral domain؟ هل
+
+111
+00:12:57,280 --> 00:13:03,440
+كل field يكون integral domain عملية العكسية؟
+
+112
+00:13:03,440 --> 00:13:09,640
+السؤال هو ال field في zero divisor؟ لأ لأن كل أنصر
+
+113
+00:13:09,640 --> 00:13:14,380
+عبارة عن unitصح ولا لا؟ مدين كل أنصار من يبقى لا
+
+114
+00:13:14,380 --> 00:13:19,820
+يمكن لل unit أن يكون zero divisor يعني مش فيها
+
+115
+00:13:19,820 --> 00:13:24,000
+zero divisor، بيبقى ايش صارت؟ Integral domain يبقى
+
+116
+00:13:24,000 --> 00:13:29,020
+any field is an integral domain لكن العكس ليس
+
+117
+00:13:29,020 --> 00:13:35,640
+بالضرورة صحيحا يعني مش كل integral domain هو field
+
+118
+00:13:36,430 --> 00:13:42,590
+لكن إذا كان الـ Integral domain finite حسب نص
+
+119
+00:13:42,590 --> 00:13:48,030
+النظرية بيكون هو field تمام؟ يبقى الـ Integral
+
+120
+00:13:48,030 --> 00:13:52,650
+domain لازم أحط عليه شرط مشان يصير field لكن ال
+
+121
+00:13:52,650 --> 00:13:57,310
+field بحطش عليه ولا شرط مشان يصير Integral domain
+
+122
+00:13:57,310 --> 00:14:06,840
+طيب ننتقل الآن إلى نتيجة على هذه النظريةالان
+
+123
+00:14:06,840 --> 00:14:11,820
+كرولري الكرولري
+
+124
+00:14:11,820 --> 00:14:21,080
+بتقول معناته for every prime P for every prime P
+
+125
+00:14:21,080 --> 00:14:33,240
+ال ZP ال ZP اللي هي the range of integers
+
+126
+00:14:34,820 --> 00:14:50,100
+موديولو P موديولو P ال P شوفناها
+
+127
+00:14:50,100 --> 00:14:54,160
+قبل ما كتبناها في المحاضرة الماضية و إيش قلنا
+
+128
+00:14:54,160 --> 00:15:00,660
+عليها Integral domain صح ولا لأ يبقى هنا بقولوا we
+
+129
+00:15:00,660 --> 00:15:14,870
+know thatاحنا بنعرف ان ZP is an integral domain من
+
+130
+00:15:14,870 --> 00:15:21,150
+وين هذا الكلام مثال سابق هي بيصف example في
+
+131
+00:15:21,150 --> 00:15:27,010
+المحاضرة السابقة مش بعيد يعني تمام؟ يبقى هذا
+
+132
+00:15:27,010 --> 00:15:33,030
+integral domain السؤال هو finite ولا لأ؟قداش عدد
+
+133
+00:15:33,030 --> 00:15:41,810
+العناصر في ايه؟ كداش؟ في ناقص واحد العنصر الأخير
+
+134
+00:15:41,810 --> 00:15:47,330
+فيه ناقص واحد لكن أول عنصر كداش؟ Zero إذا عدد
+
+135
+00:15:47,330 --> 00:15:54,050
+العناصر فيه يبقى الـLZP
+
+136
+00:15:54,050 --> 00:16:01,370
+has finite elements
+
+137
+00:16:05,520 --> 00:16:11,020
+that is P
+
+138
+00:16:11,020 --> 00:16:19,400
+elements يبقى P من العناصر يعني it is P finite
+
+139
+00:16:19,400 --> 00:16:33,480
+يبقى by the by the above theorem بالنظرية
+
+140
+00:16:33,480 --> 00:16:42,840
+السابقةZP is AP فلو
+
+141
+00:16:42,840 --> 00:16:49,860
+جيبتك سؤال في الامتحان و قولتك اثبتيلي ان ZP is AP
+
+142
+00:16:49,860 --> 00:16:57,180
+بتقدرش تثبتيلي اولا انه integral domain تمام اللي
+
+143
+00:16:57,180 --> 00:17:00,800
+هو القرآن تبع المرأة الماضية و اضيف عليه الكلمتين
+
+144
+00:17:00,800 --> 00:17:28,870
+هدولإنه finite وبالتالي بصير as a field طيب
+
+145
+00:17:28,870 --> 00:17:29,770
+example
+
+146
+00:17:37,820 --> 00:17:49,240
+زي التلاتة on I اللي هي على الصيرة كل العناصر A
+
+147
+00:17:49,240 --> 00:18:02,620
+زائد B في I such that ال A و ال B belongs to D3 من
+
+148
+00:18:02,620 --> 00:18:08,990
+العناصر هذه اللي هي تساويالـ zero والواحد والاتنين
+
+149
+00:18:08,990 --> 00:18:16,890
+وال I والواحد زائد I والاتنين زائد I والاتنين I
+
+150
+00:18:16,890 --> 00:18:27,050
+وواحد زائد اتنين I والاتنين زائد اتنين I is a
+
+151
+00:18:27,050 --> 00:18:27,490
+field
+
+152
+00:18:39,650 --> 00:18:43,590
+الـ Z3 of I طبعا الـ Z3 همين العلاصة اللي ربنا
+
+153
+00:18:43,590 --> 00:18:48,990
+ناقصها؟ Zero واحد و اتنين فقط لغير ثلاثة علاصة
+
+154
+00:18:48,990 --> 00:18:55,290
+العلاصة بتبقى Z of I على صيغة إيه زي الـ Bi في حد
+
+155
+00:18:55,290 --> 00:19:00,830
+الـ A والـ B موجودة في Z3 يعني الـ A والـ B يا إما
+
+156
+00:19:00,830 --> 00:19:05,970
+Zero يا إما واحد يا إما اتنين ما خلال ذلك مانيش
+
+157
+00:19:05,970 --> 00:19:10,670
+علاقة فيه تمام؟طيب هذه لو جيت ادور على عناصرها
+
+158
+00:19:10,670 --> 00:19:15,730
+بلاقي zero واحد و اتنين بلاقي I واحد زايد I اتنين
+
+159
+00:19:15,730 --> 00:19:21,810
+زايد I stop بتروحلى الاتنين I واحد زايد اتنين I و
+
+160
+00:19:21,810 --> 00:19:27,450
+اتنين زايد اتنين I خلصنا هى العناصر عديهم بتلاقيهم
+
+161
+00:19:27,450 --> 00:19:33,750
+هاش تسعة عناصر يجي هذا ring فيهاش الا تسعة عناصر
+
+162
+00:19:33,750 --> 00:19:42,710
+طبعا هذه commutative ringwith unity من هنا one
+
+163
+00:19:42,710 --> 00:19:54,830
+يبقى هذه because Z of تلاتة I is a commutative
+
+164
+00:19:54,830 --> 00:19:58,130
+ring
+
+165
+00:19:58,130 --> 00:20:09,710
+with unity اللي همينالواحد اللى بيساوي واحد زائد
+
+166
+00:20:09,710 --> 00:20:18,210
+زيرو في I اللى موجود في Z تلاتة او I يبقى واحد هو
+
+167
+00:20:18,210 --> 00:20:22,630
+ال unity هذا موجود في Z تلاتة لإن ابتدى الاقتبال
+
+168
+00:20:22,630 --> 00:20:27,150
+على الصيغة واحد زائد زيرو في I والواحد والزيرو
+
+169
+00:20:27,150 --> 00:20:33,410
+موجود في Z تلاتة هذا كلام مظبوط ضليش عندي اثبت انه
+
+170
+00:20:33,410 --> 00:20:37,900
+مافيهاش Zero divisorsيبقى ايه بعدي عن ال zero
+
+171
+00:20:37,900 --> 00:20:43,820
+تعالى لباقي التامة العناصر هل ممكن تظهر بأي اتنين
+
+172
+00:20:43,820 --> 00:20:52,620
+فيهم يطلع zero لأن كل واحد فيهم عبارة عن unit تمام
+
+173
+00:20:52,620 --> 00:21:04,400
+يبقى this ring has no zero divisors
+
+174
+00:21:06,840 --> 00:21:11,840
+مافيش عندى بالماضى كل أنصر عبارة عن ايش عبارة عن
+
+175
+00:21:11,840 --> 00:21:17,600
+unit طيب مابنامفش فيها zero divider لانه لايمكن
+
+176
+00:21:17,600 --> 00:21:23,620
+اضرب أنصرين غير صفرين ابدا عن zero خدي اي اتنين
+
+177
+00:21:23,620 --> 00:21:28,620
+وضربهم لايمكن يطلع صفر ديبجى this ring has no zero
+
+178
+00:21:28,620 --> 00:21:41,940
+divisor سزد تلاتة of Iis a finite finite integral
+
+179
+00:21:41,940 --> 00:21:46,340
+domain ليش
+
+180
+00:21:46,340 --> 00:21:52,860
+ان فيه كام عنصر تسعة عناصر تسعة عناصر يبقى finite
+
+181
+00:21:52,860 --> 00:22:00,140
+وintegral domain يبقى is AP يبقى هذا بتيعطينا ان Z
+
+182
+00:22:00,140 --> 00:22:03,000
+تلاتة of I
+
+183
+00:22:10,660 --> 00:22:18,740
+مشان يكون فيل كل عنصر بد يكون unit صح؟ فلينا نتاكد
+
+184
+00:22:18,740 --> 00:22:25,660
+هل فعلا كل عنصر عبارة عن unit هيسبنا zero الواحد
+
+185
+00:22:25,660 --> 00:22:33,100
+لو ضربت في واحد واحد is a unitإتنين لو ضربته في
+
+186
+00:22:33,100 --> 00:22:37,980
+اتنين يطلع أربعة في زي التلاتة بسيب تلاتة بيبقى
+
+187
+00:22:37,980 --> 00:22:44,820
+الجداش يبقى اتنين is a unit تمام نيجي لل I و اتنين
+
+188
+00:22:44,820 --> 00:22:51,600
+I العنصر هذا مع العنصر هذا لو ضربنهم في بعض بيصير
+
+189
+00:22:51,600 --> 00:22:58,760
+I كده اضبه في اتنين I يبقى اتنين في سالب واحد اللي
+
+190
+00:22:58,760 --> 00:23:04,670
+هو سالب اتنينماعنديش شريك Z3 سالب اتنين لكن سالب
+
+191
+00:23:04,670 --> 00:23:11,390
+اتنين يكافئ عمصر موجود في Z3 مين هو هذا العمصر
+
+192
+00:23:11,390 --> 00:23:18,030
+يبقى سالب اتنين زائد تلاتة لما اضيف تلاتة ومضاعفة
+
+193
+00:23:18,030 --> 00:23:23,210
+تلاتة تؤثر على العمصر يبقى مين بيطلع ال unity اللي
+
+194
+00:23:23,210 --> 00:23:29,200
+هو الواحد يبقى اتحاصر ضرب الاتنين سوا ال unityيبقى
+
+195
+00:23:29,200 --> 00:23:36,460
+هذا يخلّي ان ال I و 2 I are units يبقى هذا يخلّي
+
+196
+00:23:36,460 --> 00:23:46,960
+ان ال I و 2 I are units طيب لو مسكت ضرب تمين ضربت
+
+197
+00:23:46,960 --> 00:23:54,580
+ال واحد زائد I تمين في ال اتنين زائد ال I نشوف ايش
+
+198
+00:23:54,580 --> 00:24:01,560
+بيعطيه واحد في اتنين باتنينوحد في I ب I I في اتنين
+
+199
+00:24:01,560 --> 00:24:10,160
+ب اتنين I I في I بسالب واحد تمام سالب واحد واتنين
+
+200
+00:24:10,160 --> 00:24:17,060
+يصير واحد زائد تلاتة I تلاتة I يبقى دياشر Zero
+
+201
+00:24:17,060 --> 00:24:22,740
+يبقى الجواب يساوي واحد يبقى حاصل ضربهم يساوي واحد
+
+202
+00:24:22,740 --> 00:24:28,260
+يبقى اتنين هدول are units يبقى هدف يعطينا مينإن
+
+203
+00:24:28,260 --> 00:24:38,840
+الواحد زائد I وكذلك الاتنين زائد I are units أظن
+
+204
+00:24:38,840 --> 00:24:43,380
+مش لا ألغى الأخر اتنين كلهم
+
+205
+00:24:43,380 --> 00:24:48,000
+ضربناهم ما عدا مين ما عدا أخر اتنين يبقى لو جيت
+
+206
+00:24:48,000 --> 00:24:56,240
+هنا and رحت أخد واحد زائد اتنين I في مينفى اتنين
+
+207
+00:24:56,240 --> 00:25:03,360
+زائد اتنين I ويسار واحد فى اتنين باتنين زائد اتنين
+
+208
+00:25:03,360 --> 00:25:16,260
+I زائد اربعة I زائد اربعة I ناقص اربعة تمام ؟ طيب
+
+209
+00:25:16,260 --> 00:25:23,160
+هذا الكلام ناقص اربعة و اتنين بيظل ناقص اتنين و
+
+210
+00:25:23,160 --> 00:25:31,210
+هدول كدهشزائد ستة I التلاتة ب zero يبقى الستة كمان
+
+211
+00:25:31,210 --> 00:25:37,330
+ب zero يبقى ناتج يسوى نقص اتنين زائد تلاتة اللي هو
+
+212
+00:25:37,330 --> 00:25:42,570
+الواحد اللي هو ال unity يبقى هنا سواء واحد زائد
+
+213
+00:25:42,570 --> 00:25:53,330
+اتنين I وكذلك اتنين زائد اتنين I هدول are units
+
+214
+00:25:54,840 --> 00:26:02,700
+يبقى صار every non zero element في zi unit يبقى
+
+215
+00:26:02,700 --> 00:26:10,360
+thus و هكذا every every
+
+216
+00:26:10,360 --> 00:26:21,800
+non zero element in z3
+
+217
+00:26:21,800 --> 00:26:34,480
+of iis YOLO لذلك هذا field كما زعمنا قبل قليل طبعا
+
+218
+00:26:34,480 --> 00:26:39,960
+في الكتاب عندك راح عامل جدولة ضرب لكل العناصر
+
+219
+00:26:39,960 --> 00:26:45,320
+التسعة اللي عندك بمجالك تطلع إلى جدولة ضرب في
+
+220
+00:26:45,320 --> 00:26:51,300
+الكتاب حصل ضرب هذه العناصر مع بعضها البعض
+
+221
+00:26:56,370 --> 00:27:03,670
+طيب هذا كان مثال رقم واحد نروح لمثال رقم اتنين for
+
+222
+00:27:03,670 --> 00:27:07,830
+example اتنين
+
+223
+00:27:07,830 --> 00:27:14,670
+هذا ست اللي
+
+224
+00:27:14,670 --> 00:27:23,300
+هو Q جذر اتنين شكل يعني هذااللي هو كل العناصر اللي
+
+225
+00:27:23,300 --> 00:27:29,840
+ع صيغة a زائد b جدري اتنين بحيث ال a و ال b are
+
+226
+00:27:29,840 --> 00:27:44,520
+rational number هذه is a commutative ring with
+
+227
+00:27:44,520 --> 00:27:46,460
+unity
+
+228
+00:27:52,880 --> 00:27:59,200
+One، معقول؟ أه، هذه الكميوتة تبقى with unity one
+
+229
+00:27:59,200 --> 00:28:06,820
+لغة ساوية واحد زائد زيرو في جذري اتنين، يبقى هذا
+
+230
+00:28:06,820 --> 00:28:10,940
+هو ال unity في الست اللي عندنا هذا، وهذه الكميوتة
+
+231
+00:28:10,940 --> 00:28:14,820
+تبقى لإنها عملية ضرب ال rational number لعملية
+
+232
+00:28:14,820 --> 00:28:21,480
+إبداعية، يقول ماعنا مشكلة فيها، مش ضايلة لها.فيها
+
+233
+00:28:21,480 --> 00:28:28,540
+Zero Divisors؟ مش فيها Zero Divisors بالمرة لإنه
+
+234
+00:28:28,540 --> 00:28:34,200
+any two rational number لايمكن انه يعطينا Zero
+
+235
+00:28:34,200 --> 00:28:39,660
+بشرط ان ولا واحد فيهم يسوي Zero تمام؟ إذا ماعنديش
+
+236
+00:28:39,660 --> 00:28:46,740
+rational number ماعنديش units فيها، ماعنديش Zero
+
+237
+00:28:46,740 --> 00:28:51,310
+Divisors جدًا، بقيت اتنينIs it finite ولا
+
+238
+00:28:51,310 --> 00:28:56,870
+infinite؟ Infinite يبقى هذا السؤال مش على النظرية،
+
+239
+00:28:56,870 --> 00:29:04,090
+هذا السؤال يعتبر سؤال خارجي. يبقى أنا أدعي انه هذا
+
+240
+00:29:04,090 --> 00:29:09,230
+الآن is ايه فيه. يبقى النظرية صحيه عشان شجع ان ال
+
+241
+00:29:09,230 --> 00:29:14,270
+computer can ring with unity. تمام؟ أظل أثبت والله
+
+242
+00:29:14,270 --> 00:29:19,820
+إذا كان كل عنصرالو معكوز تحت عملية الضرر يعني
+
+243
+00:29:19,820 --> 00:29:24,400
+multiplicative inverse بتبني المفروض بصي ان ادي
+
+244
+00:29:24,400 --> 00:29:32,000
+اسم ايه فيه تمام؟ بقدر اروح اقوله I want to show
+
+245
+00:29:32,000 --> 00:29:35,400
+ان
+
+246
+00:29:35,400 --> 00:29:50,140
+الروح انبين ذات انه any none zero element ofEq of
+
+247
+00:29:50,140 --> 00:30:01,460
+جدر اتنين has a multiplicative
+
+248
+00:30:01,460 --> 00:30:06,520
+inverse.بدأت
+
+249
+00:30:06,520 --> 00:30:14,260
+انه اي عنصر غير صحي له معكس.لذلك بعدين بقوله افترض
+
+250
+00:30:14,260 --> 00:30:25,810
+ان ال a زائد bجادر اتنين لا يساوي Z بروح
+
+251
+00:30:25,810 --> 00:30:31,010
+بقول Z multiplicative
+
+252
+00:30:31,010 --> 00:30:35,710
+inverse
+
+253
+00:30:35,710 --> 00:30:47,820
+of ال A زائد B جادر اتنين is من ذاك الرقماللي لو
+
+254
+00:30:47,820 --> 00:30:52,200
+ضربته في هذا العنصر بدي أعطيه ال unity اللي هو
+
+255
+00:30:52,200 --> 00:31:01,800
+واحد مين؟ واحد على هذا المقدار تمام؟ واحد على إيه
+
+256
+00:31:01,800 --> 00:31:08,780
+لقيت بيه جذر إتنى السؤال هل العنصر هذا موجود في ال
+
+257
+00:31:08,780 --> 00:31:15,940
+IQ جذر إتنى؟ يعني هذا العنصر هل مكتوب على صيغة
+
+258
+00:31:15,940 --> 00:31:21,810
+constantزائد كنستان في جدرتنا؟ لأ مش مكتوب
+
+259
+00:31:21,810 --> 00:31:30,090
+وبالتالي يمكن نقدر نقتله ويمكن مايمكنش إذا قدرنا
+
+260
+00:31:30,090 --> 00:31:33,970
+نقتله بصير كلامنا صحيح وخلصنا من المسألة إذا
+
+261
+00:31:33,970 --> 00:31:38,890
+ماقدرناش بصير إدعائنا هذا غير صحيح بصير هذا معكس
+
+262
+00:31:38,890 --> 00:31:42,230
+لكن هذا القلم اللي جبته من الشارع أنا ماجبتوش من
+
+263
+00:31:42,230 --> 00:31:48,800
+ال ring اللي عندي تمام؟ يبقىإذا جدرت أثبت إن هذا
+
+264
+00:31:48,800 --> 00:31:54,040
+على الصيغة constant زائد constant في جذر اتنين
+
+265
+00:31:54,040 --> 00:31:59,000
+بصير موجود في الـQ فعلاً يكون هذا هو المعقول لذلك
+
+266
+00:31:59,000 --> 00:32:03,640
+إذا قُلت ضبطت في ذكرة إن غصوب ال element هذا هو ال
+
+267
+00:32:03,640 --> 00:32:12,700
+element هذا لأيش؟ هو هذا أنا أدعي أنه موجود في
+
+268
+00:32:12,700 --> 00:32:27,150
+الـQ ofof جذر اتنين cents ليش؟ لأن واحد على ا زائد
+
+269
+00:32:27,150 --> 00:32:33,970
+بيه جذر اتنين بده يساوي واحد على ا زائد بيه جذر
+
+270
+00:32:33,970 --> 00:32:40,950
+اتنين لو ضربته في مرافق المقام فبصير عند مين ايه
+
+271
+00:32:40,950 --> 00:32:48,090
+ناقص بيه جذر اتنينعلى إيه ناقص بيه جذري اتنين بهذا
+
+272
+00:32:48,090 --> 00:32:54,130
+الشكل المقام مش هو تحليل الفرق بين المراد عين بدي
+
+273
+00:32:54,130 --> 00:32:58,730
+أرجعه إلى أصله يبقى رجعناه إلى أصله بيصير
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/3RMuJHLrdR0.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/3RMuJHLrdR0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d4acc2d504cd16ee6773f8332f80ba62d66b9d33
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/3RMuJHLrdR0.srt
@@ -0,0 +1,1357 @@
+1
+00:00:21,800 --> 00:00:26,060
+بسم الله الرحمن الرحيم، نكمل ما ابتدأناه في
+
+2
+00:00:26,060 --> 00:00:31,260
+المحاضرات السابقة، وهو chapter 15. عندنا تعريف
+
+3
+00:00:31,260 --> 00:00:35,940
+وعندنا آخر نظرية في هذا الـ chapter. نتفضل اليوم إن
+
+4
+00:00:35,940 --> 00:00:43,400
+شاء الله، ثم نبدأ بحل بعض التمارين. عندي تعريف طبعًا
+
+5
+00:00:43,400 --> 00:00:48,480
+مش موجود عندك تعريف، لكن محطوط في ثانية عدة قصيرة.
+
+6
+00:00:48,480 --> 00:00:54,190
+فإحنا سحبناه وحطيناه. التعريف بيقول little f is a field
+
+7
+00:00:54,190 --> 00:01:00,390
+in the intersection of all subfields of F is a
+
+8
+00:01:00,390 --> 00:01:04,570
+subfield. بسميه الـ prime subfield من الـ field
+
+9
+00:01:04,570 --> 00:01:10,770
+الأصلي F. يبقى إحنا عندنا field F، جبنا كل الـ sub
+
+10
+00:01:10,770 --> 00:01:16,370
+fields من هذا الـ field الأصلي، عملنا لهم intersection
+
+11
+00:01:16,370 --> 00:01:21,700
+(تقاطع)، اللي عليه شيء إن شاء الله يكون العنصر الـ
+
+12
+00:01:21,700 --> 00:01:25,680
+unity أو الصفري. ما علينا، المهم جبنا الـ
+
+13
+00:01:25,680 --> 00:01:29,820
+intersection. الـ intersection هذا بيكون subfield.
+
+14
+00:01:29,820 --> 00:01:35,720
+بدنا نسميه الـ prime subfield من الـ field الأصلي.
+
+15
+00:01:35,720 --> 00:01:40,480
+ما علينا، مش ده مهمية كتيرة الآن. بدنا نروح لآخر
+
+16
+00:01:40,480 --> 00:01:44,960
+نظرية. النص بتاعها، النص بيقول little d by an
+
+17
+00:01:44,960 --> 00:01:51,430
+integral domain, then there exist a field F. شو شكله؟
+
+18
+00:01:51,430 --> 00:01:57,090
+مش عارفين حتى اللحظة. بسميه الـ quotient field أو الـ
+
+19
+00:01:57,090 --> 00:02:01,770
+field of quotients على الـ integral domain دي. that
+
+20
+00:02:01,770 --> 00:02:07,630
+contains. هذا الـ field بدي يحتوي على الـ subring. شو
+
+21
+00:02:07,630 --> 00:02:12,290
+شكلها؟ حتى الآن مش عارف. وهذا الـ subring تكون
+
+22
+00:02:12,290 --> 00:02:19,240
+isomorphic لمين؟ إلى دي. يبقى الفرعان كالتالي، طبعًا زي
+
+23
+00:02:19,240 --> 00:02:24,300
+ما أنتم شايفين نص النظرية فيه غموض كبير، لكن إن شاء
+
+24
+00:02:24,300 --> 00:02:30,180
+الله سنكشف هذا الغموض بكل سهولة ويسر. يبقى بدي
+
+25
+00:02:30,180 --> 00:02:41,180
+أبدأ أقول له: let D be an integral domain، اللي هو ما
+
+26
+00:02:41,180 --> 00:02:47,900
+أعطيناه في رأس النظرية. بعدين بدي أقول له: let S be
+
+27
+00:02:47,900 --> 00:02:53,440
+عبارة عن الـ set اللي على الشكل: عناصرها A على B
+
+28
+00:02:53,440 --> 00:02:59,560
+بحيث A وB بدي أجيبهم من الـ integral domain D، وفي
+
+29
+00:02:59,560 --> 00:03:06,280
+نفس الوقت الـ B ممنوع يتساوي zero، لأن العناصر بيصير
+
+30
+00:03:06,280 --> 00:03:15,350
+مالهاش غير معرفة. طيب، بدي أجي أقول له: define A and
+
+31
+00:03:15,350 --> 00:03:18,610
+equivalence
+
+32
+00:03:18,610 --> 00:03:28,230
+relation. relation.
+
+33
+00:03:28,230 --> 00:03:40,770
+أديها الرمز بتاع التكافؤ on S by: الـ A على B is
+
+34
+00:03:40,770 --> 00:03:51,890
+equivalent to الـ C على D إذا كان الـ A على B يساوي الـ C على D، أو الـ AD يساوي الـ BC. يعني ممكن أكتبها
+
+35
+00:03:51,890 --> 00:03:59,950
+بهذه الصياغة، وممكن أقول AD يساوي BC. هذه
+
+36
+00:03:59,950 --> 00:04:06,850
+الصياغة، وهذه الصياغة الاثنين are the same. طيب إحنا
+
+37
+00:04:06,850 --> 00:04:13,160
+عملنا relation equivalence. السؤال هو بس مجرد
+
+38
+00:04:13,160 --> 00:04:17,300
+سؤال جانبي: شو يعني equivalence relation؟ من مقدرة
+
+39
+00:04:17,300 --> 00:04:23,320
+رياضيات؟ أيوة، relation تحقق ثلاثة شروط. أيوة،
+
+40
+00:04:28,460 --> 00:04:32,300
+symmetric وtransitive
+
+41
+00:04:32,300 --> 00:04:37,000
+وreflexive.
+
+42
+00:04:37,000 --> 00:04:44,240
+يبقى relation R بقول عنها symmetric وtransitive
+
+43
+00:04:44,240 --> 00:04:49,740
+وreflexive. انتحققت الأمور الثلاثة هذه، بقول هذه
+
+44
+00:04:49,740 --> 00:04:53,940
+equivalence relation. طب إيش معناه من ناحية الرياضيات؟
+
+45
+00:04:53,940 --> 00:04:58,280
+هذا كلام بلدي، كلام عربي. تمام، لما أقول relation
+
+46
+00:04:58,280 --> 00:05:04,000
+reflexive، يعني كل عنصر مرتبط مع نفسه. الـ a are
+
+47
+00:05:04,000 --> 00:05:09,440
+related with a، أو الـ a is related with a. الآن
+
+48
+00:05:09,440 --> 00:05:15,440
+symmetric، إذا كان الـ A related with B، then B are
+
+49
+00:05:15,440 --> 00:05:20,040
+related with A. حالة transitive، لو كان الـ A
+
+50
+00:05:20,040 --> 00:05:23,720
+related with B، وB related with C، يبقى الـ A
+
+51
+00:05:23,720 --> 00:05:28,100
+related with مين؟ الـ C. هذا معنى اللي هو
+
+52
+00:05:28,100 --> 00:05:34,400
+الـ reflexive. هذا معنى الـ equivalence relation. طيب
+
+53
+00:05:34,400 --> 00:05:38,080
+كويس، الـ equivalence relation إيش بتعمل على
+
+54
+00:05:38,080 --> 00:05:45,020
+الـ set؟ ماذا بتقسمها لإيش يعني؟ Partition. ماذا
+
+55
+00:05:45,020 --> 00:05:52,040
+بيسميهم؟ equivalence classes. مش كنت... والله نسيته.
+
+56
+00:05:52,040 --> 00:05:57,460
+principles of mathematics. مبادئ الرياضيات. يبقى الـ
+
+57
+00:05:57,460 --> 00:06:01,620
+relations. أخذنا الـ relations والـ functions. كل ما
+
+58
+00:06:01,620 --> 00:06:07,080
+أخذناهم في مبادئ الرياضيات، اللي هو الأساس لباقي
+
+59
+00:06:07,080 --> 00:06:12,220
+فروع الرياضيات. وبنعتبر اللي بينجح فيها بجدارة بيصير
+
+60
+00:06:12,220 --> 00:06:17,860
+سهل عليه يدرس الرياضيات، لأن كل الرياضيات مركبة على
+
+61
+00:06:17,860 --> 00:06:24,260
+مبادئ الرياضيات. طيب عرفنا relation على S بالطريقة
+
+62
+00:06:24,260 --> 00:06:32,800
+اللي وراها دي. الآن بدي أجي أقول له: افترض F is
+
+63
+00:06:32,800 --> 00:06:36,200
+the set of all
+
+65
+00:06:40,870 --> 00:06:50,270
+equivalence classes of الـ relation اللي عندنا على
+
+66
+00:06:50,270 --> 00:06:54,670
+الـ S. يبقى
+
+67
+00:06:54,670 --> 00:07:01,250
+أنا عندي F هنا. قلنا that there exists a field F.
+
+68
+00:07:01,250 --> 00:07:06,990
+بسميه field of quotients. شو شكله؟ ما عرفتش، لكن أنا جيت
+
+69
+00:07:06,990 --> 00:07:11,870
+أخذت الـ F والـ S، وأقول equivalence classes. إذا جيت
+
+70
+00:07:11,870 --> 00:07:17,430
+أثبت إنه هذه field، يبقى تحقق الكلام اللي أنا بقوله.
+
+71
+00:07:17,430 --> 00:07:21,870
+هنا there exists a field of quotients أو quotient
+
+72
+00:07:21,870 --> 00:07:27,470
+field. كويس، يبقى أنا حتى الآن قلت S وما قلتش شو
+
+73
+00:07:27,470 --> 00:07:33,170
+العمليات اللي عليها، تمام؟ لأن إحنا الـ ring بنقول
+
+74
+00:07:33,170 --> 00:07:39,540
+S وعليها two operations، حققت الست شروط، بقول عليها
+
+75
+00:07:39,540 --> 00:07:46,400
+ring. مظبوط. يبقى أنا عندي set سميتها F. شو العمليات
+
+76
+00:07:46,400 --> 00:07:51,020
+اللي عليها؟ بدي أروح أعرف العمليات اللي على هذه
+
+77
+00:07:51,020 --> 00:08:00,280
+الـ set. يبقى بدي أجي أقول له: define addition and
+
+78
+00:08:04,280 --> 00:08:11,520
+multiplication. and multiplication
+
+79
+00:08:11,520 --> 00:08:27,580
+on F by: الـ a على b زائد c على d بتساوي ad
+
+80
+00:08:27,580 --> 00:08:39,960
+زائد bc، كله على bd. والعملية الثانية اللي هو a
+
+81
+00:08:39,960 --> 00:08:56,420
+على b مضروبة في c على d بتساوي ac على bd. أنا
+
+82
+00:08:56,420 --> 00:09:03,490
+عرفت two operations على الـ set F بالشكل اللي قدامي.
+
+83
+00:09:03,490 --> 00:09:09,770
+هي عملية الجمع، وهي عملية... عملية الضرب. طب استنى
+
+84
+00:09:09,770 --> 00:09:16,390
+شوية. السؤال هو: هل ممكن bd في يوم من الأيام
+
+85
+00:09:16,390 --> 00:09:24,390
+تكون zero؟ لأ، لأنه لا الـ b بـ zero ولا الـ d بـ zero.
+
+86
+00:09:24,390 --> 00:09:27,670
+و D كمجال تكامل يعني ما فيهوش zero
+
+87
+00:09:27,670 --> 00:09:36,720
+divisor. يبقى هنا not that، not that. لاحظوا إن الـ a
+
+88
+00:09:36,720 --> 00:09:45,560
+في b does not equal الـ b في d. الـ b في d does not
+
+89
+00:09:45,560 --> 00:09:53,080
+equal zero because اللي هو الـ b لا تساوي zero، and
+
+90
+00:09:53,080 --> 00:10:01,600
+الـ d لا تساوي zero، and D is an integral
+
+91
+00:10:01,600 --> 00:10:14,320
+domain. is an integral domain. طيب
+
+92
+00:10:14,320 --> 00:10:22,160
+الأهم يا بنات، لما نقول عناصر في S على الشكل A على
+
+93
+00:10:22,160 --> 00:10:32,180
+B، مش فيه عناصر هتطلع متساوية؟ مثلًا زي إيش؟ مثلًا زي
+
+94
+00:10:34,260 --> 00:10:40,640
+نص، إيش بقدر أكتبها؟ بقدر
+
+95
+00:10:40,640 --> 00:10:45,900
+أكتبها ثلاثة على ستة، بقدر أكتبها أربعة على ثمانية، بقدر
+
+96
+00:10:45,900 --> 00:10:51,840
+أكتبها خمسة على عشرة. زي ما بدك، تساوي حقها زي ما بدك.
+
+97
+00:10:51,840 --> 00:10:57,160
+أرقام إيه؟ يعني الـ two operations هذول يجب أن
+
+98
+00:10:57,160 --> 00:11:02,330
+نثبتهم إنهم إيه؟ والـ define حتى ما يروحوش عنصرين
+
+99
+00:11:02,330 --> 00:11:13,370
+لعنصرين ثانية. تمام. يبقى هنا want to show addition
+
+100
+00:11:13,370 --> 00:11:16,830
+and
+
+101
+00:11:16,830 --> 00:11:25,010
+multiplication on
+
+102
+00:11:25,010 --> 00:11:35,530
+الـ F are well defined.  مشان
+
+103
+00:11:35,530 --> 00:11:43,770
+هيك بندي روح نقول له: assume افترض أن الـ A على B يساوي
+
+104
+00:11:43,770 --> 00:11:53,130
+A prime على B prime، and الـ C على D يساوي C prime
+
+105
+00:11:53,130 --> 00:12:01,970
+على D prime. بندي روح نثبت له إن A على B زي C على D
+
+106
+00:12:01,970 --> 00:12:06,850
+يساوي A prime على B prime زي C prime على D prime.
+
+107
+00:12:06,850 --> 00:12:12,710
+هذه ناحية. الناحية الثانية بدي أثبت له إنه AC على
+
+108
+00:12:12,710 --> 00:12:18,930
+BD يساوي A prime C prime على B prime D prime. إذا
+
+109
+00:12:18,930 --> 00:12:23,970
+أثبتت خلاص بيصير well defined، العملية معرفة وما
+
+110
+00:12:23,970 --> 00:12:29,990
+فيها مشكلة. طيب يا بنات، هذا إيه؟ لو جيت لي هذه ممكن
+
+111
+00:12:29,990 --> 00:12:40,070
+أضرب ضرب تبادلي: بيصير ad prime، بيصير a prime b، and
+
+112
+00:12:40,070 --> 00:12:51,230
+الثانية cd prime، بيصير c prime d. هذه هنرجع لها بعد
+
+113
+00:12:51,230 --> 00:12:55,030
+قليل. الآن بدي أقول له: consider
+
+114
+00:12:57,360 --> 00:13:09,460
+عملية الجمع هذه. بدي آخذ الـ ad زائد الـ bc، بدي
+
+115
+00:13:09,460 --> 00:13:17,200
+أضربها في الـ b prime d prime، أشوف وين بدها توصلنا.
+
+116
+00:13:17,200 --> 00:13:25,010
+هذه، هذا الكلام يساوي، إن قدرت يا بنت أثبت إن هذه
+
+117
+00:13:25,010 --> 00:13:30,210
+تساوي a prime d prime زائد b prime c prime في bd
+
+118
+00:13:30,210 --> 00:13:35,450
+بيكون خلاصنا تم المطلوب. يبقى نثبتها، هذا اللي بدنا
+
+119
+00:13:35,450 --> 00:13:44,850
+نبينه الآن. بدي أفك القصة. يبقى ad في b prime d prime
+
+120
+00:13:44,850 --> 00:13:53,170
+زائد bc في b prime d prime. تمام؟
+
+121
+00:13:53,790 --> 00:13:57,950
+خاصية الـ associativity صحيحة. أولًا، الشيء الـ
+
+122
+00:13:57,950 --> 00:14:03,090
+associativity. خاصية الـ commutative لأنه فرض D
+
+123
+00:14:03,090 --> 00:14:08,390
+integral domain، يبقى commutative والـ unity. ودول
+
+124
+00:14:08,390 --> 00:14:11,770
+كلهم: الـ A، والـ B، والـ C، والـ D، والـ prime كلهم
+
+125
+00:14:11,770 --> 00:14:16,710
+عناصر في الـ integral domain. إذا بقدر أبدل زي ما
+
+126
+00:14:16,710 --> 00:14:24,080
+بدي. إذا بدي آخذ الـ A مع B prime، الـ A مع B prime، مين
+
+127
+00:14:24,080 --> 00:14:32,700
+ضال عندي؟ ضال عندي dd prime. ثانيًا بدي آخذ الآن c مع
+
+128
+00:14:32,700 --> 00:14:42,660
+d prime. بضل عندي مين؟ الـ bb prime. يساوي، طيب
+
+129
+00:14:42,660 --> 00:14:50,800
+الـ ab prime هذه وين هي؟ هي بدها تساوي a prime b.
+
+130
+00:14:51,390 --> 00:15:00,070
+يبقى هذه تساوي a prime b في dd prime. نرجع نكمل ما
+
+131
+00:15:00,070 --> 00:15:05,650
+ابتدأناه. نقول: أخذنا الـ term اللي عندنا هذا، تمام؟
+
+132
+00:15:05,650 --> 00:15:10,050
+طيب ليش أخذته؟ لأن اللي بين قوسين هو البسط اللي
+
+133
+00:15:10,050 --> 00:15:16,110
+عندي هذا. ومطلوب أني أثبت إن هذا على هذا يساوي a
+
+134
+00:15:16,110 --> 00:15:20,590
+prime d prime زائد b prime c prime على b prime d
+
+135
+00:15:20,590 --> 00:15:28,780
+prime. فرحت ضربت القصة دي في B' D'، وبده أوصل، جيت
+
+136
+00:15:28,780 --> 00:15:36,220
+فكيت القصة، فكيت القصة. أخذت الـ AB' مع بعض، ضل DD'.
+
+137
+00:15:36,980 --> 00:15:44,020
+ومن هنا أخذت الـ CD'، ضل عندي BB'. الآن بالنسبة
+
+138
+00:15:44,020 --> 00:15:51,780
+للأولى، من هنا الـ AB' يسمى A'B، والـ DD' ضلت زي ما هي. الآن CD' هي C'D. يبقى زائد C
+
+139
+00:15:59,140 --> 00:16:07,680
+Prime D. زائد C Prime D في مين؟ في الـ BB Prime. و
+
+140
+00:16:07,680 --> 00:16:14,440
+يساوي. طلعنا. بدأ أخذ الأولى مع الأخيرة، يبقى شو تصير
+
+141
+00:16:14,440 --> 00:16:23,190
+عندي؟ A Prime D Prime. بظهر لنا مين؟ الـ BD. زرعتها بدا
+
+142
+00:16:23,190 --> 00:16:31,130
+آخذ هنا الـ B Prime C Prime مضروبة فيه، اللي هو الـ
+
+143
+00:16:31,130 --> 00:16:38,070
+BD. طلعنا لهذه، وهذه الاثنين are the same. إذا بدي
+
+144
+00:16:38,070 --> 00:16:42,550
+أستخدم الـ distributive law، يعني هذا الكلام بده
+
+145
+00:16:42,550 --> 00:16:53,110
+يساوي A Prime D Prime زائد B'C' في BD. طلعنا
+
+146
+00:16:53,110 --> 00:17:03,150
+هنا وهنا. طيب؟ بدي أقسم الطرفين على BD B'D'. يبقى
+
+147
+00:17:03,150 --> 00:17:11,350
+هذا كله إيش بيعطينا؟ بيعطينا ما يأتي: الـ AD الـ AD
+
+148
+00:17:11,350 --> 00:17:21,230
+زائد الـ BC على الـ BD. بالضبط. في طرف الثاني
+
+149
+00:17:21,230 --> 00:17:34,190
+A'D' زائد B'C' على B'D'. بما صارت عملية الجمع well
+
+150
+00:17:34,190 --> 00:17:38,590
+defined. عرفنا ليش أخذنا هذا اللي أنتم بناتنا
+
+151
+00:17:38,590 --> 00:17:43,880
+ساعدتوني قبل قليل. لسه أثبتنا إن الجمع is well
+
+152
+00:17:43,880 --> 00:17:50,600
+defined. ضايل علينا عملية الضرب. يبقى بروح بقول له: and
+
+153
+00:17:50,600 --> 00:17:59,820
+وين عملية الضرب هذه؟ ضربناها له: ac على bd. بدي آخذ
+
+154
+00:17:59,820 --> 00:18:09,520
+الـ ac في مين؟ في نفس الـ b prime d prime.  yourself
+
+156
+00:18:11,880 --> 00:18:21,940
+الـ AB Prime مضروبة في CD Prime. طيب،
+
+157
+00:18:21,940 --> 00:18:27,800
+الآن نجل هذه: الـ AB Prime هي الـ A Prime B. يبقى
+
+158
+00:18:27,800 --> 00:18:34,900
+هذه A Prime B، والـ CD Prime هي C Prime D. يبقى في
+
+159
+00:18:34,900 --> 00:18:46,920
+C Prime D. يبقى يساوي A'C' في BD. طلعنا الأولى و
+
+160
+00:18:46,920 --> 00:18:54,500
+الأخيرة. بدنا نقسم الطرفين على BD B'D'. يبقى هذا
+
+161
+00:18:54,500 --> 00:19:03,640
+بدي يعطيك مين؟ اللي هو AC على BD يساوي A'C' على B'
+
+162
+00:19:04,300 --> 00:19:11,550
+D'. يعني إيه؟ يعني الـ a على b في الـ c على d يساوي a
+
+163
+00:19:11,550 --> 00:19:18,470
+prime على b prime في الـ c prime على d prime. يبقى
+
+164
+00:19:18,470 --> 00:19:24,490
+صارت عملية الضرب مالها well defined. عملية الجمع
+
+165
+00:19:24,490 --> 00:19:30,310
+وعملية من الضرب. يبقى صار عندي set وعليها two
+
+166
+00:19:30,310 --> 00:19:37,630
+binary operations. تمام. طب الـ D أصلاً integral domain.
+
+167
+00:19:37,630 --> 00:19:42,890
+يبقى الـ commutative والـ unity موجودة وجاهزة لأنه
+
+168
+00:19:42,890 --> 00:19:49,310
+كلها أخذناها من هناك. الآن يا بناتي، الـ unity و
+
+169
+00:19:49,310 --> 00:19:58,650
+الموجودة وين؟ موجودة في D. هذا معناه إنه zero على
+
+170
+00:19:58,650 --> 00:20:00,810
+واحد، وين موجود؟
+
+171
+00:20:04,570 --> 00:20:08,130
+مش الـ F هو كل equivalence classes بتاعة الـ
+
+172
+00:20:08,130 --> 00:20:11,730
+equivalence relation على الـ S. موجود في F. ممتاز.
+
+173
+00:20:11,730 --> 00:20:24,930
+يبقى موجود في F. يبقى هذا is the zero element in F.
+
+174
+00:20:24,930 --> 00:20:39,750
+
+223
+00:27:33,840 --> 00:27:36,380
+the same، نفس الشيء.
+
+224
+00:27:55,010 --> 00:28:04,810
+طبعا مثلا نتطرق إلى حل بعض المسائل بعض
+
+225
+00:28:04,810 --> 00:28:10,770
+المسائل من شكر 15 نبدأ
+
+226
+00:28:10,770 --> 00:28:18,270
+نبدأ
+
+227
+00:28:18,270 --> 00:28:21,770
+يبقى exercises on
+
+228
+00:28:31,270 --> 00:28:38,110
+السؤال التام مثلا بيقول prove that prove that
+
+229
+00:28:38,110 --> 00:28:46,510
+every ring homomorphism من الـ Z<sub>n</sub> إلى الـ Z<sub>n</sub>
+
+230
+00:28:46,510 --> 00:28:57,230
+itself has the form has the form  ϕ(x)
+
+231
+00:28:57,230 --> 00:29:06,830
+بده يساوي a في x بده يساوي a في x حيث الـ a
+
+232
+00:29:06,830 --> 00:29:17,910
+تقريبا يساوي a  أهلا
+
+233
+00:29:17,910 --> 00:29:25,070
+و مرحبا بكم يقولوا اثبتلي أن أي homomorphism من Z<sub>n</sub>
+
+234
+00:29:25,070 --> 00:29:30,630
+إلى نفس شكله بدي يكون ϕ(x) بدي يساوي الـ A
+
+235
+00:29:30,630 --> 00:29:36,190
+for x حيث الـ a بيبقوا بالكلمة. بيبقوا بسيطة.
+
+236
+00:29:36,390 --> 00:29:44,370
+تعالى نشوف  ϕ(x). هل بتطلع ax ولا شو
+
+237
+00:29:44,370 --> 00:29:50,310
+الموضوع؟ بنقول له ماشي. هذا الكلام يساوي ϕ
+
+238
+00:29:52,830 --> 00:29:57,250
+الـ x element وين؟ يعني ممكن يكون صفر، ممكن يكون
+
+239
+00:29:57,250 --> 00:30:01,890
+واحد، اتنين، تلاتة، أربعة، لغاية n -1
+
+240
+00:30:01,890 --> 00:30:08,530
+يبقى بقدر أقول واحد زائد واحد زائد واحد كم مرة يا
+
+241
+00:30:08,530 --> 00:30:15,410
+بنات؟ x مرات يبقى x من المرة. Gallify
+
+242
+00:30:15,410 --> 00:30:22,290
+homomorphism يبقى باجي بقوله الـ ϕ(1) زائد
+
+243
+00:30:22,290 --> 00:30:31,410
+ϕ(1) زائد ϕ(1)  كم مرة؟ x مرات يبقى
+
+244
+00:30:31,410 --> 00:30:38,890
+هذا بدي يساوي الـ x في ϕ(1) أو ϕ(1) في
+
+245
+00:30:38,890 --> 00:30:44,390
+x يعني تفرقش عندنا لأن الـ ring هذه commutative
+
+246
+00:30:45,720 --> 00:30:51,960
+طيب الآن لو جيت قولتلك let ϕ(1) بده يساوي
+
+247
+00:30:51,960 --> 00:30:59,600
+الـ a مثلا و الـ a موجودة في Z<sub>n</sub> يبقى هذا الكلام
+
+248
+00:30:59,600 --> 00:31:07,880
+بده يساوي الـ x في a أو الـ ax يبقى أي homomorphism
+
+249
+00:31:07,880 --> 00:31:14,380
+صار على الشكل a في x و الـ A هي عبارة عن ϕ
+
+250
+00:31:14,380 --> 00:31:19,300
+(1)، إيش ما تطلع صورتها تطلع، ما أعرفش كده إيش تطلع،
+
+251
+00:31:19,300 --> 00:31:25,420
+ما علينا. قال لي بدك تثبت أنه a<sup>2</sup> تساوي a،
+
+252
+00:31:25,420 --> 00:31:31,120
+ما أقول لك إيش مشكلة. أن الواحد الـ unity، مش هو
+
+253
+00:31:31,120 --> 00:31:36,120
+عبارة عن واحد في واحد، أثر على الطرفين بـ ϕ.
+
+254
+00:31:36,800 --> 00:31:42,760
+يبقى هذا بدي أعطيك ϕ(1) ϕ(1) في 1
+
+255
+00:31:42,760 --> 00:31:50,140
+هذا معناه أنه ϕ(1) بدي يساوي ϕ(1) في
+
+256
+00:31:50,140 --> 00:31:56,600
+ϕ(1) ϕ(1) بيبقى a في a بيبقى a
+
+257
+00:31:56,600 --> 00:32:03,680
+فيساوي a في a يبقى الـ a بدي تساوي a<sup>2</sup>
+
+258
+00:32:03,680 --> 00:32:11,740
+وهو المطلوب أي homomorphism من Z<sub>n</sub> إلى Z<sub>n</sub> نفسها
+
+259
+00:32:11,740 --> 00:32:18,080
+بديكون شكله ϕ(x) يساوي a(x) حيث الـ a بده
+
+260
+00:32:18,080 --> 00:32:25,720
+يساوي a<sup>2</sup> وهو المطلوب طيب هذا سؤال
+
+261
+00:32:25,720 --> 00:32:35,650
+ثمانية سؤال عشرة طبعا مطلوبين a و b سؤال عشرة بيسأل
+
+262
+00:32:35,650 --> 00:32:44,990
+هل الـ 2Z isomorphic لـ 3Z أم لا؟ بيقولوا
+
+263
+00:32:44,990 --> 00:32:49,470
+الله أعلم، و السؤال اللي بعده بيقول هل 2Z
+
+264
+00:32:49,470 --> 00:32:57,650
+isomorphic لـ 4Z أم لا؟ بيقولوا كمان الله أعلم،
+
+265
+00:32:57,650 --> 00:33:04,760
+كمان؟ أنا بقول لا هذا isomorphic و لا هذا isomorphic
+
+266
+00:33:04,760 --> 00:33:09,900
+هذا السؤال ببدأ السؤال عشرة  راح سؤال خمسين قال
+
+267
+00:33:09,900 --> 00:33:17,260
+أثبت إذا الـ m بتساويش الـ n يبقى الـ mZ is not
+
+268
+00:33:17,260 --> 00:33:22,880
+isomorphic to nZ يبقى automatic هدول اتنين ما لهم
+
+269
+00:33:22,880 --> 00:33:29,140
+not isomorphic خلينا نثبت واحد و الثاني بتثبته بنفس
+
+270
+00:33:29,140 --> 00:33:36,960
+الطريقة تمام؟ يبقى بالدالي أقوله as you افترض أنه
+
+271
+00:33:36,960 --> 00:33:44,240
+2Z isomorphic little أو بلاش بيقول as you
+
+272
+00:33:44,240 --> 00:33:53,860
+assume that  الـ function من 2Z إلى 3Z is an
+
+273
+00:33:53,860 --> 00:33:55,280
+isomorphism
+
+274
+00:33:59,380 --> 00:34:09,640
+طيب أمانة 2 موجودة في 2Z ولا لا؟ يبقى
+
+275
+00:34:09,640 --> 00:34:19,960
+هذا يعطينا ϕ(2)  وفي 2 يبقى 3k for
+
+276
+00:34:19,960 --> 00:34:25,900
+some k اللي موجودة في Z قد ما تطلع تطلع
+
+277
+00:34:28,540 --> 00:34:35,700
+ساكت الشعب أخدت element هنا افترض أنه صورة على
+
+278
+00:34:35,700 --> 00:34:41,800
+الشكل اللي قدامي هنا بدي أشوف يا ترى هل هذا الكلام
+
+279
+00:34:41,800 --> 00:34:46,640
+صحيح ولا لا؟ هل هذا isomorphism ولا لا؟ طيب لو
+
+280
+00:34:46,640 --> 00:34:52,960
+أخدت الآن ϕ(4) كده هتساوي هذا يا بنات؟
+
+281
+00:34:52,960 --> 00:34:59,070
+ϕ(2Z)  2 أنا جاي أقول عليه isomorphism
+
+282
+00:34:59,070 --> 00:35:05,650
+يعني homomorphism يعني ϕ(2) + ϕ(2)
+
+283
+00:35:05,650 --> 00:35:12,670
+= ϕ(2)  يبقى = 3k + 3k
+
+284
+00:35:12,670 --> 00:35:20,110
+يبقى 6k طب لو رجعت لـ ϕ(4) نفسي مش هي
+
+285
+00:35:20,110 --> 00:35:28,840
+في 2 في 2 مظبوط يعني هذا في 4 أو بـ 2 في ϕ
+
+286
+00:35:28,840 --> 00:35:35,540
+أو بـ 2 في ϕ(2) بتلاتة k مضروبة في تلاتة k
+
+287
+00:35:35,540 --> 00:35:43,060
+يبقى بتسعة k<sup>2</sup> مش هذا كلام يعني 2 متساوية
+
+288
+00:35:43,060 --> 00:35:49,160
+مش هذه ϕ(4) و هذه ϕ(4) نتيجة تانية
+
+289
+00:35:49,160 --> 00:35:56,980
+مختلفة تانية يبقى لازم الـ 9k<sup>2</sup> يساوي 6k
+
+290
+00:35:56,980 --> 00:36:07,100
+أو إن شئتم فقولوا أن الـ 9k<sup>2</sup> ناقص 6k
+
+291
+00:36:07,100 --> 00:36:17,140
+بتساوي 0 تمام؟ هذا معناه أن 3k (3k -2)
+
+292
+00:36:17,140 --> 00:36:24,690
+ناقص 2 بتساوي 0 يعني معنى هذا الكلام أن
+
+293
+00:36:24,690 --> 00:36:32,190
+الثلاثة بلاش منها يبقى k تساوي 0 أو 3k
+
+294
+00:36:32,190 --> 00:36:40,090
+ناقص 2 يساوي 0 طب خذنا الواحدة منهم  k =
+
+295
+00:36:40,090 --> 00:36:48,250
+3k - 2 يساوي 0  إن الـ k بدي تساوي
+
+296
+00:36:48,250 --> 00:36:59,910
+2/3 موجودة في Z ده في مُجاف منّه إيه؟ أخذنا الـ k
+
+297
+00:36:59,910 --> 00:37:08,190
+و وجدنا الـ k موجودة في Z هذه مش موجودة في Z يبقى هل
+
+298
+00:37:08,190 --> 00:37:15,270
+الإمكانية هذه واردة؟ لأ غير واردة و يبقى هذا معناته
+
+299
+00:37:15,670 --> 00:37:19,950
+أنه 3k - 2 تساوي 0 is
+
+300
+00:37:19,950 --> 00:37:28,750
+impossible، كلام غير ممكن، يبقى k تساوي 0،
+
+301
+00:37:28,750 --> 00:37:34,030
+مش هذا الأمر الثاني، بيجي نشوف k ممكن تساوي 0
+
+302
+00:37:34,030 --> 00:37:41,130
+وما كمان مستبعد، يمكن يكون مستبعد ولا لا؟ أكيد؟
+
+303
+00:37:41,130 --> 00:37:51,450
+أكيد، 100% لو كان الـ k تساوي 0، فأصبح ϕ ..
+
+304
+00:37:51,450 --> 00:37:57,470
+خلينا نشوف وين هنا؟ قولنا ϕ(2) يساوي 3k يجب أن يكون
+
+305
+00:37:57,470 --> 00:38:07,670
+ϕ(2) يصبح 3 في 0 لأنه سيساوي 0 فيبقوا ϕ(4)
+
+306
+00:38:07,670 --> 00:38:17,180
+سيساوي كم؟ فهو ϕ(4) بتساوي 6k  يفجأ يفجأ يفجأ
+
+307
+00:38:17,180 --> 00:38:26,540
+يفجأ يفجأ يفجأ يفجأ يفجأ يفجأ يفجأ
+
+308
+00:38:26,540 --> 00:38:37,020
+يفجأ
+
+309
+00:38:37,020 --> 00:38:46,460
+يفجأ يفجأ يفجأ يفجأ يفجأ يفجأ الـ ϕ is not one to
+
+310
+00:38:46,460 --> 00:38:55,320
+one يبقى الـ ϕ is not isomorphic هذا معناه أن
+
+311
+00:38:55,320 --> 00:39:05,800
+2Z لا يمكن أن تكون isomorphic لـ 3Z الجزء
+
+312
+00:39:05,800 --> 00:39:12,580
+الثاني بنمر بي بنفس الطريقة حرفيا إن شاء الله لما
+
+313
+00:39:12,580 --> 00:39:18,840
+نوصل لسؤال خمسين بالسلامة بروح أنبرهنه لأي عدد
+
+314
+00:39:18,840 --> 00:39:28,920
+أعطيناه بالنسبة للـ 2 أو الـ 3 سؤال 12 سؤال
+
+315
+00:39:28,920 --> 00:39:40,930
+12 يقول ما يأتي أثبت أن Z<sub>3</sub>[x] الذي كل
+
+316
+00:39:40,930 --> 00:39:47,570
+عناصره على شكل a + bx حيث a و b
+
+317
+00:39:47,570 --> 00:39:59,870
+موجودة في Z<sub>3</sub> موجودة في Z<sub>3</sub> isomorphic لمين؟ لـ Z<sub>3</sub>
+
+318
+00:39:59,870 --> 00:40:06,730
+[x]/(x<sup>2</sup>+1)
+
+319
+00:40:06,730 --> 00:40:07,870
+زائد واحد
+
+320
+00:40:15,860 --> 00:40:22,840
+complex numbers 0, 1, 2 isomorphic لـ
+
+321
+00:40:22,840 --> 00:40:28,720
+functions من الدرجة الأولى الثانية الثالثة العاشرة
+
+322
+00:40:28,720 --> 00:40:33,940
+العشرين زي ما بدك modulo of the principal ideal
+
+323
+00:40:33,940 --> 00:40:39,400
+generated by x<sup>2</sup> + 1 طيب إيه المهم هو
+
+324
+00:40:39,400 --> 00:40:43,770
+أن هذا الـ function  نثبت أنه one to one and
+
+325
+00:40:43,770 --> 00:40:49,350
+onto homomorphism بيصير isomorphism صح؟ يبقى باجي
+
+326
+00:40:49,350 --> 00:41:03,490
+أقوله define a function ϕ من Z<sub>3</sub>[x] إلى Z<sub>3</sub>[x]
+
+327
+00:41:03,490 --> 00:41:14,850
+/(x<sup>2</sup>+1) by ϕ(a + bx)
+
+328
+00:41:14,850 --> 00:41:20,690
+بدي أخلص صورته هنا الـ elements اللي في الـ Z<sub>3</sub>
+
+329
+00:41:20,690 --> 00:41:30,150
+بعد ما نختصرهم بتطلع معادلة من الدرجة الأولى
+
+330
+00:41:30,150 --> 00:41:36,570
+لأن كل اللي قبلها بنقدر نضيفه لـ x<sup>2</sup>
+
+331
+00:41:36,570 --> 00:41:44,620
+أو نتركه و ندخله مرة مرتين يبقى بقدر أقول هذا a +
+
+332
+00:41:44,620 --> 00:41:51,820
+bx + (x<sup>2</sup> + 1) يبقى بدي
+
+333
+00:41:51,820 --> 00:42:01,020
+أثبت أن الـ ϕ is homomorphism بدي أخد ϕ(
+
+334
+00:42:01,020 --> 00:42:09,630
+a + b x) + ϕ(c + dx) يبقى هذا
+
+335
+00:42:09,630 --> 00:42:19,070
+ϕ(a + c + (b+d)x) صار هذا complex
+
+336
+00:42:19,070 --> 00:42:26,730
+number إذا ϕ لو أثرت عليه بتساوي مين الـ constant
+
+337
+00:42:26,730 --> 00:42:36,550
+اللي هو a + c + (b+d)x + (x<sup>2</sup> + 1) هذا
+
+338
+00:42:36,550 --> 00:42:42,540
+يا بنات بقدر أقول a + bx + (x<sup>2</sup> + 1)
+
+339
+00:42:42,540 --> 00:42:47,560
+وهنا + c + dx + (x<sup>2</sup> + 1)
+
+340
+00:42:47,560 --> 00:42:54,620
+مظبوط هذا يعني ϕ(a + bx) + ϕ(c + dx)
+
+341
+00:42:54,620 --> 00:43:05,670
+مباشر ما فيه صعوبة ولا حاجة
+
+342
+00:43:05,670 --> 00:43:11,330
+الترتيب وماشي زي الملاحي طيب أجي آخذ and ϕ(
+
+343
+00:43:11,330 --> 00:43:19,050
+a + bx)(c + dx) يساوي اه استنى شوية
+
+344
+00:43:19,050 --> 00:43:28,330
+بدك تضرب هنا مش زي اللي قبلها اجمع وامشي يبقى بقوله
+
+345
+00:43:28,330 --> 00:43:33,610
+بدك تضرب هنا مش زي اللي قبلها اجمع و امشي يبقى بقوله
+
+346
+00:43:33,610 --> 00:43:43,250
+ϕ(ac - bd + (ad + bc)x) + (x<sup>2</sup> + 1)
+
+347
+00:43:43,250 --> 00:43:51,210
+ يبقى  (ad + bc) هذا كله في الجزء اللي بعده
+
+348
+00:43:51,210 --> 00:44:04,970
+(ad + bc) + (x<sup>2</sup>+1) يبقى حطيت حاصل الضرب
+
+349
+00:44:04,970 --> 00:44:11,150
+على شكل complex number حسب الـ definition هذا بده
+
+350
+00:44:11,150 --> 00:44:22,870
+يساوي ac - bd + (ad + bc) x + (x<sup>2</sup> + 1)
+
+351
+00:44:22,870 --> 00:44:29,290
+و بتعتبر المعادلة هذه رقم 1
+
+352
+00:44:29,830 --> 00:44:36,410
+الصعب أرجع من المعادلة هذه لحاصل ضرب الاثنين فابدأ
+
+353
+00:44:36,410 --> 00:44:45,710
+أروح آخذ حاصل ضرب الاثنين ϕ(c + dx)
+
+354
+00:44:45,710 --> 00:44:53,690
+و أشوف إيش بده يساوي هذا اللي هو a + bx + (x<sup>2</sup> + 1)
+
+355
+00:44:53,690 --> 00:45:02,320
+مضروب من مين؟ من الـ c + dx + (x<sup>2</sup> + 1)
+
+356
+00:45:02,320 --> 00:45:10,300
+تمام؟ هذا الكلام يساوي اللي هو الـ
+
+357
+00:45:10,300 --> 00:45:18,520
+a + bx (c + dx) + (x<sup>2</sup> + 1)
+
+358
+00:45:18,520 --> 00:45:24,700
+تمام؟ طب بدأ أفك هذه و أشوف أين بدأ أتوجه
+
+359
+00:45:24,700 --> 00:45:31,330
+الدنيا هل بتساوي هذه ولا بتساويش هذه؟ الله أعلم
+
+360
+00:45:31,330 --> 00:45:40,230
+يبقى هذه ac ضربنا الأول في الأول و الثاني في الثاني
+
+361
+00:45:40,230 --> 00:45:44,890
++bdx<sup>2</sup>
+
+362
+00:45:44,890 --> 00:45:57,030
++ adx + bcx + (x<sup>2</sup> + 1)
+
+363
+00:45:57,590 --> 00:46:06,350
+زائد الـ bc كل هذا bc في x + (x<sup>2</sup> + 1) طيب
+
+364
+00:46:06,350 --> 00:46:11,830
+نرجع بالذاكرة للوراء x<sup>2</sup> + 1
+
+365
+00:46:11,830 --> 00:46:18,510
+تساوي 0 x<sup>2</sup> + 1 تساوي 0 يبقى الـ x
+
+366
+00:46:24,420 --> 00:46:31,400
+تقريبا -1 -1 يبقى هذه بقد إيش يا بنات
+
+367
+00:46:31,400 --> 00:46:37,500
+أقدر أشيلها و أحط مكانها -1 يبقى بيصير
+
+368
+00:46:37,500 --> 00:46:47,700
+النتيجة ac - bd هذه ما فيه access بالمرة + ad
+
+369
+00:46:47,700 --> 00:46:54,530
++ bc في الـ x + (x<sup>2</sup> + 1)
+
+370
+00:46:54,530 --> 00:46:58,810
+فاكرين هذا لما عملناها و سويناها
+
+371
+00:46:58,810 --> 00:47:04,870
+بالواحد؟ طيب تمام يبقى هذه العلاقة رقم 2
+
+372
+00:47:04,870 --> 00:47:13,110
+بتطلعوني في 1 و 2 زي بعض؟ مدام زي بعض يبقى
+
+373
+00:47:13,110 --> 00:47:17,410
+صار الـ ϕ عبارة عن homomorphism
+
+374
+00:47:24,700 --> 00:47:34,660
+يبقى بجي بقوله from 1 and 2 we have أن الـ
+
+375
+00:47:34,660 --> 00:47:44,040
+ϕ(a + bx)(c + dx) = ϕ(a + bx) ϕ(c + dx) يبقى خلصنا
+
+376
+00:47:44,040 --> 00:47:52,750
+من إثبات أن ϕ هو homomorphism بدي أثبت ϕ is
+
+377
+00:47:52,750 --> 00:47:59,810
+one to one يبقى بدي آخذ صورتين متساويتين ϕ(a
+
+378
+00:47:59,810 --> 00:48:09,230
++ bx) = ϕ(c + dx) then
+
+379
+00:48:09,230 --> 00:48:17,530
+صورة الأول اللي هو a + bx + (x<sup>2</sup> + 1)
+
+380
+00:48:17,530 --> 00:48:25,080
+صورة الثانية c + dx + (x<sup>2</sup> + 1)
+
+381
+00:48:25,080 --> 00:48:32,120
+طيب شو رأيكم في هذه بقدر أقول a - c
+
+382
+00:48:32,120 --> 00:48:41,060
++ (b - d)x + (x<sup>2</sup> + 1)
+
+383
+00:48:41,060 --> 00:48:49,620
+= 0 + (x<sup>2</sup> + 1) يعني
+
+384
+00:48:49,620 --> 00:48:56,220
+يساوي 0 صحيح؟ يبقى هنا a - c + (b -d)x = 0
+
+385
+00:48:56,220 --> 00:49:02,880
+معادلة صفرية هذه تعني
+
+386
+00:49:02,880 --> 00:49:13,780
+أن a - c = 0 و b - d = 0
+
+387
+00:49:13,780 --> 00:49:23,070
+يبقى a = c و b = d يبقى صارت الصورتين متساويتين بدي أشوف الأصل تبعها
+
+388
+00:49:23,070 --> 00:49:30,310
+a + bx = c + dx
+
+389
+00:49:30,310 --> 00:49:37,650
+هو المطلوب خلاص ما هو المطلوب الـ m في Z[x] is onto because
+
+390
+00:49:37,650 --> 00:49:45,830
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5WB6jBEi9nU.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5WB6jBEi9nU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..18453e07686c9adc752b8abc16e034130e6b67c0
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5WB6jBEi9nU.srt
@@ -0,0 +1,1507 @@
+1
+00:00:20,690 --> 00:00:25,630
+بسم الله الرحمن الرحيم نواصل الآن اللي هو الشق الثاني
+
+2
+00:00:25,630 --> 00:00:31,710
+14 والمرة اللي فاتت أعطينا تعريف للـ ID وأخذنا عليه
+
+3
+00:00:31,710 --> 00:00:37,970
+ذلك خمسة أمثلة وهذا هو المثال السادس، المثال السادس
+
+4
+00:00:37,970 --> 00:00:41,910
+بيقول افترض أن R عبارة عن كمية  ring with unity
+
+5
+00:00:41,910 --> 00:00:46,970
+وأخذنا مجموعة من العناصر من الـ ring R وليكن A1 و
+
+6
+00:00:46,970 --> 00:00:54,480
+A2 و AN، كوّننا ست جديدة، هذه الست  مُزالها بالرمز I
+
+7
+00:00:54,480 --> 00:01:01,840
+هي الست التي تُولّد بالعناصر A1 و A2 و AN، شو شكل
+
+8
+00:01:01,840 --> 00:01:09,100
+العنصر فيها؟ كل عنصر فيها شكله R1 A1 + R2 A2 + لغاية RN
+
+9
+00:01:09,100 --> 00:01:15,700
+AN، يعني أخذت كل عنصر من عناصر الست A وضربته في
+
+10
+00:01:15,700 --> 00:01:20,820
+عنصر من عناصر R، وجمعت كل هذا، بيعطينا عنصر واحد في
+
+11
+00:01:20,820 --> 00:01:26,720
+مين؟ في الست اللي عندنا اللي هو I، يبقى هذا عبارة عن
+
+12
+00:01:26,720 --> 00:01:32,360
+ideal، بدنا نثبت صحة هذا الكلام، هذا الـ ideal اسمه
+
+13
+00:01:32,360 --> 00:01:38,280
+the ideal generated by A1 و A2 و لغاية AN، يبقى هو
+
+14
+00:01:38,280 --> 00:01:47,040
+الـ ideal اللي تكون من العناصر A1 و A2 لغاية AN
+
+15
+00:01:47,680 --> 00:01:54,000
+الاهم solution، احنا مشان نثبت أن الـ set هي عبارة
+
+16
+00:01:54,000 --> 00:02:01,100
+عن ideal، بدنا نروح نثبت ثلاث نقاط:  أولًا لو أخذت
+
+17
+00:02:01,100 --> 00:02:05,560
+عنصرين من هذه الـ set وطرحتهما، بد يكون الناتج موجود
+
+18
+00:02:05,560 --> 00:02:09,300
+في نفس الـ set، ثانيًا لو أخدت element من هذه الـ set و
+
+19
+00:02:09,300 --> 00:02:14,200
+element من R وضربته في هذا العنصر من اليمين أو من
+
+20
+00:02:14,200 --> 00:02:19,240
+الشمال، بد يكون في نفس الـ set، لأن إذا حدث ذلك، هذه
+
+21
+00:02:19,240 --> 00:02:24,840
+الـ set بسميها إيش؟ I، دي طيب، احنا الآن نجي للنقطة
+
+22
+00:02:24,840 --> 00:02:31,320
+الأولى، أنا أدعي أن هذه الـ set is non-empty، يبقى
+
+23
+00:02:31,320 --> 00:02:41,790
+باجي بقول الـ I is non-empty، ليش؟ بدنا عنصر واحد على
+
+24
+00:02:41,790 --> 00:02:49,610
+الأقل نثبته موجود فيها، because a zero، بقدر أكتب هو
+
+25
+00:02:49,610 --> 00:02:58,130
+r واحد zero + r اتنين zero + ... + r n zero، والـ R i
+
+26
+00:02:58,130 --> 00:03:04,110
+موجودة في R، مظبوط؟ كده إيش بطلع؟ zero + zero +
+
+27
+00:03:04,110 --> 00:03:09,660
+zero + zero، كله a zero فقط، يبقى الـ zero عنصر
+
+28
+00:03:09,660 --> 00:03:18,760
+هذا موجود في الـ set I، لذلك الـ I is non-empty، تمام؟
+
+29
+00:03:18,760 --> 00:03:24,620
+يبقى هنا نقول because، ما هو السبب؟ السبب خلوه
+
+30
+00:03:24,620 --> 00:03:31,800
+قدامنا، النقطة الثانية، سأخذ عنصرين في نفس الـ I،
+
+31
+00:03:31,800 --> 00:03:41,230
+يبقى let X وY موجودة في I، then بتعرف شكل الـ X والـ
+
+32
+00:03:41,230 --> 00:03:47,230
+Y عبارة عن إيه؟ يبقى الـ X في هذه الحالة أقدر أقول
+
+33
+00:03:47,230 --> 00:03:59,610
+R1 A1 + R2 A2 + ... + RN AN، والـ Ri موجودة في R،
+
+34
+00:03:59,610 --> 00:04:05,330
+طيب، والـ Y؟ R1
+
+35
+00:04:05,330 --> 00:04:13,200
+هذي نفسها؟ أو الـ R نفسها؟ لأ لأ، ليس بالضرورة الـ R
+
+36
+00:04:13,200 --> 00:04:16,600
+الثابتة،
+
+37
+00:04:16,600 --> 00:04:23,160
+هي A1 وA2 وA3 لغاية AN، يبقى الـ R هذول متغيرات،
+
+38
+00:04:23,160 --> 00:04:28,800
+ما عنهم، مش ثوابت، أي عناصر من الـ ring R، يبقى لو روحت
+
+39
+00:04:28,800 --> 00:04:40,050
+قلت S1 A1 + S2 A2 + ... + SN AN، والـ Si موجودة في R،
+
+40
+00:04:40,050 --> 00:04:47,090
+فالمطلوب أثبت أن الفرق فيما بينهما موجود في الـ I،
+
+41
+00:04:47,090 --> 00:04:54,670
+إذا بدي آخذ الـ X ناقص الـ Y، يبقى الـ X ناقص الـ Y بدي
+
+42
+00:04:54,670 --> 00:05:04,470
+أطرح كل عضو منهم، يبقى R1 ناقص S1 في الـ A1 +
+
+43
+00:05:04,470 --> 00:05:14,810
+R2 ناقص S2 في الـ A2 + ... + RN ناقص SN
+
+44
+00:05:14,810 --> 00:05:23,350
+كله في الـ AN، أليس هذا على شكل العنصر اللي فوق؟ نعم،
+
+45
+00:05:23,350 --> 00:05:33,150
+لأن الـ Ri ناقص Si موجودة في R، يبقى هذا موجود في I،
+
+46
+00:05:33,150 --> 00:05:34,050
+because
+
+47
+00:05:36,490 --> 00:05:47,610
+الـ Ri ناقص الـ Si موجود في الـ ring R، طيب، الآن
+
+48
+00:05:47,610 --> 00:05:53,770
+بدي أجد النقطة الثالثة، بدي آخذ عنصر من الـ ring R
+
+49
+00:05:53,770 --> 00:05:59,330
+وأخذ عنصر من الـ set I، وأثبت أنه حاصل ضربه من
+
+50
+00:05:59,330 --> 00:06:06,930
+اليمين ومن الشمال موجود في I، إن حدث ذلك، يبقى يقول
+
+51
+00:06:06,930 --> 00:06:12,910
+خلاص، لو صارت الـ I is an ideal، يبقى هنا باني بقوله
+
+52
+00:06:12,910 --> 00:06:21,670
+افترض أن R موجودة في R، and الـ X موجودة في الـ I،
+
+53
+00:06:21,670 --> 00:06:30,930
+then الـ RX  بتساوي R في (R1 A1 +
+
+54
+00:06:31,400 --> 00:06:42,800
+R2 A2 + ... + RN AN)، والـ Ri موجودة في الـ R، و
+
+55
+00:06:42,800 --> 00:06:50,160
+بتاخد من الواحد إلى N، يبقى لو جيت على الـ RX،
+
+56
+00:06:50,160 --> 00:06:59,280
+يساوي الـ R، ده يشيل الـ X ويحط  اليمين، اللي هي
+
+57
+00:06:59,280 --> 00:07:11,280
+الـ R1 A1 + الـ R2 A2 + ... + الـ RN AN،
+
+58
+00:07:11,280 --> 00:07:18,320
+بقدر أدخل الـ R حسب الـ distributive law على كل عنصر
+
+59
+00:07:18,320 --> 00:07:26,440
+من هذه العناصر، يعني لو دخلت، تصير مين؟ R في R1 A1 +
+
+60
+00:07:26,440 --> 00:07:40,060
+R في R2 A2 + ... + R في RN AN،
+
+61
+00:07:40,060 --> 00:07:47,920
+طيب، هذا الكلام،  بنستخدم الآن خاصية الـ
+
+62
+00:07:47,920 --> 00:07:53,260
+associativity على الـ ring R، هذول كل واحد فيهم من
+
+63
+00:07:53,260 --> 00:07:59,570
+الـ R، هذول في الـ R، هذول في الـ R، خاصية الـ associativity صحيحة على
+
+64
+00:08:03,510 --> 00:08:11,130
+الـ R، يبقى بده يعطيني (R R1) في الـ A1 + (R R2) في الـ
+
+65
+00:08:11,130 --> 00:08:22,300
+A2 + ... + (R RN) في الـ AN، هذه الصيغة مش هي
+
+66
+00:08:22,300 --> 00:08:29,200
+الصيغة اللي عندنا هذه؟ لأن RR1 في R، وRR2 في R، وRRN
+
+67
+00:08:29,200 --> 00:08:36,600
+في R، يبقى هذا الكلام كله موجود وين؟ موجود في I،
+
+68
+00:08:36,600 --> 00:08:48,620
+since، ليش؟ لأن الـ RRi موجود في الـ ring R itself، طيب،
+
+69
+00:08:48,620 --> 00:08:53,420
+بناء عليه أثبتنا الخواص الثلاث، يبقى بروح بقوله
+
+70
+00:08:53,420 --> 00:09:01,460
+إن الـ I، اللي هي الست المُولدة بالـ A1 والـ
+
+71
+00:09:01,460 --> 00:09:15,690
+A2 والـ AN، هذا is an ideal of R، إذا بتلاحظوا يا
+
+72
+00:09:15,690 --> 00:09:21,530
+بنات، هذا هو تعميم للـ principle ideal generated by
+
+73
+00:09:21,530 --> 00:09:25,490
+A، الـ principle ideal generated by A يقول كل
+
+74
+00:09:25,490 --> 00:09:31,870
+العناصر AR أو RA، لأن هذه commutative، مش مشكلة
+
+75
+00:09:31,870 --> 00:09:38,850
+عندنا فيها، يبقى كل العناصر RA بحيث الـ R موجودة في
+
+76
+00:09:38,850 --> 00:09:43,570
+R، احنا أثبتنا الـ RX بتثير
+
+78
+00:09:51,200 --> 00:09:57,260
+XR موجودة في R، بنفس الطريقة، يبقى صارت ضرب من
+
+79
+00:09:57,260 --> 00:10:02,700
+اليمين ولا ضرب من الشمال، يبقى صارت two sided ideal،
+
+80
+00:10:02,700 --> 00:10:11,480
+هذا هو المثال رقم ستة، بقى نروح للمثال رقم سبعة، مثال
+
+81
+00:10:11,480 --> 00:10:21,650
+رقم سبعة، بيقول الآن اللي هو Z of X، مين
+
+82
+00:10:21,650 --> 00:10:30,390
+هي هذه؟ مجموعة الـ polynomials اللي العوامل تبعات الـ
+
+83
+00:10:30,390 --> 00:10:37,050
+X كلهم ثوابت، والثوابت هذه ماخدينها من مين؟ الـ set
+
+84
+00:10:37,050 --> 00:10:44,510
+of integers، كلهم أعداد صحيحة، يبقى the ring of all
+
+85
+00:10:44,510 --> 00:10:54,140
+polynomials، the ring of all polynomials
+
+86
+00:10:54,140 --> 00:10:57,860
+polynomials
+
+87
+00:10:57,860 --> 00:11:05,600
+with integer coefficients،
+
+88
+00:11:05,600 --> 00:11:11,080
+كله
+
+89
+00:11:11,080 --> 00:11:22,310
+بمعاملات ذات أعداد صحيحة، بدي آخذ set I ثابت من Z of X
+
+90
+00:11:22,310 --> 00:11:35,250
+such that بحيث أن الـ I كل العناصر F of X بحيث أن
+
+91
+00:11:35,250 --> 00:11:45,390
+الـ F of X بدها تساوي AN XN + AN−1 XN−1 + ... +
+
+92
+00:11:45,950 --> 00:11:56,710
+a1 x + a2 m، والـ m موجودة في Z، والـ m
+
+93
+00:11:56,710 --> 00:12:08,990
+موجودة في Z، show that، show that،  مين؟ أن الـ I is an
+
+94
+00:12:08,990 --> 00:12:18,810
+ideal of R، بيقول إن هذا ideal of الـ R اللي يمين،
+
+95
+00:12:18,810 --> 00:12:22,250
+اللي هي Z of X،
+
+96
+00:12:36,860 --> 00:12:43,400
+نقرأ السؤال مرة ثانية، وبدي أوضح
+
+97
+00:12:43,400 --> 00:12:49,100
+الصيغة الرياضية تبعته، السؤال بيقول: خُذْ Z of X هي
+
+98
+00:12:49,100 --> 00:12:56,260
+ring، اللي هي كثيرات الحدود بحيث المعاملات تبع
+
+99
+00:12:56,260 --> 00:13:02,100
+كثيرات الحدود كلها أعداد صحيحة، طبعًا أخذناها قبل
+
+100
+00:13:02,100 --> 00:13:08,040
+ذلك، وأثبتنا أنها مجموعة،  مالها؟ الـ integer
+
+101
+00:13:08,040 --> 00:13:14,280
+coefficients، موجودة في Z، خذ لي subset من Z of X،
+
+102
+00:13:14,280 --> 00:13:21,660
+مين هي هذه الـ set؟ هي الـ set I، كل العناصر f of x such
+
+103
+00:13:21,660 --> 00:13:27,020
+that f of x تساوي الـ polynomial هذه، بس تطلع لي هنا
+
+104
+00:13:27,020 --> 00:13:33,960
+كتبناها، زائد a2 m، إيش يعني قصده يقول؟ يقول: كل الـ
+
+105
+00:13:33,960 --> 00:13:39,220
+polynomials اللي المقدار الثابت فيها هو عدد زوجي،
+
+106
+00:13:39,220 --> 00:13:44,720
+طبعًا احنا أخذناها كمثال قبلين، المقدار الثابت صفر،
+
+107
+00:13:44,720 --> 00:13:50,620
+مظبوط، وأثبتنا أنها ideal، هنا بقول اللي المقدار
+
+108
+00:13:50,620 --> 00:13:56,260
+الثابت هو عدد زوجي، مش أي عدد، وبدنا نروح نثبت أن
+
+109
+00:13:56,260 --> 00:14:03,350
+هذه عبارة عن إيش؟ عبارة عن ideal، وده بسيط جدًا، يبقى
+
+110
+00:14:03,350 --> 00:14:07,530
+الثلاث خطوات: أولًا، أن الفرق بين أي
+
+111
+00:14:07,530 --> 00:14:13,050
+عنصرين منها موجود فيها، حاصل ضرب عنصر من الـ ring
+
+112
+00:14:13,050 --> 00:14:17,730
+أو عنصر من هذه الـ set، لو ضربناهم في بعض يمين أو
+
+113
+00:14:17,730 --> 00:14:24,590
+شمال، موجود داخلها، طبعًا لو رجعنا بالذاكرة قليلًا إلى
+
+114
+00:14:24,590 --> 00:14:31,930
+أوراق المحاضرة الماضية، آخر مثال، مثال خمسة، شبيه قوي
+
+115
+00:14:31,930 --> 00:14:36,790
+وكبير جدًا ما بين هذا المثال والمثال الأول، لكن
+
+116
+00:14:36,790 --> 00:14:43,910
+بداية بدنا نثبت أن هذا .. أن هذه، أو هذه الـ set ليست
+
+117
+00:14:43,910 --> 00:14:54,430
+فارغة، non-empty، تمام؟ فبعدين بقوله الآن that the set I
+
+118
+00:14:54,430 --> 00:15:02,070
+is non-empty،  أفضل صفر موجود، زي ما عملنا، قدرنا نثبت
+
+119
+00:15:02,070 --> 00:15:09,610
+هل لي ولو عنصر واحد ثاني، because لو
+
+120
+00:15:09,610 --> 00:15:14,810
+أخذت F of zero، فإيش بده يساوي؟ zero
+
+121
+00:15:14,810 --> 00:15:19,110
+zero + zero + zero + 2m، يبقى 2m، 2m عدد
+
+122
+00:15:19,110 --> 00:15:23,910
+زوجي، polynomial والحد الثابت فيها عدد زوجي،
+
+123
+00:15:23,910 --> 00:15:32,080
+إذا هذه موجودة وين؟ في I، لأن هذا موجود في I، مدى ما
+
+124
+00:15:32,080 --> 00:15:38,220
+موجود في I، يبقى الـ I non-empty، الآن الـ
+
+125
+00:15:38,220 --> 00:15:44,360
+condition اثنين، الآن الـ condition ثلاثه are the
+
+126
+00:15:44,360 --> 00:15:52,100
+same، نفس الشكل as example خمسة،
+
+127
+00:15:53,010 --> 00:15:57,470
+لذلك مش هروح أضيع الوقت وأكرر فيه،  أو
+
+128
+00:15:57,470 --> 00:16:04,330
+راجع مثال خمسة، بتكون وصلت للإجابة، طيب، نجي
+
+129
+00:16:04,330 --> 00:16:08,770
+لسؤال، بس سؤال calculus، المرة هذه، اللي عارفينه
+
+130
+00:16:08,770 --> 00:16:12,950
+ومتذكرين، الـ calculus بتلاقوه إن شاء الله بسيط، طيب،
+
+131
+00:16:12,950 --> 00:16:21,790
+مثال رقم ثمانية، بيقول ما يأتي، اللي بيقول
+
+132
+00:16:21,790 --> 00:16:31,470
+consider the ring، consider the ring، اللي هي R،
+
+133
+00:16:31,470 --> 00:16:41,770
+تساوي، R تساوي كل العناصر F of X such that، such
+
+134
+00:16:41,770 --> 00:16:49,130
+that الـ F of X is a real valued function، is a real
+
+135
+00:16:49,710 --> 00:17:03,810
+valued function، among little s that capital S، هي كل
+
+136
+00:17:03,810 --> 00:17:11,010
+العناصر g of x اللي موجودة في الـ ring R، such that
+
+137
+00:17:11,010 --> 00:17:19,500
+الـ g is a differentiable function، دالة قابلة
+
+138
+00:17:19,500 --> 00:17:32,360
+للاشتقاق، show that، show that، بيقول إن الـ S is a sub
+
+139
+00:17:32,360 --> 00:17:42,720
+ring of R، but not an ideal،
+
+140
+00:18:19,270 --> 00:18:25,310
+السؤال مرة ثانية: يقول: خذ ring، كل الدوال التي
+
+141
+00:18:25,310 --> 00:18:31,490
+لها قيمة لو عوضنا بأي عدد حقيقي، real valued
+
+142
+00:18:31,490 --> 00:18:35,750
+function، يعني لو عوضت عدد حقيقي من الـ set في real
+
+143
+00:18:35,750 --> 00:18:40,290
+number، بلاقي إنها لها قيمة عددية، يعني الدوال
+
+144
+00:18:40,290 --> 00:18:47,600
+المعرفة، تمام؟ مين الـ S؟ كل الـ g of x الموجودة في
+
+145
+00:18:47,600 --> 00:18:53,820
+الـ ring R بحيث الـ g تكون قابلة للاشتقاق، وكل الدوال
+
+146
+00:18:53,820 --> 00:18:57,460
+قابلة للاشتقاق؟ لأ لأ لأ لأ لأ لأ لأ لأ
+
+147
+00:18:57,460 --> 00:18:58,820
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+148
+00:18:58,820 --> 00:18:59,160
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+149
+00:18:59,160 --> 00:19:01,340
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+150
+00:19:01,340 --> 00:19:09,820
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+151
+00:19:09,820 --> 00:19:11,460
+لأ،
+
+152
+00:19:12,980 --> 00:19:18,920
+لا الدالة معرفة ولا مشتقتها معرفة، بس هذه خارج
+
+153
+00:19:18,920 --> 00:19:23,860
+نطاق الـ ring R منها، احنا بنتكلم على الدوال
+
+154
+00:19:23,860 --> 00:19:30,380
+المعرفة، طيب، هي الدالة وقتاش بيكون مشتقتها does
+
+155
+00:19:30,380 --> 00:19:38,100
+not exist؟ في كام مكان؟ في كام حالة؟ في كده حالات
+
+156
+00:19:38,100 --> 00:19:44,820
+حالات في كل قلص إيه؟ في كام حالة غير قابلة للاشتقاق؟
+
+157
+00:19:44,820 --> 00:19:47,960
+تقدرش؟
+
+158
+00:19:47,960 --> 00:19:53,020
+غير متصلة؟
+
+159
+00:19:53,020 --> 00:20:00,100
+طيب، وإذا غير متصلة، غير قابلة للاشتقاق، يبقى أربع
+
+160
+00:20:00,100 --> 00:20:04,980
+حالات، الحالة الأولى: لو رسمت الرسمة، لو
+
+161
+00:20:04,980 --> 00:20:12,390
+طلع عندي corner، لو كان الرسم فيه كسر، لو كان
+
+162
+00:20:12,390 --> 00:20:18,430
+فيه Vertical Tangent، لأن المشتقة عند الـ Vertical
+
+163
+00:20:18,430 --> 00:20:23,230
+Tangent بتصير Infinity، مش معرفة، الأمر الرابع ما
+
+164
+00:20:23,230 --> 00:20:31,990
+قالته زميلتكم .. شو اسمها؟ مقداد؟
+
+165
+00:20:31,990 --> 00:20:37,590
+زغلان، زغلان، زغلان، زغلان، زغلان، زغلان، زغلان،
+
+166
+00:20:37,590 --> 00:20:37,690
+زغلان، زغلان، زغلان، زغلان، زغلان، زغلان، زغلان،
+
+167
+00:20:37,690 --> 00:20:37,750
+زغلان، زغلان، زغلان، زغلان، زغلان، زغلان، زغلان،
+
+168
+00:20:37,750 --> 00:20:41,840
+زغلان، زغلان، زغلان، زغلان، زغلان، زغلان، يبقى هي
+
+169
+00:20:41,840 --> 00:20:45,720
+الـ أربع حالات اللي الدالة بتكون عندها غير قابلة
+
+170
+00:20:45,720 --> 00:20:50,980
+للاشتقاق، مثال بسيط، عكس مقالة زميلتكم،  في
+
+223
+00:26:16,040 --> 00:26:24,940
+الإتنين exist، تمام؟ هذا معناه هذا موجود في S يبقى
+
+224
+00:26:24,940 --> 00:26:35,820
+هذا معناه أن الـ G1 ماقص G2 is different يعني G1
+
+225
+00:26:35,820 --> 00:26:45,880
+ماقص G2 موجودة في S، بدنا نروح للشرط الثالث، الشرط
+
+226
+00:26:45,880 --> 00:26:52,930
+الثالث بدنا ناخد جي واحد جي إثنين الكل prime as a
+
+227
+00:26:52,930 --> 00:26:59,870
+function of X، أظن هذا الكلام يساوي جي واحد A prime
+
+228
+00:26:59,870 --> 00:27:07,030
+في جي إثنين prime، غلط غلط، هذه مشتقة حاصل ضرب
+
+229
+00:27:07,030 --> 00:27:11,110
+الثانية، بجدال الأولى في مشتقة الثانية زي دي
+
+230
+00:27:11,110 --> 00:27:18,640
+الثانية في مشتقة الأولى، يبقى هذه الدالة الأولى في
+
+231
+00:27:18,640 --> 00:27:26,260
+مشتقة الدالة الثانية زائد مشتقة الدالة الأولى في
+
+232
+00:27:26,260 --> 00:27:32,620
+الدالة الثانية، الحين جي واحد و جي إثنين أنا ماخدهم
+
+233
+00:27:32,620 --> 00:27:39,900
+وين؟ في الـ S، يعني كل واحدة فيهم قابلة للاشتقاق، إذا
+
+234
+00:27:39,900 --> 00:27:46,490
+هذه قابلة للاشتقاق وهذه مشتقتها موجودة لأنها قابلة
+
+235
+00:27:46,490 --> 00:27:52,270
+للاشتقاق، إذا حاصل الضرب هذا كله ماله؟ موجود، قابل
+
+236
+00:27:52,270 --> 00:27:58,850
+الاشتقاق وهذا حاصل الضرب برضه قابل للاشتقاق، يبقى
+
+237
+00:27:58,850 --> 00:28:05,870
+هذه بدها تكون موجودة في S، هذا بدي يعطينا أن G1 G2
+
+238
+00:28:05,870 --> 00:28:11,500
+موجود في S بناء على هذا الكلام، بصير الـ S هي عبارة
+
+239
+00:28:11,500 --> 00:28:22,620
+عن sub ring، يبقى هنا سؤال: S is a sub ring of A
+
+240
+00:28:22,620 --> 00:28:25,700
+finally
+
+241
+00:28:25,700 --> 00:28:34,000
+أخيرا، بدي أثبت، أثبت أن الـ S هذه ما بنفعش تكون ideal
+
+242
+00:28:34,000 --> 00:28:40,040
+ما هي ideal؟ sub ring بين مشيكلك، لكن ideal يبعد
+
+243
+00:28:40,040 --> 00:28:45,360
+الله، شوف لك شغل غيرها الشغل. بيقول الآن: عشان أثبت
+
+244
+00:28:45,360 --> 00:28:50,860
+أنها ideal، بدي آخذ element من S و element من R
+
+245
+00:28:50,860 --> 00:28:57,580
+و أضربهم في بعض و أشوف هل هذا الكلام موجود في S ولا
+
+246
+00:28:57,580 --> 00:29:04,420
+غير موجود في S. إذا باجي بقوله: خد لي G موجودة في S.
+
+247
+00:29:05,550 --> 00:29:15,090
+الـ F موجودة في A، then الـ G is differentiable
+
+248
+00:29:15,090 --> 00:29:29,490
+function and الـ F is not necessarily differentiable
+
+249
+00:29:30,890 --> 00:29:34,370
+لأن الـ R تحتوي الـ differentiable و غير
+
+250
+00:29:34,370 --> 00:29:38,250
+الـ differentiable، يبقى الـ F اللي أخدتها ليس
+
+251
+00:29:38,250 --> 00:29:43,970
+بالضرورة تكون قابلة للاشتقاق. الآن لو جينا بناخذ
+
+252
+00:29:43,970 --> 00:29:53,330
+أخذنا الـ GF prime، السؤال هو: هل هذا
+
+253
+00:29:53,330 --> 00:29:59,990
+يساوي؟ والله نشوف، اليساوي في الأول. هل هذا يساوي؟
+
+254
+00:30:00,220 --> 00:30:09,600
+الـ G في الـ F prime زائد الـ G prime في الـ F؟
+
+255
+00:30:09,600 --> 00:30:14,300
+ليس بالضرورة، ليش؟ لأن هذى الـ differentiable هذى
+
+256
+00:30:14,300 --> 00:30:19,180
+ليس بالضرورة، لأن هذى الـ differentiable هذى ليس
+
+257
+00:30:19,180 --> 00:30:24,300
+بالضرورة، يبقى هذا الكلام ما بيساوي هذا إلا في حالة
+
+258
+00:30:24,300 --> 00:30:32,180
+differentiable، يبقى هذه صارت مالها؟ does not belong
+
+259
+00:30:32,180 --> 00:30:46,800
+to S because الـ F is not necessarily differentiable
+
+260
+00:30:46,800 --> 00:30:56,200
+يبقى هنا، سواء الـ S is not I
+
+261
+00:31:00,400 --> 00:31:06,860
+إحنا المحاضرة الماضية و ما أخدناه اليوم كله أمثلة
+
+262
+00:31:06,860 --> 00:31:11,940
+على حكاية مين الـ ideal و هل الـ set اللي بناخدها أو
+
+263
+00:31:11,940 --> 00:31:16,080
+الـ subset اللي بناخدها من هناك ممكن تكون ideal
+
+264
+00:31:16,080 --> 00:31:20,520
+و ممكن ما تكونش ideal، إيش يطلع عندنا ideal و إيش
+
+265
+00:31:20,520 --> 00:31:25,280
+يطلع عندنا ما هو ideal، هذا هو النقطة الأولى من
+
+266
+00:31:25,280 --> 00:31:29,440
+هذا الشابتر، النقطة الثانية أو العمود الفقري الثاني
+
+267
+00:31:29,440 --> 00:31:33,500
+من هذا الشابتر اللي هو الـ factor ring أو الـ
+
+268
+00:31:33,500 --> 00:31:39,120
+quotient ring، فنروح نعطيها التعريف وهو الذي لن
+
+269
+00:31:39,120 --> 00:31:43,520
+يختلف عن تعريف الـ factor group اللي درسناه في جبر
+
+270
+00:31:43,520 --> 00:31:51,340
+حديث واحد، if an ideal has a definition، بقول
+
+271
+00:31:51,340 --> 00:32:00,970
+لك يا بي: أنا أديك بي ring، let the A be an ideal of
+
+272
+00:32:00,970 --> 00:32:14,730
+pairing up the set of cosets، the set of cosets
+
+273
+00:32:14,730 --> 00:32:25,150
+اللي على الشكل A زائد الـ A such that الـ R موجودة
+
+274
+00:32:25,150 --> 00:32:36,250
+في R، موجودة في R، بتساوي R modulo A is called A
+
+275
+00:32:36,250 --> 00:32:45,390
+factor، is called A factor أو quotient
+
+276
+00:32:53,330 --> 00:32:58,790
+كلمة Coset هذه أول مرة نسمعها في جبر حديث إثنين
+
+277
+00:32:58,790 --> 00:33:04,490
+لكن مرّ معنا و إحنا في جبر حديث واحد، آه، بس كانت
+
+278
+00:33:04,490 --> 00:33:20,890
+ذات على الـ groups وليس على الـ rings، الآن
+
+279
+00:33:20,890 --> 00:33:28,690
+ما هي الـ Coset؟ هلأ عندي كان عندي group G، جيت
+
+280
+00:33:28,690 --> 00:33:34,410
+أخذت منها sub group H من الـ group الأصلية، جيت على
+
+281
+00:33:34,410 --> 00:33:41,870
+عناصر G و خليت العنصر، كل عنصر من G، أثّر عليها إما
+
+282
+00:33:41,870 --> 00:33:46,490
+بالضرب أو بالجمع أو العملية المعرفة على الـ group
+
+283
+00:33:46,490 --> 00:33:53,380
+كان جمع، ضرب، طرح، غيره إلى آخره، كل مرة سينتج مجموعة
+
+284
+00:33:53,380 --> 00:33:57,800
+من العناصر، و أحيانا العناصر اللي بتتساوى، اللي
+
+285
+00:33:57,800 --> 00:34:01,880
+بتتساوى برميها، علي جنب، باخذ بس واحد منهم
+
+286
+00:34:01,880 --> 00:34:05,920
+ما باخذش باقي اللي بيساووا، يمكن هذه المجموعة بتكوين
+
+287
+00:34:05,920 --> 00:34:11,400
+لي cosets من الـ group الأصلية، الـ cosets هدول
+
+288
+00:34:11,400 --> 00:34:18,220
+بيكونوا عناصر الـ factor group G modulo H، تمام
+
+289
+00:34:18,530 --> 00:34:23,530
+بجينا نقول: جي modulo H، عناصرها كذا كذا، كل عنصر من
+
+290
+00:34:23,530 --> 00:34:28,990
+عناصرها اللي هو بده يساوي مين؟ بده يساوي coset، وهذه
+
+291
+00:34:28,990 --> 00:34:35,010
+استخدمناها في إثبات النظرية المشهورة في جميع كتب
+
+292
+00:34:35,010 --> 00:34:41,950
+الجبر وهي نظرية Lagrange، Lagrange theorem، وهو إن
+
+293
+00:34:41,950 --> 00:34:48,320
+الـ order للـ subgroup بيقسم الـ order للـ group، ما دام إن
+
+294
+00:34:48,320 --> 00:34:53,360
+في عندنا فكرة قديمة بدنا نجددها، قال لي: خد لي A
+
+295
+00:34:53,360 --> 00:34:58,660
+عبارة عن الـ ideal في الـ ring R، يبقى الـ set of course it's
+
+296
+00:34:58,660 --> 00:35:04,680
+كل العناصر اللي على الصّورة R زائد A حيث R موجودة
+
+297
+00:35:04,680 --> 00:35:10,100
+في R، و اللي بدها تكون لي set جديدة اسمها R modulo A
+
+298
+00:35:10,100 --> 00:35:15,500
+كانت في الـ group نسميها G modulo H حيث الـ H هي بالـ
+
+299
+00:35:15,500 --> 00:35:22,190
+sub group، يبقى هذه اسمها Factoring أو Coseting.
+
+300
+00:35:22,270 --> 00:35:27,430
+تمام؟ طيب الآن في نظرية على الـ factor ring
+
+301
+00:35:27,430 --> 00:35:34,190
+لنتعرف على هذه النظرية و نحاول أن نبرهّنها. النظرية
+
+302
+00:35:34,190 --> 00:35:34,770
+بتقول
+
+303
+00:35:44,250 --> 00:35:51,510
+بتقول: let الـ A be a sub ring of R، let الـ A be a
+
+304
+00:35:51,510 --> 00:36:06,410
+sub ring of R، the set of cosets، the set of cosets
+
+305
+00:36:06,410 --> 00:36:13,980
+cosets، اللي هو امين؟ الـ set of cosets، اللي هي كل
+
+306
+00:36:13,980 --> 00:36:23,080
+العناصر R زائد A بحيث R موجودة في R، مالها؟ is a
+
+307
+00:36:23,080 --> 00:36:33,860
+ring، is a ring، is a ring under the operations
+
+308
+00:36:33,860 --> 00:36:38,800
+under the operations
+
+309
+00:36:41,530 --> 00:36:49,750
+تحت العملياتين اللي هو الـ S زائد الـ A زائد الـ T
+
+310
+00:36:49,750 --> 00:37:04,600
+زائد الـ A، بدي يساوي S زائد T زائد الـ A، and الـ S زائد
+
+311
+00:37:04,600 --> 00:37:16,300
+الـ A مضروب في الـ T زائد الـ A يساوي ST زائد الـ A، if
+
+312
+00:37:16,300 --> 00:37:24,480
+and only if، if and only if، الـ A is an ideal
+
+313
+00:37:42,700 --> 00:37:46,880
+مجينا نقول: في حالة الـ factor group، مشان تبقى الـ
+
+314
+00:37:46,880 --> 00:37:51,980
+group، factor group، لازم يكون الـ G modulo H، الـ H is
+
+315
+00:37:51,980 --> 00:37:57,240
+a normal sub group، تمام؟ أول ما بديت في الجبر هنا
+
+316
+00:37:57,240 --> 00:38:04,300
+قلت لكم الـ ideal اللي عندنا في جبر حديث إثنين تعادل
+
+317
+00:38:04,300 --> 00:38:09,560
+normal sub group في حالة من الـ groups، وهذا ما نحن
+
+318
+00:38:09,560 --> 00:38:15,400
+وصلنا إليه، ما قلناه لكم في أول محاضرة جئتم فيها
+
+319
+00:38:15,400 --> 00:38:21,760
+إليكم نظرية بتقول: خد لي A subring من R، مش كل
+
+320
+00:38:21,760 --> 00:38:27,900
+subring بتكون ideal، فرض الـ A subring، يبقى الـ set of
+
+321
+00:38:27,900 --> 00:38:31,380
+cosets اللي بالشكل، يعني إنها there is a ring
+
+322
+00:38:31,380 --> 00:38:38,400
+تحت العمليتين هدول، الجمع والضرب، if and only if الـ A
+
+323
+00:38:38,400 --> 00:38:44,610
+is an ideal، هذا الكلام صحيح لو كان الـ A ideal وليس
+
+324
+00:38:44,610 --> 00:38:50,330
+subring، ما هو كل ideal هو عبارة عن subring. يعني إحنا
+
+325
+00:38:50,330 --> 00:38:54,650
+ما نقدر نحكم على الـ set إنها ideal إلا إذا كانت
+
+326
+00:38:54,650 --> 00:39:00,690
+subring في الأساس. شوف يا بنات، يبقى كلمة if and
+
+327
+00:39:00,690 --> 00:39:06,630
+only if، يعني أن البرهان سيصير في اتجاهين. يبقى
+
+328
+00:39:06,630 --> 00:39:11,610
+الآن بدنا نأخذ الاتجاه الأول. يبقى بدي أجي أقوله
+
+329
+00:39:11,610 --> 00:39:25,850
+assume that، أن الـ A is an ideal، إيش بدّه يثبت؟ أن الـ R
+
+330
+00:39:25,850 --> 00:39:32,230
+modulo A is a ring، يبقى بدّه يروح يثبت أن كل الـ
+
+331
+00:39:32,230 --> 00:39:36,970
+cosets هدول عبارة عن ring تحت، من تحت العمليات
+
+332
+00:39:36,970 --> 00:39:44,720
+اللي إثنين هدول. يجي هنا: want to show، want to show
+
+333
+00:39:44,720 --> 00:39:54,340
+that، أن الـ A modulo A is a ring، طيب أنا مشان أثبت
+
+334
+00:39:54,340 --> 00:40:01,940
+إنها ring، فبدي أعمل ست خواص، و ليس ستة خواص، ست
+
+335
+00:40:01,940 --> 00:40:08,090
+خواص، وليس ستة خواص، لأن العدد يخالف المعدود من
+
+336
+00:40:08,090 --> 00:40:12,990
+ثلاثة لتسعة، إلا إذا سبق المعدود العدد، جاز
+
+337
+00:40:12,990 --> 00:40:20,330
+الوجهان. نقول: البنات الست، و ممكن نقول: البنات الستة
+
+338
+00:40:20,330 --> 00:40:25,530
+عشرتين، صح؟ لكن لما نقول: ست بنات، لازم التذكير
+
+339
+00:40:25,530 --> 00:40:31,810
+والتأنيث يحدث هنا، فهذه قاعدة نحوية، والقواعد النحوية
+
+340
+00:40:31,810 --> 00:40:38,410
+مثل ما هي الرياضيات، كذلك قواعد، وإحنا بنشتغل على هذه
+
+341
+00:40:38,410 --> 00:40:43,850
+القواعد، طيب نفترض إنّه ideal، اللي بدنا نثبت إن الـ R
+
+342
+00:40:43,850 --> 00:40:48,830
+modulo I is a ring، يبقى الخطوة الأولى بدّه يثبت إنها
+
+343
+00:40:48,830 --> 00:40:54,270
+Abelian تحت عملية الجمع، و Associative تحت عملية
+
+344
+00:40:54,270 --> 00:40:59,030
+الجمع، و Zero element تحت عملية الجمع، و ناقص element
+
+345
+00:40:59,030 --> 00:41:04,540
+تحت عملية الجمع، بضلّ الطرف، والجمع، الـ associativity
+
+346
+00:41:04,540 --> 00:41:12,160
+و الـ distributive، مظبوط؟ طيب خلينا نثبت أول خاصية، طيب
+
+347
+00:41:12,160 --> 00:41:17,300
+الآن يا بنات، لو جيت أخذت الـ R و عملتها عملية
+
+348
+00:41:17,300 --> 00:41:23,260
+الجمع، abelian ولا لا abelian group؟ جمع a و b
+
+349
+00:41:23,260 --> 00:41:27,280
+بيساوي b زائد a، عادي جدا، مش طرف عملية واحدة
+
+350
+00:41:27,280 --> 00:41:38,190
+بسيطة، يبقى هذا يعني is abelian group، طيب هذا يعني أن
+
+351
+00:41:38,190 --> 00:41:44,350
+الـ R تحت عملية الجامعة abelian ولا لا؟ يبقى هذا
+
+352
+00:41:44,350 --> 00:41:54,250
+يعني is abelian، هذا يعني أن الـ A هو الـ plus is
+
+353
+00:41:54,250 --> 00:41:54,850
+normal
+
+354
+00:41:58,870 --> 00:42:06,790
+صح؟ نسيت، مش بيجينا نقول normal subgroup ونحط الـ
+
+355
+00:42:06,790 --> 00:42:15,690
+condition إن الـ AR أو الـ AH بدها تساوي HA، نحدد ذلك
+
+356
+00:42:15,690 --> 00:42:25,050
+أو الـ HA بدها تساوي A H، وكمان صيغة ثالثة، وكمان صيغة
+
+357
+00:42:25,050 --> 00:42:28,490
+رابعة، من خلال الأسئلة لإثبات الـ Normal Subgroup.
+
+358
+00:42:28,570 --> 00:42:33,750
+لكن أخذنا القاعدة إن لو كانت الـ R أبيليان، إذن
+
+359
+00:42:33,750 --> 00:42:39,650
+عملية الإبدال سهلة جدا وبالتالي كل Abelian group،
+
+360
+00:42:40,030 --> 00:42:46,390
+any subgroup منها is Normal. يجي هذا بدي يعطينا
+
+361
+00:42:46,390 --> 00:42:58,070
+Normal in R plus. ما دام Normal، يبقى سؤال: الـ R
+
+362
+00:42:58,070 --> 00:43:07,710
+modulo A، مع عملية الجمع exist؟
+
+363
+00:43:07,710 --> 00:43:14,190
+و abelian exist، و abelian في نفسها exist، and
+
+364
+00:43:14,190 --> 00:43:23,500
+abelian، الـ R abelian و الـ A abelian، و الـ A صارت
+
+365
+00:43:23,500 --> 00:43:27,580
+normal subgroup، و الـ R modulo A exist، و في نفس
+
+366
+00:43:27,580 --> 00:43:32,160
+الوقت abelian، إذا هنا يتحقق الـ condition الأول ولا
+
+367
+00:43:32,160 --> 00:43:38,340
+لا؟ من الـ ring، إذا الـ condition الأول خلصنا منه،
+
+368
+00:43:38,340 --> 00:43:43,020
+أيه، قولي؟ إحنا
+
+369
+00:43:43,020 --> 00:43:47,900
+أخذنا عملية الجمع بس، فإتكلم عن R تحت عملية
+
+370
+00:43:47,900 --> 00:43:52,940
+الجمع، إتكلمتش عن الضرب لسه، كلمنا على الجمع، لكن لو
+
+371
+00:43:52,940 --> 00:43:57,480
+حطيت ضرب، فهو سيصبح ضرب أبيليان، من الضرب وليس
+
+372
+00:43:57,480 --> 00:44:03,900
+بالجمع، وبيطلع يتعمق، تحفظك زائد زائد زائد، طبعا؟
+
+373
+00:44:03,900 --> 00:44:08,380
+أنا بتكلم كإني بأشتغل في الـ groups، لسه ما قلت
+
+374
+00:44:08,380 --> 00:44:14,340
+شريط، طبعا؟ طيب، R plus is abelian، تمام
+
+375
+00:44:14,340 --> 00:44:19,660
+طيب، صارت هذه abelian group، يبقى إحنا حققنا الـ
+
+376
+00:44:19,660 --> 00:44:24,280
+condition الأول من مين؟ من الـ ring، نيجي لـ الـ
+
+377
+00:44:24,280 --> 00:44:28,420
+condition الثاني، الـ condition الثاني قال لي: خاصية
+
+378
+00:44:28,420 --> 00:44:37,480
+الـ associativity برضه صحيحة، يبقى الـ check ذات
+
+379
+00:44:37,910 --> 00:44:45,150
+إكتشف لي إن the associative
+
+380
+00:44:45,150 --> 00:44:49,490
+law
+
+381
+00:44:49,490 --> 00:44:58,170
+قانون الـ associativity، الـ associativity is hold
+
+382
+00:44:58,170 --> 00:45:03,310
+under addition
+
+383
+00:45:03,310 --> 00:45:05,570
+تحت عملية الجمع
+
+384
+00:45:10,160 --> 00:45:13,300
+يبقى air condition الثاني، بدنا نيجي إلى الـ zero
+
+385
+00:45:13,300 --> 00:45:26,840
+element، الـ A is the zero، أو الـ A، أو الـ zero زائد A
+
+386
+00:45:26,840 --> 00:45:38,440
+يساوي A، is the zero element of R modulo A، because
+
+387
+00:45:40,890 --> 00:45:48,250
+و بيثبت إن فعلا هذا هو zero element، because if الـ A
+
+388
+00:45:48,250 --> 00:45:58,230
+زائد الـ A موجود في الـ A modulo A، then لو أخذت الـ A
+
+389
+00:45:58,230 --> 00:46:06,750
+زائد الـ A زائد الـ zero زائد الـ A حسب الـ definition
+
+390
+00:46:06,750 --> 00:46:12,640
+اللي إحنا حاطينه على الجمع، هذا، يبقى هذا الكلام
+
+391
+00:46:12,640 --> 00:46:19,780
+بالنسبة للـ R زائد الـ zero زائد الـ A، يعني الـ R
+
+392
+00:46:19,780 --> 00:46:26,500
+زائد الـ A، لأن الـ
+
+445
+00:53:09,370 --> 00:53:16,690
+إذا بدأت آخذ يا بنات الـ S زائد الـ A، بدأ أضربها في
+
+446
+00:53:16,690 --> 00:53:23,530
+مين؟ في الـ T زائد الـ A، وشوف وين بدأ توصيل هذا الكلام.
+
+447
+00:53:23,530 --> 00:53:30,780
+بده يساوي S B زائد الـ A، هذا الكلام يساوي S زائد الـ A.
+
+448
+00:53:30,780 --> 00:53:35,940
+أو بدي آخذ الأولى.
+
+449
+00:53:35,940 --> 00:53:45,200
+S زائد الـ A يساوي S prime زائد الـ A، إيش ممكن أكتب؟
+
+450
+00:53:45,200 --> 00:53:53,040
+هذه، ممكن أكتب S ناقص S prime زائد الـ A يساوي الـ A.
+
+451
+00:53:53,300 --> 00:53:59,960
+أضفنا سالب S prime للطرفين، هذا إيش معناه؟ أن
+
+452
+00:53:59,960 --> 00:54:04,500
+الـ elements زائد A يساوي الـ A itself، إيش معناه؟
+
+453
+00:54:04,500 --> 00:54:11,120
+أن هذا العنصر موجود في A، هذا معناه
+
+454
+00:54:11,120 --> 00:54:18,580
+أن الـ S ناقص S prime موجود في A، هذا معناه أن الـ S
+
+455
+00:54:18,580 --> 00:54:28,070
+ناقص S prime تساوي a، for some a اللي موجود في A.
+
+456
+00:54:28,070 --> 00:54:40,150
+أو الـ S تساوي S prime زائد اللي هو من الـ A، أضف
+
+457
+00:54:40,150 --> 00:54:46,490
+نضيف S prime للطرفين، بنفس الطريقة، similarly
+
+458
+00:54:50,810 --> 00:54:58,250
+Similarly، الـ T تساوي T prime زائد الـ B، والـ A والـ
+
+459
+00:54:58,250 --> 00:55:04,930
+B موجودة في الـ A، هاي يقول لنا A موجود في A، وكذلك الـ
+
+460
+00:55:04,930 --> 00:55:11,630
+B موجود في B، طب احنا إيش بدنا؟ بدنا الـ S في T، إذا
+
+461
+00:55:11,630 --> 00:55:17,910
+لو ضربت الـ S في T، يبقى الـ S في T يساوي S prime
+
+462
+00:55:17,910 --> 00:55:25,710
+زائد الـ A في T prime زائد الـ B، نفكر قصة، يبقى هذا
+
+463
+00:55:25,710 --> 00:55:33,930
+بدّه يعطينا S prime T prime زائد A T prime زائد S
+
+464
+00:55:33,930 --> 00:55:46,430
+prime B زائد A B، طيب احنا بدنا S T زائد A، بدنا الـ
+
+465
+00:55:46,430 --> 00:55:52,750
+S T زائد A يساوي هذا زائد A، يبقى هذا الكلام يساوي S'
+
+466
+00:55:53,370 --> 00:56:04,810
+T' A T' S' B زائد A B زائد A، إذا احنا وصلنا لإنه
+
+467
+00:56:04,810 --> 00:56:11,830
+S T يساوي هذا العنصر، إذا S T زي الـ A، عادل، سيساوي هذا
+
+468
+00:56:11,830 --> 00:56:19,130
+العنصر زي A، السؤال هو: هذا موجود في A؟ لأن A و B
+
+469
+00:56:19,130 --> 00:56:29,670
+موجودة في A، و A و B موجودة في A، و B موجودة
+
+470
+00:56:29,670 --> 00:56:33,250
+في A، و S موجودة في R، و A موجودة في A، و S موجودة في R
+
+471
+00:56:33,250 --> 00:56:34,290
+و A موجودة في A، و S موجودة في R، و A موجودة في A، و S
+
+472
+00:56:34,290 --> 00:56:37,530
+موجودة في R، و A موجودة في A، و S موجودة في A، و S
+
+473
+00:56:37,530 --> 00:56:39,830
+موجودة في R، و A موجودة في A، و S موجودة في R، و A
+
+474
+00:56:39,830 --> 00:56:46,990
+موجودة في A، و S موجودة في A، و S موجودة في A، و S
+
+475
+00:56:47,200 --> 00:56:54,700
+الـ A L M I D، يبقى هذا مش بيعطينا أمان، بيعطينا أن
+
+476
+00:56:54,700 --> 00:57:00,840
+الـ S T زائد الـ A، يسبق هذا، مادام كله موجود فيها.
+
+477
+00:57:00,840 --> 00:57:07,580
+يبقى هذا الجمع بده يعطينا A، يبقى S prime T prime
+
+478
+00:57:07,580 --> 00:57:15,160
+زائد A، قبل هذا، وهو المطلوب، ليه بروح بقوله: Thus
+
+479
+00:57:15,880 --> 00:57:26,900
+وهكذا، بص اللي هو الـ R modulo A is a ring، اللي هي
+
+480
+00:57:26,900 --> 00:57:34,060
+الـ factoring، طبعاً؟ ضايع الاتجاه الثاني الآن، لو كان
+
+481
+00:57:34,060 --> 00:57:40,100
+لأ، لو كانت هذه factoring، يبقى الـ A بتاعت الـ person
+
+482
+00:57:40,100 --> 00:57:44,320
+ID، للمرة القادمة إن شاء الله.
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e1ff8332c1f0dbeaf6ca1023b09204ec9de85770
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA_postprocess.srt
@@ -0,0 +1,1816 @@
+1
+00:00:20,820 --> 00:00:25,440
+بسم الله الرحمن الرحيم نكمل ما ابتدأنا به في المرة
+
+2
+00:00:25,440 --> 00:00:31,420
+الماضية وهو حل أسئلة من أسئلة التمرين على chapter
+
+3
+00:00:31,420 --> 00:00:37,640
+17 وصلنا المرة اللي فاتت إلى chapter 10 إلى سؤال
+
+4
+00:00:37,640 --> 00:00:43,320
+10 وفي سؤال 10 مكون من عدة نقاط تعرضنا للنقطة
+
+5
+00:00:43,320 --> 00:00:49,390
+الأولى والثالثة وقلنا التنتين هدول زي بعضو كذلك
+
+6
+00:00:49,390 --> 00:00:54,410
+تعرضنا للثانية و الآن الرابعة التالتية الرابعة
+
+7
+00:00:54,410 --> 00:00:58,810
+اللي هي نمرة دي و الخامسة أخدنا مثل زي هي بقى لا
+
+8
+00:00:58,810 --> 00:01:03,810
+داعي نضيع وقت فيها نيجي لمين؟ للخامسة اللي عندنا
+
+9
+00:01:03,810 --> 00:01:11,010
+بدي أروح الآن على اللي هو ال field z2 بس بدنا نروح
+
+10
+00:01:11,010 --> 00:01:16,520
+نجيب ال F barالسؤال هو هل هذه irreducible والبقى
+
+11
+00:01:16,520 --> 00:01:22,920
+irreducible عالميا على اللي هو reduced operational
+
+12
+00:01:22,920 --> 00:01:29,660
+number يبقى بجي بقوله solution on
+
+13
+00:01:29,660 --> 00:01:39,440
+Z2 بدي يصير عندنا ال F bar of X تساوم ل X أص خمسة
+
+14
+00:01:39,440 --> 00:01:46,230
+زجمهينزايد X تربيع زايد واحد انه الخمسة اتنين زايد
+
+15
+00:01:46,230 --> 00:01:50,250
+اتنين زايد واحد اتنينات مع السلامة اللي لها في Z2
+
+16
+00:01:50,250 --> 00:01:55,090
+وضلها اتنين واحد يبقى آلة ال F bar of X الى X روز
+
+17
+00:01:55,090 --> 00:02:01,210
+خمسة زايد X تربيع زايد واحد الان بدنا نشوف هل لها
+
+18
+00:02:01,210 --> 00:02:07,870
+هذه أصفر والله مالهاش أصفر الان لو جيت حطيت Zero
+
+19
+00:02:07,870 --> 00:02:15,890
+Zero واحديبقى Zero ليس صفرا من أصفرها طيب الواحد
+
+20
+00:02:15,890 --> 00:02:22,790
+واحد واحد واحد تلاتة في زيته واحد يبقى مالهاش أصفر
+
+21
+00:02:22,790 --> 00:02:29,970
+يبقى ال F of Zero يبقى يسوى واحد وال F of واحد
+
+22
+00:02:29,970 --> 00:02:37,830
+كذلك يبقى يسوى واحد هذا بدي يعطينا ان F bar has
+
+23
+00:02:39,160 --> 00:02:49,720
+Zeros in the two يعني معناته الدرجة الأولى مستبعدة
+
+24
+00:02:49,720 --> 00:02:56,480
+و الدرجة التالتة مستبعدة يبقى هذا بده يعطينا if
+
+25
+00:02:56,480 --> 00:03:10,050
+bar of x has no factor of degree oneتمام؟ يبقى
+
+26
+00:03:10,050 --> 00:03:16,350
+معناته هذه مافيش عندي element أو factor منها ال
+
+27
+00:03:16,350 --> 00:03:20,190
+degree اللي واحد أو has no linear degree linear
+
+28
+00:03:20,190 --> 00:03:26,110
+factor ماعنديش factor يكون خطيا يبقى في المقابل
+
+29
+00:03:26,110 --> 00:03:30,110
+ماعنديش factor من الدرجة الرابعة لإن الدرجة
+
+30
+00:03:30,110 --> 00:03:34,130
+الرابعة مع الدرجة الأولى بيعطينا الدرجة الخامسة
+
+31
+00:03:34,130 --> 00:03:49,420
+and so ولذلكالـ F bar has no factor of degree for
+
+32
+00:03:49,420 --> 00:03:53,400
+لا من الدرجة الأولى ولا من الدرجة الراجعى يبقى
+
+33
+00:03:53,400 --> 00:03:59,180
+لضايل عند الدرجة التانية أو الدرجة التالتة لأن لو
+
+34
+00:03:59,180 --> 00:04:05,140
+افترضنا ان عندنا factor من الدرجة التالتة بدنا
+
+35
+00:04:05,140 --> 00:04:11,380
+نشوف شو شكلهومين ممكن يجيبلي عناصر تمام يبقى مضاجي
+
+36
+00:04:11,380 --> 00:04:21,920
+اقوله assume افترض ان ال F bar of X has a factor
+
+37
+00:04:21,920 --> 00:04:25,600
+of
+
+38
+00:04:25,600 --> 00:04:40,280
+degree 2 من الدرجة الثانية مثلا that isI am هذا ال
+
+39
+00:04:40,280 --> 00:04:49,180
+factor that is in the form يبقى في الشكل التالي
+
+40
+00:04:49,180 --> 00:04:58,780
+اللي هو ال X ترمية زائد X زائد V بتشوف في أكم
+
+41
+00:04:58,780 --> 00:05:07,100
+احتمال لهذه في Z2 يبقى بادي بقول we have4
+
+42
+00:05:07,100 --> 00:05:10,480
+possibilities
+
+43
+00:05:10,480 --> 00:05:14,780
+يبقى
+
+44
+00:05:14,780 --> 00:05:20,360
+في عندي أربع احتمالات للدرجة الثانية احتمال ان
+
+45
+00:05:20,360 --> 00:05:29,000
+يكون x تربيع فقط واحتمال ان يكون x تربيع زائد x
+
+46
+00:05:29,000 --> 00:05:38,810
+واحتمال ان يكون x تربيع زائد 1و احتمال ان يكون X
+
+47
+00:05:38,810 --> 00:05:45,090
+تربية زائد X زائد واحد في ال X نجي للاحتمالات
+
+48
+00:05:45,090 --> 00:05:49,790
+الأول يبقى الاحتمال الأول لو كان X تربية بقدر
+
+49
+00:05:49,790 --> 00:05:56,630
+احلله X في X تمام؟ و لو كان لي احتمالي الثاني بقدر
+
+50
+00:05:56,630 --> 00:06:02,510
+احلله X في X زائد واحد و لو كان لي احتمالي التالت
+
+51
+00:06:02,510 --> 00:06:11,780
+بقدر احلله X زائد واحدX زائد واحد طبعا اللي تاخد X
+
+52
+00:06:11,780 --> 00:06:18,020
+في X ب X ترابيعه زائد X و زايد X ب 2 X و احنا
+
+53
+00:06:18,020 --> 00:06:23,300
+بنشتغل في Z2 يبقى ب Zero مع السلامة ماضلش الا واحد
+
+54
+00:06:23,300 --> 00:06:28,440
+في واحد اليومين بواحد التلات احتمالات دول حللهم
+
+55
+00:06:28,440 --> 00:06:34,400
+الى حاصل ضرب عاملين من الدرجة الأولى هل هذا ممكن؟
+
+56
+00:06:34,870 --> 00:06:41,050
+لأ لإن استبعدنا الدرجة الأولى فوق هيو يبقى هذا كله
+
+57
+00:06:41,050 --> 00:06:50,270
+impossible يبقى هذا impossible كل احتمالات هذه غير
+
+58
+00:06:50,270 --> 00:06:57,370
+ممكنة السبب because because
+
+59
+00:06:57,370 --> 00:07:15,840
+ال F bar of X hasno factor of first degree بيظل
+
+60
+00:07:15,840 --> 00:07:21,480
+احتماله ثاني للي عندناها الان لو جسمنا ال
+
+61
+00:07:21,480 --> 00:07:26,680
+polynomial أصلية على ال polynomial هذه لا يمكن
+
+62
+00:07:26,680 --> 00:07:32,140
+يطلع هذا أحد العوامل يعني لا يمكن يطلع الناتجبدون
+
+63
+00:07:32,140 --> 00:07:36,480
+باقي، لازم يطلع النتج بمين؟ بباقي، يبقى لو راحت
+
+64
+00:07:36,480 --> 00:07:42,800
+كيك ومسكت القلم وقسمت ال polynomial اللي عندنا على
+
+65
+00:07:42,800 --> 00:07:48,360
+هذه هتلاقي لازم يبقى باقي، وأظن أن الباقي هو واحد
+
+66
+00:07:48,360 --> 00:07:55,380
+صحيح، تمام؟ وبالتالي هذه لا تقسم من اللي فوق، يبقى
+
+67
+00:07:55,380 --> 00:08:00,840
+باجي بقوله هذه by long division
+
+68
+00:08:03,750 --> 00:08:16,050
+الـ X تربيع زيد X زيد واحد is not a factor of F
+
+69
+00:08:16,050 --> 00:08:23,930
+bar of X معناته ان هو factor of second degree
+
+70
+00:08:23,930 --> 00:08:37,470
+تمام؟ يبقى هنا no factor off part of x of second
+
+71
+00:08:37,470 --> 00:08:43,130
+degree مدام
+
+72
+00:08:43,130 --> 00:08:46,790
+مافيش من الدرجة الثانية ممكن يكون من الدرجة
+
+73
+00:08:46,790 --> 00:08:51,810
+الثالثة برضه لأ لإنه حاصل ضربه ويحطينه 100 الدرجة
+
+74
+00:08:51,810 --> 00:08:59,250
+الخامسة يبقى هذا يقن كذلك now factor of third
+
+75
+00:08:59,250 --> 00:09:00,090
+degree
+
+76
+00:09:02,330 --> 00:09:09,630
+ال degree يبقى ايش تفسيرنا لهذا الكلام ان ال F bar
+
+77
+00:09:09,630 --> 00:09:15,890
+is irreducible على Z2 بس ضالت واحدة بشكل ان يكون
+
+78
+00:09:15,890 --> 00:09:21,770
+ال degree ل F هي degree ل F bar يبقى الان بقى اللي
+
+79
+00:09:21,770 --> 00:09:30,570
+بقوله since ال degree لل F هي نفس ال degreeللـ F
+
+80
+00:09:30,570 --> 00:09:39,730
+bar اللي هي تساوي خمسة We have ان ال F bar of X
+
+81
+00:09:39,730 --> 00:09:48,870
+اللي تساوي X أُص خمسة زائد X ترابية زائد واحد is
+
+82
+00:09:48,870 --> 00:10:00,250
+irreducible over زائد 2 هذا بدي يعطينا ايه؟by a
+
+83
+00:10:00,250 --> 00:10:08,790
+previous theorem by a previous theorem بنظرية
+
+84
+00:10:08,790 --> 00:10:17,150
+السابقة ال F of X اللي هي تساوي X أُس خمسة زائد
+
+85
+00:10:17,150 --> 00:10:26,050
+خمسة X ترابيع زائد واحد is irreducible over
+
+86
+00:10:28,200 --> 00:10:34,960
+الـ Q على
+
+87
+00:10:34,960 --> 00:10:40,780
+هيك بيقول ان هنا سؤال عشرة بدنا نروح لسؤال 11 سؤال
+
+88
+00:10:40,780 --> 00:10:47,220
+11 بيقول لي show that ال X أُس 4 زي 1 is reducible
+
+89
+00:10:47,220 --> 00:10:55,160
+على ال Q but reducible على مين؟ على A سؤال 11
+
+90
+00:10:55,160 --> 00:11:05,160
+بيقول showthat إن ال X أُس أربع زائد واحد is
+
+91
+00:11:05,160 --> 00:11:18,400
+irreducible over اكيوم but reducible over R
+
+92
+00:11:39,300 --> 00:11:46,800
+بويس يقول يبينلي ان ال X أُس 4 زي 1 is irreducible
+
+93
+00:11:46,800 --> 00:11:55,580
+على ال field Q اللي هي 6 rational number لكنه ليس
+
+94
+00:11:55,580 --> 00:12:02,480
+irreducible يعني irreducible على من؟ على R نقوله
+
+95
+00:12:02,480 --> 00:12:06,700
+بسيطة، بدنا نرجع لأي نظرية من النظريات اللي
+
+96
+00:12:06,700 --> 00:12:12,030
+درسناهاأو اي سؤال سابق من المسائل اللي اتعرضنا
+
+97
+00:12:12,030 --> 00:12:19,050
+عليهم ونحاول نحل المسألة الان الان لو جيتلي هذه
+
+98
+00:12:19,050 --> 00:12:27,350
+المثلة وروحت سميت هذه F of X يبقى ال F of X بيساوي
+
+99
+00:12:27,350 --> 00:12:34,850
+X أُص أربع زائد واحد لو روحت يابانا جيب F of X
+
+100
+00:12:34,850 --> 00:12:37,750
+زائد واحد على سبيل المثال
+
+101
+00:12:40,510 --> 00:12:47,390
+يبقى بدي أشيل كل X و أحط مكانها X زائد واحد يبقى
+
+102
+00:12:47,390 --> 00:12:55,010
+هذي بدي أساول X زائد واحد أصفر زائد واحد بدي أضغط
+
+103
+00:12:55,010 --> 00:12:59,650
+هذي و أشوفها جديش ابتدي طبعا X زائد واحد لكل
+
+104
+00:12:59,650 --> 00:13:06,230
+ترابية في X زائد واحد لكل ترابية تمام؟يبقى هذه
+
+105
+00:13:06,230 --> 00:13:12,110
+عبارة عن X تربية زائد اتنين X زائد واحد X تربية
+
+106
+00:13:12,110 --> 00:13:18,270
+زائد اتنين X زائد واحد بتعطيني فك الجوش اللي عندنا
+
+107
+00:13:18,270 --> 00:13:25,690
+هذا تمام؟ بقولك كويس يبقى هذه X أُص أربع زائد
+
+108
+00:13:25,690 --> 00:13:34,670
+اتنين X تكيب زائد X تربية زائد اتنين X تكيبزائد
+
+109
+00:13:34,670 --> 00:13:43,830
+اربعة X ترابيع زائد اتنين X وهنا X ترابيع زائد
+
+110
+00:13:43,830 --> 00:13:52,230
+اتنين X زائد واحد بيجي نجمع بصير عندنا ال F of X
+
+111
+00:13:52,230 --> 00:13:59,550
+زائد واحد على الشكل التالف X وصف اربعة هذه اربعة X
+
+112
+00:13:59,550 --> 00:14:10,250
+تكيينزائد أربع X تكييف زائد ستة X ترابيع زائد أربع
+
+113
+00:14:10,250 --> 00:14:16,030
+X زائد اتنين عندنا زائد واحد و هنا عندنا واحد يبقى
+
+114
+00:14:16,030 --> 00:14:22,110
+هاي اتنين يبقى هذا الشكل ال polynomial اندعى واضح
+
+115
+00:14:22,110 --> 00:14:29,350
+ان هالي ال polynomial موجودة في Z of X
+
+116
+00:14:30,260 --> 00:14:36,320
+تمام؟ كل هذه موجودة المعاملة تبعتها أعداد صحيحة
+
+117
+00:14:36,320 --> 00:14:41,960
+طيب بتروح دور على prime مين أول prime جابلنا في
+
+118
+00:14:41,960 --> 00:14:47,560
+الدنيا؟ اتنين اتنين بتجسم المعاملات هذه كلها
+
+119
+00:14:47,560 --> 00:14:57,620
+معادات مربع اربعة اتنين طبعا يبقى بادي بيقوله نعم
+
+120
+00:14:59,010 --> 00:15:05,650
+الاتنين لا يقسم الواحد هو معامل اكسوس أربع اتنين
+
+121
+00:15:05,650 --> 00:15:13,010
+بيقسم الأربع اتنين بيقسم الست اتنين بيقسم الأربع
+
+122
+00:15:13,010 --> 00:15:21,530
+اتنين بيقسم اتنين and اتنين تربيه يسوى أربع لا
+
+123
+00:15:21,530 --> 00:15:28,990
+يقسم اتنين by a previous theoremهذا الـ F of X
+
+124
+00:15:28,990 --> 00:15:37,530
+زائد واحد is irreducible على الـ U نبقى بعد ايه
+
+125
+00:15:37,530 --> 00:15:50,030
+الـ previous theorem بنظرية سابقة الـ F of X زائد
+
+126
+00:15:50,030 --> 00:16:03,380
+واحد is irreducible overThank you.طيب
+
+127
+00:16:03,380 --> 00:16:09,420
+المرة الأولى بدأناكم بصورة رقم خمسة وقلنا خمسة C
+
+128
+00:16:09,420 --> 00:16:15,000
+وروحنا على C وروحنا أثبتنا F of X زاد C مين ما
+
+129
+00:16:15,000 --> 00:16:19,420
+تكون الـC موجودة في الفيلم صحيح؟ تبقى أنا عندي هنا
+
+130
+00:16:19,420 --> 00:16:24,520
+C في قداشر؟ إيه بواحد إذا كانت هذه irreducible فال
+
+131
+00:16:24,520 --> 00:16:34,680
+F of X is reducibleيبقى هنا by exercises
+
+132
+00:16:34,680 --> 00:16:46,540
+خمسة part C ال F of X اللي هي الأصلية is R reduce
+
+133
+00:16:46,540 --> 00:16:51,280
+seven over the Q
+
+134
+00:16:55,690 --> 00:17:01,050
+خلاص المطبق كله ولا بس نصه؟ نص المطبق ده اللي اثبت
+
+135
+00:17:01,050 --> 00:17:05,790
+ان ال polynomial هذه irreducible على ال EQ لكنها
+
+136
+00:17:05,790 --> 00:17:15,610
+irreducible على مين؟ على R طيب بطيب لو جيت لل X قص
+
+137
+00:17:15,610 --> 00:17:21,970
+4 زائد 1 دي فرق بين المربعين و الله مجموع مربعين
+
+138
+00:17:23,080 --> 00:17:29,100
+مجموع مرفعين يبقى حسب علمنا القديم، مالهاش تحليل،
+
+139
+00:17:29,100 --> 00:17:33,380
+مظبوط؟ مافيش رأيك؟ زد اتنين الى تحليل؟ كيف؟ زد
+
+140
+00:17:33,380 --> 00:17:37,220
+اتنين الى تحليل؟ احنا مالمش زد اتنين، احنا مش عالش
+
+141
+00:17:37,220 --> 00:17:41,600
+في زد اتنين، احنا الان في Q، صحيح ولا لأ؟ يعني
+
+142
+00:17:41,600 --> 00:17:46,340
+احنا لم نتعرض لزد اتنين، لإن احنا ماجيبناش F bar
+
+143
+00:17:46,340 --> 00:17:51,070
+على الإطلاق، تمام؟ في هذا السؤال، تمام؟بدي بقول
+
+144
+00:17:51,070 --> 00:17:57,290
+لكن ممكن انحللها و احنا مش دارى كيف انحللها يبقى
+
+145
+00:17:57,290 --> 00:18:07,170
+هاتي بقدر اقول X ترابية زائد جذري اتنين في X زائد
+
+146
+00:18:07,170 --> 00:18:16,790
+واحد في X ترابية نقص جذري اتنين X زائد واحد معقول
+
+147
+00:18:16,790 --> 00:18:23,420
+معقولX تربيه في X تربيه هي X نص أربع وواحد في واحد
+
+148
+00:18:23,420 --> 00:18:29,060
+هي واحد هذا موجب مع سالب لما نظر واحد هيطلع عكس
+
+149
+00:18:29,060 --> 00:18:34,100
+التاني واحد بإشارة موجب وواحد بإشارة سالب لكن هل
+
+150
+00:18:34,100 --> 00:18:40,300
+هذا موجود في Q يا بنات؟ لأ لإن الـQ is irrational
+
+151
+00:18:40,300 --> 00:18:45,110
+مش rational الـQ ده set of rational numberيبقى هذا
+
+152
+00:18:45,110 --> 00:18:49,570
+مش موجود في الـQ، لكن هو موجود وين؟ في R، لأن الـR
+
+153
+00:18:49,570 --> 00:18:55,730
+تشمل ال rational و ال irrational number.طيب، الان
+
+154
+00:18:55,730 --> 00:19:03,670
+باجي بقوله اللي هو ال X تربيع زائد جذر اتنين X
+
+155
+00:19:03,670 --> 00:19:10,290
+زائد واحد، وال X تربيع ناقص جذر اتنين X زائد واحد،
+
+156
+00:19:10,290 --> 00:19:17,450
+does not belong to Q.مش موجودة في نكرة السبب جالري
+
+157
+00:19:17,450 --> 00:19:22,790
+2 هو اللي جابنا مش موجودة في نكرة مش موجودة بـ Q
+
+158
+00:19:22,790 --> 00:19:32,970
+but belonging to R لكنها موجودة في R مادة موجودة
+
+159
+00:19:32,970 --> 00:19:39,630
+في R إذا حللنا ال X plus 4 زي 1 على صورة حصل ضرب
+
+160
+00:19:39,930 --> 00:19:43,870
+two polynomials وهذه ال polynomials موجودة في
+
+161
+00:19:43,870 --> 00:19:50,310
+ارمان ردو سبل ارمان صحيح ولا لأ يبقى باجي بقوله
+
+162
+00:19:50,310 --> 00:20:02,930
+this means that هذا يعني ان ال X مسارة زائد واحد
+
+163
+00:20:02,930 --> 00:20:07,370
+is reduceable
+
+164
+00:20:17,920 --> 00:20:23,980
+فى واحد أشطر مننا شوية دارس ال complex كويس ناخد
+
+165
+00:20:23,980 --> 00:20:30,140
+مادة في ال complex وناجح فيها بجدارة راح حلل x أس
+
+166
+00:20:30,140 --> 00:20:35,770
+4 زائد 1 إلى أربع تعوان ال complexوانتوا عارفين
+
+167
+00:20:35,770 --> 00:20:41,810
+عمل بيجى العنصر ومرافقه الكنجوكي التابع تمام؟ تحلل
+
+168
+00:20:41,810 --> 00:20:46,050
+عنصر ومرافقه، عنصر ومرافقه هى الأربعة حلول لما
+
+169
+00:20:46,050 --> 00:20:51,530
+انضرب العنصر مع مرافقه صلى ريان البرهان والعنصر
+
+170
+00:20:51,530 --> 00:20:56,090
+التالي مع مرافقه صلى عهد تمام؟ يبقى هو من ال
+
+171
+00:20:56,090 --> 00:20:59,610
+complex وصل لمين؟ للريال، يعني في ال complex
+
+172
+00:20:59,610 --> 00:21:04,580
+رديوسه ولبس أربعة عناصرحوّلها لـ Real لستوا الـ
+
+173
+00:21:04,580 --> 00:21:09,080
+Real نفسهم و اتنين فقط لغيره وبالتالي طلعت الـ
+
+174
+00:21:09,080 --> 00:21:13,100
+Radius من هذه واضحة هذه ماتفرقش عندنا لإتنين كل
+
+175
+00:21:13,100 --> 00:21:17,840
+واحد فيهم يعتبر حل في هذه المسألة سواء الحل اللي
+
+176
+00:21:17,840 --> 00:21:25,100
+حلنا احنا أو الحل الآخر اللي أشرنا اليه شافويًا
+
+177
+00:21:32,570 --> 00:21:39,790
+هذا كان سؤال احداش، سؤال اتناش جالي بيبينلي ان هذه
+
+178
+00:21:39,790 --> 00:21:46,550
+ال polynomial is irreducible على زي ده احداش سؤال
+
+179
+00:21:46,550 --> 00:21:57,650
+اتناش بيقول show that show that ان ال F of X تساوي
+
+180
+00:21:57,650 --> 00:22:07,320
+X تربية زي X زي 4x² plus x plus 4 is irreducible
+
+181
+00:22:07,320 --> 00:22:12,560
+على z11 is
+
+182
+00:22:12,560 --> 00:22:16,160
+irreducible
+
+183
+00:22:16,160 --> 00:22:21,240
+over z11
+
+184
+00:22:29,610 --> 00:22:33,690
+طبعا على زد اتنين وزد تلاتة بنقول سهلة ويمكن زد
+
+185
+00:22:33,690 --> 00:22:38,870
+خمسة كمان مقبولة بس لما نطلع لفوق بتكبر الحسابات
+
+186
+00:22:38,870 --> 00:22:45,150
+لكن قصة بسيطة جدا وسهلة كيف بسيطة وسهلة هذا ما
+
+187
+00:22:45,150 --> 00:22:55,150
+سنجيب عليه الآن ان شاء الله هاري
+
+188
+00:22:55,150 --> 00:23:03,110
+بركة الان زد احداشية كم عنصر11 عنصة بيجي نجرب إذا
+
+189
+00:23:03,110 --> 00:23:08,930
+ل 11 عنصة ولا واحد صفر الدالة خلاها بصفر إذا
+
+190
+00:23:08,930 --> 00:23:13,730
+ماعنديش linear factor يعني ماعنديش factor من
+
+191
+00:23:13,730 --> 00:23:18,490
+الدرجة طب و ال polynomial من الدرجة أيه؟ بيقول
+
+192
+00:23:18,490 --> 00:23:23,010
+خلصنا، بيقول ال reduce و الدوري مباشرة، لا بدة بحث
+
+193
+00:23:23,010 --> 00:23:28,630
+ولا تنقيب بعد ذلك، ماشي؟ طب نشتغل شفاوي؟هو بسيط و
+
+194
+00:23:28,630 --> 00:23:32,590
+بيخليك الحسابات اللي ضار تشتغليها انت براحة لإن
+
+195
+00:23:32,590 --> 00:23:36,910
+تعالي و تشتغليها هاي القران عامة F of zero باربعة
+
+196
+00:23:36,910 --> 00:23:43,510
+F of واحد بستة احنا بنشتغل في زد احداشر دير بالك
+
+197
+00:23:43,510 --> 00:23:50,070
+يبقى مضل زي ما هي F of اتنين اربعة و اتنين ستة
+
+198
+00:23:50,070 --> 00:23:56,490
+واربع عشرة زي ما هي لاتساوي دير F of تلاتة تسعة و
+
+199
+00:23:56,490 --> 00:24:04,640
+تلاتةاطلاش واربع ستاش زد احداش وضل خمسة مش صفر طب
+
+200
+00:24:04,640 --> 00:24:11,840
+هفو باربع اربع في اربع ستاش واربع عشرين واربع شيلي
+
+201
+00:24:11,840 --> 00:24:16,320
+منهم اتنين وعشرين وابقى قد احداش وضل قداش يقو صف
+
+202
+00:24:16,320 --> 00:24:21,560
+على شك هفو خمسة خمسة وعشرين وخمسة تلاتين واربع
+
+203
+00:24:21,560 --> 00:24:26,540
+اربع تلاتين احداش في تلاتة تلاتة تلاتين بضاله صف
+
+204
+00:24:26,540 --> 00:24:31,770
+جانبهيبقى الخمسة نجي للستة في ستة ستة و تلاتين و
+
+205
+00:24:31,770 --> 00:24:37,510
+ستة نين و أربعين و أربع ستة و أربعين أحد عاشر و
+
+206
+00:24:37,510 --> 00:24:42,190
+أربع و أربع يبقى الأتنين جنبهم سبعة سبعة في سبعة
+
+207
+00:24:42,190 --> 00:24:47,650
+تسعة و أربعين تسعة و أربعين و سبعة ستة و خمسين و
+
+208
+00:24:47,650 --> 00:24:53,730
+أربع ستين بتكسب على أحداش جنبهم يبقى تمانية في
+
+209
+00:24:53,730 --> 00:24:59,660
+تمانيةأربعة وستين، أربعة وستين وتمانية، نين وسبعين
+
+210
+00:24:59,660 --> 00:25:04,860
+وأربعة، ستة وسبعين، هم مضاعفات لأحداشر؟ لأ، فيها
+
+211
+00:25:04,860 --> 00:25:08,640
+عشرة، لأن أحداشر في سبعة في سبعة وسبعين، حق أنا
+
+212
+00:25:08,640 --> 00:25:12,760
+جمه، تسعة في تسعة، بواحد و تمانين، واحد تمانين
+
+213
+00:25:12,760 --> 00:25:20,510
+وتسعة، ميةهي قصة تسعين تسعين واربعة واربعة و تسعين
+
+214
+00:25:20,510 --> 00:25:22,950
+هي أحداشر في التمانية و تمانية و تمانية و مضال
+
+215
+00:25:22,950 --> 00:25:28,270
+الخامسة مضالة ستة يبقى حطيها شجرة يبقى ضالش ولا
+
+216
+00:25:28,270 --> 00:25:33,390
+عشرة عشرة في عشرة مية و عشرة مية و أربعتاشر بتقسمش
+
+217
+00:25:33,390 --> 00:25:41,110
+على هذا يبقى ولا واحد فيهم Zero يبقى Any Element
+
+218
+00:25:41,110 --> 00:25:43,730
+Any
+
+219
+00:25:45,900 --> 00:25:55,660
+E11 is a zero of an element in Z11 is not a zero
+
+220
+00:25:55,660 --> 00:26:01,260
+in
+
+221
+00:26:01,260 --> 00:26:04,320
+Z11
+
+222
+00:26:04,320 --> 00:26:14,180
+is not a zero of the polynomial
+
+223
+00:26:19,500 --> 00:26:26,640
+F of X يساوي X ترمية زي X زي أرفع.معناته فيها
+
+224
+00:26:26,640 --> 00:26:33,980
+factor من الدرجة الأولى؟لأ هذا بده يعطينا ان ال F
+
+225
+00:26:33,980 --> 00:26:44,820
+of X has no linear factor او no factor of degree
+
+226
+00:26:46,770 --> 00:26:50,930
+معنديش ولا واحد من الدرجة الأولى طب هي من الدرجة
+
+227
+00:26:50,930 --> 00:26:54,870
+الثانية لو تتحدث عن الدرجة الأولى فدرجة الأولى طب
+
+228
+00:26:54,870 --> 00:26:59,230
+ولا واحد من الدرجة الأولى يبقى لا يمكن تحليلها لأن
+
+229
+00:26:59,230 --> 00:27:05,350
+الدرجة الأولى irreducible كذلك مالهاش تحليل الدرجة
+
+230
+00:27:05,350 --> 00:27:11,570
+الأولى يبقى هذا بده يعطينا ان ال F of X is
+
+231
+00:27:11,570 --> 00:27:15,490
+irreducible over
+
+232
+00:27:17,840 --> 00:27:24,980
+زي احدى هذا
+
+233
+00:27:24,980 --> 00:27:31,660
+كان سؤال اتنين سؤال اربعة عشر ال F of X ماعطيني
+
+234
+00:27:31,660 --> 00:27:36,280
+هذه right of X as a product of reducible
+
+235
+00:27:36,280 --> 00:27:42,380
+polynomials سؤال
+
+236
+00:27:42,380 --> 00:27:50,810
+اربعة عشر اربعة عشر بيقول ال F of X اللي بدها
+
+237
+00:27:50,810 --> 00:28:02,910
+تساوي X تكيب زائد X ترابيع زائد X زائد واحد موجودة
+
+238
+00:28:02,910 --> 00:28:15,930
+في Z2 of X طيب write ال F of X write ال F of X as
+
+239
+00:28:16,360 --> 00:28:26,020
+aproduct of irreducible pronoun of irreducible
+
+240
+00:28:26,020 --> 00:28:34,660
+pronoun أنزلت
+
+241
+00:28:47,150 --> 00:28:56,810
+كم تحنات اليوم؟ نرجع لسؤالنا مرة ثانية قريبا كده
+
+242
+00:28:56,810 --> 00:29:01,130
+ماعطيني polynomial و ال polynomial موجودة في Z2
+
+243
+00:29:01,130 --> 00:29:06,250
+وقولوا اكتب لل F of X as a product of reusable
+
+244
+00:29:06,250 --> 00:29:14,270
+polynomials على Z2 السؤال هو هل هذا معناه ان ال F
+
+245
+00:29:14,270 --> 00:29:19,290
+of X هذهRadiusable وما .. إيه ال Radiusable على
+
+246
+00:29:19,290 --> 00:29:24,090
+زته؟ Radiusable .. Radiusable .. Radiusable ..
+
+247
+00:29:24,090 --> 00:29:26,950
+Radiusable .. Radiusable .. Radiusable ..
+
+248
+00:29:26,950 --> 00:29:27,550
+Radiusable .. Radiusable .. Radiusable ..
+
+249
+00:29:27,550 --> 00:29:27,850
+Radiusable .. Radiusable .. Radiusable ..
+
+250
+00:29:27,850 --> 00:29:28,890
+Radiusable .. Radiusable .. Radiusable ..
+
+251
+00:29:28,890 --> 00:29:31,690
+Radiusable .. Radiusable .. Radiusable ..
+
+252
+00:29:31,690 --> 00:29:32,570
+Radiusable .. Radiusable .. Radiusable ..
+
+253
+00:29:32,570 --> 00:29:35,450
+Radiusable .. Radiusable .. Radiusable ..
+
+254
+00:29:35,450 --> 00:29:37,810
+Radiusable .. Radiusable .. Radiusable ..
+
+255
+00:29:37,810 --> 00:29:42,430
+Radiusable .. Radiusable .. Radiusable ..
+
+256
+00:29:42,430 --> 00:29:45,430
+Radiusable
+
+257
+00:29:45,690 --> 00:29:50,390
+لكن كل واحدة من التنتين أو التلاتة هي ال
+
+258
+00:29:50,390 --> 00:29:55,170
+reduceable إذا قدرت أعمل البرنامج العصر درجة two
+
+259
+00:29:55,170 --> 00:30:00,030
+factors أو three factors على الأكثر لأننا من
+
+260
+00:30:00,030 --> 00:30:04,690
+الدرجة الثالثة يبقى يا two factors يا three
+
+261
+00:30:04,690 --> 00:30:10,190
+factors وكل واحد من الاتنين أو التلاتة بتكون ال
+
+262
+00:30:10,190 --> 00:30:14,330
+reduceableيبقى كل factor irreducible لكن ال
+
+263
+00:30:14,330 --> 00:30:18,390
+polynomial الأصلي يبقى irreducible لإني جدرت
+
+264
+00:30:18,390 --> 00:30:22,830
+أحللها وأكتبها على صيغة حاصل ضغط طيب ماشي نيجي ده
+
+265
+00:30:22,830 --> 00:30:28,930
+قال يكتبلي هذه على صيغة حاصل ضغط irreducible
+
+266
+00:30:28,930 --> 00:30:33,870
+polynomial بقوله ماشي بجي لأول وقت بقول F of zero
+
+267
+00:30:33,870 --> 00:30:39,700
+و واحد حقهش ايه طيب F of واحدفزيه ويبقى صار ال X
+
+268
+00:30:39,700 --> 00:30:46,560
+نقل واحد is a factor طبعا هذا لو فكرت في حكاية
+
+269
+00:30:46,560 --> 00:30:51,620
+التعوين في واحد شاطر في التحليل قال ايه؟ قال انا
+
+270
+00:30:51,620 --> 00:30:55,780
+راح ادري تحليل وخلص و بجيب عامل من الطريقة الأولى
+
+271
+00:30:55,780 --> 00:30:59,060
+زي ما جيبت انت عامل هو هو نفس العامل بالضبط ومثل
+
+272
+00:30:59,060 --> 00:31:05,320
+كده قالي هذا ال F of X you said بتاخد هدول مع بعض
+
+273
+00:31:05,320 --> 00:31:10,380
+و هدول مع بعض كله ماشيقال بدي أخد X تربيع من
+
+274
+00:31:10,380 --> 00:31:15,420
+الأولى والتانية بدي أخليها زي ما هي قولله تمام قال
+
+275
+00:31:15,420 --> 00:31:21,400
+من قانون التوزيع هاي X تربيع برة بظل X زائد واحد
+
+276
+00:31:21,400 --> 00:31:27,440
+زائد القوس اللي ضايل X زائد واحد قولله تمام قاللي
+
+277
+00:31:27,440 --> 00:31:35,040
+علي التوزيع كمان مرة يبقى كمان مرة بصير Xزائد واحد
+
+278
+00:31:35,040 --> 00:31:41,500
+هى وخدناه برا بظلف مين في X تربية زائد واحد قلنا
+
+279
+00:31:41,500 --> 00:31:46,760
+له والله سيجعلها يتكتب كده على حاصل two factors
+
+280
+00:31:46,760 --> 00:31:52,280
+واحد منهم ال radius اقولنا انه من الدرجة الأولى
+
+281
+00:31:52,280 --> 00:31:58,180
+والتانية مصير خير بنشوف لكن احنا قلنا ان الواحد هو
+
+282
+00:31:58,180 --> 00:32:04,550
+صفر لهذه الدليل X ناقص واحد هو احد العواملانت طالع
+
+283
+00:32:04,550 --> 00:32:10,730
+عندك هنا X ناقص واحد غلط الله صح صح صح صح صح صح صح
+
+284
+00:32:10,730 --> 00:32:13,670
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+285
+00:32:13,670 --> 00:32:13,710
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+286
+00:32:13,710 --> 00:32:16,310
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+287
+00:32:16,310 --> 00:32:22,890
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+288
+00:32:22,890 --> 00:32:25,530
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+289
+00:32:25,530 --> 00:32:31,630
+صح صح صح صح صح صح صح صح صح صح صح صح
+
+290
+00:32:31,630 --> 00:32:38,530
+صهذه ال X زايد واحد اللي برا وهذه بدي أحللها X
+
+291
+00:32:38,530 --> 00:32:43,870
+زايد واحد X زايد واحد هتيجي تقولي هو مجموع
+
+292
+00:32:43,870 --> 00:32:49,470
+المربعين بتحلل لكنك بتشتغل وين؟ بتشتغل في الريال و
+
+293
+00:32:49,470 --> 00:32:52,690
+الله في زد اتنين، تقولي في زد اتنين، بيقولها لا
+
+294
+00:32:52,690 --> 00:32:55,950
+يبقى الريال مالوش داوة هذه المجموع المربعين اللي
+
+295
+00:32:55,950 --> 00:32:59,710
+بلغتنا القديمة مالهاش تتبعت الإعدادية، مالهاش
+
+296
+00:32:59,710 --> 00:33:03,780
+تحليل هذالكن كوانا بنشتغل في زد اتنين إذا اختلف
+
+297
+00:33:03,780 --> 00:33:08,760
+الوضع هدول لو ضربتهم في بعض بيعطوني هذه الإجابة
+
+298
+00:33:08,760 --> 00:33:15,580
+نعم X في X X تلفية هيئة زائد X و زائد X بزائد
+
+299
+00:33:15,580 --> 00:33:20,500
+اتنين X في زد اتنين Zero مع السلامة راحة تظل واحد
+
+300
+00:33:20,500 --> 00:33:25,440
+في واحد في واحد هيئة يبقى تحليلنا سليم مئة بالمئة
+
+301
+00:33:25,440 --> 00:33:32,620
+يبقى هذا عبارة عن جوس الكل تكييفيبقى الحل سبعها X
+
+302
+00:33:32,620 --> 00:33:38,520
+يساوي واحد O multiplicity ثلاث طبعا طيب
+
+303
+00:33:38,520 --> 00:33:42,300
+multiplicity ثلاث و الله مش ثلاث كل واحد فيهم من
+
+304
+00:33:42,300 --> 00:33:50,160
+أي درجة الدرجة الأولى Irreducible يبقى هنا since
+
+305
+00:33:50,160 --> 00:33:57,340
+إما ان اني Linear Polynomial
+
+306
+00:34:12,430 --> 00:34:21,890
+F of X is a product of
+
+307
+00:34:21,890 --> 00:34:28,930
+irreducible polynomials
+
+308
+00:34:45,460 --> 00:34:52,980
+لازم اجيبلكوا polynomial زيك و تشوفوا ما يناسبها
+
+309
+00:34:52,980 --> 00:34:57,820
+من هالنظريات اللي فاتوها و تشوفوها irreducible
+
+310
+00:34:57,820 --> 00:35:04,680
+والله irreducibleأه طبعا لازم أجيبك حلولة و أحددلي
+
+311
+00:35:04,680 --> 00:35:09,760
+أقولك شوفيها لي هل هي reducible ولا irreducible
+
+312
+00:35:09,760 --> 00:35:14,500
+على ال field فلان و أعطيك field مين يطلع مش عارف
+
+313
+00:35:14,500 --> 00:35:18,960
+رغم اني ماعطيتش ولا سؤال بالامتحان حتى هذه اللحظة
+
+314
+00:35:18,960 --> 00:35:23,560
+لكن انا في تصوري اني هجيب سؤال بالشكل اللي عندنا
+
+315
+00:35:23,560 --> 00:35:30,960
+طيب هذا كان سؤال أربعة عشر بدنا سؤال تلاتة و عشرين
+
+316
+00:35:31,180 --> 00:35:37,520
+سؤال 23 عارف والله يا بنت الحلقه ليش اللي بديها
+
+317
+00:35:37,520 --> 00:35:48,440
+سؤال 23 بيقول ما يكفي find all zeros find all
+
+318
+00:35:48,440 --> 00:35:57,280
+zeros and multiplicities and their multiplicities
+
+319
+00:35:57,280 --> 00:36:00,460
+and their
+
+320
+00:36:07,250 --> 00:36:13,490
+multiplicities multiplicities of
+
+321
+00:36:13,490 --> 00:36:25,950
+ال F of X قدر ساب اللي هو X أُس خمسة زائد اللي هو
+
+322
+00:36:25,950 --> 00:36:33,590
+أربعة X أُس أربعةاربع اكس اكس اربع زائد اربع اكس
+
+323
+00:36:33,590 --> 00:36:46,750
+تكيب ناقص اكس ترابيع ناقص اربع اكس زائد واحد زائد
+
+324
+00:36:46,750 --> 00:36:54,410
+واحد over z five over
+
+325
+00:36:54,410 --> 00:36:57,750
+z
+
+326
+00:36:58,760 --> 00:37:04,880
+خمس نقرأ
+
+327
+00:37:04,880 --> 00:37:09,640
+السؤال ونشوف بما يوحي السؤال قبل أن نبدأ الحلول
+
+328
+00:37:09,640 --> 00:37:16,160
+هذه كل ال zeros و ال multiplicities تبعها من ال F
+
+329
+00:37:16,160 --> 00:37:22,080
+of X على Z الخمس السؤال هو هل هذا يعنيإن ال F of X
+
+330
+00:37:22,080 --> 00:37:27,240
+is reducible و الله إيه Reducible؟ رجالي هاتل
+
+331
+00:37:27,240 --> 00:37:31,520
+زيروز معناته في عوامل و أول شي بنبدأ بالدرجة
+
+332
+00:37:31,520 --> 00:37:36,400
+الأولى يبقى أنا بدأ أروح على Z خمسة أشوف في أصفار
+
+333
+00:37:36,400 --> 00:37:41,080
+لهذه ال polynomial أم لا طبعا F of Zero يسوى Zero
+
+334
+00:37:41,080 --> 00:37:49,040
+يبقى Zero حُط على شكلني GF of واحد واحد يعطينا هذا
+
+335
+00:37:49,040 --> 00:37:59,120
+و هذا خمسةو .. و هذا اربع و هنا ناقص واحد بثلاثة
+
+336
+00:37:59,120 --> 00:38:06,360
+او ناقص اربع زي اربع مع ثلاثة يظل هنا ناقص واحد زي
+
+337
+00:38:06,360 --> 00:38:13,260
+واحد يساوي زيه يبقى بالي بقوله ال F of واحد يساوي
+
+338
+00:38:13,260 --> 00:38:20,640
+زيه نيجي لل F of اتنين اتنين باتنين و تلاتينفي Z
+
+339
+00:38:20,640 --> 00:38:27,760
+خمسة بيظل كده؟ إتنين. هذا ستاشر في Z خمسة بيظل
+
+340
+00:38:27,760 --> 00:38:32,560
+واحد في أربعة بأربعة واتنين. ستة بيظل معانا واحد.
+
+341
+00:38:33,160 --> 00:38:37,020
+هذا تمانية في أربعة باتنين وتلاتية اتنين واحد
+
+342
+00:38:37,020 --> 00:38:45,520
+تلاتة تلاتة وهنا عندك ناقص أربعة بيظل ناقص واحد
+
+343
+00:38:45,520 --> 00:38:52,370
+ناقص واحد وو مابس .. اه كدهش احنا قولنا؟ نظروا فى
+
+344
+00:38:52,370 --> 00:39:00,750
+كدهش؟ تانى مرة اتين؟ اتنين هذه اتنين و تلاتين بيظل
+
+345
+00:39:00,750 --> 00:39:08,410
+اتنين تمام؟ و هذه ستاشر اربع اربع و ستين اربع و
+
+346
+00:39:08,410 --> 00:39:14,070
+ستين بيظل خمسة بيظل زائد اربع و اتنين ستة بيظل
+
+347
+00:39:14,070 --> 00:39:20,560
+واحديجي لهذه تمانية في أربعة باتنين وتلاتين تلاتين
+
+348
+00:39:20,560 --> 00:39:21,960
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+349
+00:39:21,960 --> 00:39:22,980
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+350
+00:39:22,980 --> 00:39:28,960
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+351
+00:39:28,960 --> 00:39:29,240
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+352
+00:39:29,240 --> 00:39:32,960
+تلاتين تلاتين تلاتين تلاتين تلاتين
+
+353
+00:39:32,960 --> 00:39:39,700
+تلاتين تلاتين تلاتين
+
+354
+00:39:41,600 --> 00:39:46,640
+لأ بدأت على Zero كيف هذا مرة تانية مرة تانية مرة
+
+355
+00:39:46,640 --> 00:39:50,880
+تانية تلاتة بتطلع Zero تلاتة بتطلع Zero هذا بيطلع
+
+356
+00:39:50,880 --> 00:39:55,280
+اتنين هذا بيطلع اتنين هذا بيطلع اتناشر Zero بيبقى
+
+357
+00:39:55,280 --> 00:39:59,200
+ناقص اتنين و بعدين بيبقى اتنين يبقى لايمكن ان
+
+358
+00:39:59,200 --> 00:40:07,400
+تساوي Zero فبنشوف F of تلاتة F of تلاتة معاكم
+
+359
+00:40:07,400 --> 00:40:13,300
+Calculator؟بتدخل تلاتة في تلاتة بتسعة تسعة في تسعة
+
+360
+00:40:13,300 --> 00:40:17,880
+وواحد و تمانين و بيضل معايا واحد بيضل مين؟ بيضل
+
+361
+00:40:17,880 --> 00:40:26,240
+واحد اللي هو تلاتة تلاتة في واحد بتلاتة بيضل تلاتة
+
+362
+00:40:26,240 --> 00:40:31,940
+من الأول، مظبوط؟ طيب، إذا لو روحنا على Z خمسة
+
+363
+00:40:31,940 --> 00:40:37,600
+بنلاقي إن ال polynomial هذه الأصفر تبعها فقط واحد
+
+364
+00:40:37,600 --> 00:40:46,880
+و تلاتةيبقى هنا R أنا بدي أضمن الواحد and ثلاثة
+
+365
+00:40:46,880 --> 00:41:01,380
+are the only zeros of ال F of X. So ال X ماقص واحد
+
+366
+00:41:01,380 --> 00:41:16,120
+and ال X ماقص ثلاثة RFactors of F of X that is IM
+
+367
+00:41:16,120 --> 00:41:25,740
+F of X بده يسافر X ناقص واحد في X ناقص ثلاثة في
+
+368
+00:41:25,740 --> 00:41:30,770
+أقصر قديش هنا عندنا معادلة من الدرجة الخامسة هدول
+
+369
+00:41:30,770 --> 00:41:34,110
+من الدرجة التانية بتطلع معادلة EI من الدرجة
+
+370
+00:41:34,110 --> 00:41:38,690
+التاسعة. إذا بنتروح أجسم جسمة مطولة المعادلة اللي
+
+371
+00:41:38,690 --> 00:41:43,110
+عندنا على حاصل ضرب هدول، بروح في الهام الشيء،
+
+372
+00:41:43,110 --> 00:41:49,350
+بقوله X plus خمسة زيادة أربعة X plus أربعة زيادة
+
+373
+00:41:49,350 --> 00:41:56,090
+أربعة X تقريبا ماقصة X تقريبا ماقصة أربعة X زيادة
+
+374
+00:41:56,090 --> 00:42:02,010
+واحد مقسمة على حاصل ضرب هدولة منها.هي X تنبيه ،
+
+375
+00:42:02,010 --> 00:42:10,730
+ناقص X ، ناقص تلاتة X ، ناقص أربع X زائد تلاتة.
+
+376
+00:42:12,330 --> 00:42:22,430
+سمعون؟ هذه فيها X تكيينة، X أُص خمسة ناقص أربع X
+
+377
+00:42:22,430 --> 00:42:31,380
+أُص أربعة وهنا زائد تلاتة X تكيينةزائد بيصير ناقص
+
+378
+00:42:31,380 --> 00:42:39,640
+وهذه زائد وهذه ناقص لا يوجد هنا تمانية اكس أس اربع
+
+379
+00:42:39,640 --> 00:42:49,740
+في زيت خمسة زيت جتلاتة اكس أس اربع هذه ناقص اكس
+
+380
+00:42:49,740 --> 00:42:56,220
+تكييرإن ثلاثة راجع أربعة هذي بالموج و بعدها بالسلم
+
+381
+00:42:56,220 --> 00:43:02,520
+و بضال ناقص X تربيع أربعة أربعة ناقص مو زاد أربعة
+
+382
+00:43:02,520 --> 00:43:08,720
+اه زائد X تكريم زائد X تكريم ثلاثة و بضال عندنا
+
+383
+00:43:08,720 --> 00:43:16,140
+ناقص X تربيع ناقص أربعة X زي ده نواصل القسم يبقى
+
+384
+00:43:16,140 --> 00:43:24,370
+زائد ثلاثة X تربيعبصير عندى تلاتة X أُص أربعة ناقص
+
+385
+00:43:24,370 --> 00:43:33,310
+اتناشر X تكيب و هنا زايد تسعة X ترمية زايد تسعة X
+
+386
+00:43:33,310 --> 00:43:38,790
+ترمية زايد بصير ناقص وهذه زايد وهذه ناقص هذه مع
+
+387
+00:43:38,790 --> 00:43:45,310
+السلامة بصير عندنا اتناشر X تكيب و X تكيب
+
+388
+00:43:48,820 --> 00:43:55,660
+طبعا كان مرة تانية مرة تانية الآن تلاتة X تربيع في
+
+389
+00:43:55,660 --> 00:44:02,240
+X تربيع تلاتة X أُس الله تلاتة في أربعة اتناشر X
+
+390
+00:44:02,240 --> 00:44:09,800
+تكييب اتناشر X تكييب بالسنة بدنا نخليها موجة وهذه
+
+391
+00:44:09,800 --> 00:44:18,950
+نزلت هنا ال X تكييب اجتنعهاأدت من فوق يبقى X تقريب
+
+392
+00:44:18,950 --> 00:44:28,050
+و .. و هذه اللي هي الجداشر ناقص 9 X تربيه هذه 12 و
+
+393
+00:44:28,050 --> 00:44:33,930
+هذه 13 مش صحيح لأ لأ فيها شغل ليست صحيح دكتور هو
+
+394
+00:44:33,930 --> 00:44:39,810
+من الأول يدفع ان يخلي سالب أرفع اه هذه حقك هذه حقك
+
+395
+00:44:39,810 --> 00:44:46,900
+مظلومة منك الكلام هو صحيح هذه الأصلمن البداية إذا
+
+396
+00:44:46,900 --> 00:44:54,480
+كنا نقول X plus 5 زي ما كان زائد X تمام؟ إذا نخلّح
+
+397
+00:44:54,480 --> 00:45:06,460
+هذه ونقول هذه X ترابيع زائد X زائد 3 هذا حصل ضغط 2
+
+398
+00:45:06,460 --> 00:45:13,830
+في Z 5 تمام؟ إذا ال X ترابيعلما ضربناها كانت على
+
+399
+00:45:13,830 --> 00:45:24,570
+الشكل التالي X تكييب ب X أُص خمسة زائد تلاتة زائد
+
+400
+00:45:24,570 --> 00:45:36,370
+X تكييب زائد X أُص أربعة ومنا زائد تسعة X تربيع
+
+401
+00:45:36,370 --> 00:45:43,090
+الشكل اللي عندنا تمامهذه زيك بصير ناقص واحد وهذه
+
+402
+00:45:43,090 --> 00:45:51,370
+بصير ناقص بضلي ثلاثة X أس أربع وهذه بصير ناقص شير
+
+403
+00:45:51,370 --> 00:45:57,550
+أربع بض ناقص خمسة اللي هي في زيرو أربع وناقص تسعة
+
+404
+00:46:03,180 --> 00:46:08,740
+اه استني شوية تلاتة
+
+405
+00:46:08,740 --> 00:46:15,180
+اكسة شوفوا هذه الأولى هذه اكس أُس خمسة هذه اكس أُس
+
+406
+00:46:15,180 --> 00:46:26,040
+أربعة هذه تلاتة اكس تكريم تلاتة وهذه اكس تكريم
+
+407
+00:46:26,040 --> 00:46:34,050
+مظبوط يقول صحيح هذه راحةتبقى تلاتة اكس اربعة يبقى
+
+408
+00:46:34,050 --> 00:46:40,890
+بضال زائد اكس تكريم واحدة ناقص اكس تربيع ناقص
+
+409
+00:46:40,890 --> 00:46:47,590
+اربعة اكس زائد واحدة هذه على هذه التلاتة اكس تربيع
+
+410
+00:46:47,590 --> 00:46:51,250
+تلاتة اكس تربيع بصير تلاتة
+
+411
+00:46:59,790 --> 00:47:07,070
+تلاتة X تكييب زي تسعة X ترمية زي تسعة X ترمية هذه
+
+412
+00:47:07,070 --> 00:47:14,010
+زي ناقص مع السلامة هذه ناقص هذه ناقص ناقص تلاتة X
+
+413
+00:47:14,010 --> 00:47:21,630
+تكييب و X تكييبه بقى ناقصينين X تكييب اللي يتعادل
+
+414
+00:47:21,630 --> 00:47:30,250
+تلاتة X تكييب يبقى هذه تلاتة X تكييبوعندك هذه ناقص
+
+415
+00:47:30,250 --> 00:47:37,710
+عشرة راحت تبقى ناقص أربعة X زائد واحدة تلاتة X
+
+416
+00:47:37,710 --> 00:47:45,190
+تقيم على X تربيعي زائد تلاتة X زائد تلاتة X تقيم
+
+417
+00:47:45,190 --> 00:47:49,630
+على X تربيعي زائد تلاتة X تقيم على X تربيعي زائد
+
+418
+00:47:49,630 --> 00:47:54,790
+تلاتة X تقيم على X تربيعي زائد تلاتة X تقيم على X
+
+419
+00:47:54,790 --> 00:47:55,430
+تربيعي
+
+420
+00:47:58,250 --> 00:48:05,530
+زائد تسعة X عندك هذه زائد بالصير ناقص وهذه بالصير
+
+421
+00:48:05,530 --> 00:48:13,190
+ناقص وهذه ناقص ناقص تلاتة X ترابية اللي هو زائد
+
+422
+00:48:13,190 --> 00:48:22,710
+اتنين X ترابية وعندك هنا ناقص اربعة X وناقص تسعة X
+
+423
+00:48:22,710 --> 00:48:31,140
+وناقص تلات عشر Xيعني ناقص ثلاثة X ناقص ثلاثة X
+
+424
+00:48:31,140 --> 00:48:39,460
+زائد واحد تمام مين X تربيع على X تربيع يبقى زائد
+
+425
+00:48:39,460 --> 00:48:48,780
+اتنين اتنين X تربيع وهذه زائد اتنين X زائد اتنين X
+
+426
+00:49:01,870 --> 00:49:09,550
+وهذه عندك ناقص خمسة X بزيرو وعندك هنا ناقص خمسة
+
+427
+00:49:09,550 --> 00:49:16,470
+كمان بزيرو يبقى Zero Zero Zero إذا أصبحت هذه X
+
+428
+00:49:16,470 --> 00:49:24,170
+تكعيف زائد تلاتة X ترابيع زائد تلاتة X زائد بكتير
+
+429
+00:49:24,170 --> 00:49:29,930
+لان يا طول المقار هذا بدنا نشوف ال multiplicity
+
+430
+00:49:29,930 --> 00:49:35,470
+تبع هذولهل يا طول الواحد هو أحد العوامل لهذه ولا
+
+431
+00:49:35,470 --> 00:49:41,390
+لا؟ واحد وثلاثة، أربع وثلاثة، سبعة واثنين، تسعة لا
+
+432
+00:49:41,390 --> 00:49:46,510
+يساوى زيرو. تبقى لها خطة مشاكلة، تجي لتلاتة. تلاتة
+
+433
+00:49:46,510 --> 00:49:54,750
+تكيب لسبعة وعشرين، تبقى لإتنين، وكمان اتنين، اربع،
+
+434
+00:49:54,750 --> 00:50:01,640
+اربع وتسعة، تلتاش، تلاتة واثنين، خمسة، زيرو.فلو
+
+435
+00:50:01,640 --> 00:50:08,460
+قلنا ان g of x يساوي الـ x تقريب زائد تلاتة x
+
+436
+00:50:08,460 --> 00:50:14,180
+ترمية زائد x زائد اتنين هذا بدي يقيل ليه g of
+
+437
+00:50:14,180 --> 00:50:20,520
+تلاتة بيساوي جدار زيلة. يبقى x ناقص تلاتة هو أحد
+
+438
+00:50:20,520 --> 00:50:28,080
+العواني. يبقى صارة ال F of x يساوي x ناقص واحد في
+
+439
+00:50:28,080 --> 00:50:37,260
+x ناقص تلاتةالكل تربيع تمين نروح نجسم X تكيّب زائد
+
+440
+00:50:37,260 --> 00:50:45,540
+تلاتة X تربيع زائد تلاتة X زائد اتنين كل هذا تفسير
+
+441
+00:50:45,540 --> 00:50:53,940
+من تفسير ال X زائد اتنين و X ناقص تلاتة تعني X
+
+442
+00:50:53,940 --> 00:50:58,780
+زائد اتنين يبقى هاي X تربيع
+
+443
+00:51:00,410 --> 00:51:08,970
+بصير X تكيين زائد اتنين X تربيع زائد بصير ناقص هذه
+
+444
+00:51:08,970 --> 00:51:17,170
+بتروح وبظل عندنا X تربيع واحدة زائد تلاتة X زائد
+
+445
+00:51:17,170 --> 00:51:27,590
+اتنين يبقى زائد X X تربيع زائد اتنين X زائد اتنين
+
+446
+00:51:27,590 --> 00:51:35,530
+Xفهقط لغيره هذه زائد بيصير ناقص وهذه ناقص بيبقى ال
+
+447
+00:51:35,530 --> 00:51:43,570
+X زائد اتنين يبقى زائد واحد ب X زائد اتنين Zero و
+
+448
+00:51:43,570 --> 00:51:51,430
+Zero إذا صارت المثل هذه X ترابيع زائد X زائد واحد
+
+449
+00:51:51,430 --> 00:51:58,420
+هل الواحد بيخليها صفر؟طبعاً لأ، التلاتة بيخليها
+
+450
+00:51:58,420 --> 00:52:05,400
+صفر؟ لأ، يبقى ولا واحد فيهم بأصفار تمام؟ يبقى هنا
+
+451
+00:52:05,400 --> 00:52:12,220
+صار the zeros zeros
+
+452
+00:52:12,220 --> 00:52:23,460
+are one of one dct one تمام؟ and
+
+453
+00:52:34,120 --> 00:52:41,800
+طيب هنا انتهينا من هذا ال section وبعد غد ان شاء
+
+454
+00:52:41,800 --> 00:52:47,420
+الله سنبدأ اخر section في المقرر
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..16aa9b1ad5bd9e8f123ca927d31b99ce2e041432
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/5jHSCddQfXA_raw.srt
@@ -0,0 +1,1852 @@
+1
+00:00:20,820 --> 00:00:25,440
+بسم الله الرحمن الرحيم نكمل ما ابتدأنا به في المرة
+
+2
+00:00:25,440 --> 00:00:31,420
+الماضية وهو حل أسئلة من أسئلة التمرين على chapter
+
+3
+00:00:31,420 --> 00:00:37,640
+17 وصلنا المرة اللي فاتت إلى chapter 10 إلى سؤال
+
+4
+00:00:37,640 --> 00:00:43,320
+10 وفي سؤال 10 مكون من عدة نقاط تعرضنا للنقطة
+
+5
+00:00:43,320 --> 00:00:49,390
+الأولى والثالثة وقلنا التنتين هدول زي بعضو كذلك
+
+6
+00:00:49,390 --> 00:00:54,410
+تعرضنا للثانية و الآن الرابعة التالتية الرابعة
+
+7
+00:00:54,410 --> 00:00:58,810
+اللي هي نمرة دي و الخامسة أخدنا مثل زي هي بقى لا
+
+8
+00:00:58,810 --> 00:01:03,810
+داعي نضيع وقت فيها نيجي لمين؟ للخامسة اللي عندنا
+
+9
+00:01:03,810 --> 00:01:11,010
+بدي أروح الآن على اللي هو ال field z2 بس بدنا نروح
+
+10
+00:01:11,010 --> 00:01:16,520
+نجيب ال F barالسؤال هو هل هذه irreducible والبقى
+
+11
+00:01:16,520 --> 00:01:22,920
+irreducible عالميا على اللي هو reduced operational
+
+12
+00:01:22,920 --> 00:01:29,660
+number يبقى بجي بقوله solution on
+
+13
+00:01:29,660 --> 00:01:39,440
+Z2 بدي يصير عندنا ال F bar of X تساوم ل X أص خمسة
+
+14
+00:01:39,440 --> 00:01:46,230
+زجمهينزايد X تربيع زايد واحد انه الخمسة اتنين زايد
+
+15
+00:01:46,230 --> 00:01:50,250
+اتنين زايد واحد اتنينات مع السلامة اللي لها في Z2
+
+16
+00:01:50,250 --> 00:01:55,090
+وضلها اتنين واحد يبقى آلة ال F bar of X الى X روز
+
+17
+00:01:55,090 --> 00:02:01,210
+خمسة زايد X تربيع زايد واحد الان بدنا نشوف هل لها
+
+18
+00:02:01,210 --> 00:02:07,870
+هذه أصفر والله مالهاش أصفر الان لو جيت حطيت Zero
+
+19
+00:02:07,870 --> 00:02:15,890
+Zero واحديبقى Zero ليس صفرا من أصفرها طيب الواحد
+
+20
+00:02:15,890 --> 00:02:22,790
+واحد واحد واحد تلاتة في زيته واحد يبقى مالهاش أصفر
+
+21
+00:02:22,790 --> 00:02:29,970
+يبقى ال F of Zero يبقى يسوى واحد وال F of واحد
+
+22
+00:02:29,970 --> 00:02:37,830
+كذلك يبقى يسوى واحد هذا بدي يعطينا ان F bar has
+
+23
+00:02:39,160 --> 00:02:49,720
+Zeros in the two يعني معناته الدرجة الأولى مستبعدة
+
+24
+00:02:49,720 --> 00:02:56,480
+و الدرجة التالتة مستبعدة يبقى هذا بده يعطينا if
+
+25
+00:02:56,480 --> 00:03:10,050
+bar of x has no factor of degree oneتمام؟ يبقى
+
+26
+00:03:10,050 --> 00:03:16,350
+معناته هذه مافيش عندي element أو factor منها ال
+
+27
+00:03:16,350 --> 00:03:20,190
+degree اللي واحد أو has no linear degree linear
+
+28
+00:03:20,190 --> 00:03:26,110
+factor ماعنديش factor يكون خطيا يبقى في المقابل
+
+29
+00:03:26,110 --> 00:03:30,110
+ماعنديش factor من الدرجة الرابعة لإن الدرجة
+
+30
+00:03:30,110 --> 00:03:34,130
+الرابعة مع الدرجة الأولى بيعطينا الدرجة الخامسة
+
+31
+00:03:34,130 --> 00:03:49,420
+and so ولذلكالـ F bar has no factor of degree for
+
+32
+00:03:49,420 --> 00:03:53,400
+لا من الدرجة الأولى ولا من الدرجة الراجعى يبقى
+
+33
+00:03:53,400 --> 00:03:59,180
+لضايل عند الدرجة التانية أو الدرجة التالتة لأن لو
+
+34
+00:03:59,180 --> 00:04:05,140
+افترضنا ان عندنا factor من الدرجة التالتة بدنا
+
+35
+00:04:05,140 --> 00:04:11,380
+نشوف شو شكلهومين ممكن يجيبلي عناصر تمام يبقى مضاجي
+
+36
+00:04:11,380 --> 00:04:21,920
+اقوله assume افترض ان ال F bar of X has a factor
+
+37
+00:04:21,920 --> 00:04:25,600
+of
+
+38
+00:04:25,600 --> 00:04:40,280
+degree 2 من الدرجة الثانية مثلا that isI am هذا ال
+
+39
+00:04:40,280 --> 00:04:49,180
+factor that is in the form يبقى في الشكل التالي
+
+40
+00:04:49,180 --> 00:04:58,780
+اللي هو ال X ترمية زائد X زائد V بتشوف في أكم
+
+41
+00:04:58,780 --> 00:05:07,100
+احتمال لهذه في Z2 يبقى بادي بقول we have4
+
+42
+00:05:07,100 --> 00:05:10,480
+possibilities
+
+43
+00:05:10,480 --> 00:05:14,780
+يبقى
+
+44
+00:05:14,780 --> 00:05:20,360
+في عندي أربع احتمالات للدرجة الثانية احتمال ان
+
+45
+00:05:20,360 --> 00:05:29,000
+يكون x تربيع فقط واحتمال ان يكون x تربيع زائد x
+
+46
+00:05:29,000 --> 00:05:38,810
+واحتمال ان يكون x تربيع زائد 1و احتمال ان يكون X
+
+47
+00:05:38,810 --> 00:05:45,090
+تربية زائد X زائد واحد في ال X نجي للاحتمالات
+
+48
+00:05:45,090 --> 00:05:49,790
+الأول يبقى الاحتمال الأول لو كان X تربية بقدر
+
+49
+00:05:49,790 --> 00:05:56,630
+احلله X في X تمام؟ و لو كان لي احتمالي الثاني بقدر
+
+50
+00:05:56,630 --> 00:06:02,510
+احلله X في X زائد واحد و لو كان لي احتمالي التالت
+
+51
+00:06:02,510 --> 00:06:11,780
+بقدر احلله X زائد واحدX زائد واحد طبعا اللي تاخد X
+
+52
+00:06:11,780 --> 00:06:18,020
+في X ب X ترابيعه زائد X و زايد X ب 2 X و احنا
+
+53
+00:06:18,020 --> 00:06:23,300
+بنشتغل في Z2 يبقى ب Zero مع السلامة ماضلش الا واحد
+
+54
+00:06:23,300 --> 00:06:28,440
+في واحد اليومين بواحد التلات احتمالات دول حللهم
+
+55
+00:06:28,440 --> 00:06:34,400
+الى حاصل ضرب عاملين من الدرجة الأولى هل هذا ممكن؟
+
+56
+00:06:34,870 --> 00:06:41,050
+لأ لإن استبعدنا الدرجة الأولى فوق هيو يبقى هذا كله
+
+57
+00:06:41,050 --> 00:06:50,270
+impossible يبقى هذا impossible كل احتمالات هذه غير
+
+58
+00:06:50,270 --> 00:06:57,370
+ممكنة السبب because because
+
+59
+00:06:57,370 --> 00:07:15,840
+ال F bar of X hasno factor of first degree بيظل
+
+60
+00:07:15,840 --> 00:07:21,480
+احتماله ثاني للي عندناها الان لو جسمنا ال
+
+61
+00:07:21,480 --> 00:07:26,680
+polynomial أصلية على ال polynomial هذه لا يمكن
+
+62
+00:07:26,680 --> 00:07:32,140
+يطلع هذا أحد العوامل يعني لا يمكن يطلع الناتجبدون
+
+63
+00:07:32,140 --> 00:07:36,480
+باقي، لازم يطلع النتج بمين؟ بباقي، يبقى لو راحت
+
+64
+00:07:36,480 --> 00:07:42,800
+كيك ومسكت القلم وقسمت ال polynomial اللي عندنا على
+
+65
+00:07:42,800 --> 00:07:48,360
+هذه هتلاقي لازم يبقى باقي، وأظن أن الباقي هو واحد
+
+66
+00:07:48,360 --> 00:07:55,380
+صحيح، تمام؟ وبالتالي هذه لا تقسم من اللي فوق، يبقى
+
+67
+00:07:55,380 --> 00:08:00,840
+باجي بقوله هذه by long division
+
+68
+00:08:03,750 --> 00:08:16,050
+الـ X تربيع زيد X زيد واحد is not a factor of F
+
+69
+00:08:16,050 --> 00:08:23,930
+bar of X معناته ان هو factor of second degree
+
+70
+00:08:23,930 --> 00:08:37,470
+تمام؟ يبقى هنا no factor off part of x of second
+
+71
+00:08:37,470 --> 00:08:43,130
+degree مدام
+
+72
+00:08:43,130 --> 00:08:46,790
+مافيش من الدرجة الثانية ممكن يكون من الدرجة
+
+73
+00:08:46,790 --> 00:08:51,810
+الثالثة برضه لأ لإنه حاصل ضربه ويحطينه 100 الدرجة
+
+74
+00:08:51,810 --> 00:08:59,250
+الخامسة يبقى هذا يقن كذلك now factor of third
+
+75
+00:08:59,250 --> 00:09:00,090
+degree
+
+76
+00:09:02,330 --> 00:09:09,630
+ال degree يبقى ايش تفسيرنا لهذا الكلام ان ال F bar
+
+77
+00:09:09,630 --> 00:09:15,890
+is irreducible على Z2 بس ضالت واحدة بشكل ان يكون
+
+78
+00:09:15,890 --> 00:09:21,770
+ال degree ل F هي degree ل F bar يبقى الان بقى اللي
+
+79
+00:09:21,770 --> 00:09:30,570
+بقوله since ال degree لل F هي نفس ال degreeللـ F
+
+80
+00:09:30,570 --> 00:09:39,730
+bar اللي هي تساوي خمسة We have ان ال F bar of X
+
+81
+00:09:39,730 --> 00:09:48,870
+اللي تساوي X أُص خمسة زائد X ترابية زائد واحد is
+
+82
+00:09:48,870 --> 00:10:00,250
+irreducible over زائد 2 هذا بدي يعطينا ايه؟by a
+
+83
+00:10:00,250 --> 00:10:08,790
+previous theorem by a previous theorem بنظرية
+
+84
+00:10:08,790 --> 00:10:17,150
+السابقة ال F of X اللي هي تساوي X أُس خمسة زائد
+
+85
+00:10:17,150 --> 00:10:26,050
+خمسة X ترابيع زائد واحد is irreducible over
+
+86
+00:10:28,200 --> 00:10:34,960
+الـ Q على
+
+87
+00:10:34,960 --> 00:10:40,780
+هيك بيقول ان هنا سؤال عشرة بدنا نروح لسؤال 11 سؤال
+
+88
+00:10:40,780 --> 00:10:47,220
+11 بيقول لي show that ال X أُس 4 زي 1 is reducible
+
+89
+00:10:47,220 --> 00:10:55,160
+على ال Q but reducible على مين؟ على A سؤال 11
+
+90
+00:10:55,160 --> 00:11:05,160
+بيقول showthat إن ال X أُس أربع زائد واحد is
+
+91
+00:11:05,160 --> 00:11:18,400
+irreducible over اكيوم but reducible over R
+
+92
+00:11:39,300 --> 00:11:46,800
+بويس يقول يبينلي ان ال X أُس 4 زي 1 is irreducible
+
+93
+00:11:46,800 --> 00:11:55,580
+على ال field Q اللي هي 6 rational number لكنه ليس
+
+94
+00:11:55,580 --> 00:12:02,480
+irreducible يعني irreducible على من؟ على R نقوله
+
+95
+00:12:02,480 --> 00:12:06,700
+بسيطة، بدنا نرجع لأي نظرية من النظريات اللي
+
+96
+00:12:06,700 --> 00:12:12,030
+درسناهاأو اي سؤال سابق من المسائل اللي اتعرضنا
+
+97
+00:12:12,030 --> 00:12:19,050
+عليهم ونحاول نحل المسألة الان الان لو جيتلي هذه
+
+98
+00:12:19,050 --> 00:12:27,350
+المثلة وروحت سميت هذه F of X يبقى ال F of X بيساوي
+
+99
+00:12:27,350 --> 00:12:34,850
+X أُص أربع زائد واحد لو روحت يابانا جيب F of X
+
+100
+00:12:34,850 --> 00:12:37,750
+زائد واحد على سبيل المثال
+
+101
+00:12:40,510 --> 00:12:47,390
+يبقى بدي أشيل كل X و أحط مكانها X زائد واحد يبقى
+
+102
+00:12:47,390 --> 00:12:55,010
+هذي بدي أساول X زائد واحد أصفر زائد واحد بدي أضغط
+
+103
+00:12:55,010 --> 00:12:59,650
+هذي و أشوفها جديش ابتدي طبعا X زائد واحد لكل
+
+104
+00:12:59,650 --> 00:13:06,230
+ترابية في X زائد واحد لكل ترابية تمام؟يبقى هذه
+
+105
+00:13:06,230 --> 00:13:12,110
+عبارة عن X تربية زائد اتنين X زائد واحد X تربية
+
+106
+00:13:12,110 --> 00:13:18,270
+زائد اتنين X زائد واحد بتعطيني فك الجوش اللي عندنا
+
+107
+00:13:18,270 --> 00:13:25,690
+هذا تمام؟ بقولك كويس يبقى هذه X أُص أربع زائد
+
+108
+00:13:25,690 --> 00:13:34,670
+اتنين X تكيب زائد X تربية زائد اتنين X تكيبزائد
+
+109
+00:13:34,670 --> 00:13:43,830
+اربعة X ترابيع زائد اتنين X وهنا X ترابيع زائد
+
+110
+00:13:43,830 --> 00:13:52,230
+اتنين X زائد واحد بيجي نجمع بصير عندنا ال F of X
+
+111
+00:13:52,230 --> 00:13:59,550
+زائد واحد على الشكل التالف X وصف اربعة هذه اربعة X
+
+112
+00:13:59,550 --> 00:14:10,250
+تكيينزائد أربع X تكييف زائد ستة X ترابيع زائد أربع
+
+113
+00:14:10,250 --> 00:14:16,030
+X زائد اتنين عندنا زائد واحد و هنا عندنا واحد يبقى
+
+114
+00:14:16,030 --> 00:14:22,110
+هاي اتنين يبقى هذا الشكل ال polynomial اندعى واضح
+
+115
+00:14:22,110 --> 00:14:29,350
+ان هالي ال polynomial موجودة في Z of X
+
+116
+00:14:30,260 --> 00:14:36,320
+تمام؟ كل هذه موجودة المعاملة تبعتها أعداد صحيحة
+
+117
+00:14:36,320 --> 00:14:41,960
+طيب بتروح دور على prime مين أول prime جابلنا في
+
+118
+00:14:41,960 --> 00:14:47,560
+الدنيا؟ اتنين اتنين بتجسم المعاملات هذه كلها
+
+119
+00:14:47,560 --> 00:14:57,620
+معادات مربع اربعة اتنين طبعا يبقى بادي بيقوله نعم
+
+120
+00:14:59,010 --> 00:15:05,650
+الاتنين لا يقسم الواحد هو معامل اكسوس أربع اتنين
+
+121
+00:15:05,650 --> 00:15:13,010
+بيقسم الأربع اتنين بيقسم الست اتنين بيقسم الأربع
+
+122
+00:15:13,010 --> 00:15:21,530
+اتنين بيقسم اتنين and اتنين تربيه يسوى أربع لا
+
+123
+00:15:21,530 --> 00:15:28,990
+يقسم اتنين by a previous theoremهذا الـ F of X
+
+124
+00:15:28,990 --> 00:15:37,530
+زائد واحد is irreducible على الـ U نبقى بعد ايه
+
+125
+00:15:37,530 --> 00:15:50,030
+الـ previous theorem بنظرية سابقة الـ F of X زائد
+
+126
+00:15:50,030 --> 00:16:03,380
+واحد is irreducible overThank you.طيب
+
+127
+00:16:03,380 --> 00:16:09,420
+المرة الأولى بدأناكم بصورة رقم خمسة وقلنا خمسة C
+
+128
+00:16:09,420 --> 00:16:15,000
+وروحنا على C وروحنا أثبتنا F of X زاد C مين ما
+
+129
+00:16:15,000 --> 00:16:19,420
+تكون الـC موجودة في الفيلم صحيح؟ تبقى أنا عندي هنا
+
+130
+00:16:19,420 --> 00:16:24,520
+C في قداشر؟ إيه بواحد إذا كانت هذه irreducible فال
+
+131
+00:16:24,520 --> 00:16:34,680
+F of X is reducibleيبقى هنا by exercises
+
+132
+00:16:34,680 --> 00:16:46,540
+خمسة part C ال F of X اللي هي الأصلية is R reduce
+
+133
+00:16:46,540 --> 00:16:51,280
+seven over the Q
+
+134
+00:16:55,690 --> 00:17:01,050
+خلاص المطبق كله ولا بس نصه؟ نص المطبق ده اللي اثبت
+
+135
+00:17:01,050 --> 00:17:05,790
+ان ال polynomial هذه irreducible على ال EQ لكنها
+
+136
+00:17:05,790 --> 00:17:15,610
+irreducible على مين؟ على R طيب بطيب لو جيت لل X قص
+
+137
+00:17:15,610 --> 00:17:21,970
+4 زائد 1 دي فرق بين المربعين و الله مجموع مربعين
+
+138
+00:17:23,080 --> 00:17:29,100
+مجموع مرفعين يبقى حسب علمنا القديم، مالهاش تحليل،
+
+139
+00:17:29,100 --> 00:17:33,380
+مظبوط؟ مافيش رأيك؟ زد اتنين الى تحليل؟ كيف؟ زد
+
+140
+00:17:33,380 --> 00:17:37,220
+اتنين الى تحليل؟ احنا مالمش زد اتنين، احنا مش عالش
+
+141
+00:17:37,220 --> 00:17:41,600
+في زد اتنين، احنا الان في Q، صحيح ولا لأ؟ يعني
+
+142
+00:17:41,600 --> 00:17:46,340
+احنا لم نتعرض لزد اتنين، لإن احنا ماجيبناش F bar
+
+143
+00:17:46,340 --> 00:17:51,070
+على الإطلاق، تمام؟ في هذا السؤال، تمام؟بدي بقول
+
+144
+00:17:51,070 --> 00:17:57,290
+لكن ممكن انحللها و احنا مش دارى كيف انحللها يبقى
+
+145
+00:17:57,290 --> 00:18:07,170
+هاتي بقدر اقول X ترابية زائد جذري اتنين في X زائد
+
+146
+00:18:07,170 --> 00:18:16,790
+واحد في X ترابية نقص جذري اتنين X زائد واحد معقول
+
+147
+00:18:16,790 --> 00:18:23,420
+معقولX تربيه في X تربيه هي X نص أربع وواحد في واحد
+
+148
+00:18:23,420 --> 00:18:29,060
+هي واحد هذا موجب مع سالب لما نظر واحد هيطلع عكس
+
+149
+00:18:29,060 --> 00:18:34,100
+التاني واحد بإشارة موجب وواحد بإشارة سالب لكن هل
+
+150
+00:18:34,100 --> 00:18:40,300
+هذا موجود في Q يا بنات؟ لأ لإن الـQ is irrational
+
+151
+00:18:40,300 --> 00:18:45,110
+مش rational الـQ ده set of rational numberيبقى هذا
+
+152
+00:18:45,110 --> 00:18:49,570
+مش موجود في الـQ، لكن هو موجود وين؟ في R، لأن الـR
+
+153
+00:18:49,570 --> 00:18:55,730
+تشمل ال rational و ال irrational number.طيب، الان
+
+154
+00:18:55,730 --> 00:19:03,670
+باجي بقوله اللي هو ال X تربيع زائد جذر اتنين X
+
+155
+00:19:03,670 --> 00:19:10,290
+زائد واحد، وال X تربيع ناقص جذر اتنين X زائد واحد،
+
+156
+00:19:10,290 --> 00:19:17,450
+does not belong to Q.مش موجودة في نكرة السبب جالري
+
+157
+00:19:17,450 --> 00:19:22,790
+2 هو اللي جابنا مش موجودة في نكرة مش موجودة بـ Q
+
+158
+00:19:22,790 --> 00:19:32,970
+but belonging to R لكنها موجودة في R مادة موجودة
+
+159
+00:19:32,970 --> 00:19:39,630
+في R إذا حللنا ال X plus 4 زي 1 على صورة حصل ضرب
+
+160
+00:19:39,930 --> 00:19:43,870
+two polynomials وهذه ال polynomials موجودة في
+
+161
+00:19:43,870 --> 00:19:50,310
+ارمان ردو سبل ارمان صحيح ولا لأ يبقى باجي بقوله
+
+162
+00:19:50,310 --> 00:20:02,930
+this means that هذا يعني ان ال X مسارة زائد واحد
+
+163
+00:20:02,930 --> 00:20:07,370
+is reduceable
+
+164
+00:20:17,920 --> 00:20:23,980
+فى واحد أشطر مننا شوية دارس ال complex كويس ناخد
+
+165
+00:20:23,980 --> 00:20:30,140
+مادة في ال complex وناجح فيها بجدارة راح حلل x أس
+
+166
+00:20:30,140 --> 00:20:35,770
+4 زائد 1 إلى أربع تعوان ال complexوانتوا عارفين
+
+167
+00:20:35,770 --> 00:20:41,810
+عمل بيجى العنصر ومرافقه الكنجوكي التابع تمام؟ تحلل
+
+168
+00:20:41,810 --> 00:20:46,050
+عنصر ومرافقه، عنصر ومرافقه هى الأربعة حلول لما
+
+169
+00:20:46,050 --> 00:20:51,530
+انضرب العنصر مع مرافقه صلى ريان البرهان والعنصر
+
+170
+00:20:51,530 --> 00:20:56,090
+التالي مع مرافقه صلى عهد تمام؟ يبقى هو من ال
+
+171
+00:20:56,090 --> 00:20:59,610
+complex وصل لمين؟ للريال، يعني في ال complex
+
+172
+00:20:59,610 --> 00:21:04,580
+رديوسه ولبس أربعة عناصرحوّلها لـ Real لستوا الـ
+
+173
+00:21:04,580 --> 00:21:09,080
+Real نفسهم و اتنين فقط لغيره وبالتالي طلعت الـ
+
+174
+00:21:09,080 --> 00:21:13,100
+Radius من هذه واضحة هذه ماتفرقش عندنا لإتنين كل
+
+175
+00:21:13,100 --> 00:21:17,840
+واحد فيهم يعتبر حل في هذه المسألة سواء الحل اللي
+
+176
+00:21:17,840 --> 00:21:25,100
+حلنا احنا أو الحل الآخر اللي أشرنا اليه شافويًا
+
+177
+00:21:32,570 --> 00:21:39,790
+هذا كان سؤال احداش، سؤال اتناش جالي بيبينلي ان هذه
+
+178
+00:21:39,790 --> 00:21:46,550
+ال polynomial is irreducible على زي ده احداش سؤال
+
+179
+00:21:46,550 --> 00:21:57,650
+اتناش بيقول show that show that ان ال F of X تساوي
+
+180
+00:21:57,650 --> 00:22:07,320
+X تربية زي X زي 4x² plus x plus 4 is irreducible
+
+181
+00:22:07,320 --> 00:22:12,560
+على z11 is
+
+182
+00:22:12,560 --> 00:22:16,160
+irreducible
+
+183
+00:22:16,160 --> 00:22:21,240
+over z11
+
+184
+00:22:29,610 --> 00:22:33,690
+طبعا على زد اتنين وزد تلاتة بنقول سهلة ويمكن زد
+
+185
+00:22:33,690 --> 00:22:38,870
+خمسة كمان مقبولة بس لما نطلع لفوق بتكبر الحسابات
+
+186
+00:22:38,870 --> 00:22:45,150
+لكن قصة بسيطة جدا وسهلة كيف بسيطة وسهلة هذا ما
+
+187
+00:22:45,150 --> 00:22:55,150
+سنجيب عليه الآن ان شاء الله هاري
+
+188
+00:22:55,150 --> 00:23:03,110
+بركة الان زد احداشية كم عنصر11 عنصة بيجي نجرب إذا
+
+189
+00:23:03,110 --> 00:23:08,930
+ل 11 عنصة ولا واحد صفر الدالة خلاها بصفر إذا
+
+190
+00:23:08,930 --> 00:23:13,730
+ماعنديش linear factor يعني ماعنديش factor من
+
+191
+00:23:13,730 --> 00:23:18,490
+الدرجة طب و ال polynomial من الدرجة أيه؟ بيقول
+
+192
+00:23:18,490 --> 00:23:23,010
+خلصنا، بيقول ال reduce و الدوري مباشرة، لا بدة بحث
+
+193
+00:23:23,010 --> 00:23:28,630
+ولا تنقيب بعد ذلك، ماشي؟ طب نشتغل شفاوي؟هو بسيط و
+
+194
+00:23:28,630 --> 00:23:32,590
+بيخليك الحسابات اللي ضار تشتغليها انت براحة لإن
+
+195
+00:23:32,590 --> 00:23:36,910
+تعالي و تشتغليها هاي القران عامة F of zero باربعة
+
+196
+00:23:36,910 --> 00:23:43,510
+F of واحد بستة احنا بنشتغل في زد احداشر دير بالك
+
+197
+00:23:43,510 --> 00:23:50,070
+يبقى مضل زي ما هي F of اتنين اربعة و اتنين ستة
+
+198
+00:23:50,070 --> 00:23:56,490
+واربع عشرة زي ما هي لاتساوي دير F of تلاتة تسعة و
+
+199
+00:23:56,490 --> 00:24:04,640
+تلاتةاطلاش واربع ستاش زد احداش وضل خمسة مش صفر طب
+
+200
+00:24:04,640 --> 00:24:11,840
+هفو باربع اربع في اربع ستاش واربع عشرين واربع شيلي
+
+201
+00:24:11,840 --> 00:24:16,320
+منهم اتنين وعشرين وابقى قد احداش وضل قداش يقو صف
+
+202
+00:24:16,320 --> 00:24:21,560
+على شك هفو خمسة خمسة وعشرين وخمسة تلاتين واربع
+
+203
+00:24:21,560 --> 00:24:26,540
+اربع تلاتين احداش في تلاتة تلاتة تلاتين بضاله صف
+
+204
+00:24:26,540 --> 00:24:31,770
+جانبهيبقى الخمسة نجي للستة في ستة ستة و تلاتين و
+
+205
+00:24:31,770 --> 00:24:37,510
+ستة نين و أربعين و أربع ستة و أربعين أحد عاشر و
+
+206
+00:24:37,510 --> 00:24:42,190
+أربع و أربع يبقى الأتنين جنبهم سبعة سبعة في سبعة
+
+207
+00:24:42,190 --> 00:24:47,650
+تسعة و أربعين تسعة و أربعين و سبعة ستة و خمسين و
+
+208
+00:24:47,650 --> 00:24:53,730
+أربع ستين بتكسب على أحداش جنبهم يبقى تمانية في
+
+209
+00:24:53,730 --> 00:24:59,660
+تمانيةأربعة وستين، أربعة وستين وتمانية، نين وسبعين
+
+210
+00:24:59,660 --> 00:25:04,860
+وأربعة، ستة وسبعين، هم مضاعفات لأحداشر؟ لأ، فيها
+
+211
+00:25:04,860 --> 00:25:08,640
+عشرة، لأن أحداشر في سبعة في سبعة وسبعين، حق أنا
+
+212
+00:25:08,640 --> 00:25:12,760
+جمه، تسعة في تسعة، بواحد و تمانين، واحد تمانين
+
+213
+00:25:12,760 --> 00:25:20,510
+وتسعة، ميةهي قصة تسعين تسعين واربعة واربعة و تسعين
+
+214
+00:25:20,510 --> 00:25:22,950
+هي أحداشر في التمانية و تمانية و تمانية و مضال
+
+215
+00:25:22,950 --> 00:25:28,270
+الخامسة مضالة ستة يبقى حطيها شجرة يبقى ضالش ولا
+
+216
+00:25:28,270 --> 00:25:33,390
+عشرة عشرة في عشرة مية و عشرة مية و أربعتاشر بتقسمش
+
+217
+00:25:33,390 --> 00:25:41,110
+على هذا يبقى ولا واحد فيهم Zero يبقى Any Element
+
+218
+00:25:41,110 --> 00:25:43,730
+Any
+
+219
+00:25:45,900 --> 00:25:55,660
+E11 is a zero of an element in Z11 is not a zero
+
+220
+00:25:55,660 --> 00:26:01,260
+in
+
+221
+00:26:01,260 --> 00:26:04,320
+Z11
+
+222
+00:26:04,320 --> 00:26:14,180
+is not a zero of the polynomial
+
+223
+00:26:19,500 --> 00:26:26,640
+F of X يساوي X ترمية زي X زي أرفع.معناته فيها
+
+224
+00:26:26,640 --> 00:26:33,980
+factor من الدرجة الأولى؟لأ هذا بده يعطينا ان ال F
+
+225
+00:26:33,980 --> 00:26:44,820
+of X has no linear factor او no factor of degree
+
+226
+00:26:46,770 --> 00:26:50,930
+معنديش ولا واحد من الدرجة الأولى طب هي من الدرجة
+
+227
+00:26:50,930 --> 00:26:54,870
+الثانية لو تتحدث عن الدرجة الأولى فدرجة الأولى طب
+
+228
+00:26:54,870 --> 00:26:59,230
+ولا واحد من الدرجة الأولى يبقى لا يمكن تحليلها لأن
+
+229
+00:26:59,230 --> 00:27:05,350
+الدرجة الأولى irreducible كذلك مالهاش تحليل الدرجة
+
+230
+00:27:05,350 --> 00:27:11,570
+الأولى يبقى هذا بده يعطينا ان ال F of X is
+
+231
+00:27:11,570 --> 00:27:15,490
+irreducible over
+
+232
+00:27:17,840 --> 00:27:24,980
+زي احدى هذا
+
+233
+00:27:24,980 --> 00:27:31,660
+كان سؤال اتنين سؤال اربعة عشر ال F of X ماعطيني
+
+234
+00:27:31,660 --> 00:27:36,280
+هذه right of X as a product of reducible
+
+235
+00:27:36,280 --> 00:27:42,380
+polynomials سؤال
+
+236
+00:27:42,380 --> 00:27:50,810
+اربعة عشر اربعة عشر بيقول ال F of X اللي بدها
+
+237
+00:27:50,810 --> 00:28:02,910
+تساوي X تكيب زائد X ترابيع زائد X زائد واحد موجودة
+
+238
+00:28:02,910 --> 00:28:15,930
+في Z2 of X طيب write ال F of X write ال F of X as
+
+239
+00:28:16,360 --> 00:28:26,020
+aproduct of irreducible pronoun of irreducible
+
+240
+00:28:26,020 --> 00:28:34,660
+pronoun أنزلت
+
+241
+00:28:47,150 --> 00:28:56,810
+كم تحنات اليوم؟ نرجع لسؤالنا مرة ثانية قريبا كده
+
+242
+00:28:56,810 --> 00:29:01,130
+ماعطيني polynomial و ال polynomial موجودة في Z2
+
+243
+00:29:01,130 --> 00:29:06,250
+وقولوا اكتب لل F of X as a product of reusable
+
+244
+00:29:06,250 --> 00:29:14,270
+polynomials على Z2 السؤال هو هل هذا معناه ان ال F
+
+245
+00:29:14,270 --> 00:29:19,290
+of X هذهRadiusable وما .. إيه ال Radiusable على
+
+246
+00:29:19,290 --> 00:29:24,090
+زته؟ Radiusable .. Radiusable .. Radiusable ..
+
+247
+00:29:24,090 --> 00:29:26,950
+Radiusable .. Radiusable .. Radiusable ..
+
+248
+00:29:26,950 --> 00:29:27,550
+Radiusable .. Radiusable .. Radiusable ..
+
+249
+00:29:27,550 --> 00:29:27,850
+Radiusable .. Radiusable .. Radiusable ..
+
+250
+00:29:27,850 --> 00:29:27,850
+Radiusable .. Radiusable .. Radiusable ..
+
+251
+00:29:27,850 --> 00:29:27,850
+Radiusable .. Radiusable .. Radiusable ..
+
+252
+00:29:27,850 --> 00:29:28,890
+Radiusable .. Radiusable .. Radiusable ..
+
+253
+00:29:28,890 --> 00:29:31,690
+Radiusable .. Radiusable .. Radiusable ..
+
+254
+00:29:31,690 --> 00:29:32,570
+Radiusable .. Radiusable .. Radiusable ..
+
+255
+00:29:32,570 --> 00:29:32,570
+Radiusable .. Radiusable .. Radiusable ..
+
+256
+00:29:32,570 --> 00:29:32,570
+Radiusable .. Radiusable .. Radiusable ..
+
+257
+00:29:32,570 --> 00:29:32,570
+Radiusable .. Radiusable .. Radiusable ..
+
+258
+00:29:32,570 --> 00:29:32,570
+Radiusable .. Radiusable .. Radiusable ..
+
+259
+00:29:32,570 --> 00:29:32,570
+Radiusable .. Radiusable .. Radiusable ..
+
+260
+00:29:32,570 --> 00:29:35,450
+Radiusable .. Radiusable .. Radiusable ..
+
+261
+00:29:35,450 --> 00:29:37,810
+Radiusable .. Radiusable .. Radiusable ..
+
+262
+00:29:37,810 --> 00:29:42,430
+Radiusable .. Radiusable .. Radiusable ..
+
+263
+00:29:42,430 --> 00:29:45,430
+Radiusable
+
+264
+00:29:45,690 --> 00:29:50,390
+لكن كل واحدة من التنتين أو التلاتة هي ال
+
+265
+00:29:50,390 --> 00:29:55,170
+reduceable إذا قدرت أعمل البرنامج العصر درجة two
+
+266
+00:29:55,170 --> 00:30:00,030
+factors أو three factors على الأكثر لأننا من
+
+267
+00:30:00,030 --> 00:30:04,690
+الدرجة الثالثة يبقى يا two factors يا three
+
+268
+00:30:04,690 --> 00:30:10,190
+factors وكل واحد من الاتنين أو التلاتة بتكون ال
+
+269
+00:30:10,190 --> 00:30:14,330
+reduceableيبقى كل factor irreducible لكن ال
+
+270
+00:30:14,330 --> 00:30:18,390
+polynomial الأصلي يبقى irreducible لإني جدرت
+
+271
+00:30:18,390 --> 00:30:22,830
+أحللها وأكتبها على صيغة حاصل ضغط طيب ماشي نيجي ده
+
+272
+00:30:22,830 --> 00:30:28,930
+قال يكتبلي هذه على صيغة حاصل ضغط irreducible
+
+273
+00:30:28,930 --> 00:30:33,870
+polynomial بقوله ماشي بجي لأول وقت بقول F of zero
+
+274
+00:30:33,870 --> 00:30:39,700
+و واحد حقهش ايه طيب F of واحدفزيه ويبقى صار ال X
+
+275
+00:30:39,700 --> 00:30:46,560
+نقل واحد is a factor طبعا هذا لو فكرت في حكاية
+
+276
+00:30:46,560 --> 00:30:51,620
+التعوين في واحد شاطر في التحليل قال ايه؟ قال انا
+
+277
+00:30:51,620 --> 00:30:55,780
+راح ادري تحليل وخلص و بجيب عامل من الطريقة الأولى
+
+278
+00:30:55,780 --> 00:30:59,060
+زي ما جيبت انت عامل هو هو نفس العامل بالضبط ومثل
+
+279
+00:30:59,060 --> 00:31:05,320
+كده قالي هذا ال F of X you said بتاخد هدول مع بعض
+
+280
+00:31:05,320 --> 00:31:10,380
+و هدول مع بعض كله ماشيقال بدي أخد X تربيع من
+
+281
+00:31:10,380 --> 00:31:15,420
+الأولى والتانية بدي أخليها زي ما هي قولله تمام قال
+
+282
+00:31:15,420 --> 00:31:21,400
+من قانون التوزيع هاي X تربيع برة بظل X زائد واحد
+
+283
+00:31:21,400 --> 00:31:27,440
+زائد القوس اللي ضايل X زائد واحد قولله تمام قاللي
+
+284
+00:31:27,440 --> 00:31:35,040
+علي التوزيع كمان مرة يبقى كمان مرة بصير Xزائد واحد
+
+285
+00:31:35,040 --> 00:31:41,500
+هى وخدناه برا بظلف مين في X تربية زائد واحد قلنا
+
+286
+00:31:41,500 --> 00:31:46,760
+له والله سيجعلها يتكتب كده على حاصل two factors
+
+287
+00:31:46,760 --> 00:31:52,280
+واحد منهم ال radius اقولنا انه من الدرجة الأولى
+
+288
+00:31:52,280 --> 00:31:58,180
+والتانية مصير خير بنشوف لكن احنا قلنا ان الواحد هو
+
+289
+00:31:58,180 --> 00:32:04,550
+صفر لهذه الدليل X ناقص واحد هو احد العواملانت طالع
+
+290
+00:32:04,550 --> 00:32:10,730
+عندك هنا X ناقص واحد غلط الله صح صح صح صح صح صح صح
+
+291
+00:32:10,730 --> 00:32:13,670
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+292
+00:32:13,670 --> 00:32:13,710
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+293
+00:32:13,710 --> 00:32:16,310
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+294
+00:32:16,310 --> 00:32:22,890
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+295
+00:32:22,890 --> 00:32:25,530
+صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح صح
+
+296
+00:32:25,530 --> 00:32:31,630
+صح صح صح صح صح صح صح صح صح صح صح صح
+
+297
+00:32:31,630 --> 00:32:38,530
+صهذه ال X زايد واحد اللي برا وهذه بدي أحللها X
+
+298
+00:32:38,530 --> 00:32:43,870
+زايد واحد X زايد واحد هتيجي تقولي هو مجموع
+
+299
+00:32:43,870 --> 00:32:49,470
+المربعين بتحلل لكنك بتشتغل وين؟ بتشتغل في الريال و
+
+300
+00:32:49,470 --> 00:32:52,690
+الله في زد اتنين، تقولي في زد اتنين، بيقولها لا
+
+301
+00:32:52,690 --> 00:32:55,950
+يبقى الريال مالوش داوة هذه المجموع المربعين اللي
+
+302
+00:32:55,950 --> 00:32:59,710
+بلغتنا القديمة مالهاش تتبعت الإعدادية، مالهاش
+
+303
+00:32:59,710 --> 00:33:03,780
+تحليل هذالكن كوانا بنشتغل في زد اتنين إذا اختلف
+
+304
+00:33:03,780 --> 00:33:08,760
+الوضع هدول لو ضربتهم في بعض بيعطوني هذه الإجابة
+
+305
+00:33:08,760 --> 00:33:15,580
+نعم X في X X تلفية هيئة زائد X و زائد X بزائد
+
+306
+00:33:15,580 --> 00:33:20,500
+اتنين X في زد اتنين Zero مع السلامة راحة تظل واحد
+
+307
+00:33:20,500 --> 00:33:25,440
+في واحد في واحد هيئة يبقى تحليلنا سليم مئة بالمئة
+
+308
+00:33:25,440 --> 00:33:32,620
+يبقى هذا عبارة عن جوس الكل تكييفيبقى الحل سبعها X
+
+309
+00:33:32,620 --> 00:33:38,520
+يساوي واحد O multiplicity ثلاث طبعا طيب
+
+310
+00:33:38,520 --> 00:33:42,300
+multiplicity ثلاث و الله مش ثلاث كل واحد فيهم من
+
+311
+00:33:42,300 --> 00:33:50,160
+أي درجة الدرجة الأولى Irreducible يبقى هنا since
+
+312
+00:33:50,160 --> 00:33:57,340
+إما ان اني Linear Polynomial
+
+313
+00:34:12,430 --> 00:34:21,890
+F of X is a product of
+
+314
+00:34:21,890 --> 00:34:28,930
+irreducible polynomials
+
+315
+00:34:45,460 --> 00:34:52,980
+لازم اجيبلكوا polynomial زيك و تشوفوا ما يناسبها
+
+316
+00:34:52,980 --> 00:34:57,820
+من هالنظريات اللي فاتوها و تشوفوها irreducible
+
+317
+00:34:57,820 --> 00:35:04,680
+والله irreducibleأه طبعا لازم أجيبك حلولة و أحددلي
+
+318
+00:35:04,680 --> 00:35:09,760
+أقولك شوفيها لي هل هي reducible ولا irreducible
+
+319
+00:35:09,760 --> 00:35:14,500
+على ال field فلان و أعطيك field مين يطلع مش عارف
+
+320
+00:35:14,500 --> 00:35:18,960
+رغم اني ماعطيتش ولا سؤال بالامتحان حتى هذه اللحظة
+
+321
+00:35:18,960 --> 00:35:23,560
+لكن انا في تصوري اني هجيب سؤال بالشكل اللي عندنا
+
+322
+00:35:23,560 --> 00:35:30,960
+طيب هذا كان سؤال أربعة عشر بدنا سؤال تلاتة و عشرين
+
+323
+00:35:31,180 --> 00:35:37,520
+سؤال 23 عارف والله يا بنت الحلقه ليش اللي بديها
+
+324
+00:35:37,520 --> 00:35:48,440
+سؤال 23 بيقول ما يكفي find all zeros find all
+
+325
+00:35:48,440 --> 00:35:57,280
+zeros and multiplicities and their multiplicities
+
+326
+00:35:57,280 --> 00:36:00,460
+and their
+
+327
+00:36:07,250 --> 00:36:13,490
+multiplicities multiplicities of
+
+328
+00:36:13,490 --> 00:36:25,950
+ال F of X قدر ساب اللي هو X أُس خمسة زائد اللي هو
+
+329
+00:36:25,950 --> 00:36:33,590
+أربعة X أُس أربعةاربع اكس اكس اربع زائد اربع اكس
+
+330
+00:36:33,590 --> 00:36:46,750
+تكيب ناقص اكس ترابيع ناقص اربع اكس زائد واحد زائد
+
+331
+00:36:46,750 --> 00:36:54,410
+واحد over z five over
+
+332
+00:36:54,410 --> 00:36:57,750
+z
+
+333
+00:36:58,760 --> 00:37:04,880
+خمس نقرأ
+
+334
+00:37:04,880 --> 00:37:09,640
+السؤال ونشوف بما يوحي السؤال قبل أن نبدأ الحلول
+
+335
+00:37:09,640 --> 00:37:16,160
+هذه كل ال zeros و ال multiplicities تبعها من ال F
+
+336
+00:37:16,160 --> 00:37:22,080
+of X على Z الخمس السؤال هو هل هذا يعنيإن ال F of X
+
+337
+00:37:22,080 --> 00:37:27,240
+is reducible و الله إيه Reducible؟ رجالي هاتل
+
+338
+00:37:27,240 --> 00:37:31,520
+زيروز معناته في عوامل و أول شي بنبدأ بالدرجة
+
+339
+00:37:31,520 --> 00:37:36,400
+الأولى يبقى أنا بدأ أروح على Z خمسة أشوف في أصفار
+
+340
+00:37:36,400 --> 00:37:41,080
+لهذه ال polynomial أم لا طبعا F of Zero يسوى Zero
+
+341
+00:37:41,080 --> 00:37:49,040
+يبقى Zero حُط على شكلني GF of واحد واحد يعطينا هذا
+
+342
+00:37:49,040 --> 00:37:59,120
+و هذا خمسةو .. و هذا اربع و هنا ناقص واحد بثلاثة
+
+343
+00:37:59,120 --> 00:38:06,360
+او ناقص اربع زي اربع مع ثلاثة يظل هنا ناقص واحد زي
+
+344
+00:38:06,360 --> 00:38:13,260
+واحد يساوي زيه يبقى بالي بقوله ال F of واحد يساوي
+
+345
+00:38:13,260 --> 00:38:20,640
+زيه نيجي لل F of اتنين اتنين باتنين و تلاتينفي Z
+
+346
+00:38:20,640 --> 00:38:27,760
+خمسة بيظل كده؟ إتنين. هذا ستاشر في Z خمسة بيظل
+
+347
+00:38:27,760 --> 00:38:32,560
+واحد في أربعة بأربعة واتنين. ستة بيظل معانا واحد.
+
+348
+00:38:33,160 --> 00:38:37,020
+هذا تمانية في أربعة باتنين وتلاتية اتنين واحد
+
+349
+00:38:37,020 --> 00:38:45,520
+تلاتة تلاتة وهنا عندك ناقص أربعة بيظل ناقص واحد
+
+350
+00:38:45,520 --> 00:38:52,370
+ناقص واحد وو مابس .. اه كدهش احنا قولنا؟ نظروا فى
+
+351
+00:38:52,370 --> 00:39:00,750
+كدهش؟ تانى مرة اتين؟ اتنين هذه اتنين و تلاتين بيظل
+
+352
+00:39:00,750 --> 00:39:08,410
+اتنين تمام؟ و هذه ستاشر اربع اربع و ستين اربع و
+
+353
+00:39:08,410 --> 00:39:14,070
+ستين بيظل خمسة بيظل زائد اربع و اتنين ستة بيظل
+
+354
+00:39:14,070 --> 00:39:20,560
+واحديجي لهذه تمانية في أربعة باتنين وتلاتين تلاتين
+
+355
+00:39:20,560 --> 00:39:21,960
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+356
+00:39:21,960 --> 00:39:22,980
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+357
+00:39:22,980 --> 00:39:28,960
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+358
+00:39:28,960 --> 00:39:29,240
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+359
+00:39:29,240 --> 00:39:29,240
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+360
+00:39:29,240 --> 00:39:29,240
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+361
+00:39:29,240 --> 00:39:32,960
+تلاتين تلاتين تلاتين تلاتين تلاتين
+
+362
+00:39:32,960 --> 00:39:39,700
+تلاتين تلاتين تلاتين
+
+363
+00:39:41,600 --> 00:39:46,640
+لأ بدأت على Zero كيف هذا مرة تانية مرة تانية مرة
+
+364
+00:39:46,640 --> 00:39:50,880
+تانية تلاتة بتطلع Zero تلاتة بتطلع Zero هذا بيطلع
+
+365
+00:39:50,880 --> 00:39:55,280
+اتنين هذا بيطلع اتنين هذا بيطلع اتناشر Zero بيبقى
+
+366
+00:39:55,280 --> 00:39:59,200
+ناقص اتنين و بعدين بيبقى اتنين يبقى لايمكن ان
+
+367
+00:39:59,200 --> 00:40:07,400
+تساوي Zero فبنشوف F of تلاتة F of تلاتة معاكم
+
+368
+00:40:07,400 --> 00:40:13,300
+Calculator؟بتدخل تلاتة في تلاتة بتسعة تسعة في تسعة
+
+369
+00:40:13,300 --> 00:40:17,880
+وواحد و تمانين و بيضل معايا واحد بيضل مين؟ بيضل
+
+370
+00:40:17,880 --> 00:40:26,240
+واحد اللي هو تلاتة تلاتة في واحد بتلاتة بيضل تلاتة
+
+371
+00:40:26,240 --> 00:40:31,940
+من الأول، مظبوط؟ طيب، إذا لو روحنا على Z خمسة
+
+372
+00:40:31,940 --> 00:40:37,600
+بنلاقي إن ال polynomial هذه الأصفر تبعها فقط واحد
+
+373
+00:40:37,600 --> 00:40:46,880
+و تلاتةيبقى هنا R أنا بدي أضمن الواحد and ثلاثة
+
+374
+00:40:46,880 --> 00:41:01,380
+are the only zeros of ال F of X. So ال X ماقص واحد
+
+375
+00:41:01,380 --> 00:41:16,120
+and ال X ماقص ثلاثة RFactors of F of X that is IM
+
+376
+00:41:16,120 --> 00:41:25,740
+F of X بده يسافر X ناقص واحد في X ناقص ثلاثة في
+
+377
+00:41:25,740 --> 00:41:30,770
+أقصر قديش هنا عندنا معادلة من الدرجة الخامسة هدول
+
+378
+00:41:30,770 --> 00:41:34,110
+من الدرجة التانية بتطلع معادلة EI من الدرجة
+
+379
+00:41:34,110 --> 00:41:38,690
+التاسعة. إذا بنتروح أجسم جسمة مطولة المعادلة اللي
+
+380
+00:41:38,690 --> 00:41:43,110
+عندنا على حاصل ضرب هدول، بروح في الهام الشيء،
+
+381
+00:41:43,110 --> 00:41:49,350
+بقوله X plus خمسة زيادة أربعة X plus أربعة زيادة
+
+382
+00:41:49,350 --> 00:41:56,090
+أربعة X تقريبا ماقصة X تقريبا ماقصة أربعة X زيادة
+
+383
+00:41:56,090 --> 00:42:02,010
+واحد مقسمة على حاصل ضرب هدولة منها.هي X تنبيه ،
+
+384
+00:42:02,010 --> 00:42:10,730
+ناقص X ، ناقص تلاتة X ، ناقص أربع X زائد تلاتة.
+
+385
+00:42:12,330 --> 00:42:22,430
+سمعون؟ هذه فيها X تكيينة، X أُص خمسة ناقص أربع X
+
+386
+00:42:22,430 --> 00:42:31,380
+أُص أربعة وهنا زائد تلاتة X تكيينةزائد بيصير ناقص
+
+387
+00:42:31,380 --> 00:42:39,640
+وهذه زائد وهذه ناقص لا يوجد هنا تمانية اكس أس اربع
+
+388
+00:42:39,640 --> 00:42:49,740
+في زيت خمسة زيت جتلاتة اكس أس اربع هذه ناقص اكس
+
+389
+00:42:49,740 --> 00:42:56,220
+تكييرإن ثلاثة راجع أربعة هذي بالموج و بعدها بالسلم
+
+390
+00:42:56,220 --> 00:43:02,520
+و بضال ناقص X تربيع أربعة أربعة ناقص مو زاد أربعة
+
+391
+00:43:02,520 --> 00:43:08,720
+اه زائد X تكريم زائد X تكريم ثلاثة و بضال عندنا
+
+392
+00:43:08,720 --> 00:43:16,140
+ناقص X تربيع ناقص أربعة X زي ده نواصل القسم يبقى
+
+393
+00:43:16,140 --> 00:43:24,370
+زائد ثلاثة X تربيعبصير عندى تلاتة X أُص أربعة ناقص
+
+394
+00:43:24,370 --> 00:43:33,310
+اتناشر X تكيب و هنا زايد تسعة X ترمية زايد تسعة X
+
+395
+00:43:33,310 --> 00:43:38,790
+ترمية زايد بصير ناقص وهذه زايد وهذه ناقص هذه مع
+
+396
+00:43:38,790 --> 00:43:45,310
+السلامة بصير عندنا اتناشر X تكيب و X تكيب
+
+397
+00:43:48,820 --> 00:43:55,660
+طبعا كان مرة تانية مرة تانية الآن تلاتة X تربيع في
+
+398
+00:43:55,660 --> 00:44:02,240
+X تربيع تلاتة X أُس الله تلاتة في أربعة اتناشر X
+
+399
+00:44:02,240 --> 00:44:09,800
+تكييب اتناشر X تكييب بالسنة بدنا نخليها موجة وهذه
+
+400
+00:44:09,800 --> 00:44:18,950
+نزلت هنا ال X تكييب اجتنعهاأدت من فوق يبقى X تقريب
+
+401
+00:44:18,950 --> 00:44:28,050
+و .. و هذه اللي هي الجداشر ناقص 9 X تربيه هذه 12 و
+
+402
+00:44:28,050 --> 00:44:33,930
+هذه 13 مش صحيح لأ لأ فيها شغل ليست صحيح دكتور هو
+
+403
+00:44:33,930 --> 00:44:39,810
+من الأول يدفع ان يخلي سالب أرفع اه هذه حقك هذه حقك
+
+404
+00:44:39,810 --> 00:44:46,900
+مظلومة منك الكلام هو صحيح هذه الأصلمن البداية إذا
+
+405
+00:44:46,900 --> 00:44:54,480
+كنا نقول X plus 5 زي ما كان زائد X تمام؟ إذا نخلّح
+
+406
+00:44:54,480 --> 00:45:06,460
+هذه ونقول هذه X ترابيع زائد X زائد 3 هذا حصل ضغط 2
+
+407
+00:45:06,460 --> 00:45:13,830
+في Z 5 تمام؟ إذا ال X ترابيعلما ضربناها كانت على
+
+408
+00:45:13,830 --> 00:45:24,570
+الشكل التالي X تكييب ب X أُص خمسة زائد تلاتة زائد
+
+409
+00:45:24,570 --> 00:45:36,370
+X تكييب زائد X أُص أربعة ومنا زائد تسعة X تربيع
+
+410
+00:45:36,370 --> 00:45:43,090
+الشكل اللي عندنا تمامهذه زيك بصير ناقص واحد وهذه
+
+411
+00:45:43,090 --> 00:45:51,370
+بصير ناقص بضلي ثلاثة X أس أربع وهذه بصير ناقص شير
+
+412
+00:45:51,370 --> 00:45:57,550
+أربع بض ناقص خمسة اللي هي في زيرو أربع وناقص تسعة
+
+413
+00:46:03,180 --> 00:46:08,740
+اه استني شوية تلاتة
+
+414
+00:46:08,740 --> 00:46:15,180
+اكسة شوفوا هذه الأولى هذه اكس أُس خمسة هذه اكس أُس
+
+415
+00:46:15,180 --> 00:46:26,040
+أربعة هذه تلاتة اكس تكريم تلاتة وهذه اكس تكريم
+
+416
+00:46:26,040 --> 00:46:34,050
+مظبوط يقول صحيح هذه راحةتبقى تلاتة اكس اربعة يبقى
+
+417
+00:46:34,050 --> 00:46:40,890
+بضال زائد اكس تكريم واحدة ناقص اكس تربيع ناقص
+
+418
+00:46:40,890 --> 00:46:47,590
+اربعة اكس زائد واحدة هذه على هذه التلاتة اكس تربيع
+
+419
+00:46:47,590 --> 00:46:51,250
+تلاتة اكس تربيع بصير تلاتة
+
+420
+00:46:59,790 --> 00:47:07,070
+تلاتة X تكييب زي تسعة X ترمية زي تسعة X ترمية هذه
+
+421
+00:47:07,070 --> 00:47:14,010
+زي ناقص مع السلامة هذه ناقص هذه ناقص ناقص تلاتة X
+
+422
+00:47:14,010 --> 00:47:21,630
+تكييب و X تكييبه بقى ناقصينين X تكييب اللي يتعادل
+
+423
+00:47:21,630 --> 00:47:30,250
+تلاتة X تكييب يبقى هذه تلاتة X تكييبوعندك هذه ناقص
+
+424
+00:47:30,250 --> 00:47:37,710
+عشرة راحت تبقى ناقص أربعة X زائد واحدة تلاتة X
+
+425
+00:47:37,710 --> 00:47:45,190
+تقيم على X تربيعي زائد تلاتة X زائد تلاتة X تقيم
+
+426
+00:47:45,190 --> 00:47:49,630
+على X تربيعي زائد تلاتة X تقيم على X تربيعي زائد
+
+427
+00:47:49,630 --> 00:47:54,790
+تلاتة X تقيم على X تربيعي زائد تلاتة X تقيم على X
+
+428
+00:47:54,790 --> 00:47:55,430
+تربيعي
+
+429
+00:47:58,250 --> 00:48:05,530
+زائد تسعة X عندك هذه زائد بالصير ناقص وهذه بالصير
+
+430
+00:48:05,530 --> 00:48:13,190
+ناقص وهذه ناقص ناقص تلاتة X ترابية اللي هو زائد
+
+431
+00:48:13,190 --> 00:48:22,710
+اتنين X ترابية وعندك هنا ناقص اربعة X وناقص تسعة X
+
+432
+00:48:22,710 --> 00:48:31,140
+وناقص تلات عشر Xيعني ناقص ثلاثة X ناقص ثلاثة X
+
+433
+00:48:31,140 --> 00:48:39,460
+زائد واحد تمام مين X تربيع على X تربيع يبقى زائد
+
+434
+00:48:39,460 --> 00:48:48,780
+اتنين اتنين X تربيع وهذه زائد اتنين X زائد اتنين X
+
+435
+00:49:01,870 --> 00:49:09,550
+وهذه عندك ناقص خمسة X بزيرو وعندك هنا ناقص خمسة
+
+436
+00:49:09,550 --> 00:49:16,470
+كمان بزيرو يبقى Zero Zero Zero إذا أصبحت هذه X
+
+437
+00:49:16,470 --> 00:49:24,170
+تكعيف زائد تلاتة X ترابيع زائد تلاتة X زائد بكتير
+
+438
+00:49:24,170 --> 00:49:29,930
+لان يا طول المقار هذا بدنا نشوف ال multiplicity
+
+439
+00:49:29,930 --> 00:49:35,470
+تبع هذولهل يا طول الواحد هو أحد العوامل لهذه ولا
+
+440
+00:49:35,470 --> 00:49:41,390
+لا؟ واحد وثلاثة، أربع وثلاثة، سبعة واثنين، تسعة لا
+
+441
+00:49:41,390 --> 00:49:46,510
+يساوى زيرو. تبقى لها خطة مشاكلة، تجي لتلاتة. تلاتة
+
+442
+00:49:46,510 --> 00:49:54,750
+تكيب لسبعة وعشرين، تبقى لإتنين، وكمان اتنين، اربع،
+
+443
+00:49:54,750 --> 00:50:01,640
+اربع وتسعة، تلتاش، تلاتة واثنين، خمسة، زيرو.فلو
+
+444
+00:50:01,640 --> 00:50:08,460
+قلنا ان g of x يساوي الـ x تقريب زائد تلاتة x
+
+445
+00:50:08,460 --> 00:50:14,180
+ترمية زائد x زائد اتنين هذا بدي يقيل ليه g of
+
+446
+00:50:14,180 --> 00:50:20,520
+تلاتة بيساوي جدار زيلة. يبقى x ناقص تلاتة هو أحد
+
+447
+00:50:20,520 --> 00:50:28,080
+العواني. يبقى صارة ال F of x يساوي x ناقص واحد في
+
+448
+00:50:28,080 --> 00:50:37,260
+x ناقص تلاتةالكل تربيع تمين نروح نجسم X تكيّب زائد
+
+449
+00:50:37,260 --> 00:50:45,540
+تلاتة X تربيع زائد تلاتة X زائد اتنين كل هذا تفسير
+
+450
+00:50:45,540 --> 00:50:53,940
+من تفسير ال X زائد اتنين و X ناقص تلاتة تعني X
+
+451
+00:50:53,940 --> 00:50:58,780
+زائد اتنين يبقى هاي X تربيع
+
+452
+00:51:00,410 --> 00:51:08,970
+بصير X تكيين زائد اتنين X تربيع زائد بصير ناقص هذه
+
+453
+00:51:08,970 --> 00:51:17,170
+بتروح وبظل عندنا X تربيع واحدة زائد تلاتة X زائد
+
+454
+00:51:17,170 --> 00:51:27,590
+اتنين يبقى زائد X X تربيع زائد اتنين X زائد اتنين
+
+455
+00:51:27,590 --> 00:51:35,530
+Xفهقط لغيره هذه زائد بيصير ناقص وهذه ناقص بيبقى ال
+
+456
+00:51:35,530 --> 00:51:43,570
+X زائد اتنين يبقى زائد واحد ب X زائد اتنين Zero و
+
+457
+00:51:43,570 --> 00:51:51,430
+Zero إذا صارت المثل هذه X ترابيع زائد X زائد واحد
+
+458
+00:51:51,430 --> 00:51:58,420
+هل الواحد بيخليها صفر؟طبعاً لأ، التلاتة بيخليها
+
+459
+00:51:58,420 --> 00:52:05,400
+صفر؟ لأ، يبقى ولا واحد فيهم بأصفار تمام؟ يبقى هنا
+
+460
+00:52:05,400 --> 00:52:12,220
+صار the zeros zeros
+
+461
+00:52:12,220 --> 00:52:23,460
+are one of one dct one تمام؟ and
+
+462
+00:52:34,120 --> 00:52:41,800
+طيب هنا انتهينا من هذا ال section وبعد غد ان شاء
+
+463
+00:52:41,800 --> 00:52:47,420
+الله سنبدأ اخر section في المقرر
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/6jfA6QVWjz4_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/6jfA6QVWjz4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fb06bd1c1c55c208ec7137933652af3837c51a1b
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/6jfA6QVWjz4_postprocess.srt
@@ -0,0 +1,1296 @@
+1
+00:00:20,920 --> 00:00:26,780
+بسم الله الرحمن الرحيم نبدأ اليوم chapter جديد
+
+2
+00:00:26,780 --> 00:00:30,780
+اللي هو chapter 18 اللي هو divisibility in
+
+3
+00:00:30,780 --> 00:00:36,120
+integral domains يعني القسمة داخل ال integral
+
+4
+00:00:36,120 --> 00:00:41,760
+domains أو التحليل داخل ال integral domains في
+
+5
+00:00:41,760 --> 00:00:46,840
+عندنا تلتة تعريف أساسية للبدأ في هذا ال chapter هي
+
+6
+00:00:46,840 --> 00:00:52,180
+التلت تعريف قدامنا بنحاول نقرأهاونفهم مفهوم كل
+
+7
+00:00:52,180 --> 00:00:57,440
+تعريف من التعريف الثلاثة التعريف الأول بيقول two
+
+8
+00:00:57,440 --> 00:01:02,500
+elements here and here وما حط الشرط عليهم صفر غير
+
+9
+00:01:02,500 --> 00:01:06,660
+صفر units مايعني اي two elements موجودات في ال
+
+10
+00:01:06,660 --> 00:01:11,520
+integral domain D بيقول ال art code associates
+
+11
+00:01:11,520 --> 00:01:18,420
+اتنين هدول بيكونوا مرتبطين مع بعض كإذا كان واحد
+
+12
+00:01:18,420 --> 00:01:25,700
+منهمقدرت أكد و حاصل ضرب ثاني في element تاني ال
+
+13
+00:01:25,700 --> 00:01:31,060
+element التاني اللي هو you هذا is a unit يعني ال a
+
+14
+00:01:31,060 --> 00:01:35,740
+بده يتساوي بي مضغوبا في unit و ال unit هذا من ال
+
+15
+00:01:35,740 --> 00:01:40,540
+integral domain اللي عليا إن حدث ذلك يبقى بقول ال
+
+16
+00:01:40,540 --> 00:01:45,320
+a و ال b are associates يبقى اتنين مرتبطين مع بعض
+
+17
+00:01:45,320 --> 00:01:50,410
+تماماالتعريف الثاني بيقول a non-zero element of an
+
+18
+00:01:50,410 --> 00:01:55,750
+integral domain دي بيحط شرم ان العمصر غير صفر لكن
+
+19
+00:01:55,750 --> 00:02:02,270
+في التعريف الأول ماحطش هذا الشرم طبعا يبقى a non
+
+20
+00:02:02,270 --> 00:02:06,230
+-zero element of an integral domain دي is called
+
+21
+00:02:06,230 --> 00:02:12,350
+irreducible يعني لا يمكن افككه اللي حصل ضرب two
+
+22
+00:02:12,350 --> 00:02:18,760
+elementsأو أحلله إلى حاصل ضرب two elements إذا كان
+
+23
+00:02:18,760 --> 00:02:27,340
+الـA not unit يبقى هذا الشرط أساسي إن الـA is not
+
+24
+00:02:27,340 --> 00:02:31,980
+a unit هذا النقطة الأولى النقطة الثانية ال
+
+25
+00:02:31,980 --> 00:02:38,940
+universe P وC موجودة في P with الـA يسوى حاصل ضرب
+
+26
+00:02:38,940 --> 00:02:44,950
+P في Cيبقى الشرط التاني لو لقيت عنصرين فيه وحاصل
+
+27
+00:02:44,950 --> 00:02:50,610
+ضربهما سواء ال element a اللي هو غير الصفري و اللي
+
+28
+00:02:50,610 --> 00:02:55,390
+هو ال irreducible يبقى ال P و ال C واحدة منهم لازم
+
+29
+00:02:55,390 --> 00:03:03,670
+تكون main unit طيب يبقى هنا العنصر بقول عنه
+
+30
+00:03:03,670 --> 00:03:10,250
+irreducible إذا تحقق شرطانالشرط الأول ان ال a is
+
+31
+00:03:10,250 --> 00:03:16,470
+not unit تمام الشرط الثاني لو لقيت حاصل ضرب عنصرين
+
+32
+00:03:16,470 --> 00:03:21,870
+يزاوي هذا العنصر معناته واحد فيهم لازم يكون a unit
+
+33
+00:03:21,870 --> 00:03:27,530
+ال a مش unit هدول واحد منهم بدي يكون ماله بدي يكون
+
+34
+00:03:27,530 --> 00:03:33,390
+is a unit هذا معنى ال irreducible الآن بننتقل الى
+
+35
+00:03:33,390 --> 00:03:37,740
+التعريف الثالثبرضه non zero element in integral
+
+36
+00:03:37,740 --> 00:03:44,840
+domain D is called A prime associated irreducible
+
+37
+00:03:44,840 --> 00:03:49,520
+A prime التعريف التالف يبقى بتقول عنه A prime إذا
+
+38
+00:03:49,520 --> 00:03:55,000
+تحقق شرطان الشرط الأولاني برضه قالوا ما هوش units
+
+39
+00:03:55,000 --> 00:04:00,720
+زي مين زي الحالة الأولى من التعريف الثاني والشرط
+
+40
+00:04:00,720 --> 00:04:05,810
+الثاني لو كان A بيقسم ال B في Cيبقى بده يقسم
+
+41
+00:04:05,810 --> 00:04:13,490
+أحدهما يا إما بيقسم ال B يا إما بيقسم ال C نبدأ
+
+42
+00:04:13,490 --> 00:04:21,130
+نعطي بعض الأمثلة البسيطة فمثلا لو جيت بولز أنا بدي
+
+43
+00:04:21,130 --> 00:04:29,850
+أخد ال Z is an integral domain صحيح؟ اه it is an
+
+44
+00:04:29,850 --> 00:04:35,820
+integral domain تمام؟لو وجد حصل ضرب عنصر N يساوي
+
+45
+00:04:35,820 --> 00:04:41,360
+صفر ليس يمكن أن يحدث ذلك إلا إذا كان هدومة يساوي
+
+46
+00:04:41,360 --> 00:04:48,180
+صفر على الأقل يبقى أنا عندي Z an integral domain
+
+47
+00:04:48,180 --> 00:04:53,680
+طيب بدي أشوف أحكاية ال irreducible و ال
+
+48
+00:04:53,680 --> 00:04:58,720
+irreducible لو رحت أخدت any integer N
+
+49
+00:05:01,030 --> 00:05:08,850
+مرتبط مع مين؟ مرتبط مع نفسه مع ناقص N مظبوط؟ طيب
+
+50
+00:05:08,850 --> 00:05:14,090
+ليش؟ مرتبط مع نفسه لإنه لا يوجد units في Z إلا
+
+51
+00:05:14,090 --> 00:05:20,050
+اتنين الواحد والسالج واحد، مظبوط؟ يبقى ال N بقدر
+
+52
+00:05:20,050 --> 00:05:25,750
+اكتب واحد في N والسالج ب N بقدر اكتب وسالج واحد في
+
+53
+00:05:25,750 --> 00:05:31,470
+N تمام؟يبقى صار مين؟ صار سالب ان يسوي سالب واحد ان
+
+54
+00:05:31,470 --> 00:05:37,550
+السالب واحد is a unit والأولان الواحد is a unit
+
+55
+00:05:37,550 --> 00:05:44,670
+كذلك يبقى هذا طبقا للتعريف الأول انتجرال دومين وال
+
+56
+00:05:44,670 --> 00:05:49,290
+A وB موجودات فيها يبقى اتنين associated إذا كان
+
+57
+00:05:49,290 --> 00:05:53,910
+واحد كتبته بدلالته الثانية بس اللي بدي اضرب فيه
+
+58
+00:05:53,910 --> 00:05:58,670
+بديكون ايه اش؟ بديكون unit تمام؟مش حيال الله يعني
+
+59
+00:05:58,670 --> 00:06:04,250
+مش اي رقم كويس طيب المثال اللي انت سمعته فبنروح
+
+60
+00:06:04,250 --> 00:06:09,910
+نسجله مشان ما يضيع ايش مننا و احنا بنذكر يبقى
+
+61
+00:06:09,910 --> 00:06:15,670
+النقطة الأولى بدي اخد every non zero integer every
+
+62
+00:06:15,670 --> 00:06:24,530
+non zero integer in
+
+63
+00:06:27,670 --> 00:06:38,110
+has exactly has exactly بالضبط has exactly two
+
+64
+00:06:38,110 --> 00:06:43,590
+associates two associates
+
+65
+00:06:43,590 --> 00:06:47,690
+in
+
+66
+00:06:47,690 --> 00:06:52,590
+them اللي
+
+67
+00:06:52,590 --> 00:07:03,060
+هم مين ال in andناقص in because the
+
+68
+00:07:03,060 --> 00:07:19,880
+only units in z اللي هو زائد او ناقص واحد that is
+
+69
+00:07:19,880 --> 00:07:23,600
+in ال
+
+70
+00:07:25,060 --> 00:07:32,960
+بدا تساوي واحد مضروبة في N الـ Salib N يساوي سالب
+
+71
+00:07:32,960 --> 00:07:43,860
+واحد مضروبة في N لكل الـ N اللي موجودة في ذلك.
+
+72
+00:07:44,120 --> 00:07:50,560
+طيب المثال الثاني المثال
+
+73
+00:07:50,560 --> 00:07:59,410
+الثانيقول the irreducible elements the irreducible
+
+74
+00:07:59,410 --> 00:08:05,770
+elements
+
+75
+00:08:05,770 --> 00:08:20,030
+the irreducible elements in that are just the
+
+76
+00:08:20,030 --> 00:08:22,010
+أبصارمي
+
+77
+00:08:32,660 --> 00:08:39,420
+مين يا بنات؟ من العناصر اللي موجودة في ذلك اللي
+
+78
+00:08:39,420 --> 00:08:45,440
+ماقدرش أحللها، إلا إذا كان قلت العنصر فيه unit.
+
+79
+00:08:46,420 --> 00:08:50,680
+الابراعي الممتاز جدا. يبقى الابراعي زمين مكان يكون
+
+80
+00:08:50,680 --> 00:08:53,860
+اتنين، تلاتة، خمسة، سبعة، احداشر، تلاتاشر،
+
+81
+00:08:53,860 --> 00:08:58,930
+سبعتاشر، تسعتاشر، إلى آخرين.يبقى هدول ضبضب هم ال
+
+82
+00:08:58,930 --> 00:09:09,350
+prime integers يبقى just the prime integers لإن ال
+
+83
+00:09:09,350 --> 00:09:14,330
+prime integers لا يقسم إلا على نفسه وعلى الواحد
+
+84
+00:09:14,330 --> 00:09:18,550
+الصحيح because
+
+85
+00:09:18,550 --> 00:09:25,150
+the only divisors
+
+86
+00:09:27,070 --> 00:09:40,050
+the only divisors of A prime P او
+
+87
+00:09:40,050 --> 00:09:49,610
+ناقص P لـ X Associate Its
+
+88
+00:09:49,610 --> 00:09:52,410
+Associates and
+
+89
+00:09:54,880 --> 00:10:05,800
+زاد او ناقص واحد اللي هم ال units زد يبقى ال units
+
+90
+00:10:05,800 --> 00:10:15,760
+الموجودة في الذات ال I am ال P
+
+91
+00:10:15,760 --> 00:10:30,520
+is not a unit ما هوش ان ال andالـ P بدأت ساوي واحد
+
+92
+00:10:30,520 --> 00:10:45,040
+مضروب في P هذا بدي أعطيك واحد is a unit يبقى
+
+93
+00:10:45,040 --> 00:10:49,980
+المثال الثاني يقول the irreducible elements في Z
+
+94
+00:10:49,980 --> 00:10:55,910
+هم بالضبط ل prime numbers تمام؟الـPrimal مرة
+
+95
+00:10:55,910 --> 00:11:01,110
+بيحدّله الرمز P، ليش؟ لأن الـonly divisor of
+
+96
+00:11:01,110 --> 00:11:06,070
+الـPrimal P له الـP وثالث P، والواحد وثالث واحد
+
+97
+00:11:06,070 --> 00:11:10,570
+مافيش رغمه، فلو قلت الـP وثالث P، بيهدول ال
+
+98
+00:11:10,570 --> 00:11:18,130
+associates طبق للتعريف الأول، تمام؟ و .. و كذلك ال
+
+99
+00:11:18,130 --> 00:11:24,060
+units اللي هم زائد أو ناقص واحد، ليش؟لأنه لما نقلة
+
+100
+00:11:24,060 --> 00:11:30,220
+ال irreducible تعريفه يبقى هو non zero integer هذا
+
+101
+00:11:30,220 --> 00:11:35,600
+بنسميه نفسه إذا كان not unit يبقى قولنا هنا ال P
+
+102
+00:11:35,600 --> 00:11:41,060
+not unit ما هوش unit تمام؟ and whenever وإذا كان
+
+103
+00:11:41,060 --> 00:11:46,620
+حصل ضربهما بده يساوي هذا ال element يبقى واحد منهم
+
+104
+00:11:46,620 --> 00:11:52,840
+بده يكون هو عبارة عن unitطيب نجي لأول ملاحظة في
+
+105
+00:11:52,840 --> 00:12:02,640
+هذا ال section يبقى remark يقول
+
+106
+00:12:02,640 --> 00:12:09,880
+little a belong to
+
+107
+00:12:09,880 --> 00:12:11,260
+an integral domain
+
+108
+00:12:21,550 --> 00:12:31,130
+والـ A لا تساوي زيه ال A لا تساوي زيه ثم ال A is a
+
+109
+00:12:31,130 --> 00:12:40,870
+prime ال A is a prime if and only if if and only
+
+110
+00:12:40,870 --> 00:12:49,010
+if the principle ideal generated by A is a prime
+
+111
+00:12:49,010 --> 00:12:50,650
+ideal
+
+112
+00:13:03,930 --> 00:13:10,310
+D مرة تانية أخدنا عنصر A مولد في ال integral
+
+113
+00:13:10,310 --> 00:13:15,630
+domain D والعنصر A لا يسوى Zero يبقى non-zero
+
+114
+00:13:15,630 --> 00:13:20,290
+element زي ما اشتغلتها في التعريف الاتنين دول non
+
+115
+00:13:20,290 --> 00:13:25,550
+-zero elementقال الـ A is a prime يبقى هذا بدي
+
+116
+00:13:25,550 --> 00:13:29,090
+يكون ال prime number اف ان والي اف ال principle
+
+117
+00:13:29,090 --> 00:13:34,750
+ideal generated by A is a prime ideal يبقى البرهام
+
+118
+00:13:34,750 --> 00:13:42,330
+بدي يصيحه باتجاهين يبقى بترجع يقوله assume افترض
+
+119
+00:13:42,330 --> 00:13:49,630
+ان ال A is a prime ايش بده نطبق ده بناته؟إنه هذا
+
+120
+00:13:49,630 --> 00:13:55,090
+هو prime ideal. طب هذا احنا عارفين إنه هو ideal
+
+121
+00:13:55,090 --> 00:13:59,470
+لإن ال principle ideal generated by ايه؟ يبقى we
+
+122
+00:13:59,470 --> 00:14:11,010
+know that. We know that ان هذا is an ideal. اللي
+
+123
+00:14:11,010 --> 00:14:17,540
+بيضل عليه نسبتاش يبقى بتاخد عنصرين في ديوفترض ان
+
+124
+00:14:17,540 --> 00:14:23,040
+حاصل ضربهم موجود في ال ideal دي اذا قلت اثبت ان
+
+125
+00:14:23,040 --> 00:14:27,840
+احدهم موجود في هذا ال ideal بصير ال ideal هذا a
+
+126
+00:14:27,840 --> 00:14:32,820
+prime مش هيك تعرف ال prime ideal يبقى بروح بقوله
+
+127
+00:14:32,820 --> 00:14:40,200
+let ال X و ال Y موجودة وين في ال integral domain D
+
+128
+00:14:40,200 --> 00:14:49,760
+such thatبحيث ان ال X Y موجودة في ال principle
+
+129
+00:14:49,760 --> 00:14:55,780
+ideal generated by A ايش بدي احاول اثبت؟ بدي احاول
+
+130
+00:14:55,780 --> 00:15:01,160
+اثبت ان ال X موجود في ال ideal هذا او ال Y موجود
+
+131
+00:15:01,160 --> 00:15:05,660
+في ال ideal هذا ان جدرنا يبقى على طول الخط بصير ال
+
+132
+00:15:05,660 --> 00:15:11,180
+ideal هذا ال prime ideal وبكون برهنة لاتجاه الاول
+
+133
+00:15:14,780 --> 00:15:20,020
+من خلال تعريف ال principle idealية من ال X Y شبه
+
+134
+00:15:20,020 --> 00:15:29,740
+ما اقدر اكتبها A في B يبقى هذا A في B for some B
+
+135
+00:15:29,740 --> 00:15:37,580
+اللي موجودة وين في ال integral domain D كويسة
+
+136
+00:15:37,580 --> 00:15:44,500
+فماشي معناه هذا الكلام ان A تقسم ال X Y صح ولا لا
+
+137
+00:15:44,860 --> 00:15:55,280
+يبقى هنا سا ال a تقسم ال x في y طيب احنا فاقين و
+
+138
+00:15:55,280 --> 00:16:01,300
+هذا يعيش لا pride نيدي لليه pride هذا التاني هو
+
+139
+00:16:01,300 --> 00:16:06,260
+التاني هو تعريف ال pride لو كانت a تقسم اللي يبقى
+
+140
+00:16:06,260 --> 00:16:18,750
+هتقسم أحدهما يبقى هذا then ال aبتقسم ال X او ال A
+
+141
+00:16:18,750 --> 00:16:28,030
+بتقسم ال Y طيب مدام ال A بتقسم ال X او ال A بتقسم
+
+142
+00:16:28,030 --> 00:16:33,710
+ال Y يبقى بدنا نشوف ايش بدنا نستنتج من هذا الكلام
+
+143
+00:16:33,710 --> 00:16:39,890
+من هذا الكلام نستنتج ان ال X بدي سوى ال A في عنصر
+
+144
+00:16:39,890 --> 00:16:48,790
+اخر يبقى هذا بدي يعطيناإن ال X بدها تساوي A مثلا
+
+145
+00:16:48,790 --> 00:17:02,670
+في B1 تمام Or ال Y بدها تساوي مثلا A في B2 و ال B1
+
+146
+00:17:02,670 --> 00:17:14,470
+و ال B2 موجودة في D و ال B1 و ال B2 موجودة فيطيب
+
+147
+00:17:14,470 --> 00:17:22,430
+ما هو تفسيرك لهذا ال X يسوى ايه ايه في عنصر تاني
+
+148
+00:17:22,430 --> 00:17:26,650
+يبقى في ال principle ideal generated by او ال Y
+
+149
+00:17:26,650 --> 00:17:30,830
+موجود في ال principle ideal generated يبقى هنا
+
+150
+00:17:30,830 --> 00:17:36,730
+this means this
+
+151
+00:17:36,730 --> 00:17:46,240
+means that هذا يعنيإن ال X belongs to the
+
+152
+00:17:46,240 --> 00:17:52,740
+principle ideal generated by A او ال Y belong to
+
+153
+00:17:52,740 --> 00:17:56,580
+the principle ideal generated by A ايش معناه هذا
+
+154
+00:17:56,580 --> 00:18:02,680
+الكلام ان هذا ال ideal is a prime هذا بده يعطينا
+
+155
+00:18:02,680 --> 00:18:14,260
+ال ideal اللي عندنا هذا is a prime ideal in Dيبقى
+
+156
+00:18:14,260 --> 00:18:18,040
+انتهينا من الاتجاه الأول بما نروح الاتجاه الثاني
+
+157
+00:18:18,040 --> 00:18:27,940
+بروح نقول ده ايه converse تمام يبقى assume that
+
+158
+00:18:27,940 --> 00:18:34,620
+طرف انه ال principle ideal generated by A is
+
+159
+00:18:34,620 --> 00:18:39,320
+maximal ideal
+
+160
+00:18:44,670 --> 00:18:52,730
+prime اه صحيح prime ideal بنفترض
+
+161
+00:18:52,730 --> 00:19:04,590
+هذا is a prime ideal indeed إيش بدنا نثبت ان ال A
+
+162
+00:19:04,590 --> 00:19:10,230
+في حد ذاتها is a primeاي unit بدنا نثبت ان ال A is
+
+163
+00:19:10,230 --> 00:19:15,330
+a product لو راجعنا هنا معناته بدنا نثبت نقطتين
+
+164
+00:19:15,330 --> 00:19:22,270
+النقطة الأولى بدنا نثبت ان هذه is not a unit هذه
+
+165
+00:19:22,270 --> 00:19:27,950
+واحدة والثانية لو أخدنا A بتقسم ال B في C يبقى يا
+
+166
+00:19:27,950 --> 00:19:35,390
+إما ال A في B يا إما ال A في C يا إما ال A بتقسم
+
+167
+00:19:35,390 --> 00:19:41,800
+من A to Cيبقى بدأت بتشغيل team يبقى نجي للشغل
+
+168
+00:19:41,800 --> 00:19:47,360
+قاللي هذا يفرضوا انه prime ideal السؤال هو ممكن
+
+169
+00:19:47,360 --> 00:19:55,240
+الـA تكون هنا؟
+
+170
+00:19:55,240 --> 00:20:01,640
+ممكن أنا بس السؤال لسه ممكن؟ ممنوع، بدنا نعرف ليش،
+
+171
+00:20:01,640 --> 00:20:14,020
+كويس؟ يبقى هنابنقول معناه الـ A is not ionic هو
+
+172
+00:20:14,020 --> 00:20:25,980
+الشرط الأول because السبب because if ال A is ionic
+
+173
+00:20:25,980 --> 00:20:30,800
+then الواحد
+
+174
+00:20:30,800 --> 00:20:35,960
+الصحيح بيكون مولد في ال principle هذا ولا لاإن
+
+175
+00:20:35,960 --> 00:20:42,640
+الـA unit كل العناصر بتبقى موجودة فيه، مظبوط يبقى
+
+176
+00:20:42,640 --> 00:20:50,920
+هنا then الواحد belong to me للـA فأخدنا remark
+
+177
+00:20:50,920 --> 00:20:56,980
+صغيرة، لو ال ideal احتوى على ال unity تبع ال ring،
+
+178
+00:20:56,980 --> 00:21:02,520
+يبقى ال ideal بتساوي ال ring كلها، مظبوط، يبقى
+
+179
+00:21:02,520 --> 00:21:08,050
+then هذا بده يعطيناإن ال principle ideal generated
+
+180
+00:21:08,050 --> 00:21:15,050
+R by F بدي يسوي ال integral domain كله هذا كلام
+
+181
+00:21:15,050 --> 00:21:23,210
+صحيح؟ ال prime ideal و ال maximum ideal مش يبقى
+
+182
+00:21:23,210 --> 00:21:28,070
+وقار يبقى يقولوا يمكن أن يحدث ذلك يبقى value
+
+183
+00:21:28,070 --> 00:21:31,910
+يقولوا this is impossible
+
+184
+00:21:34,530 --> 00:21:39,590
+هذا الكلام لا يمكن أن يكون صحيحا، إيه السبب؟
+
+185
+00:21:39,590 --> 00:21:48,250
+Because ال principle ID generated by A is proper
+
+186
+00:21:48,250 --> 00:21:58,110
+يبقى فرضنا اللي فرضنا هذا هو صحيح، not a unit لما
+
+187
+00:21:58,110 --> 00:22:04,530
+نقول لو كان unit وصلنا إلى نتيجة قاطعةيبقى هذا
+
+188
+00:22:04,530 --> 00:22:11,870
+يؤكد النقطة الأولى اللى قلناها إذا النقطة الأولى
+
+189
+00:22:11,870 --> 00:22:21,430
+من تعريف الـ prime ideal تحققت مين هي أن الـA هذا
+
+190
+00:22:21,430 --> 00:22:28,790
+is not A يبقى بدي أفرض الآن أن الـA هذا بدي يقسم
+
+191
+00:22:28,790 --> 00:22:39,140
+two elementsيبقى باجي بيقوله F L A بتيقسم X في ال
+
+192
+00:22:39,140 --> 00:22:45,420
+Y مثلا طب نيجي نشوف احنا ايش فرضنا هنا من ال
+
+193
+00:22:45,420 --> 00:22:53,700
+conversely افترض ان هذا هو ال prime صح؟ طيب نشوف
+
+194
+00:22:53,700 --> 00:23:00,000
+نستفيد منه و الله مانستفيدش F
+
+195
+00:23:00,470 --> 00:23:11,810
+الـ A بيقسم ال X Y then ال X Y بتساوي قدر A في B
+
+196
+00:23:11,810 --> 00:23:25,030
+for some B اللي موجودة في D طب هذا ايش معنى ان ال
+
+197
+00:23:25,030 --> 00:23:30,920
+X Y موجودة في ال principle صحيح ولا لأ هذا معناهإن
+
+198
+00:23:30,920 --> 00:23:36,720
+ال X في ال Y موجودة في ال principle ideal طيب هذا
+
+199
+00:23:36,720 --> 00:23:41,400
+prime يبقى يا العنصر الأول موجود فيه يا العنصر
+
+200
+00:23:41,400 --> 00:23:48,600
+التاني موجود فيه يبقى هذا بده يعطينا إن ال X موجود
+
+201
+00:23:48,600 --> 00:23:54,100
+في ال principle ideal generated by A or ال X
+
+202
+00:23:54,100 --> 00:24:01,840
+belongs في ال principle ideal or ال Yوجودة في ال
+
+203
+00:24:01,840 --> 00:24:08,440
+principle ideal generated by A تمام؟ هذا معناه
+
+204
+00:24:08,440 --> 00:24:13,720
+إيش؟ همسك الأول يبقى معنى هذا الكلام إن ال H
+
+205
+00:24:13,720 --> 00:24:25,800
+بتساوي A في B1 مثلا or Y يساوي A في B2 مثلا or
+
+206
+00:24:25,800 --> 00:24:35,560
+some B1 وB2اللي موجودة في الـ D الـ integral
+
+207
+00:24:35,560 --> 00:24:43,900
+domain D طب هذا معناه إيش؟ نمسك هذا يبجى
+
+208
+00:24:43,900 --> 00:24:50,760
+ال A بتقسم ال X يبجى هذا معناه إن ال A تقسم ال X
+
+209
+00:24:50,760 --> 00:24:59,340
+or ال A تقسم ال Yأخدنا a بتقسم اتنين وطلع ال a
+
+210
+00:24:59,340 --> 00:25:05,760
+بتقسم أحدهم اه ليس هذا هو معنى ال prime يبقى
+
+211
+00:25:05,760 --> 00:25:11,720
+أثبتنا النقطة الأولى ان هذا a is not a unit اتنين
+
+212
+00:25:11,720 --> 00:25:16,800
+أخدنا a بتقسم حاصل الضرب بستنجح ان ال a بتقسم
+
+213
+00:25:16,800 --> 00:25:23,700
+الأول او اتنين او اتنين اثانى يبقى this means
+
+214
+00:25:25,640 --> 00:25:34,940
+لأ، هذا يعني ان الـ A is prime. وافق. حد فيكم
+
+215
+00:25:34,940 --> 00:25:42,780
+بتسأل أي سؤال هنا؟ سهل أظن؟ طب كمان واحدة. ويبهبنه
+
+216
+00:25:42,780 --> 00:25:49,360
+المحاضرة يعني. نشط معاه ليه كل يوم. كمان remark
+
+217
+00:25:49,360 --> 00:25:49,940
+تانية.
+
+218
+00:25:54,490 --> 00:26:05,830
+الـ remark بتقول ما يأتي let
+
+219
+00:26:05,830 --> 00:26:17,310
+his day belongs to z such that بحيث ان ال day does
+
+220
+00:26:17,310 --> 00:26:22,890
+not equal one and
+
+221
+00:26:24,320 --> 00:26:33,340
+الـ D is not divisible لاتقسم
+
+222
+00:26:33,340 --> 00:26:45,460
+او لا تنقسم by the square by
+
+223
+00:26:45,460 --> 00:26:59,650
+the square of a primeby the square of A prime on
+
+224
+00:26:59,650 --> 00:27:08,510
+the integral domain on
+
+225
+00:27:08,510 --> 00:27:17,590
+the integral domain اللي هو Z of جدري D مين هو
+
+226
+00:27:17,590 --> 00:27:26,490
+هذا؟ كل العناصر Aزائد بي جدر دي بحيث ال a و ال b
+
+227
+00:27:26,490 --> 00:27:36,930
+أعداد صحيحة define a function
+
+228
+00:27:36,930 --> 00:27:48,610
+عرف الدالة in من z of جدر دي إلى زر plus
+
+229
+00:27:51,040 --> 00:28:02,580
+By الـ N of A زائد B جدر الـ D. N زائد B في جدر
+
+230
+00:28:02,580 --> 00:28:10,460
+الـ D. بدل ساوي absolute value للـ A تربيع ناقص
+
+231
+00:28:10,460 --> 00:28:17,900
+الـ B بـ B تربيع. Then النقطة
+
+232
+00:28:17,900 --> 00:28:27,680
+الأولىال N of X بده يساوي Zero if and only if ال X
+
+233
+00:28:27,680 --> 00:28:35,700
+بده يساوي Zero النقطة الثانية نمره بيه ال N of X
+
+234
+00:28:35,700 --> 00:28:44,800
+هو Y لو ال N of X في Y يساوي ال N of X في ال N of
+
+235
+00:28:44,800 --> 00:28:54,340
+Y لكلالـ X والـ Y اللي موجودة في Z of the square
+
+236
+00:28:54,340 --> 00:28:59,880
+root لـ D النقطة
+
+237
+00:28:59,880 --> 00:29:13,300
+C الـ X is a unit if and only if ال N of X يسوى
+
+238
+00:29:13,300 --> 00:29:13,800
+واحد
+
+239
+00:29:17,500 --> 00:29:30,920
+مقطع نمرة D if ال N of X is A' is
+
+240
+00:29:30,920 --> 00:29:40,160
+A' then ال X is irreducible
+
+241
+00:29:40,160 --> 00:29:44,020
+is irreducible
+
+242
+00:30:12,470 --> 00:30:18,440
+طبعا الكتاب ترى كل كنت تفرحه للريضةوانتوا طبعا
+
+243
+00:30:18,440 --> 00:30:24,640
+قارئين يبقى ممكن تقولوا انهم انتوا طبعا طيب ما
+
+244
+00:30:24,640 --> 00:30:28,460
+علينا نيجي
+
+245
+00:30:28,460 --> 00:30:33,560
+نرجع لنص ال remark اللي هنا يقول الكل دي موجودة في
+
+246
+00:30:33,560 --> 00:30:38,580
+الزد و الدي لا يساوي الواحد وفي نفس الوقت دي is
+
+247
+00:30:38,580 --> 00:30:44,060
+not divisible by a square of a prime يعني لو أخدنا
+
+248
+00:30:44,060 --> 00:30:49,230
+عدد أولي وربعنايبقى هذا ال element لا يُقسم بها
+
+249
+00:30:49,230 --> 00:30:54,110
+بمربع العدد الأولى عشان أقل على ال integral domain
+
+250
+00:30:54,110 --> 00:30:59,390
+هذا المعرف بهذا الشكل بدي أعرف function من ال
+
+251
+00:30:59,390 --> 00:31:03,810
+integral domain هذا إلى مجموعة الأعداد الصحيحة
+
+252
+00:31:03,810 --> 00:31:10,670
+الموجبة سالف ماعندهش صفر ماعندهش بقلل N هي
+
+253
+00:31:10,670 --> 00:31:16,910
+function من Z of D إلى Z plus بايإن لما تأثر على
+
+254
+00:31:16,910 --> 00:31:23,610
+الـ Element اللي هناها بده يسوى المربع الأول ناقص
+
+255
+00:31:23,610 --> 00:31:28,790
+D في المربع الثاني المربع هذا بطل اللي يربص على
+
+256
+00:31:28,790 --> 00:31:33,830
+الـ D وهذا الـ D اللي هي الـ D الثالثة فيه عندي
+
+257
+00:31:33,830 --> 00:31:38,430
+أربع نقاط النقطة الأولى N of X سوى Zero F عندهم F
+
+258
+00:31:38,430 --> 00:31:44,640
+X سوى Zero الـ N of X هو يسوى N of X في N أو Yلكل
+
+259
+00:31:44,640 --> 00:31:50,260
+ال X ال Y الموجودة في Z of جذر يتيح اتة تا X زي
+
+260
+00:31:50,260 --> 00:31:55,360
+ونة F عن طولي F ال N ال N of X تسوّع ال N of X is
+
+261
+00:31:55,360 --> 00:32:01,440
+defined ان ال X is irreducible على مين على Z يبقى
+
+262
+00:32:01,440 --> 00:32:06,180
+كله على التعريف اللي عندها ده وليه دالك مضيت شمسة
+
+263
+00:32:06,180 --> 00:32:11,300
+التعريف وخلتها حتى لو تحضرها متى لازم أقوله نمسك
+
+264
+00:32:11,300 --> 00:32:19,630
+الأوليبقى ال N of X بده يساوي 0 if and only if بدي
+
+265
+00:32:19,630 --> 00:32:25,190
+أمشي لغاية ما أوصل إلى X يساوي قدها يساوي 0 طب ال
+
+266
+00:32:25,190 --> 00:32:30,450
+N of X ال X هو اللي موجودة يبقى الشكلها A زائد B
+
+267
+00:32:30,450 --> 00:32:43,010
+جادرة 2 يبقى N of A زائد B جادرة D بده يساوي 0هذا
+
+268
+00:32:43,010 --> 00:32:49,610
+الكلام صحيح if and only if هذا اللي هو ال absolute
+
+269
+00:32:49,610 --> 00:32:59,650
+value لل a ترابية ناقص d بي ترابية يسوى zero طيب
+
+270
+00:32:59,650 --> 00:33:07,690
+هذا الكلام صحيح إذا كان ال a ترابية ناقص ال d بي
+
+271
+00:33:07,690 --> 00:33:15,950
+ترابية يسوى zero مظبوط؟صح؟ طيب، أليس هذا فرق بين
+
+272
+00:33:15,950 --> 00:33:23,330
+المربعين؟ يبقى البقزر أكت وعلص إلى التانية اللي هو
+
+273
+00:33:23,330 --> 00:33:32,490
+ال A ناقص B جدر ال D في ال A زائد ال B جدر ال D
+
+274
+00:33:32,490 --> 00:33:38,020
+يبدو سوى Zero طب احنا بنشتغل وياه؟في integral
+
+275
+00:33:38,020 --> 00:33:43,320
+domain وحاصل ضرب عنصرين يساوي zero يبقى ولا حد
+
+276
+00:33:43,320 --> 00:33:49,520
+منهم بده يساوي zero مظبوط؟ يبقى هذا الكلام صحيح if
+
+277
+00:33:49,520 --> 00:33:56,540
+and only if ال a ناقص b جذر ال d بده يساوي zero او
+
+278
+00:33:56,540 --> 00:34:03,400
+ال a زائد ال b جذر ال d بده يساوي zero ليش هذا
+
+279
+00:34:03,400 --> 00:34:14,530
+since ال dis an integral domain
+
+280
+00:34:14,530 --> 00:34:17,930
+طيب
+
+281
+00:34:17,930 --> 00:34:25,950
+الكلام هذا صحيح if and only if الاولاري بقدر اقول
+
+282
+00:34:25,950 --> 00:34:38,940
+a بدي سوى b في جذري d او ال aبتساوي ناقص P في جذري
+
+283
+00:34:38,940 --> 00:34:47,900
+D هذا الكلام صحيح F and only F شكل ال X اللي
+
+284
+00:34:47,900 --> 00:34:54,040
+موجودة في ال integral domain هذا بده يساوي A زائد
+
+285
+00:34:54,040 --> 00:35:05,030
+P جذري 2 مظبوط؟ طيب هنا ال A بداشا بناهابجذر اتنين
+
+286
+00:35:05,030 --> 00:35:13,750
+صحيح يفقد بده يساوي ال a زائد ال a اللي هو بقداش
+
+287
+00:35:13,750 --> 00:35:25,790
+باتنين a او ال x بده يساوي a ناقص a مش ال a ناقص b
+
+288
+00:35:25,790 --> 00:35:32,320
+جذري اتنينيبقى بده اشيل هذه A زي .. ايها يا بني
+
+289
+00:35:32,320 --> 00:35:38,580
+هذه واحدة و هي تانية مش عندنا A زي B جذري تانية X
+
+290
+00:35:38,580 --> 00:35:45,760
+خلت الـ A زي .. بي جذري ال D بي جذري ال D هذه خطأة
+
+291
+00:35:45,760 --> 00:35:51,580
+طبيعية تمام؟ يبقى بي جذري ال D طب انا عندي بي جذري
+
+292
+00:35:51,580 --> 00:35:58,820
+ال D ب Aيبقى شلطة وحطت مكان ا و ا باتنين ا او ال X
+
+293
+00:35:58,820 --> 00:36:04,980
+من النقرة تانية بتاخد هذا يبقى ال A كما هي
+
+294
+00:36:04,980 --> 00:36:12,380
+والتانية B جادة يرددهم سالب A هذا سالب يجد اسه
+
+295
+00:36:12,380 --> 00:36:18,320
+ساوي Zero يبقى هذه هو المطلوب خلاص مخلصها من
+
+296
+00:36:18,320 --> 00:36:20,540
+الجهود كم؟
+
+297
+00:36:22,270 --> 00:36:27,310
+قال ماشي، مالحين هي هذه أو هذه، تمام؟ يبقى هذه و
+
+298
+00:36:27,310 --> 00:36:31,370
+هذه يبقى stop أيضا طبيعي، واحدة منهم، أنا بدي أخد
+
+299
+00:36:31,370 --> 00:36:39,010
+X بساوي Z، تمام؟ يكفيني ذلك، تمام؟ طيب، نمر بيه؟
+
+300
+00:36:39,010 --> 00:36:44,270
+نمر بيه بسيطة جدا، لو سألتي، بتقولك هذا الشو؟
+
+301
+00:36:44,270 --> 00:36:49,010
+بتقوللي هذا هو الشرط التاني من شروط ال homorphism
+
+302
+00:36:49,490 --> 00:36:54,970
+يبقى انا بتبدأ و اخليك تكبلي انت فالدار لحالك كيف
+
+303
+00:36:54,970 --> 00:37:02,810
+بدنا نبدأ سعالى شوف الحين ال N of X في Y يبقى ال N
+
+304
+00:37:02,810 --> 00:37:07,970
+ار بده اشيل ال X و احطها من ال from ال integral
+
+305
+00:37:07,970 --> 00:37:16,790
+domain هذا يبقى ايش بده يصير ايوة A زائد B جذري D
+
+306
+00:37:16,790 --> 00:37:27,420
+سبعمضروبة في C زائد E جدر ال D بتكتر ضربيها حتى
+
+307
+00:37:27,420 --> 00:37:34,420
+تقدر تبقاش اللي عندك النقطة هذه يبقى هذا بتساوي N
+
+308
+00:37:34,420 --> 00:37:47,110
+R A C زائد B E Dفانا هذه مع هذه و هذه مع هذه طريقة
+
+309
+00:37:47,110 --> 00:37:59,290
+تظهر الآن A مع الأخيرة يبقى A E زائد A E زائد B C
+
+310
+00:37:59,290 --> 00:38:08,190
+B C كله في جذر ال T يبقى
+
+311
+00:38:08,190 --> 00:38:16,080
+M يؤثر على هذا ال Mيبقى المربع الأول ناقص C في
+
+312
+00:38:16,080 --> 00:38:22,280
+المربع الثاني يبقى هذا الكلام في الديسير اللي هو
+
+313
+00:38:22,280 --> 00:38:31,660
+ال A C زائد B E D لكل تربيع ك absolute value ناقص
+
+314
+00:38:31,660 --> 00:38:42,330
+D في ال A E زائد ال B C لكل تربيع بالمثلبدك تروح
+
+315
+00:38:42,330 --> 00:38:50,030
+تجيبي N of X في ال N of Y يبقى جاهزة كده إيش بده
+
+316
+00:38:50,030 --> 00:39:00,090
+يسياري ال N of A زائد B جذر ال D فاهمين؟ في ال N
+
+317
+00:39:00,090 --> 00:39:11,970
+اللي هو C زائد ال E جذر ال Dهذا بالدرسية ال
+
+318
+00:39:11,970 --> 00:39:19,930
+absolute value ا تربيع ناقص ال D بي تربيع مضروب في
+
+319
+00:39:19,930 --> 00:39:31,730
+مين في ال C تربيع ناقص ال D اي تربيع الحين مطلوب
+
+320
+00:39:31,730 --> 00:39:38,980
+انك تثبتيإن الاتنين هدول are equal يبقى بيك تروحش
+
+321
+00:39:38,980 --> 00:39:44,880
+تضغط تفكي هذه تفكي هذه تفكي هذه هتلاقي اتنين نساوة
+
+322
+00:39:44,880 --> 00:39:54,340
+و بعض يبقى هدول are equal قد بني منك ت check عليهم
+
+323
+00:39:54,340 --> 00:40:03,790
+شكلي عليهم تمام؟ بقى النقطتينللمرة القادمة، إن شاء
+
+324
+00:40:03,790 --> 00:40:05,090
+الله تعالى.
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/6jfA6QVWjz4_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/6jfA6QVWjz4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fb06bd1c1c55c208ec7137933652af3837c51a1b
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/6jfA6QVWjz4_raw.srt
@@ -0,0 +1,1296 @@
+1
+00:00:20,920 --> 00:00:26,780
+بسم الله الرحمن الرحيم نبدأ اليوم chapter جديد
+
+2
+00:00:26,780 --> 00:00:30,780
+اللي هو chapter 18 اللي هو divisibility in
+
+3
+00:00:30,780 --> 00:00:36,120
+integral domains يعني القسمة داخل ال integral
+
+4
+00:00:36,120 --> 00:00:41,760
+domains أو التحليل داخل ال integral domains في
+
+5
+00:00:41,760 --> 00:00:46,840
+عندنا تلتة تعريف أساسية للبدأ في هذا ال chapter هي
+
+6
+00:00:46,840 --> 00:00:52,180
+التلت تعريف قدامنا بنحاول نقرأهاونفهم مفهوم كل
+
+7
+00:00:52,180 --> 00:00:57,440
+تعريف من التعريف الثلاثة التعريف الأول بيقول two
+
+8
+00:00:57,440 --> 00:01:02,500
+elements here and here وما حط الشرط عليهم صفر غير
+
+9
+00:01:02,500 --> 00:01:06,660
+صفر units مايعني اي two elements موجودات في ال
+
+10
+00:01:06,660 --> 00:01:11,520
+integral domain D بيقول ال art code associates
+
+11
+00:01:11,520 --> 00:01:18,420
+اتنين هدول بيكونوا مرتبطين مع بعض كإذا كان واحد
+
+12
+00:01:18,420 --> 00:01:25,700
+منهمقدرت أكد و حاصل ضرب ثاني في element تاني ال
+
+13
+00:01:25,700 --> 00:01:31,060
+element التاني اللي هو you هذا is a unit يعني ال a
+
+14
+00:01:31,060 --> 00:01:35,740
+بده يتساوي بي مضغوبا في unit و ال unit هذا من ال
+
+15
+00:01:35,740 --> 00:01:40,540
+integral domain اللي عليا إن حدث ذلك يبقى بقول ال
+
+16
+00:01:40,540 --> 00:01:45,320
+a و ال b are associates يبقى اتنين مرتبطين مع بعض
+
+17
+00:01:45,320 --> 00:01:50,410
+تماماالتعريف الثاني بيقول a non-zero element of an
+
+18
+00:01:50,410 --> 00:01:55,750
+integral domain دي بيحط شرم ان العمصر غير صفر لكن
+
+19
+00:01:55,750 --> 00:02:02,270
+في التعريف الأول ماحطش هذا الشرم طبعا يبقى a non
+
+20
+00:02:02,270 --> 00:02:06,230
+-zero element of an integral domain دي is called
+
+21
+00:02:06,230 --> 00:02:12,350
+irreducible يعني لا يمكن افككه اللي حصل ضرب two
+
+22
+00:02:12,350 --> 00:02:18,760
+elementsأو أحلله إلى حاصل ضرب two elements إذا كان
+
+23
+00:02:18,760 --> 00:02:27,340
+الـA not unit يبقى هذا الشرط أساسي إن الـA is not
+
+24
+00:02:27,340 --> 00:02:31,980
+a unit هذا النقطة الأولى النقطة الثانية ال
+
+25
+00:02:31,980 --> 00:02:38,940
+universe P وC موجودة في P with الـA يسوى حاصل ضرب
+
+26
+00:02:38,940 --> 00:02:44,950
+P في Cيبقى الشرط التاني لو لقيت عنصرين فيه وحاصل
+
+27
+00:02:44,950 --> 00:02:50,610
+ضربهما سواء ال element a اللي هو غير الصفري و اللي
+
+28
+00:02:50,610 --> 00:02:55,390
+هو ال irreducible يبقى ال P و ال C واحدة منهم لازم
+
+29
+00:02:55,390 --> 00:03:03,670
+تكون main unit طيب يبقى هنا العنصر بقول عنه
+
+30
+00:03:03,670 --> 00:03:10,250
+irreducible إذا تحقق شرطانالشرط الأول ان ال a is
+
+31
+00:03:10,250 --> 00:03:16,470
+not unit تمام الشرط الثاني لو لقيت حاصل ضرب عنصرين
+
+32
+00:03:16,470 --> 00:03:21,870
+يزاوي هذا العنصر معناته واحد فيهم لازم يكون a unit
+
+33
+00:03:21,870 --> 00:03:27,530
+ال a مش unit هدول واحد منهم بدي يكون ماله بدي يكون
+
+34
+00:03:27,530 --> 00:03:33,390
+is a unit هذا معنى ال irreducible الآن بننتقل الى
+
+35
+00:03:33,390 --> 00:03:37,740
+التعريف الثالثبرضه non zero element in integral
+
+36
+00:03:37,740 --> 00:03:44,840
+domain D is called A prime associated irreducible
+
+37
+00:03:44,840 --> 00:03:49,520
+A prime التعريف التالف يبقى بتقول عنه A prime إذا
+
+38
+00:03:49,520 --> 00:03:55,000
+تحقق شرطان الشرط الأولاني برضه قالوا ما هوش units
+
+39
+00:03:55,000 --> 00:04:00,720
+زي مين زي الحالة الأولى من التعريف الثاني والشرط
+
+40
+00:04:00,720 --> 00:04:05,810
+الثاني لو كان A بيقسم ال B في Cيبقى بده يقسم
+
+41
+00:04:05,810 --> 00:04:13,490
+أحدهما يا إما بيقسم ال B يا إما بيقسم ال C نبدأ
+
+42
+00:04:13,490 --> 00:04:21,130
+نعطي بعض الأمثلة البسيطة فمثلا لو جيت بولز أنا بدي
+
+43
+00:04:21,130 --> 00:04:29,850
+أخد ال Z is an integral domain صحيح؟ اه it is an
+
+44
+00:04:29,850 --> 00:04:35,820
+integral domain تمام؟لو وجد حصل ضرب عنصر N يساوي
+
+45
+00:04:35,820 --> 00:04:41,360
+صفر ليس يمكن أن يحدث ذلك إلا إذا كان هدومة يساوي
+
+46
+00:04:41,360 --> 00:04:48,180
+صفر على الأقل يبقى أنا عندي Z an integral domain
+
+47
+00:04:48,180 --> 00:04:53,680
+طيب بدي أشوف أحكاية ال irreducible و ال
+
+48
+00:04:53,680 --> 00:04:58,720
+irreducible لو رحت أخدت any integer N
+
+49
+00:05:01,030 --> 00:05:08,850
+مرتبط مع مين؟ مرتبط مع نفسه مع ناقص N مظبوط؟ طيب
+
+50
+00:05:08,850 --> 00:05:14,090
+ليش؟ مرتبط مع نفسه لإنه لا يوجد units في Z إلا
+
+51
+00:05:14,090 --> 00:05:20,050
+اتنين الواحد والسالج واحد، مظبوط؟ يبقى ال N بقدر
+
+52
+00:05:20,050 --> 00:05:25,750
+اكتب واحد في N والسالج ب N بقدر اكتب وسالج واحد في
+
+53
+00:05:25,750 --> 00:05:31,470
+N تمام؟يبقى صار مين؟ صار سالب ان يسوي سالب واحد ان
+
+54
+00:05:31,470 --> 00:05:37,550
+السالب واحد is a unit والأولان الواحد is a unit
+
+55
+00:05:37,550 --> 00:05:44,670
+كذلك يبقى هذا طبقا للتعريف الأول انتجرال دومين وال
+
+56
+00:05:44,670 --> 00:05:49,290
+A وB موجودات فيها يبقى اتنين associated إذا كان
+
+57
+00:05:49,290 --> 00:05:53,910
+واحد كتبته بدلالته الثانية بس اللي بدي اضرب فيه
+
+58
+00:05:53,910 --> 00:05:58,670
+بديكون ايه اش؟ بديكون unit تمام؟مش حيال الله يعني
+
+59
+00:05:58,670 --> 00:06:04,250
+مش اي رقم كويس طيب المثال اللي انت سمعته فبنروح
+
+60
+00:06:04,250 --> 00:06:09,910
+نسجله مشان ما يضيع ايش مننا و احنا بنذكر يبقى
+
+61
+00:06:09,910 --> 00:06:15,670
+النقطة الأولى بدي اخد every non zero integer every
+
+62
+00:06:15,670 --> 00:06:24,530
+non zero integer in
+
+63
+00:06:27,670 --> 00:06:38,110
+has exactly has exactly بالضبط has exactly two
+
+64
+00:06:38,110 --> 00:06:43,590
+associates two associates
+
+65
+00:06:43,590 --> 00:06:47,690
+in
+
+66
+00:06:47,690 --> 00:06:52,590
+them اللي
+
+67
+00:06:52,590 --> 00:07:03,060
+هم مين ال in andناقص in because the
+
+68
+00:07:03,060 --> 00:07:19,880
+only units in z اللي هو زائد او ناقص واحد that is
+
+69
+00:07:19,880 --> 00:07:23,600
+in ال
+
+70
+00:07:25,060 --> 00:07:32,960
+بدا تساوي واحد مضروبة في N الـ Salib N يساوي سالب
+
+71
+00:07:32,960 --> 00:07:43,860
+واحد مضروبة في N لكل الـ N اللي موجودة في ذلك.
+
+72
+00:07:44,120 --> 00:07:50,560
+طيب المثال الثاني المثال
+
+73
+00:07:50,560 --> 00:07:59,410
+الثانيقول the irreducible elements the irreducible
+
+74
+00:07:59,410 --> 00:08:05,770
+elements
+
+75
+00:08:05,770 --> 00:08:20,030
+the irreducible elements in that are just the
+
+76
+00:08:20,030 --> 00:08:22,010
+أبصارمي
+
+77
+00:08:32,660 --> 00:08:39,420
+مين يا بنات؟ من العناصر اللي موجودة في ذلك اللي
+
+78
+00:08:39,420 --> 00:08:45,440
+ماقدرش أحللها، إلا إذا كان قلت العنصر فيه unit.
+
+79
+00:08:46,420 --> 00:08:50,680
+الابراعي الممتاز جدا. يبقى الابراعي زمين مكان يكون
+
+80
+00:08:50,680 --> 00:08:53,860
+اتنين، تلاتة، خمسة، سبعة، احداشر، تلاتاشر،
+
+81
+00:08:53,860 --> 00:08:58,930
+سبعتاشر، تسعتاشر، إلى آخرين.يبقى هدول ضبضب هم ال
+
+82
+00:08:58,930 --> 00:09:09,350
+prime integers يبقى just the prime integers لإن ال
+
+83
+00:09:09,350 --> 00:09:14,330
+prime integers لا يقسم إلا على نفسه وعلى الواحد
+
+84
+00:09:14,330 --> 00:09:18,550
+الصحيح because
+
+85
+00:09:18,550 --> 00:09:25,150
+the only divisors
+
+86
+00:09:27,070 --> 00:09:40,050
+the only divisors of A prime P او
+
+87
+00:09:40,050 --> 00:09:49,610
+ناقص P لـ X Associate Its
+
+88
+00:09:49,610 --> 00:09:52,410
+Associates and
+
+89
+00:09:54,880 --> 00:10:05,800
+زاد او ناقص واحد اللي هم ال units زد يبقى ال units
+
+90
+00:10:05,800 --> 00:10:15,760
+الموجودة في الذات ال I am ال P
+
+91
+00:10:15,760 --> 00:10:30,520
+is not a unit ما هوش ان ال andالـ P بدأت ساوي واحد
+
+92
+00:10:30,520 --> 00:10:45,040
+مضروب في P هذا بدي أعطيك واحد is a unit يبقى
+
+93
+00:10:45,040 --> 00:10:49,980
+المثال الثاني يقول the irreducible elements في Z
+
+94
+00:10:49,980 --> 00:10:55,910
+هم بالضبط ل prime numbers تمام؟الـPrimal مرة
+
+95
+00:10:55,910 --> 00:11:01,110
+بيحدّله الرمز P، ليش؟ لأن الـonly divisor of
+
+96
+00:11:01,110 --> 00:11:06,070
+الـPrimal P له الـP وثالث P، والواحد وثالث واحد
+
+97
+00:11:06,070 --> 00:11:10,570
+مافيش رغمه، فلو قلت الـP وثالث P، بيهدول ال
+
+98
+00:11:10,570 --> 00:11:18,130
+associates طبق للتعريف الأول، تمام؟ و .. و كذلك ال
+
+99
+00:11:18,130 --> 00:11:24,060
+units اللي هم زائد أو ناقص واحد، ليش؟لأنه لما نقلة
+
+100
+00:11:24,060 --> 00:11:30,220
+ال irreducible تعريفه يبقى هو non zero integer هذا
+
+101
+00:11:30,220 --> 00:11:35,600
+بنسميه نفسه إذا كان not unit يبقى قولنا هنا ال P
+
+102
+00:11:35,600 --> 00:11:41,060
+not unit ما هوش unit تمام؟ and whenever وإذا كان
+
+103
+00:11:41,060 --> 00:11:46,620
+حصل ضربهما بده يساوي هذا ال element يبقى واحد منهم
+
+104
+00:11:46,620 --> 00:11:52,840
+بده يكون هو عبارة عن unitطيب نجي لأول ملاحظة في
+
+105
+00:11:52,840 --> 00:12:02,640
+هذا ال section يبقى remark يقول
+
+106
+00:12:02,640 --> 00:12:09,880
+little a belong to
+
+107
+00:12:09,880 --> 00:12:11,260
+an integral domain
+
+108
+00:12:21,550 --> 00:12:31,130
+والـ A لا تساوي زيه ال A لا تساوي زيه ثم ال A is a
+
+109
+00:12:31,130 --> 00:12:40,870
+prime ال A is a prime if and only if if and only
+
+110
+00:12:40,870 --> 00:12:49,010
+if the principle ideal generated by A is a prime
+
+111
+00:12:49,010 --> 00:12:50,650
+ideal
+
+112
+00:13:03,930 --> 00:13:10,310
+D مرة تانية أخدنا عنصر A مولد في ال integral
+
+113
+00:13:10,310 --> 00:13:15,630
+domain D والعنصر A لا يسوى Zero يبقى non-zero
+
+114
+00:13:15,630 --> 00:13:20,290
+element زي ما اشتغلتها في التعريف الاتنين دول non
+
+115
+00:13:20,290 --> 00:13:25,550
+-zero elementقال الـ A is a prime يبقى هذا بدي
+
+116
+00:13:25,550 --> 00:13:29,090
+يكون ال prime number اف ان والي اف ال principle
+
+117
+00:13:29,090 --> 00:13:34,750
+ideal generated by A is a prime ideal يبقى البرهام
+
+118
+00:13:34,750 --> 00:13:42,330
+بدي يصيحه باتجاهين يبقى بترجع يقوله assume افترض
+
+119
+00:13:42,330 --> 00:13:49,630
+ان ال A is a prime ايش بده نطبق ده بناته؟إنه هذا
+
+120
+00:13:49,630 --> 00:13:55,090
+هو prime ideal. طب هذا احنا عارفين إنه هو ideal
+
+121
+00:13:55,090 --> 00:13:59,470
+لإن ال principle ideal generated by ايه؟ يبقى we
+
+122
+00:13:59,470 --> 00:14:11,010
+know that. We know that ان هذا is an ideal. اللي
+
+123
+00:14:11,010 --> 00:14:17,540
+بيضل عليه نسبتاش يبقى بتاخد عنصرين في ديوفترض ان
+
+124
+00:14:17,540 --> 00:14:23,040
+حاصل ضربهم موجود في ال ideal دي اذا قلت اثبت ان
+
+125
+00:14:23,040 --> 00:14:27,840
+احدهم موجود في هذا ال ideal بصير ال ideal هذا a
+
+126
+00:14:27,840 --> 00:14:32,820
+prime مش هيك تعرف ال prime ideal يبقى بروح بقوله
+
+127
+00:14:32,820 --> 00:14:40,200
+let ال X و ال Y موجودة وين في ال integral domain D
+
+128
+00:14:40,200 --> 00:14:49,760
+such thatبحيث ان ال X Y موجودة في ال principle
+
+129
+00:14:49,760 --> 00:14:55,780
+ideal generated by A ايش بدي احاول اثبت؟ بدي احاول
+
+130
+00:14:55,780 --> 00:15:01,160
+اثبت ان ال X موجود في ال ideal هذا او ال Y موجود
+
+131
+00:15:01,160 --> 00:15:05,660
+في ال ideal هذا ان جدرنا يبقى على طول الخط بصير ال
+
+132
+00:15:05,660 --> 00:15:11,180
+ideal هذا ال prime ideal وبكون برهنة لاتجاه الاول
+
+133
+00:15:14,780 --> 00:15:20,020
+من خلال تعريف ال principle idealية من ال X Y شبه
+
+134
+00:15:20,020 --> 00:15:29,740
+ما اقدر اكتبها A في B يبقى هذا A في B for some B
+
+135
+00:15:29,740 --> 00:15:37,580
+اللي موجودة وين في ال integral domain D كويسة
+
+136
+00:15:37,580 --> 00:15:44,500
+فماشي معناه هذا الكلام ان A تقسم ال X Y صح ولا لا
+
+137
+00:15:44,860 --> 00:15:55,280
+يبقى هنا سا ال a تقسم ال x في y طيب احنا فاقين و
+
+138
+00:15:55,280 --> 00:16:01,300
+هذا يعيش لا pride نيدي لليه pride هذا التاني هو
+
+139
+00:16:01,300 --> 00:16:06,260
+التاني هو تعريف ال pride لو كانت a تقسم اللي يبقى
+
+140
+00:16:06,260 --> 00:16:18,750
+هتقسم أحدهما يبقى هذا then ال aبتقسم ال X او ال A
+
+141
+00:16:18,750 --> 00:16:28,030
+بتقسم ال Y طيب مدام ال A بتقسم ال X او ال A بتقسم
+
+142
+00:16:28,030 --> 00:16:33,710
+ال Y يبقى بدنا نشوف ايش بدنا نستنتج من هذا الكلام
+
+143
+00:16:33,710 --> 00:16:39,890
+من هذا الكلام نستنتج ان ال X بدي سوى ال A في عنصر
+
+144
+00:16:39,890 --> 00:16:48,790
+اخر يبقى هذا بدي يعطيناإن ال X بدها تساوي A مثلا
+
+145
+00:16:48,790 --> 00:17:02,670
+في B1 تمام Or ال Y بدها تساوي مثلا A في B2 و ال B1
+
+146
+00:17:02,670 --> 00:17:14,470
+و ال B2 موجودة في D و ال B1 و ال B2 موجودة فيطيب
+
+147
+00:17:14,470 --> 00:17:22,430
+ما هو تفسيرك لهذا ال X يسوى ايه ايه في عنصر تاني
+
+148
+00:17:22,430 --> 00:17:26,650
+يبقى في ال principle ideal generated by او ال Y
+
+149
+00:17:26,650 --> 00:17:30,830
+موجود في ال principle ideal generated يبقى هنا
+
+150
+00:17:30,830 --> 00:17:36,730
+this means this
+
+151
+00:17:36,730 --> 00:17:46,240
+means that هذا يعنيإن ال X belongs to the
+
+152
+00:17:46,240 --> 00:17:52,740
+principle ideal generated by A او ال Y belong to
+
+153
+00:17:52,740 --> 00:17:56,580
+the principle ideal generated by A ايش معناه هذا
+
+154
+00:17:56,580 --> 00:18:02,680
+الكلام ان هذا ال ideal is a prime هذا بده يعطينا
+
+155
+00:18:02,680 --> 00:18:14,260
+ال ideal اللي عندنا هذا is a prime ideal in Dيبقى
+
+156
+00:18:14,260 --> 00:18:18,040
+انتهينا من الاتجاه الأول بما نروح الاتجاه الثاني
+
+157
+00:18:18,040 --> 00:18:27,940
+بروح نقول ده ايه converse تمام يبقى assume that
+
+158
+00:18:27,940 --> 00:18:34,620
+طرف انه ال principle ideal generated by A is
+
+159
+00:18:34,620 --> 00:18:39,320
+maximal ideal
+
+160
+00:18:44,670 --> 00:18:52,730
+prime اه صحيح prime ideal بنفترض
+
+161
+00:18:52,730 --> 00:19:04,590
+هذا is a prime ideal indeed إيش بدنا نثبت ان ال A
+
+162
+00:19:04,590 --> 00:19:10,230
+في حد ذاتها is a primeاي unit بدنا نثبت ان ال A is
+
+163
+00:19:10,230 --> 00:19:15,330
+a product لو راجعنا هنا معناته بدنا نثبت نقطتين
+
+164
+00:19:15,330 --> 00:19:22,270
+النقطة الأولى بدنا نثبت ان هذه is not a unit هذه
+
+165
+00:19:22,270 --> 00:19:27,950
+واحدة والثانية لو أخدنا A بتقسم ال B في C يبقى يا
+
+166
+00:19:27,950 --> 00:19:35,390
+إما ال A في B يا إما ال A في C يا إما ال A بتقسم
+
+167
+00:19:35,390 --> 00:19:41,800
+من A to Cيبقى بدأت بتشغيل team يبقى نجي للشغل
+
+168
+00:19:41,800 --> 00:19:47,360
+قاللي هذا يفرضوا انه prime ideal السؤال هو ممكن
+
+169
+00:19:47,360 --> 00:19:55,240
+الـA تكون هنا؟
+
+170
+00:19:55,240 --> 00:20:01,640
+ممكن أنا بس السؤال لسه ممكن؟ ممنوع، بدنا نعرف ليش،
+
+171
+00:20:01,640 --> 00:20:14,020
+كويس؟ يبقى هنابنقول معناه الـ A is not ionic هو
+
+172
+00:20:14,020 --> 00:20:25,980
+الشرط الأول because السبب because if ال A is ionic
+
+173
+00:20:25,980 --> 00:20:30,800
+then الواحد
+
+174
+00:20:30,800 --> 00:20:35,960
+الصحيح بيكون مولد في ال principle هذا ولا لاإن
+
+175
+00:20:35,960 --> 00:20:42,640
+الـA unit كل العناصر بتبقى موجودة فيه، مظبوط يبقى
+
+176
+00:20:42,640 --> 00:20:50,920
+هنا then الواحد belong to me للـA فأخدنا remark
+
+177
+00:20:50,920 --> 00:20:56,980
+صغيرة، لو ال ideal احتوى على ال unity تبع ال ring،
+
+178
+00:20:56,980 --> 00:21:02,520
+يبقى ال ideal بتساوي ال ring كلها، مظبوط، يبقى
+
+179
+00:21:02,520 --> 00:21:08,050
+then هذا بده يعطيناإن ال principle ideal generated
+
+180
+00:21:08,050 --> 00:21:15,050
+R by F بدي يسوي ال integral domain كله هذا كلام
+
+181
+00:21:15,050 --> 00:21:23,210
+صحيح؟ ال prime ideal و ال maximum ideal مش يبقى
+
+182
+00:21:23,210 --> 00:21:28,070
+وقار يبقى يقولوا يمكن أن يحدث ذلك يبقى value
+
+183
+00:21:28,070 --> 00:21:31,910
+يقولوا this is impossible
+
+184
+00:21:34,530 --> 00:21:39,590
+هذا الكلام لا يمكن أن يكون صحيحا، إيه السبب؟
+
+185
+00:21:39,590 --> 00:21:48,250
+Because ال principle ID generated by A is proper
+
+186
+00:21:48,250 --> 00:21:58,110
+يبقى فرضنا اللي فرضنا هذا هو صحيح، not a unit لما
+
+187
+00:21:58,110 --> 00:22:04,530
+نقول لو كان unit وصلنا إلى نتيجة قاطعةيبقى هذا
+
+188
+00:22:04,530 --> 00:22:11,870
+يؤكد النقطة الأولى اللى قلناها إذا النقطة الأولى
+
+189
+00:22:11,870 --> 00:22:21,430
+من تعريف الـ prime ideal تحققت مين هي أن الـA هذا
+
+190
+00:22:21,430 --> 00:22:28,790
+is not A يبقى بدي أفرض الآن أن الـA هذا بدي يقسم
+
+191
+00:22:28,790 --> 00:22:39,140
+two elementsيبقى باجي بيقوله F L A بتيقسم X في ال
+
+192
+00:22:39,140 --> 00:22:45,420
+Y مثلا طب نيجي نشوف احنا ايش فرضنا هنا من ال
+
+193
+00:22:45,420 --> 00:22:53,700
+conversely افترض ان هذا هو ال prime صح؟ طيب نشوف
+
+194
+00:22:53,700 --> 00:23:00,000
+نستفيد منه و الله مانستفيدش F
+
+195
+00:23:00,470 --> 00:23:11,810
+الـ A بيقسم ال X Y then ال X Y بتساوي قدر A في B
+
+196
+00:23:11,810 --> 00:23:25,030
+for some B اللي موجودة في D طب هذا ايش معنى ان ال
+
+197
+00:23:25,030 --> 00:23:30,920
+X Y موجودة في ال principle صحيح ولا لأ هذا معناهإن
+
+198
+00:23:30,920 --> 00:23:36,720
+ال X في ال Y موجودة في ال principle ideal طيب هذا
+
+199
+00:23:36,720 --> 00:23:41,400
+prime يبقى يا العنصر الأول موجود فيه يا العنصر
+
+200
+00:23:41,400 --> 00:23:48,600
+التاني موجود فيه يبقى هذا بده يعطينا إن ال X موجود
+
+201
+00:23:48,600 --> 00:23:54,100
+في ال principle ideal generated by A or ال X
+
+202
+00:23:54,100 --> 00:24:01,840
+belongs في ال principle ideal or ال Yوجودة في ال
+
+203
+00:24:01,840 --> 00:24:08,440
+principle ideal generated by A تمام؟ هذا معناه
+
+204
+00:24:08,440 --> 00:24:13,720
+إيش؟ همسك الأول يبقى معنى هذا الكلام إن ال H
+
+205
+00:24:13,720 --> 00:24:25,800
+بتساوي A في B1 مثلا or Y يساوي A في B2 مثلا or
+
+206
+00:24:25,800 --> 00:24:35,560
+some B1 وB2اللي موجودة في الـ D الـ integral
+
+207
+00:24:35,560 --> 00:24:43,900
+domain D طب هذا معناه إيش؟ نمسك هذا يبجى
+
+208
+00:24:43,900 --> 00:24:50,760
+ال A بتقسم ال X يبجى هذا معناه إن ال A تقسم ال X
+
+209
+00:24:50,760 --> 00:24:59,340
+or ال A تقسم ال Yأخدنا a بتقسم اتنين وطلع ال a
+
+210
+00:24:59,340 --> 00:25:05,760
+بتقسم أحدهم اه ليس هذا هو معنى ال prime يبقى
+
+211
+00:25:05,760 --> 00:25:11,720
+أثبتنا النقطة الأولى ان هذا a is not a unit اتنين
+
+212
+00:25:11,720 --> 00:25:16,800
+أخدنا a بتقسم حاصل الضرب بستنجح ان ال a بتقسم
+
+213
+00:25:16,800 --> 00:25:23,700
+الأول او اتنين او اتنين اثانى يبقى this means
+
+214
+00:25:25,640 --> 00:25:34,940
+لأ، هذا يعني ان الـ A is prime. وافق. حد فيكم
+
+215
+00:25:34,940 --> 00:25:42,780
+بتسأل أي سؤال هنا؟ سهل أظن؟ طب كمان واحدة. ويبهبنه
+
+216
+00:25:42,780 --> 00:25:49,360
+المحاضرة يعني. نشط معاه ليه كل يوم. كمان remark
+
+217
+00:25:49,360 --> 00:25:49,940
+تانية.
+
+218
+00:25:54,490 --> 00:26:05,830
+الـ remark بتقول ما يأتي let
+
+219
+00:26:05,830 --> 00:26:17,310
+his day belongs to z such that بحيث ان ال day does
+
+220
+00:26:17,310 --> 00:26:22,890
+not equal one and
+
+221
+00:26:24,320 --> 00:26:33,340
+الـ D is not divisible لاتقسم
+
+222
+00:26:33,340 --> 00:26:45,460
+او لا تنقسم by the square by
+
+223
+00:26:45,460 --> 00:26:59,650
+the square of a primeby the square of A prime on
+
+224
+00:26:59,650 --> 00:27:08,510
+the integral domain on
+
+225
+00:27:08,510 --> 00:27:17,590
+the integral domain اللي هو Z of جدري D مين هو
+
+226
+00:27:17,590 --> 00:27:26,490
+هذا؟ كل العناصر Aزائد بي جدر دي بحيث ال a و ال b
+
+227
+00:27:26,490 --> 00:27:36,930
+أعداد صحيحة define a function
+
+228
+00:27:36,930 --> 00:27:48,610
+عرف الدالة in من z of جدر دي إلى زر plus
+
+229
+00:27:51,040 --> 00:28:02,580
+By الـ N of A زائد B جدر الـ D. N زائد B في جدر
+
+230
+00:28:02,580 --> 00:28:10,460
+الـ D. بدل ساوي absolute value للـ A تربيع ناقص
+
+231
+00:28:10,460 --> 00:28:17,900
+الـ B بـ B تربيع. Then النقطة
+
+232
+00:28:17,900 --> 00:28:27,680
+الأولىال N of X بده يساوي Zero if and only if ال X
+
+233
+00:28:27,680 --> 00:28:35,700
+بده يساوي Zero النقطة الثانية نمره بيه ال N of X
+
+234
+00:28:35,700 --> 00:28:44,800
+هو Y لو ال N of X في Y يساوي ال N of X في ال N of
+
+235
+00:28:44,800 --> 00:28:54,340
+Y لكلالـ X والـ Y اللي موجودة في Z of the square
+
+236
+00:28:54,340 --> 00:28:59,880
+root لـ D النقطة
+
+237
+00:28:59,880 --> 00:29:13,300
+C الـ X is a unit if and only if ال N of X يسوى
+
+238
+00:29:13,300 --> 00:29:13,800
+واحد
+
+239
+00:29:17,500 --> 00:29:30,920
+مقطع نمرة D if ال N of X is A' is
+
+240
+00:29:30,920 --> 00:29:40,160
+A' then ال X is irreducible
+
+241
+00:29:40,160 --> 00:29:44,020
+is irreducible
+
+242
+00:30:12,470 --> 00:30:18,440
+طبعا الكتاب ترى كل كنت تفرحه للريضةوانتوا طبعا
+
+243
+00:30:18,440 --> 00:30:24,640
+قارئين يبقى ممكن تقولوا انهم انتوا طبعا طيب ما
+
+244
+00:30:24,640 --> 00:30:28,460
+علينا نيجي
+
+245
+00:30:28,460 --> 00:30:33,560
+نرجع لنص ال remark اللي هنا يقول الكل دي موجودة في
+
+246
+00:30:33,560 --> 00:30:38,580
+الزد و الدي لا يساوي الواحد وفي نفس الوقت دي is
+
+247
+00:30:38,580 --> 00:30:44,060
+not divisible by a square of a prime يعني لو أخدنا
+
+248
+00:30:44,060 --> 00:30:49,230
+عدد أولي وربعنايبقى هذا ال element لا يُقسم بها
+
+249
+00:30:49,230 --> 00:30:54,110
+بمربع العدد الأولى عشان أقل على ال integral domain
+
+250
+00:30:54,110 --> 00:30:59,390
+هذا المعرف بهذا الشكل بدي أعرف function من ال
+
+251
+00:30:59,390 --> 00:31:03,810
+integral domain هذا إلى مجموعة الأعداد الصحيحة
+
+252
+00:31:03,810 --> 00:31:10,670
+الموجبة سالف ماعندهش صفر ماعندهش بقلل N هي
+
+253
+00:31:10,670 --> 00:31:16,910
+function من Z of D إلى Z plus بايإن لما تأثر على
+
+254
+00:31:16,910 --> 00:31:23,610
+الـ Element اللي هناها بده يسوى المربع الأول ناقص
+
+255
+00:31:23,610 --> 00:31:28,790
+D في المربع الثاني المربع هذا بطل اللي يربص على
+
+256
+00:31:28,790 --> 00:31:33,830
+الـ D وهذا الـ D اللي هي الـ D الثالثة فيه عندي
+
+257
+00:31:33,830 --> 00:31:38,430
+أربع نقاط النقطة الأولى N of X سوى Zero F عندهم F
+
+258
+00:31:38,430 --> 00:31:44,640
+X سوى Zero الـ N of X هو يسوى N of X في N أو Yلكل
+
+259
+00:31:44,640 --> 00:31:50,260
+ال X ال Y الموجودة في Z of جذر يتيح اتة تا X زي
+
+260
+00:31:50,260 --> 00:31:55,360
+ونة F عن طولي F ال N ال N of X تسوّع ال N of X is
+
+261
+00:31:55,360 --> 00:32:01,440
+defined ان ال X is irreducible على مين على Z يبقى
+
+262
+00:32:01,440 --> 00:32:06,180
+كله على التعريف اللي عندها ده وليه دالك مضيت شمسة
+
+263
+00:32:06,180 --> 00:32:11,300
+التعريف وخلتها حتى لو تحضرها متى لازم أقوله نمسك
+
+264
+00:32:11,300 --> 00:32:19,630
+الأوليبقى ال N of X بده يساوي 0 if and only if بدي
+
+265
+00:32:19,630 --> 00:32:25,190
+أمشي لغاية ما أوصل إلى X يساوي قدها يساوي 0 طب ال
+
+266
+00:32:25,190 --> 00:32:30,450
+N of X ال X هو اللي موجودة يبقى الشكلها A زائد B
+
+267
+00:32:30,450 --> 00:32:43,010
+جادرة 2 يبقى N of A زائد B جادرة D بده يساوي 0هذا
+
+268
+00:32:43,010 --> 00:32:49,610
+الكلام صحيح if and only if هذا اللي هو ال absolute
+
+269
+00:32:49,610 --> 00:32:59,650
+value لل a ترابية ناقص d بي ترابية يسوى zero طيب
+
+270
+00:32:59,650 --> 00:33:07,690
+هذا الكلام صحيح إذا كان ال a ترابية ناقص ال d بي
+
+271
+00:33:07,690 --> 00:33:15,950
+ترابية يسوى zero مظبوط؟صح؟ طيب، أليس هذا فرق بين
+
+272
+00:33:15,950 --> 00:33:23,330
+المربعين؟ يبقى البقزر أكت وعلص إلى التانية اللي هو
+
+273
+00:33:23,330 --> 00:33:32,490
+ال A ناقص B جدر ال D في ال A زائد ال B جدر ال D
+
+274
+00:33:32,490 --> 00:33:38,020
+يبدو سوى Zero طب احنا بنشتغل وياه؟في integral
+
+275
+00:33:38,020 --> 00:33:43,320
+domain وحاصل ضرب عنصرين يساوي zero يبقى ولا حد
+
+276
+00:33:43,320 --> 00:33:49,520
+منهم بده يساوي zero مظبوط؟ يبقى هذا الكلام صحيح if
+
+277
+00:33:49,520 --> 00:33:56,540
+and only if ال a ناقص b جذر ال d بده يساوي zero او
+
+278
+00:33:56,540 --> 00:34:03,400
+ال a زائد ال b جذر ال d بده يساوي zero ليش هذا
+
+279
+00:34:03,400 --> 00:34:14,530
+since ال dis an integral domain
+
+280
+00:34:14,530 --> 00:34:17,930
+طيب
+
+281
+00:34:17,930 --> 00:34:25,950
+الكلام هذا صحيح if and only if الاولاري بقدر اقول
+
+282
+00:34:25,950 --> 00:34:38,940
+a بدي سوى b في جذري d او ال aبتساوي ناقص P في جذري
+
+283
+00:34:38,940 --> 00:34:47,900
+D هذا الكلام صحيح F and only F شكل ال X اللي
+
+284
+00:34:47,900 --> 00:34:54,040
+موجودة في ال integral domain هذا بده يساوي A زائد
+
+285
+00:34:54,040 --> 00:35:05,030
+P جذري 2 مظبوط؟ طيب هنا ال A بداشا بناهابجذر اتنين
+
+286
+00:35:05,030 --> 00:35:13,750
+صحيح يفقد بده يساوي ال a زائد ال a اللي هو بقداش
+
+287
+00:35:13,750 --> 00:35:25,790
+باتنين a او ال x بده يساوي a ناقص a مش ال a ناقص b
+
+288
+00:35:25,790 --> 00:35:32,320
+جذري اتنينيبقى بده اشيل هذه A زي .. ايها يا بني
+
+289
+00:35:32,320 --> 00:35:38,580
+هذه واحدة و هي تانية مش عندنا A زي B جذري تانية X
+
+290
+00:35:38,580 --> 00:35:45,760
+خلت الـ A زي .. بي جذري ال D بي جذري ال D هذه خطأة
+
+291
+00:35:45,760 --> 00:35:51,580
+طبيعية تمام؟ يبقى بي جذري ال D طب انا عندي بي جذري
+
+292
+00:35:51,580 --> 00:35:58,820
+ال D ب Aيبقى شلطة وحطت مكان ا و ا باتنين ا او ال X
+
+293
+00:35:58,820 --> 00:36:04,980
+من النقرة تانية بتاخد هذا يبقى ال A كما هي
+
+294
+00:36:04,980 --> 00:36:12,380
+والتانية B جادة يرددهم سالب A هذا سالب يجد اسه
+
+295
+00:36:12,380 --> 00:36:18,320
+ساوي Zero يبقى هذه هو المطلوب خلاص مخلصها من
+
+296
+00:36:18,320 --> 00:36:20,540
+الجهود كم؟
+
+297
+00:36:22,270 --> 00:36:27,310
+قال ماشي، مالحين هي هذه أو هذه، تمام؟ يبقى هذه و
+
+298
+00:36:27,310 --> 00:36:31,370
+هذه يبقى stop أيضا طبيعي، واحدة منهم، أنا بدي أخد
+
+299
+00:36:31,370 --> 00:36:39,010
+X بساوي Z، تمام؟ يكفيني ذلك، تمام؟ طيب، نمر بيه؟
+
+300
+00:36:39,010 --> 00:36:44,270
+نمر بيه بسيطة جدا، لو سألتي، بتقولك هذا الشو؟
+
+301
+00:36:44,270 --> 00:36:49,010
+بتقوللي هذا هو الشرط التاني من شروط ال homorphism
+
+302
+00:36:49,490 --> 00:36:54,970
+يبقى انا بتبدأ و اخليك تكبلي انت فالدار لحالك كيف
+
+303
+00:36:54,970 --> 00:37:02,810
+بدنا نبدأ سعالى شوف الحين ال N of X في Y يبقى ال N
+
+304
+00:37:02,810 --> 00:37:07,970
+ار بده اشيل ال X و احطها من ال from ال integral
+
+305
+00:37:07,970 --> 00:37:16,790
+domain هذا يبقى ايش بده يصير ايوة A زائد B جذري D
+
+306
+00:37:16,790 --> 00:37:27,420
+سبعمضروبة في C زائد E جدر ال D بتكتر ضربيها حتى
+
+307
+00:37:27,420 --> 00:37:34,420
+تقدر تبقاش اللي عندك النقطة هذه يبقى هذا بتساوي N
+
+308
+00:37:34,420 --> 00:37:47,110
+R A C زائد B E Dفانا هذه مع هذه و هذه مع هذه طريقة
+
+309
+00:37:47,110 --> 00:37:59,290
+تظهر الآن A مع الأخيرة يبقى A E زائد A E زائد B C
+
+310
+00:37:59,290 --> 00:38:08,190
+B C كله في جذر ال T يبقى
+
+311
+00:38:08,190 --> 00:38:16,080
+M يؤثر على هذا ال Mيبقى المربع الأول ناقص C في
+
+312
+00:38:16,080 --> 00:38:22,280
+المربع الثاني يبقى هذا الكلام في الديسير اللي هو
+
+313
+00:38:22,280 --> 00:38:31,660
+ال A C زائد B E D لكل تربيع ك absolute value ناقص
+
+314
+00:38:31,660 --> 00:38:42,330
+D في ال A E زائد ال B C لكل تربيع بالمثلبدك تروح
+
+315
+00:38:42,330 --> 00:38:50,030
+تجيبي N of X في ال N of Y يبقى جاهزة كده إيش بده
+
+316
+00:38:50,030 --> 00:39:00,090
+يسياري ال N of A زائد B جذر ال D فاهمين؟ في ال N
+
+317
+00:39:00,090 --> 00:39:11,970
+اللي هو C زائد ال E جذر ال Dهذا بالدرسية ال
+
+318
+00:39:11,970 --> 00:39:19,930
+absolute value ا تربيع ناقص ال D بي تربيع مضروب في
+
+319
+00:39:19,930 --> 00:39:31,730
+مين في ال C تربيع ناقص ال D اي تربيع الحين مطلوب
+
+320
+00:39:31,730 --> 00:39:38,980
+انك تثبتيإن الاتنين هدول are equal يبقى بيك تروحش
+
+321
+00:39:38,980 --> 00:39:44,880
+تضغط تفكي هذه تفكي هذه تفكي هذه هتلاقي اتنين نساوة
+
+322
+00:39:44,880 --> 00:39:54,340
+و بعض يبقى هدول are equal قد بني منك ت check عليهم
+
+323
+00:39:54,340 --> 00:40:03,790
+شكلي عليهم تمام؟ بقى النقطتينللمرة القادمة، إن شاء
+
+324
+00:40:03,790 --> 00:40:05,090
+الله تعالى.
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/7NReVjSKs-k_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/7NReVjSKs-k_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3987e4f54e4491173a9c32b098fe1b13021ef9a6
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/7NReVjSKs-k_postprocess.srt
@@ -0,0 +1,1800 @@
+1
+00:00:20,960 --> 00:00:25,780
+بسم الله الرحمن الرحيم مواصل اليوم ما ابتدأناه في
+
+2
+00:00:25,780 --> 00:00:31,800
+المقابلات السابقة وهذه هي اخر نظرية في هذا ال
+
+3
+00:00:31,800 --> 00:00:38,760
+chapter ان شاء الله تبارك وتعالى نص النظرية كتالي
+
+4
+00:00:38,760 --> 00:00:44,520
+بناخد ال F عبارة عن fields ال P of X polynomial في
+
+5
+00:00:44,520 --> 00:00:50,430
+كارتن F of Xالـprinciple ideal generated by P of X
+
+6
+00:00:50,430 --> 00:00:55,970
+is maximum ideal في capital F of X if and only if
+
+7
+00:00:55,970 --> 00:01:02,610
+P of X عبارة عن الـreducible عالميا على F فالورحان
+
+8
+00:01:02,610 --> 00:01:07,810
+بده يصير في اتجاهين بسبب وجود ال F and only if
+
+9
+00:01:07,810 --> 00:01:13,230
+الأن بناخد الاتجاه الأول و بعد أن ننتهي منه ننتقل
+
+10
+00:01:13,230 --> 00:01:19,620
+الى الاتجاه الثانيالاتجاه الأول بدي افترض ان ال P
+
+11
+00:01:19,620 --> 00:01:25,460
+of X موجودة في capital F of X و P of X هو عبارة عن
+
+12
+00:01:25,460 --> 00:01:33,820
+maximal ID يبقى let ال P of X موجودة في capital F
+
+13
+00:01:33,820 --> 00:01:42,840
+of X such that بحيث ان ال P of X لprinciple ID
+
+14
+00:01:42,840 --> 00:01:51,550
+generated by P of Xis a maximal ideal
+
+15
+00:01:51,550 --> 00:01:56,970
+in capital
+
+16
+00:01:56,970 --> 00:02:01,890
+F of X قبل
+
+17
+00:02:01,890 --> 00:02:07,730
+ما اكمل اروح ال P of X is irreducible بدي اسألي
+
+18
+00:02:07,730 --> 00:02:09,090
+السؤال التالت
+
+19
+00:02:14,980 --> 00:02:21,860
+السؤال هو هل ممكن ال P of X تكون كونستان؟ لأ، في
+
+20
+00:02:21,860 --> 00:02:27,060
+الشمكانية السبب أنه إذا كانت P of X عبارة عن
+
+21
+00:02:27,060 --> 00:02:32,700
+كونستان بالprinciple ideal generated by X يا إما
+
+22
+00:02:32,700 --> 00:02:39,660
+Zero فقط يا إما كل capital F of Xليش؟ انه constant
+
+23
+00:02:39,660 --> 00:02:43,440
+polynomial any constant .. any non-zero constant
+
+24
+00:02:43,440 --> 00:02:49,460
+polynomial is a unit ومدام unit بديه يجيب لمين؟ كل
+
+25
+00:02:49,460 --> 00:02:54,620
+عناصر اللي هو ال capital F of X والسؤال هو هل ال
+
+26
+00:02:54,620 --> 00:03:00,740
+capital F of X is maximal؟ لأ لإن هي تناقض مع مين؟
+
+27
+00:03:00,740 --> 00:03:05,720
+مع ال proper any prime ideal أو maximal ideal is
+
+28
+00:03:05,720 --> 00:03:10,370
+properيبقى ليه يمكن ال P of X تبقى constant
+
+29
+00:03:10,370 --> 00:03:15,910
+polynomial خلينا نكتب المعلومة هذه مشان تلزج في
+
+30
+00:03:15,910 --> 00:03:22,490
+دماغنا لإن ربما تلزم و احنا نشترك يبقى P of X is
+
+31
+00:03:22,490 --> 00:03:31,010
+maximal ideal هنا بنكتب note that لاحظي ان ال P of
+
+32
+00:03:31,010 --> 00:03:35,410
+X is non constant
+
+33
+00:03:39,810 --> 00:03:48,270
+Polynomial شو السبب because if
+
+34
+00:03:48,270 --> 00:03:59,190
+P of X is constant then ال
+
+35
+00:03:59,190 --> 00:04:06,090
+capital P of X لprinciple هذا بده يساوي zero or
+
+36
+00:04:08,430 --> 00:04:16,230
+الـP of X is a unit وهذه
+
+37
+00:04:16,230 --> 00:04:22,030
+ستجعل الـprinciple ideal generated by P of X يكون
+
+38
+00:04:22,030 --> 00:04:40,890
+كابتل F of X and neither Zero nor F of Xis maximum
+
+39
+00:04:40,890 --> 00:04:44,670
+لا
+
+40
+00:04:44,670 --> 00:04:49,370
+هذا maximum ولا هذا maximum إذا ضروري ال P of X ما
+
+41
+00:04:49,370 --> 00:04:55,150
+تكونش constant طبعا بتبقى polynomial لكنها ليست
+
+42
+00:04:55,150 --> 00:05:01,810
+constant الآن هذه بس مجرد ملاحظة كان جملة اعتراضية
+
+43
+00:05:01,810 --> 00:05:06,790
+و بدنا نيجي إيشبدنا نثبت ان ال P of X is
+
+44
+00:05:06,790 --> 00:05:17,590
+irreducible يبقى الأن بقوله now want to show that
+
+45
+00:05:17,590 --> 00:05:27,850
+ان ال P of X is irreducible over X
+
+46
+00:05:33,870 --> 00:05:38,790
+الشفتر هذا كل البرهين كانت في ال contradiction
+
+47
+00:05:38,790 --> 00:05:43,630
+وماحدش أحسن من حد و هذه تلحقهم كمان يبقى هقوله
+
+48
+00:05:43,630 --> 00:05:51,230
+assume نعم يبقى هنا هقوله assume ان ال P of X is
+
+49
+00:05:51,230 --> 00:05:56,510
+reducible تمام
+
+50
+00:05:56,510 --> 00:06:06,150
+يبقى reducible over Fفماش اللي بده يحصل يبقى then
+
+51
+00:06:06,150 --> 00:06:15,810
+ال P of X هذه حد ساوي ال G of X في ال H of X where
+
+52
+00:06:15,810 --> 00:06:29,210
+حيث ال G of X و ال H of X موجودات في capital F of
+
+53
+00:06:29,210 --> 00:06:41,840
+X andR of lower degree ايش
+
+54
+00:06:41,840 --> 00:06:46,820
+يعني lower degree يعني درجة كل واحدة فيهم من GH
+
+55
+00:06:46,820 --> 00:06:54,260
+اقل من درجة من P of X ممتاز جدا يبقى الآن صار
+
+56
+00:06:54,260 --> 00:07:00,030
+عندنا شبنان صار عندنا P of Xيساوي حاصل ضرب two
+
+57
+00:07:00,030 --> 00:07:06,730
+polynomials تمام ليش ان ال P of X ليست constant
+
+58
+00:07:06,730 --> 00:07:11,670
+polynomial إذا كتبناها على حاصل الضرب وكل واحدة
+
+59
+00:07:11,670 --> 00:07:19,370
+فيهم درجتها أقل من درجة مين أقل من درجة P of X طيب
+
+60
+00:07:19,370 --> 00:07:24,710
+بتكتب هالجملة هذه وشوف والي صح ولا غلط أنا أزعم
+
+61
+00:07:24,710 --> 00:07:32,720
+الآنإن ال principle ideal generated by P of X هو
+
+62
+00:07:32,720 --> 00:07:39,820
+subset من ال principle ideal generated by G of X
+
+63
+00:07:39,820 --> 00:07:50,780
+هذه أقل من أو subset من اللي هو capital F of X طب
+
+64
+00:07:50,780 --> 00:07:57,060
+نمشي واحدة واحدة غطيت هذه هذه صحيحة؟هذه ما حد
+
+65
+00:07:57,060 --> 00:08:01,340
+يشيلوا عليها ترى تمام طيب ضالة تالت هل ال
+
+66
+00:08:01,340 --> 00:08:06,440
+principle ideal generated by P of X subset من ال G
+
+67
+00:08:06,440 --> 00:08:12,060
+of X طبقا لهذه المعادلة؟
+
+68
+00:08:12,060 --> 00:08:20,640
+في شكك؟ طيب سانوزيل الشك سانوزيل الشك main subset
+
+69
+00:08:20,640 --> 00:08:29,310
+من التانية 2Z دهوالله أربعة زد صبشت
+
+70
+00:08:29,310 --> 00:08:34,910
+تمام اليمين أربعة زد أصغر من اتنين زد و الله أكبر
+
+71
+00:08:34,910 --> 00:08:42,210
+أصغر تمام يبقى اتنين زد هي الرقم تبعها صغير بس
+
+72
+00:08:42,210 --> 00:08:49,270
+الأربعة زد رقمها أكبر يبقى صارت صارت مين صارت
+
+73
+00:08:49,270 --> 00:08:55,560
+الأربعة زد صبشت من مينمن اتنين زد رغم انهم اربعة
+
+74
+00:08:55,560 --> 00:09:02,180
+اكبر من من اكبر من اتنين على ضوء هذه ممكن ان نفهم
+
+75
+00:09:02,180 --> 00:09:07,000
+ان ال P of X ال principle ideal اصغر من ال
+
+76
+00:09:07,000 --> 00:09:12,820
+principle ideal generated by اللي هو G of X اي
+
+77
+00:09:12,820 --> 00:09:19,860
+واحدة ثانية هو ال P of X maximum ولا لا maximum
+
+78
+00:09:21,230 --> 00:09:28,390
+أيوة تمام طيب الآن صاروا هدول اتنين subset من بعض
+
+79
+00:09:28,390 --> 00:09:34,290
+هذه subset من هذه وهذه subset من هذه تمام؟ بدهاري
+
+80
+00:09:34,290 --> 00:09:41,410
+الآن اخد كل واحدة منها على ايش فارض؟ فارض ان ال
+
+81
+00:09:41,410 --> 00:09:46,630
+principle ID generated by P of X is a maximal ID
+
+82
+00:09:46,630 --> 00:09:52,270
+وكتبناه كتبناه هىمدام maximum لو عندى العبارة هذه
+
+83
+00:09:52,270 --> 00:09:59,270
+يبقى يا إما هذه تساوي هذه أو هذه تساوي هذه صح يبقى
+
+84
+00:09:59,270 --> 00:10:04,930
+باجي بقوله بما أنه يبقى since the principle ideal
+
+85
+00:10:04,930 --> 00:10:16,890
+generated by P of X is maximum we have أحد أمرين
+
+86
+00:10:17,350 --> 00:10:22,610
+الأمر الأول يا إما ال principle ideal generated by
+
+87
+00:10:22,610 --> 00:10:27,650
+P of X بده يساوي ال principle ideal generated by G
+
+88
+00:10:27,650 --> 00:10:34,310
+of X or ال principle ideal generated by G of X بده
+
+89
+00:10:34,310 --> 00:10:43,470
+يساوي capital F of X كله طب بتاخد كل حالة منهم
+
+90
+00:10:43,470 --> 00:10:51,960
+وشوف إيش بتعطينيالان لو كان F F اللي هو ال
+
+91
+00:10:51,960 --> 00:10:57,080
+principle ideal generated by P of X بده يساوي ال
+
+92
+00:10:57,080 --> 00:11:02,120
+principle ideal generated by G of X ما هي العلاقة
+
+93
+00:11:02,120 --> 00:11:13,280
+بين درجة ال P ودرجة ال G؟ وبعد يبقى then اللي هو
+
+94
+00:11:13,280 --> 00:11:27,200
+درجةالـ P of X بدها تساوي درجة الـ G of X تمام؟
+
+95
+00:11:27,200 --> 00:11:31,420
+لسه .. بدنا نجيب الباقي لسه في احتمال تاني يعني
+
+96
+00:11:31,420 --> 00:11:34,840
+انت بدك تنفي .. بدك تنفي الاحتمالين مش تنفي واحد و
+
+97
+00:11:34,840 --> 00:11:39,580
+التاني لا لأن احنا بنقول يا إما هذا يا إما هذا في
+
+98
+00:11:39,580 --> 00:11:44,150
+التساوي إذا بدنا نروح للحالة الثانيةيبقى باجي
+
+99
+00:11:44,150 --> 00:11:50,370
+بقوله هنا F ال principle ideal generated by G of X
+
+100
+00:11:50,370 --> 00:11:58,530
+بده ساوي capital F of X هذا حد فيكم بتقدر تقولي
+
+101
+00:11:58,530 --> 00:12:06,870
+يبقى G of X شو درجتها؟ كونصا صحيح يبقى ال G of X
+
+102
+00:12:06,870 --> 00:12:11,150
+بده تكون كونصا لأن هذه كل ال field اللي عندنا
+
+103
+00:12:11,530 --> 00:12:18,890
+Constant يعني unit صح يبقى مدام unit هي من الدرجة
+
+104
+00:12:18,890 --> 00:12:26,710
+الصفرية هتكون على طول الخط يبقى then ال degree لل
+
+105
+00:12:26,710 --> 00:12:34,250
+G بده يساوي zero يعني هذا يا بنات مش ممكن ال
+
+106
+00:12:34,250 --> 00:12:37,730
+principle ideal generated by G of X يساوي ال F of
+
+107
+00:12:37,730 --> 00:12:43,320
+X إلا إذا كانالـ g of x is constant مدام constant
+
+108
+00:12:43,320 --> 00:12:50,000
+يبقى unit مدام constant إذا ال degree تبعته تساوي
+
+109
+00:12:50,000 --> 00:12:55,200
+zero طب مدام ال degree تبعته تساوي zero إيش مضل
+
+110
+00:12:55,200 --> 00:13:05,520
+عندنا بصير عندنا ال degree ال degree لمن
+
+111
+00:13:05,520 --> 00:13:14,750
+لل g of xبدها تساوي ال degree أبصر لمين ال degree
+
+112
+00:13:14,750 --> 00:13:20,930
+ل G تساوي Zero يبقاش مضلع لنا ال degree ل P بدها
+
+113
+00:13:20,930 --> 00:13:24,630
+تساوي ال degree ل G كمان والله إيش احنا أخدنا هذه
+
+114
+00:13:24,630 --> 00:13:29,630
+في الأول بدنا نجيب التاني ال degree ل G بدها تساوي
+
+115
+00:13:29,630 --> 00:13:34,170
+ال degree ل H بس
+
+116
+00:13:34,170 --> 00:13:38,040
+خمس استغل شوية واحدة واحدةالحين احنا خدنا الحالة
+
+117
+00:13:38,040 --> 00:13:41,560
+الأولى ال principle ideal يسوي اذا ال degree ل P
+
+118
+00:13:41,560 --> 00:13:45,300
+بديه يسوي ال degree ل G الحالة التانية صارت ال
+
+119
+00:13:45,300 --> 00:13:51,380
+degree ل G Zero يبقى ال G هذه صارت constant يبقى
+
+120
+00:13:51,380 --> 00:13:56,160
+بصير ال degree ل P تسوي مين ال degree ل H يبقى ال
+
+121
+00:13:56,160 --> 00:14:03,920
+degree على P ال degree ل P ل P of X بديه يسوي ال
+
+122
+00:14:03,920 --> 00:14:10,810
+degree ل Hطب اتطلعيله للاتنين مع بعض هذا
+
+123
+00:14:10,810 --> 00:14:16,090
+contradiction ولا لا؟ هذه قالت ال degree ل P هي
+
+124
+00:14:16,090 --> 00:14:20,770
+degree ل G وهذا قالت ال degree ل P هي degree ل H و
+
+125
+00:14:20,770 --> 00:14:27,010
+degree ل P وH are of lower degree than P of X
+
+126
+00:14:27,010 --> 00:14:33,110
+تناقض ولا لا؟ يعني على كلا الحالتين صار عندي تناقض
+
+127
+00:14:33,470 --> 00:14:41,130
+يبقى هذا Contradiction هو
+
+128
+00:14:41,130 --> 00:14:50,650
+Contradicts تخليني أضحى Contradicts that ان ال G
+
+129
+00:14:50,650 --> 00:15:02,250
+of X and ال H of X are of lower degree than
+
+130
+00:15:03,600 --> 00:15:08,300
+الـ P of X تمام؟
+
+131
+00:15:08,300 --> 00:15:13,760
+ايوة طالع لما قلنا هنا قلنا where الـ R of lower
+
+132
+00:15:13,760 --> 00:15:18,200
+degree طلعوا بضريتين زي بعض يبقى هذا التناقض ما
+
+133
+00:15:18,200 --> 00:15:23,620
+الذي جاء بهذا التناقض؟ الفرض الخاطئ ما هو الفرض
+
+134
+00:15:23,620 --> 00:15:30,680
+الخاطئ؟ ان فرقت ان ال P of X is reducible
+
+135
+00:15:34,250 --> 00:15:38,950
+هذا فرضنا ان ال P of X is irreducible يبقى هذا
+
+136
+00:15:38,950 --> 00:15:44,230
+الفرض الخاطق إذا وصلنا إلى هنا يبقى باجي بقوله
+
+137
+00:15:44,230 --> 00:15:55,950
+Thus وهكذا ال P of X is irreducible over
+
+138
+00:15:55,950 --> 00:16:04,550
+اللي هو ال F نمشي .. نمشيالاتجاه المعاكس يبقى
+
+139
+00:16:04,550 --> 00:16:19,630
+conversely assume that ان ال P of X is irreducible
+
+140
+00:16:19,630 --> 00:16:23,870
+over F
+
+141
+00:16:30,110 --> 00:16:33,390
+ان ال principle ideal generated by P of X is
+
+142
+00:16:33,390 --> 00:16:41,490
+maximum يبقى انا want to show that
+
+143
+00:16:41,490 --> 00:16:46,790
+بدنا نحاول نثبت ان ال principle ideal generated by
+
+144
+00:16:46,790 --> 00:16:53,750
+P of X is maximum طيب
+
+145
+00:16:54,690 --> 00:16:59,930
+كيف كنا بنثبت ال ideal عبارة عن maximum؟ بطريقة
+
+146
+00:16:59,930 --> 00:17:06,090
+تانية النظرية و التعريف مظبوط لو قدرنا نثبت ان ال
+
+147
+00:17:06,090 --> 00:17:12,670
+factor ring عبارة عن field يبقى ال principle ideal
+
+148
+00:17:12,670 --> 00:17:17,710
+اللي نتج منها هو maximum يا أما التعريف طب روح
+
+149
+00:17:17,710 --> 00:17:25,390
+ناخد التعريف يبقى لان بداجي أقول له لأالـ I be an
+
+150
+00:17:25,390 --> 00:17:37,450
+ideal in الهميم in ال capital F of X such that و
+
+151
+00:17:37,450 --> 00:17:44,990
+بحيث أن ال P of X ال principle ideal generated by
+
+152
+00:17:44,990 --> 00:17:52,220
+P of X سبسط من I و I في الحقيقة سبسط من مينمن
+
+153
+00:17:52,220 --> 00:17:57,680
+capital F of X طرد
+
+154
+00:17:57,680 --> 00:18:02,340
+انه عندي ideal I بحيث ال principle ideal generated
+
+155
+00:18:02,340 --> 00:18:08,300
+by P of X ب subset من I و I subset من capital F of
+
+156
+00:18:08,300 --> 00:18:12,960
+X يبقى مطموض مننا نثبت ان ال principle ideal
+
+157
+00:18:12,960 --> 00:18:18,800
+generated by P of X هو I او ال I يساوي ال field
+
+158
+00:18:19,390 --> 00:18:24,510
+مظبوط ان اثبتنا ذلك بصير ال I is maximum. السؤال
+
+159
+00:18:24,510 --> 00:18:32,150
+هو ال F عبارة عن ايه؟ Field. هي في رأس المثل. ال F
+
+160
+00:18:32,150 --> 00:18:38,150
+عبارة عن field. مدام field. Any ideal في هذا ال
+
+161
+00:18:38,150 --> 00:18:44,590
+field عبارة عن ايه؟principal ideal خدناها نظرية
+
+162
+00:18:44,590 --> 00:18:49,330
+قبل ذلك إذا ال F هي عبارة عن field يبقى any ideal
+
+163
+00:18:49,330 --> 00:18:55,270
+عبارة عن principal ideal يبقى باجي بقول هنا since
+
+164
+00:18:55,270 --> 00:19:07,910
+ال F is a field يبقى any ideal
+
+165
+00:19:10,060 --> 00:19:15,760
+ال F is a principle ايش
+
+166
+00:19:15,760 --> 00:19:21,720
+معناه هذا الكلام هذا معناه ان ال I اللي عندنا هي
+
+167
+00:19:21,720 --> 00:19:33,200
+principle ideal generated by G of X for some G
+
+168
+00:19:33,200 --> 00:19:42,730
+of X اللي موجودة في capital F of Xمظبوط؟ نظرا لإن
+
+169
+00:19:42,730 --> 00:19:47,630
+ال F عبارة عن field يبقى أي ideal is a principle
+
+170
+00:19:47,630 --> 00:19:51,630
+ليش؟ لأن ال field عبارة عن principle، ideal،
+
+171
+00:19:51,630 --> 00:19:58,150
+domain تمام؟ يبقى ال ideal هذا زي ولد ب polynomial
+
+172
+00:19:58,150 --> 00:20:05,730
+وولد تكون على سبيل المثال g of x إذن هديها بقدر
+
+173
+00:20:05,730 --> 00:20:11,170
+أصيها صياغة جديدةالجهد ده بده يعطينا ان ال
+
+174
+00:20:11,170 --> 00:20:17,030
+principle ID generated by P of X subset من ال
+
+175
+00:20:17,030 --> 00:20:22,650
+principle ID generated by G of X subset من capital
+
+176
+00:20:22,650 --> 00:20:29,630
+F of X طيب
+
+177
+00:20:29,630 --> 00:20:34,610
+تعالى نشوف الآن اش اللي بده يحصل احنا اش اللي بنا
+
+178
+00:20:34,610 --> 00:20:40,910
+نثبته؟بنثبت ان ال ideal is maximum يعني بدي أثبت
+
+179
+00:20:40,910 --> 00:20:46,530
+ان اتنين هذول بتساوى او اتنين هذول بتساوى تمام؟
+
+180
+00:20:46,530 --> 00:20:52,550
+نيجي للحالة الأول الآن بدي اثبت ان اتنين هذول
+
+181
+00:20:52,550 --> 00:21:00,770
+بيتساوى ان امكن ذلك تمام؟ طب احنا في حاجة كتبناها
+
+182
+00:21:00,770 --> 00:21:09,280
+ومستفدناش منها ال radio setأخدنا إن الـ P-O-Fix is
+
+183
+00:21:09,280 --> 00:21:16,360
+irreducible. حتى الآن لم نستفد منها شيء. مظبوط؟
+
+184
+00:21:16,360 --> 00:21:22,740
+طيب، هذه نرجع لقبل شوية. إيش اللي أخدناها قبل
+
+185
+00:21:22,740 --> 00:21:28,940
+شوية؟ أخدناها شيء؟ لأ ما أخدناها شيء، اتفقتنا بس
+
+186
+00:21:28,940 --> 00:21:33,710
+للاتجاهين الأول.طيب يبقى ال F of X اللي عندنا هذه
+
+187
+00:21:33,710 --> 00:21:40,430
+is irreducible وين بتلزم؟ بدياها طيب نرجع الآن ال
+
+188
+00:21:40,430 --> 00:21:46,570
+P of X هذا subset من هذه بستفيد منها شغلة ما هي
+
+189
+00:21:46,570 --> 00:21:52,490
+الشغلة هذه؟ ال P of X موجودة في ال principle ideal
+
+190
+00:21:52,490 --> 00:21:59,380
+generated by P of X حد بتقدر ينكر هذا؟طيب هذه ال
+
+191
+00:21:59,380 --> 00:22:06,100
+subset من هذه هذا معناته ان ال P of X موجودة في ال
+
+192
+00:22:06,100 --> 00:22:11,520
+principle ideal generated by G of X صحيح ولا لأ؟
+
+193
+00:22:11,520 --> 00:22:20,940
+طيب هذا معناه ان ال P of X شو شكل العنصر هنا؟ G of
+
+194
+00:22:20,940 --> 00:22:25,840
+X مضروب في Pronomial تاني حسب تعريف ال principle
+
+195
+00:22:25,840 --> 00:22:32,660
+ideal مظبوط؟يبقى هذا ال P of X بده يساوي ال G of X
+
+196
+00:22:32,660 --> 00:22:43,640
+ب H of X for او بلاش for و ال H of X هذي موجودة في
+
+197
+00:22:43,640 --> 00:22:49,600
+capital F of X هذا
+
+198
+00:22:49,600 --> 00:22:58,250
+الفرق انه هذا irreducible اذا طلعت منكتناقض؟ لأ مش
+
+199
+00:22:58,250 --> 00:23:04,930
+تناقض ايوة هذا اللي بدنا نوصله يبقى هذا الكلام
+
+200
+00:23:04,930 --> 00:23:10,650
+صحيح في حالة واحدة انه ممكن تكون ال G of X
+
+201
+00:23:10,650 --> 00:23:17,870
+constant او ال H of X constant صح ولا لا؟ يبقى هذا
+
+202
+00:23:17,870 --> 00:23:24,310
+بني بقول since بما ان ال P of X is
+
+203
+00:23:28,230 --> 00:23:37,610
+irreducible over if we have ان ال g of x constant
+
+204
+00:23:37,610 --> 00:23:44,310
+او ال h of x constant we have ان ال g of x is
+
+205
+00:23:44,310 --> 00:23:51,510
+constant or ال h of x is constant
+
+206
+00:23:54,640 --> 00:24:01,520
+تمام ؟ الى ان نمشي الحالة الأولى لو كانت ال g of x
+
+207
+00:24:01,520 --> 00:24:06,600
+is constant لو
+
+208
+00:24:06,600 --> 00:24:12,400
+كانت ال g of x ممتاز
+
+209
+00:24:12,400 --> 00:24:19,590
+جدا لو كانت ال g of x constant يبقى هذا معناهإن ال
+
+210
+00:24:19,590 --> 00:24:24,890
+principle ideal generated by g of x بتسوي capital
+
+211
+00:24:24,890 --> 00:24:32,590
+F of X كله صح لأنه unit مظبوط يبقى هذا هجيبلي
+
+212
+00:24:32,590 --> 00:24:37,550
+capital F و ناخد الحالة التانية الحالة التانية لو
+
+213
+00:24:37,550 --> 00:24:45,930
+كانت ال H of X is constant يبقى is constant
+
+214
+00:24:49,250 --> 00:24:56,610
+طلع اليه ال H of X constant ليبقى إيش مضال عندنا؟
+
+215
+00:24:56,610 --> 00:24:59,710
+ال principle ideal generated by P of X هو ال
+
+216
+00:24:59,710 --> 00:25:03,150
+principle ideal generated by G of X لأن هذا
+
+217
+00:25:03,150 --> 00:25:09,890
+constant ليبقى then ال principle ideal generated
+
+218
+00:25:09,890 --> 00:25:18,450
+by P of X هولـ principal ideal generated by g of
+
+219
+00:25:18,450 --> 00:25:26,530
+x. إيش معنى هذا الكلام؟ ال P of X maximum. يبقى من
+
+220
+00:25:26,530 --> 00:25:35,290
+الإتنين هذول بستنتج ل principal id generated by P
+
+221
+00:25:35,290 --> 00:25:40,710
+of X ماله is maximum.
+
+222
+00:25:44,520 --> 00:25:45,500
+وهو المطلوب.
+
+223
+00:25:48,120 --> 00:25:52,040
+خليني أرجعك النظرية مرة تانية بس على السريع مشان
+
+224
+00:25:52,040 --> 00:25:56,560
+أثبت المعلومة لإن دوخناكوا شوية. ابقى ركزي معايا
+
+225
+00:25:56,560 --> 00:26:02,140
+حتى ترسخ النظرية. النظرية بيقول ياخد F فيه وخد P
+
+226
+00:26:02,140 --> 00:26:05,760
+of X في capital F of X. from the principle ID
+
+227
+00:26:05,760 --> 00:26:10,280
+generated by P of X عبارة عن maximum ID if and
+
+228
+00:26:10,280 --> 00:26:14,690
+only if P of X is irreducible.بدأ امشي الانتجاه
+
+229
+00:26:14,690 --> 00:26:19,330
+هنا ماخد P of X موجودة في capital F of X بحيث ال
+
+230
+00:26:19,330 --> 00:26:26,350
+capital P of X is maximal ideal هذا الكلام صحيح لو
+
+231
+00:26:26,350 --> 00:26:32,350
+كانت ال P of X لا تساوي constant لأن لو كانت ال P
+
+232
+00:26:32,350 --> 00:26:37,750
+of X constant يبقى هذا بدي أعطيني أحد أمرين يا إما
+
+233
+00:26:37,750 --> 00:26:43,090
+ال zero ideals يا إما الفيل نفسه وعلى كل الأمرين
+
+234
+00:26:43,410 --> 00:26:49,250
+مشي proper وبالتالي ماهواش maximum إذا لازم تكون
+
+235
+00:26:49,250 --> 00:26:57,670
+polynomial وليس constant تمام نيجي لغاية فرضت ان
+
+236
+00:26:57,670 --> 00:27:06,950
+ال P of X is maximum كويس بدنا نحاول نثبت ان P of
+
+237
+00:27:06,950 --> 00:27:12,430
+X is irreduciblewant to show is irreducible بدي
+
+238
+00:27:12,430 --> 00:27:16,890
+ابرهن بالتناقض وان افرض الكلام مش صحيح مش صحيح
+
+239
+00:27:16,890 --> 00:27:21,950
+يعني ايش يعني reducible مدام reducible اذا بقدر
+
+240
+00:27:21,950 --> 00:27:26,610
+اكتبه على شكل حاصل ضرب two polynomials of lower
+
+241
+00:27:26,610 --> 00:27:31,190
+degree الدرجة تبعتهم اقل في نفس ال field اللي هو
+
+242
+00:27:31,190 --> 00:27:37,610
+capital F of X طيب الان ال ideal اللي عندكsubset
+
+243
+00:27:37,610 --> 00:27:41,430
+من ال ideal subset من ال field الأصلي أو من ال
+
+244
+00:27:41,430 --> 00:27:47,610
+ring الأصلي الآن هذا maximum مدار maximum يبقى يا
+
+245
+00:27:47,610 --> 00:27:52,610
+هدول اتنين بتساوي يا اتنين هدول بتساوي هاي التساوي
+
+246
+00:27:52,610 --> 00:27:57,030
+أو هذا ناخد التساوي الأول انطلع اتنين هدول بتساوي
+
+247
+00:27:57,030 --> 00:28:02,950
+وبتنين نفس الدرجة يبقى صلة ال degree تبعت ال P
+
+248
+00:28:02,950 --> 00:28:11,100
+تساويالـ Degree تبع الـ G لو كان الـ G of X بدري
+
+249
+00:28:11,100 --> 00:28:15,700
+يسوي الـ capital F of X يبقى ال degree ل G Zero
+
+250
+00:28:15,700 --> 00:28:21,020
+لانه بيصير constant وبالتالي بيولد لي جميع عناصر
+
+251
+00:28:21,020 --> 00:28:25,080
+الفيه إذا ان ال degree بتسوي Zero هذا مع ال degree
+
+252
+00:28:25,080 --> 00:28:29,540
+اللي فيه بتسوي مين ال degree اللي اتش يبقى صرا ان
+
+253
+00:28:29,540 --> 00:28:33,220
+ال degree اللي فيه تسوي ال degree اللي جيه وهذا مش
+
+254
+00:28:33,220 --> 00:28:38,300
+صحيحلأنه يناقض ال lower degree او ال degree لم
+
+255
+00:28:38,300 --> 00:28:42,760
+يبقى يسوى ال degree لكشف وهذا كمان يناقض ال lower
+
+256
+00:28:42,760 --> 00:28:46,440
+degree وصار ال contradiction يبقى الفرض اللي فرضته
+
+257
+00:28:46,440 --> 00:28:50,360
+غلط وعكسه هو الصح يبقى صار ال P of X is
+
+258
+00:28:50,360 --> 00:28:56,600
+irreducible على نمشي العكس نفترض ان P of X is
+
+259
+00:28:56,600 --> 00:29:02,490
+irreducible عالمياعليك لنثبت ان ال principle ideal
+
+260
+00:29:02,490 --> 00:29:07,450
+generated by P of X is maximum لشان maximum قدامنا
+
+261
+00:29:07,450 --> 00:29:12,190
+طريقيا فاخترنا طريقة التعريف ولم نختار طريقة نظرية
+
+262
+00:29:12,190 --> 00:29:16,570
+فقلنا افترض ان عندي ideal I موجود في capital F of
+
+263
+00:29:16,570 --> 00:29:21,470
+X بحيث ال P of X من principle ideal subset من I
+
+264
+00:29:21,470 --> 00:29:26,920
+subset من ال field capital F of Xال F of X عبارة
+
+265
+00:29:26,920 --> 00:29:30,740
+عن فين؟ هو عبارة عن principle, ideal, domain يعني
+
+266
+00:29:30,740 --> 00:29:36,620
+كل ideal فيه is a principle تمام؟ مدام كل ideal
+
+267
+00:29:36,620 --> 00:29:40,900
+فيه is a principle يبقى هذه بدي أروح أكتبها على
+
+268
+00:29:40,900 --> 00:29:46,740
+الشكل اللي عندنا هذا بهذا الشكل طيب بالدليل الأول
+
+269
+00:29:46,740 --> 00:29:50,920
+ال P of X موجود في ال ideal هذا هذا subset من هذا
+
+270
+00:29:50,920 --> 00:29:55,730
+إذا ال P of X موجود هنامدان موجود هنا إذا بدأ أكتب
+
+271
+00:29:55,730 --> 00:30:01,250
+على حاصل ضرب P of X في كولونومي الأخرى صار حاصل
+
+272
+00:30:01,250 --> 00:30:04,850
+ضرب two كولونومي زي ما انتوا شايفينه لكن احنا
+
+273
+00:30:04,850 --> 00:30:10,990
+فرضنا الأساسي ان P of X is irreducible يبقى هذا
+
+274
+00:30:10,990 --> 00:30:15,950
+الكلام لا يمكن ان يكون صحيحا إلا إذا كان أحدهم
+
+275
+00:30:15,950 --> 00:30:21,180
+بمقدار ثالثيبقى يا إما الـG of X مقدار ثابت يا إما
+
+276
+00:30:21,180 --> 00:30:26,860
+الـH of X مقدار ثابت بدي أخد كل من الحالتين و نشوف
+
+277
+00:30:26,860 --> 00:30:31,580
+شو نستفيد منه فبعدين بقول لو كانت الـG constant
+
+278
+00:30:31,580 --> 00:30:39,700
+يبقى بدها صير unit يعني بدها جبل ال field كله
+
+279
+00:30:39,700 --> 00:30:44,980
+الحالة التانية لو كانت الـH constant بظل ال
+
+280
+00:30:44,980 --> 00:30:49,390
+polynomial فيههي ال polynomial .. هي ال polynomial
+
+281
+00:30:49,390 --> 00:30:54,850
+تبع ال G يبقى هذا و هذا ايش معناه؟ معناه ال P is
+
+282
+00:30:54,850 --> 00:31:00,750
+maximum I هذه هي النظرية، الآن على هذه النظرية في
+
+283
+00:31:00,750 --> 00:31:06,730
+two equilateralism واحدة بسيطة ع السريع و واحدة
+
+284
+00:31:06,730 --> 00:31:08,030
+أطول شوية
+
+285
+00:31:21,150 --> 00:31:26,870
+نجي الـ Crawler الأولى الـ Crawler بتقول معاكي أن
+
+286
+00:31:26,870 --> 00:31:34,670
+الـ FBA field and
+
+287
+00:31:34,670 --> 00:31:37,790
+P
+
+288
+00:31:37,790 --> 00:31:41,350
+of X is irreducible
+
+289
+00:31:44,600 --> 00:31:55,900
+is irreducible polynomial over
+
+290
+00:31:55,900 --> 00:32:00,620
+F.Then
+
+291
+00:32:00,620 --> 00:32:03,720
+F
+
+292
+00:32:03,720 --> 00:32:10,500
+of X modularly principal idea generated by P of X
+
+293
+00:32:11,020 --> 00:32:25,900
+is a field مرة
+
+294
+00:32:25,900 --> 00:32:31,920
+تانية ال F field أخدنا polynomial ال polynomial
+
+295
+00:32:31,920 --> 00:32:37,920
+irreducible على F يبقى ال factor ring او ال factor
+
+296
+00:32:37,920 --> 00:32:44,960
+field صار ان هذابندفت انه عبارة عن P X بسيطة جدا
+
+297
+00:32:44,960 --> 00:32:50,800
+البرهان بدي اخد من الفرض و ابدأ يبقى بداشي اقوله
+
+298
+00:32:50,800 --> 00:33:01,840
+assume افترض ان P of X is irreducible polynomial
+
+299
+00:33:01,840 --> 00:33:06,040
+polynomial
+
+300
+00:33:06,040 --> 00:33:07,780
+over
+
+301
+00:33:09,190 --> 00:33:17,330
+كامة ال F طبقا للنظرية ال maximum يبقى ماجي بقوله
+
+302
+00:33:17,330 --> 00:33:27,850
+by the above theorem بالنظرية اعلى ال P of X او ال
+
+303
+00:33:27,850 --> 00:33:35,330
+principle id generated by P of X is maximum خذنا
+
+304
+00:33:35,330 --> 00:33:42,160
+نظرية سابقة لو عندى feelوعندي maximal ideal يبقى
+
+305
+00:33:42,160 --> 00:33:49,180
+الفاكتور field الفاكتور بصير ايش؟ بصير field يبقى
+
+306
+00:33:49,180 --> 00:33:57,440
+هنا برضه by ايه؟ previous term الذاكرين هذا من هذا
+
+307
+00:33:57,440 --> 00:34:04,400
+ولا لا؟ لما كان prime لما كان prime بصير integral
+
+308
+00:34:04,400 --> 00:34:10,430
+domain لما كان maximal بصير fieldيبقى my previous
+
+309
+00:34:10,430 --> 00:34:18,490
+theorem F of X modular principle ID generated by X
+
+310
+00:34:18,490 --> 00:34:24,930
+is A3 خلّي
+
+311
+00:34:24,930 --> 00:34:31,770
+المعلومة عندك لازملي أرجعلها بعد قليل كرولر اتنين
+
+312
+00:34:31,770 --> 00:34:36,190
+النتيجة رقم اتنين
+
+313
+00:34:40,300 --> 00:34:48,080
+النص تبعها كانت تالية بيقول
+
+314
+00:34:48,080 --> 00:34:57,620
+let ال FB إيه فيهم let كانت ال FB إيه فيهم and let
+
+315
+00:34:57,620 --> 00:35:01,360
+ال
+
+316
+00:35:01,360 --> 00:35:10,510
+P of X و ال A of X و ال P of Xموجودة في capital F
+
+317
+00:35:10,510 --> 00:35:16,870
+of X F ال
+
+318
+00:35:16,870 --> 00:35:31,410
+P of X is irreducible is irreducible over F over
+
+319
+00:35:31,410 --> 00:35:43,900
+FN ال P of Xdivides ال a of x في ال b of x then ال
+
+320
+00:35:43,900 --> 00:35:54,300
+p of x divides ال a of x or ال p of x divides ال b
+
+321
+00:35:54,300 --> 00:35:55,840
+of x
+
+322
+00:36:29,960 --> 00:36:37,200
+نقرأه نرجع للنص مرة تانية if فيه أخدت three
+
+323
+00:36:37,200 --> 00:36:43,770
+polynomials موجوداتفي capital F of X عندي معلومتين
+
+324
+00:36:43,770 --> 00:36:48,330
+المعلومة الأولى ان P of X is reducible على F
+
+325
+00:36:48,330 --> 00:36:54,830
+المعلومة الثانية P of X تقسم حاصل ضاربهما ان حدث
+
+326
+00:36:54,830 --> 00:36:59,350
+ذلك اذا القولنومية الأولى بتقسم القولنومية التانية
+
+327
+00:36:59,350 --> 00:37:05,430
+او القولنومية الأولى بتقسمها P of X بتقسمها بدون
+
+328
+00:37:05,430 --> 00:37:12,630
+باقي يعنيلو قسمنا P of .. لو قسمنا A of X على P of
+
+329
+00:37:12,630 --> 00:37:18,450
+X تنتهي القسمة بدون باب طيب نيجي للبرهان اللي
+
+330
+00:37:18,450 --> 00:37:23,990
+عندنا يبقى بدي افترض ان ال P of X is irreducible
+
+331
+00:37:23,990 --> 00:37:34,310
+على F يبقى assume that ان ال P of X is
+
+332
+00:37:37,090 --> 00:37:47,010
+irreducible over if. من النظرية إيش بنستنتج؟ إن ال
+
+333
+00:37:47,010 --> 00:37:55,790
+P of X is maximal ID. إذا بقولوا هنا by the above
+
+334
+00:37:55,790 --> 00:38:01,610
+theorem ال
+
+335
+00:38:01,610 --> 00:38:09,590
+ID اللي عندنا هذاis maximal طيب
+
+336
+00:38:09,590 --> 00:38:20,730
+الكرولري اللي فوق يادى field يبقى بي كرولري one
+
+337
+00:38:20,730 --> 00:38:30,770
+capital F of X modular principle ID generated by P
+
+338
+00:38:30,770 --> 00:38:39,520
+is a fieldطب ينفع يكون integral domain؟ اه ينفع
+
+339
+00:38:39,520 --> 00:38:45,400
+يكون انتجرال دومين ينفع يكون انتجرال دومين ينفع
+
+340
+00:38:45,400 --> 00:38:51,520
+يكون انتجرال
+
+341
+00:38:51,520 --> 00:38:59,440
+دومين ينفع يكون انتجرال دومين ينفع يكون انتجرال
+
+342
+00:38:59,440 --> 00:39:06,360
+دومين ينفع يكون انتجرال دومينالشماكة بال natural
+
+343
+00:39:06,360 --> 00:39:14,100
+homomorphism ال homomorphism الطبيعي وهي من ال
+
+344
+00:39:14,100 --> 00:39:21,280
+ring ل ring موديلويدية صحيح ولا لأ يبقى هنا define
+
+345
+00:39:21,280 --> 00:39:30,420
+the natural homomorphism
+
+346
+00:39:34,440 --> 00:39:43,360
+Homomorphism Phi من اللي هو capital F of X إلى
+
+347
+00:39:43,360 --> 00:39:51,140
+capital F of X modulo لprinciple ideal generated
+
+348
+00:39:51,140 --> 00:40:01,340
+by P of X. Phi شو شكل المعادلة؟ Phiلما تأثر على ال
+
+349
+00:40:01,340 --> 00:40:06,760
+element F of X اللي موجودة في capital F of X بدي
+
+350
+00:40:06,760 --> 00:40:12,680
+يعطينا ال F of X itself زائد ال principle ideal
+
+351
+00:40:12,680 --> 00:40:20,040
+generated by P of X حتى الآن كل الشغل اشتغلناه
+
+352
+00:40:20,040 --> 00:40:26,080
+بمعلومة واحدة المعلومة التانية لسه مامسكناش مظبوط؟
+
+353
+00:40:26,080 --> 00:40:35,500
+طيب ده بيقول sinceبما ان ال P of X بتقسم ال A of X
+
+354
+00:40:35,500 --> 00:40:45,140
+في ال P of X We have ان ال A of X في ال P of X
+
+355
+00:40:45,140 --> 00:40:54,340
+يساوي ال P of X في فانكشن تانية والتكن P of X for
+
+356
+00:40:54,340 --> 00:41:02,450
+someG of X اللي موجودة في capital F of X نظرها لإن
+
+357
+00:41:02,450 --> 00:41:07,910
+ال P of X بتقسم حاصل الضرب إذا الحاصل الضرب بيساوي
+
+358
+00:41:07,910 --> 00:41:12,750
+P of X في ال polynomial التالي السؤال هو هذه أين
+
+359
+00:41:12,750 --> 00:41:17,930
+موجودة يا عزيزي؟ ال principle ID حسب التعريف
+
+360
+00:41:17,930 --> 00:41:24,450
+فمعناته هذه موجودة في ال principle ID مظبوط؟ يبقى
+
+361
+00:41:24,450 --> 00:41:33,220
+هناالآن ال A of X في ال B of X يساوي ال P of X في
+
+362
+00:41:33,220 --> 00:41:38,700
+ال G of X موجودة في ال principle ideal generated
+
+363
+00:41:38,700 --> 00:41:44,500
+by P of X ليش؟ لأن هذا تعريف ال principle ideal
+
+364
+00:41:44,500 --> 00:41:50,300
+معناته صار ال A في B موجود في ال principle يبقى
+
+365
+00:41:50,300 --> 00:41:56,820
+هذا معناته أن ال A of Xفي ال P of X موجود في ال
+
+366
+00:41:56,820 --> 00:42:03,800
+principle ideal generated by P of X طيب لو جتنا ال
+
+367
+00:42:03,800 --> 00:42:12,180
+homomorphism Phi of AX BX حسب ال definition اللي
+
+368
+00:42:12,180 --> 00:42:19,180
+احنا جايبينه فوق بده يساوي A of X في P of Xزائد
+
+369
+00:42:19,180 --> 00:42:25,380
+لـPrincipal Ideal Generated by Geographics. أكيد ؟
+
+370
+00:42:25,380 --> 00:42:30,700
+طيب هذا وين موجود ؟ ان هذا كله قد مش بديه ساوي.
+
+371
+00:42:31,080 --> 00:42:37,080
+بديه ساوي اللي هو الـPrincipal Ideal Generated by
+
+372
+00:42:37,080 --> 00:42:43,640
+Geographics. مش هذا هو الـzero element في الفكرة
+
+373
+00:42:43,640 --> 00:42:50,010
+اللي عندنا هنا صح ولا لا ؟P of X هو ال .. ال .. ال
+
+374
+00:42:50,010 --> 00:42:55,270
+zero element في ال factor field اللي عندناها طيب
+
+375
+00:42:55,270 --> 00:43:04,630
+لو جيت أخدت ال Phi of A of X فال Phi of ال P of X
+
+376
+00:43:04,630 --> 00:43:11,830
+حسب التعريف اللي فوق بده يساوي ال A of X زائد ال
+
+377
+00:43:11,830 --> 00:43:21,190
+principle ideal generatedby P of X في P of X زائد
+
+378
+00:43:21,190 --> 00:43:30,630
+ال principle ideal generated by P of X طبقا
+
+379
+00:43:30,630 --> 00:43:36,010
+اللي حصل ضرب ال lift cassettes هذا الكلام شو بده
+
+380
+00:43:36,010 --> 00:43:43,090
+يساوي ال A of X في P of Xزائد لـ Principle Ideal
+
+381
+00:43:43,090 --> 00:43:53,550
+Generated by P of X طيب هذه كم هتعطينا Principle
+
+382
+00:43:53,550 --> 00:44:01,310
+Ideal يبقى هذه بتعطينا Principle Ideal فقط لإن ال
+
+383
+00:44:01,310 --> 00:44:07,050
+AX والBX موجودة في ال Principle طيب تعالوا نشوف
+
+384
+00:44:07,050 --> 00:44:13,480
+إيش رأيكوا في الموضوع خلي بالكوا هناحاصر ضرر two
+
+385
+00:44:13,480 --> 00:44:18,960
+elements بديوا يساوي ال zero element في main في ال
+
+386
+00:44:18,960 --> 00:44:25,860
+factor ring اللي عندنا مظبوط يبقى ال factor ايش
+
+387
+00:44:25,860 --> 00:44:31,000
+قولنا عليه integral domain مادام integral domain
+
+388
+00:44:31,000 --> 00:44:35,920
+يا هذا بال zero يا التاني بال zero يبقى بالي بقول
+
+389
+00:44:35,920 --> 00:44:43,940
+since بما ان ال F of Xmoderate principle ideal
+
+390
+00:44:43,940 --> 00:44:56,880
+generated by is an integral domain we have بده
+
+391
+00:44:56,880 --> 00:45:02,520
+يصير عندنا ال a of x زائد ال principle ideal
+
+392
+00:45:02,520 --> 00:45:08,740
+generated by p of x بده يساوي ال zero elementاللي
+
+393
+00:45:08,740 --> 00:45:15,440
+هو ال principle ideal generated by P of X او او
+
+394
+00:45:15,440 --> 00:45:21,720
+التانية اللي هو P of X زائد ال principle ideal
+
+395
+00:45:21,720 --> 00:45:26,380
+generated by P of X بده يساوي ال principle ideal
+
+396
+00:45:26,380 --> 00:45:32,580
+generated by P of X اما هذه او غيرها طب ايش تفسيرك
+
+397
+00:45:32,580 --> 00:45:42,800
+لهذه ال P of X موجودة وين؟هذا معناته ان ال A of X
+
+398
+00:45:42,800 --> 00:45:51,100
+موجود في ال principle ideal generated by P of X او
+
+399
+00:45:51,100 --> 00:45:57,660
+ال P of X موجود في ال principle ideal generated by
+
+400
+00:45:57,660 --> 00:46:07,040
+P of X طب هذا ايش معناه؟بتساوي A of X بتساوي P of
+
+401
+00:46:07,040 --> 00:46:16,240
+X في Polynomial أخرى يفجر هذا معناته ان ال A of X
+
+402
+00:46:16,240 --> 00:46:28,340
+بتساوي P of X في G1 of X and ال P of X بتساوي P of
+
+403
+00:46:28,340 --> 00:46:39,810
+X في G2 of Xالكلام هذا صحيح for الصام G1 of X وجيه
+
+404
+00:46:39,810 --> 00:46:47,730
+اتنين of X اللي موجودة في capital F of X ايش
+
+405
+00:46:47,730 --> 00:46:52,990
+تفسيرك ليه هذا الجدار؟ ان ال P of X بتقسم ال A of
+
+406
+00:46:52,990 --> 00:47:03,220
+X لإن هذا معناته ان ال P of X بتقسم ال A of Xor P
+
+407
+00:47:03,220 --> 00:47:12,120
+of X تقسم P of X هذا المقال مطلوب؟ مقال مطلوب لو
+
+408
+00:47:12,120 --> 00:47:18,000
+كانت ال F is irreducible وبتقسم حصل ضرر two
+
+409
+00:47:18,000 --> 00:47:23,080
+polynomials P of X لازم تقسم ال polynomial الأولى
+
+410
+00:47:23,080 --> 00:47:29,490
+أو تقسم ال polynomial الثانيةبدنا نعطي إشارة عربية
+
+411
+00:47:29,490 --> 00:47:36,710
+بسيطة give
+
+412
+00:47:36,710 --> 00:47:49,030
+you example one example one construct a
+
+413
+00:47:49,030 --> 00:47:55,690
+field of order 8
+
+414
+00:47:57,560 --> 00:48:04,740
+مش يعني انشؤونا field ال order إله يسوى تماما
+
+415
+00:48:04,740 --> 00:48:08,960
+باستخدام الكرولاريز باستخدام النظرية اللي بدكوا
+
+416
+00:48:08,960 --> 00:48:14,500
+يعملها مشكلة القصة بسيطة جدا بدي أختار polynomial
+
+417
+00:48:14,500 --> 00:48:20,680
+و أختار field بحيث تبقى ال polynomial irreducible
+
+418
+00:48:20,680 --> 00:48:25,720
+على هذا ال field يبقى هنا solution
+
+419
+00:48:28,690 --> 00:48:37,290
+ودا يقولوا let f of x ده ساول x تكعيب مثلا زائد x
+
+420
+00:48:37,290 --> 00:48:48,430
+زائد واحد هاي polynomial وهنا let كمان let الفيه
+
+421
+00:48:48,430 --> 00:48:55,870
+let z اتنين بيه الفيه
+
+422
+00:48:59,980 --> 00:49:04,840
+بدى اشوف هذه الـreduce و لا على z2 ولا لا يبقى بدي
+
+423
+00:49:04,840 --> 00:49:13,460
+اخد f of 0 جداش تساوي واحد طب و ال f of واحد z2
+
+424
+00:49:13,460 --> 00:49:19,220
+مصبوط ولا لا يبقى معناته ليش ماعنديش zeros لهذه ال
+
+425
+00:49:19,220 --> 00:49:26,740
+function في z2 يبقى هذا معناته ان ال f of x has no
+
+426
+00:49:26,740 --> 00:49:37,260
+zerosNZ2 هذا معناته ايه N Radio 7 هذا معناته ان F
+
+427
+00:49:37,260 --> 00:49:51,360
+of X is Radio 7 over Z2 تمام يبقى ال ID للمكون
+
+428
+00:49:51,360 --> 00:49:59,110
+بيكون maximum صح بالنص النظريةيبقى بقى دي بقوله by
+
+429
+00:49:59,110 --> 00:50:09,690
+the above theorem the principle ideal generated by
+
+430
+00:50:09,690 --> 00:50:16,550
+the highest maximal مدام
+
+431
+00:50:16,550 --> 00:50:24,750
+maximal هذا الآل بده يعطينا ان z2 modulo هذا ال
+
+432
+00:50:24,750 --> 00:50:39,100
+idealماله؟ as a field يبقى as a field طبعا ايه شكل
+
+433
+00:50:39,100 --> 00:50:49,280
+هذا ال field؟ z to modulo x تكرير زائد x زائد واحد
+
+434
+00:50:49,280 --> 00:51:00,140
+بالديسام انا ازعمأنه على شكل تالت A X تربيع زائد B
+
+435
+00:51:00,140 --> 00:51:05,600
+X زائد C زائد ال principle ideal generated by X
+
+436
+00:51:05,600 --> 00:51:11,880
+تكييف زائد X زائد 1 بحيث ال A والB والC موجودة في
+
+437
+00:51:11,880 --> 00:51:20,480
+زيادة 2.معقول هيك يكون صحيح؟ طب هم البرنامج يكون
+
+438
+00:51:20,480 --> 00:51:25,100
+من ضلالي الرابع أو الخمسة أو السلسة أو ميلادبنضم
+
+439
+00:51:25,100 --> 00:51:32,000
+لهذه وضل أقل من الدرجات التي همين الدرجات التانية
+
+440
+00:51:32,000 --> 00:51:39,500
+أنا أزعم أن هذا لا يوجد فيه إلا ثمانية عناصر و ال
+
+441
+00:51:39,500 --> 00:51:43,720
+exercise اللي كنا المرة القادمة بس يجيبلي شكل
+
+442
+00:51:43,720 --> 00:51:48,080
+العناصر والله يعطيك العفو يجيب أول ما نيجي المرة
+
+443
+00:51:48,080 --> 00:51:54,850
+جاى بدنا ناقش شكل العناصركيف؟ ليش ايه؟ مين اللي
+
+444
+00:51:54,850 --> 00:52:00,790
+بتسأل؟ انا بسأل لسه معرفة ما هي مطلوبة انك تجيب
+
+445
+00:52:00,790 --> 00:52:07,230
+عليها من هنا؟ انا بسأل لسه من هنا؟ انا بسأل لسه من
+
+446
+00:52:07,230 --> 00:52:07,830
+هنا؟ انا بسأل لسه من هنا؟ انا بسأل لسه من هنا؟ انا
+
+447
+00:52:07,830 --> 00:52:09,370
+انا بسأل لسه من هنا؟ انا بسأل لسه من هنا؟ انا بسأل
+
+448
+00:52:09,370 --> 00:52:14,130
+لسه من هنا؟ انا بسأل لسه من هنا؟ انا بسأل لسه من
+
+449
+00:52:14,130 --> 00:52:30,730
+هنا؟ انا بسأل لسالجبال يوجد فقط 8 علماء منهم المرة
+
+450
+00:52:30,730 --> 00:52:32,470
+القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..dd2752423ce13b4f76b2c028e55040c2f6cec70b
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY_postprocess.srt
@@ -0,0 +1,976 @@
+1
+00:00:20,890 --> 00:00:26,230
+بسم الله الرحمن الرحيم أحنا المرة الماضية كتبنا
+
+2
+00:00:26,230 --> 00:00:31,690
+آخر نظرية ونظرا لقصر الوقت لم نتمكن من مرهانها وها
+
+3
+00:00:31,690 --> 00:00:37,010
+نحن سنبرهنها في هذا اليوم إن شاء الله نظرية نص
+
+4
+00:00:37,010 --> 00:00:43,330
+ماتتبعك وبيقول A non-empty subset S of A ring R is
+
+5
+00:00:43,330 --> 00:00:48,330
+A sub ring إذا كان الـA ومينوس الـB موجود في الـS
+
+6
+00:00:48,630 --> 00:00:54,850
+لكل ال A والB الموجودة في S وكذلك A في B بدي يكون
+
+7
+00:00:54,850 --> 00:00:59,970
+موجود في subset S إذا كان ال A والB موجود وين في
+
+8
+00:00:59,970 --> 00:01:07,270
+ال S طيب يبقى إحنا عندنا ring A أخدنا subset منها
+
+9
+00:01:07,270 --> 00:01:15,220
+S عندي شرطين هدول موجودين تماموالشرط الأول أن الـ
+
+10
+00:01:15,220 --> 00:01:20,080
+non-empty يبقى ثلاثة شروط في الحقيقة تحت هذه
+
+11
+00:01:20,080 --> 00:01:25,680
+الشروط الثلاثة الاسم لنثبت أنها subring يبقى
+
+12
+00:01:25,680 --> 00:01:29,660
+بالنسبة للنقطة الأولى يبقى بالدرجة أقول له let
+
+13
+00:01:29,660 --> 00:01:40,540
+الاسم be non-empty subset of
+
+14
+00:01:40,540 --> 00:01:42,560
+a ring
+
+15
+00:01:45,920 --> 00:01:51,500
+بعدين الخطوات اللي عندي لكي أثبت أنها رقص خطوات
+
+16
+00:01:51,500 --> 00:01:57,300
+التلاتة اللي عندي بدي أبين أن هم عبارة عن الست
+
+17
+00:01:57,300 --> 00:02:04,020
+نقاط اللي قلنا هدول بيكونوا رمين الرجل الآن بدأجي
+
+18
+00:02:04,020 --> 00:02:08,600
+أخد اللي هو خاصية ال associativity بالنسبة لعملية
+
+19
+00:02:08,600 --> 00:02:14,720
+الجامعة و كذلك خاصية الإبداع يبقى بدأجي أقول له ال
+
+20
+00:02:14,720 --> 00:02:23,830
+leftالـ A والـ B موجود في S ثم الـ A والـ B موجودة
+
+21
+00:02:23,830 --> 00:02:30,650
+في R ولا لأ؟ لأن الـ S هي subset من من؟ من الـ A
+
+22
+00:02:30,650 --> 00:02:38,050
+مدام هيك يبقى الـ A زائد الـ B بدي شاوي الـ B زائد
+
+23
+00:02:38,050 --> 00:02:41,690
+الـ A هل
+
+24
+00:02:41,690 --> 00:02:48,050
+الفلام صحيح؟لكل ال a و ال b اللي موجودة في ال 6S
+
+25
+00:02:48,050 --> 00:02:55,510
+زيادة على درجة لو جيت قول خديل ال a و ال b و ال c
+
+26
+00:02:55,510 --> 00:03:03,190
+موجودة في ال S then ال a و ال b و ال c موجودة في R
+
+27
+00:03:03,190 --> 00:03:09,130
+يبقى هذا معناه ان ال distributive ماله صحيح هذا
+
+28
+00:03:09,130 --> 00:03:12,310
+يعني ان ال distributive
+
+29
+00:03:17,540 --> 00:03:23,140
+law whole وكذلك
+
+30
+00:03:23,140 --> 00:03:33,340
+خاصية الدمج برضه تعتد ضارب صحيحة distributive law
+
+31
+00:03:33,340 --> 00:03:42,360
+whole and ال associativity whole
+
+32
+00:03:43,880 --> 00:03:48,540
+يبقى قانون التوزيع وقانون الدمج اتنين صحيحات لان
+
+33
+00:03:48,540 --> 00:03:56,760
+جميع العناصر اللي عندنا موجودة في A طيب نجب نثبت
+
+34
+00:03:56,760 --> 00:04:04,580
+ان ال zero موجود في A يبقى باجي بقوله since بما ان
+
+35
+00:04:04,580 --> 00:04:12,580
+ال a ناقص ال b موجود في Sلكل ال a و ال b اللي
+
+36
+00:04:12,580 --> 00:04:19,240
+موجود في S لو أخدت
+
+37
+00:04:19,240 --> 00:04:29,020
+ال a في b we have ان ال a ناقص ال a موجود في S
+
+38
+00:04:29,020 --> 00:04:35,480
+طبعا لمن؟ ل ال condition الأول we have هذا من ال
+
+39
+00:04:35,480 --> 00:04:39,940
+first conditionطيب الـ A ناقص اللي هي بتعطينا مين؟
+
+40
+00:04:39,940 --> 00:04:45,540
+الـ Zero يبقى الـ Zero موجودة وين؟ في S يبقى
+
+41
+00:04:45,540 --> 00:04:49,420
+معناها الكلمة من الـ S is non-empty زي ما احنا
+
+42
+00:04:49,420 --> 00:04:56,480
+فرضين قبل وزيادة على ذلك الـ Zero موجود في S يبقى
+
+43
+00:04:56,480 --> 00:05:00,720
+هاي الـ Zero element موجود في S وبالتالي الـ S is
+
+44
+00:05:00,720 --> 00:05:06,490
+non-empty طيب بتجي لنفسي ال conditionمش هغيره،
+
+45
+00:05:06,490 --> 00:05:11,870
+الحين عندي الـ zero موجود في S والـ B موجود في S
+
+46
+00:05:11,870 --> 00:05:24,490
+يبقى إذا بقوله for any B اللي موجود في S from
+
+47
+00:05:24,490 --> 00:05:28,290
+واحد،
+
+48
+00:05:28,290 --> 00:05:33,850
+من واحد ليه النقطة الأولى؟ الـ zero ناقص الـ B
+
+49
+00:05:34,210 --> 00:05:40,770
+موجود في S أخد بي في S و Zero أصلا موجود في S تبقى
+
+50
+00:05:40,770 --> 00:05:45,950
+أخدت الفرق في ما بينهما هذا إيش بده يعطيني بده
+
+51
+00:05:45,950 --> 00:05:51,770
+يعطيني إنه ناقص ال بي موجود في S إذا المعكوس
+
+52
+00:05:51,770 --> 00:05:58,370
+الجمعي لأي عنصر موجود في S بده يكون ماله موجود في
+
+53
+00:05:58,370 --> 00:06:02,440
+S يبقى سالب ال elementموجود في اسم ال
+
+54
+00:06:02,440 --> 00:06:09,080
+conditionالرابع من من من ال conditions تبعات ال
+
+55
+00:06:09,080 --> 00:06:14,020
+ring ممتاز يبقى ال zero موجود في اسم السالب بي
+
+56
+00:06:14,020 --> 00:06:19,820
+موجود في اسم هنا الخاصية الإبدال صحيحة بالنسبة
+
+57
+00:06:19,820 --> 00:06:24,700
+للجامعة وكذلك بالنسبة لل associativity عملية الضرب
+
+58
+00:06:24,700 --> 00:06:28,990
+وخاصية ال distributive كذلكبالنسبة لعملية الجامعة
+
+59
+00:06:28,990 --> 00:06:34,050
+هو الضرب اتنين مع بعض محققة لأن جميع العناصر في ا
+
+60
+00:06:34,050 --> 00:06:40,850
+بايلاند يش بس نثبت احكاية ال binary operation تمام
+
+61
+00:06:40,850 --> 00:06:49,530
+الان from condition from
+
+62
+00:06:49,530 --> 00:06:59,010
+condition two من اتنين ان ال a في bموجودة في S لكل
+
+63
+00:06:59,010 --> 00:07:06,750
+ال A و ال B اللي موجودة في S مدام هذا موجود في S
+
+64
+00:07:06,750 --> 00:07:14,810
+حصل الضرب لكل ال A اللي موجودة في S we have ان ال
+
+65
+00:07:14,810 --> 00:07:20,290
+multiplication multiplication is
+
+66
+00:07:24,230 --> 00:07:29,470
+A binary operation
+
+67
+00:07:29,470 --> 00:07:33,030
+is
+
+68
+00:07:33,030 --> 00:07:42,190
+a binary operation on S بقى البس علينا حاجة واحدة
+
+69
+00:07:42,190 --> 00:07:47,270
+ما هي هذه الحاجة نثبت ان عملية الجماعة كذلك هي
+
+70
+00:07:47,270 --> 00:07:59,990
+binary operation على Sيبقى finally و أخيرا ال سالب
+
+71
+00:07:59,990 --> 00:08:10,730
+بيه موجود في اسم ايه تمام يبقى بداجي اقوله ان from
+
+72
+00:08:10,730 --> 00:08:13,970
+condition
+
+73
+00:08:13,970 --> 00:08:17,450
+to
+
+74
+00:08:17,450 --> 00:08:27,280
+بدى يكون عند مينالـ A سالب سالب B أخدت العنصر A
+
+75
+00:08:27,280 --> 00:08:32,060
+والسالب B واخدت ال condition .. ال condition .. لأ
+
+76
+00:08:32,060 --> 00:08:36,160
+condition one مش condition two condition one يا
+
+77
+00:08:36,160 --> 00:08:41,680
+بني يبقى ال condition one يبقى الأول ناقص الثاني
+
+78
+00:08:41,680 --> 00:08:47,440
+يبقى الأول ناقص الثاني لأخدته مين ناقص ال .. ياشبط
+
+79
+00:08:47,440 --> 00:08:55,680
+الشاويتساوي a زائد b موجود في this ايش يعني يعني
+
+80
+00:08:55,680 --> 00:09:00,480
+closed under addition يبقى هذي strategy binary
+
+81
+00:09:00,480 --> 00:09:10,120
+operation يبقى this means that
+
+82
+00:09:10,120 --> 00:09:15,320
+addition is
+
+83
+00:09:16,840 --> 00:09:21,360
+A binary operation
+
+84
+00:09:21,360 --> 00:09:26,940
+on
+
+85
+00:09:26,940 --> 00:09:35,220
+set S ممتاز
+
+86
+00:09:35,220 --> 00:09:41,640
+يبقى بناء عليه تحققت كل شروط ال sub ring ومن هنا
+
+87
+00:09:41,640 --> 00:09:51,500
+ال S is a sub ring يبقى داصرو هكذا ال S is a sub
+
+88
+00:09:51,500 --> 00:10:00,680
+ring of R اذا هذه النتيجة او اللي بتسميها sub ring
+
+89
+00:10:00,680 --> 00:10:06,940
+تس اختصرتلي اللي هو شروط ال ring الستة و ال two
+
+90
+00:10:06,940 --> 00:10:09,880
+binary operation اللي عليهم يعني بيعتبر تمانية
+
+91
+00:10:09,880 --> 00:10:15,850
+اختصرتهم للقداد لتلاتةالان لو عندى ring واخدت منها
+
+92
+00:10:15,850 --> 00:10:21,810
+subset اذا اثبت انها ال subset هذه non-empty اتنين
+
+93
+00:10:21,810 --> 00:10:25,910
+اخدت عنصرين منها لجد الفرق في بينهم موجود في نفس
+
+94
+00:10:25,910 --> 00:10:30,050
+ال set S اخدت عنصرين من S وضلت لجد انها تجي موجود
+
+95
+00:10:30,050 --> 00:10:34,310
+في S تبقى بناء عليه automatic بحكم على S انها sub
+
+96
+00:10:34,310 --> 00:10:39,990
+ring من مين من ال ring S ممتاز طيب الان بدنا نبدأ
+
+97
+00:10:39,990 --> 00:10:45,980
+ناخد أمثلة مختلفةعالميا على ال sub ring بس جابي
+
+98
+00:10:45,980 --> 00:10:51,560
+المثال لو جابي المبدأ أخد أمثلة لو كانت ال ring
+
+99
+00:10:51,560 --> 00:10:56,760
+فيها unity هل ضروري ال sub ring يكون فيها نفس ال
+
+100
+00:10:56,760 --> 00:11:02,780
+unity؟ لأ لأ ممكن مايكونش هناك بالمرة ويمكن يكون
+
+101
+00:11:02,780 --> 00:11:08,020
+فيها unity غير ال unity تبع ال ring كما سنرى بعد
+
+102
+00:11:08,020 --> 00:11:13,130
+قليل ان شاء الله من خلال بعض الأمثلةيبقى بنا نيجي
+
+103
+00:11:13,130 --> 00:11:22,790
+لأول مثال و بدي أبدأ بأبسط مثال example أول
+
+104
+00:11:22,790 --> 00:11:28,090
+مثال خليني
+
+105
+00:11:28,090 --> 00:11:32,970
+أجعل ال group قليلا ثم نتقل إلى ال ringفي حاجة
+
+106
+00:11:32,970 --> 00:11:36,450
+بيبقى نسميها بنات الـtrivial subgroup مين
+
+107
+00:11:36,450 --> 00:11:40,730
+الـtrivial subgroup؟ اللي فيها بس الـsubgroup اللي
+
+108
+00:11:40,730 --> 00:11:46,650
+فيها مين؟ الـidentity element بس تمام يبقى ال set
+
+109
+00:11:46,650 --> 00:11:50,930
+اللي فيش فيها ال zero هي عبارة عن subgroup كمان
+
+110
+00:11:50,930 --> 00:11:57,950
+سؤال من مبادئ الرياضيات أخدنا any set is a subset
+
+111
+00:11:57,950 --> 00:12:03,730
+of itself تمام كمان هناany ring is a sub ring of
+
+112
+00:12:03,730 --> 00:12:09,490
+itself لأن كل شروط متبقية عليها يبقى هنا ال zero
+
+113
+00:12:09,490 --> 00:12:23,450
+and ال R are sub rings of the ring R
+
+114
+00:12:32,200 --> 00:12:38,260
+etrivial ring etrivial
+
+115
+00:12:38,260 --> 00:12:43,620
+يعني من العربي تافه بس احنا مابقولش تافه يعني أبسط
+
+116
+00:12:43,620 --> 00:12:49,920
+حاجة لل etrivial البديهي يبقى هذه ها بنسميها
+
+117
+00:12:49,920 --> 00:12:55,360
+الحلقة الجزئية البديهية من ال ring الأصلية اللي هي
+
+118
+00:12:55,360 --> 00:13:09,060
+ا مثال اتنين مثال اتنينيقول Z6 Z6 اللي على صراحة
+
+119
+00:13:09,060 --> 00:13:14,020
+اها اللي هو Zero و واحد و اتنين و تلاتة و اربعة و
+
+120
+00:13:14,020 --> 00:13:30,140
+خمسة كلهم هذول is a ring of integers Modulo
+
+121
+00:13:30,140 --> 00:13:47,510
+6modulo 6 with unity 1 with unity 1 that's it لو
+
+122
+00:13:47,510 --> 00:13:56,530
+أخدنا ال 6 التانية يجي 0 2 4 نرجع
+
+123
+00:13:56,530 --> 00:14:03,460
+مرة تانية أنا روحت أخدت ال ring z 6على السرعة يعني
+
+124
+00:14:03,460 --> 00:14:07,640
+من Zero لغاية خمسة طبعا لو روحتوا لبعضا كنتوا ممكن
+
+125
+00:14:07,640 --> 00:14:13,580
+تكتبوش زي ما احنا كتبنا لو تكتب Zero Six واحد سيكس
+
+126
+00:14:13,580 --> 00:14:15,140
+اتنين سيكس اتنين سيكس اتنين سيكس اتنين سيكس اتنين
+
+127
+00:14:15,140 --> 00:14:15,360
+سيكس اتنين سيكس اتنين سيكس اتنين سيكس اتنين سيكس
+
+128
+00:14:15,360 --> 00:14:20,260
+اتنين سيكس اتنين سيكس اتنين سيكس اتنين سيكس اتنين
+
+129
+00:14:20,260 --> 00:14:24,280
+سيكس اتنين
+
+130
+00:14:24,280 --> 00:14:29,440
+سيكس اتنين سيكس اتنين سيكس اتنين سيكس اتنين سيكس
+
+131
+00:14:29,440 --> 00:14:34,130
+اتنين سيكطبعا هذه هي ال unity اللي هو ال identity
+
+132
+00:14:34,130 --> 00:14:39,330
+element أو ال unity بالنسبة ال روحنا أخدنا منها
+
+133
+00:14:39,330 --> 00:14:46,850
+مجموعة جزئية V0 2 4 هل هذه ال sub ring بمعنى non
+
+134
+00:14:46,850 --> 00:14:55,740
+-empty لو طرحت أي اتنين من بعض موجود داخل ال Z6لو
+
+135
+00:14:55,740 --> 00:15:00,320
+ضربت اي اتنين في بعض بده لاجيه موجود داخل ال Z6
+
+136
+00:15:00,320 --> 00:15:07,480
+مثال و ذلك لو قولتك اربعة زائد اتنين جدد؟ زير ايه
+
+137
+00:15:07,480 --> 00:15:14,520
+لو قولتك اربعة ناقص اتنين يسوي جدد؟ اتنين ايه اذا
+
+138
+00:15:14,520 --> 00:15:22,240
+قولتك اتنين ناقص اربعةسالب اتنين اربعة اتنين اربعة
+
+139
+00:15:22,240 --> 00:15:27,280
+اتنين سالب اربعة بسالب اتنين سالب اتنين هذه بسلب
+
+140
+00:15:27,280 --> 00:15:31,320
+ماعنديش سالب اتنين لكن سالب اتنين هو كافة مين ضيف
+
+141
+00:15:31,320 --> 00:15:35,000
+عليها ستة لما ضيف عليها ستة مش ماتلعب اربعة موجودة
+
+142
+00:15:35,000 --> 00:15:39,160
+ولا لا إذا سالب اتنين موجودة بمعنى اربعة مين
+
+143
+00:15:39,160 --> 00:15:47,140
+موجودة لما نقول يا بنات الهام الشهيرإنه اتنين سالف
+
+144
+00:15:47,140 --> 00:15:52,540
+أربعة تساوي سالف اتنين كله modular 6 لو أضفت لها
+
+145
+00:15:52,540 --> 00:15:57,720
+ستة يعني كأنه أضفت صفر بالنسبالها يبقى هذا بدي
+
+146
+00:15:57,720 --> 00:16:05,620
+يعطينا 104 موجودة داخل Z6 إذا السالف اتنين هيالي
+
+147
+00:16:05,620 --> 00:16:15,390
+سالف اتنين تساوي هذا كله موجود داخل Z6هل هذه فيها
+
+148
+00:16:15,390 --> 00:16:20,390
+unity؟ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+149
+00:16:20,390 --> 00:16:20,490
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+150
+00:16:20,490 --> 00:16:23,410
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+151
+00:16:23,410 --> 00:16:24,750
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+152
+00:16:24,750 --> 00:16:25,330
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+153
+00:16:25,330 --> 00:16:34,790
+لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+154
+00:16:34,790 --> 00:16:35,370
+ل
+
+155
+00:16:44,520 --> 00:16:46,800
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+156
+00:16:46,800 --> 00:16:48,480
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+157
+00:16:48,480 --> 00:16:53,200
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+158
+00:16:53,200 --> 00:16:54,820
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+159
+00:16:54,820 --> 00:16:56,580
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+160
+00:16:56,580 --> 00:16:59,040
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+161
+00:16:59,040 --> 00:17:01,660
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+162
+00:17:01,660 --> 00:17:04,620
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،هو
+
+163
+00:17:04,620 --> 00:17:07,900
+مالوش علاقة بال unity تبع ال ring الأصلية هذي يلها
+
+164
+00:17:07,900 --> 00:17:12,640
+unity وهذه unity تاني كما أشرتنا إلى ذلك قبل أن
+
+165
+00:17:12,640 --> 00:17:19,320
+نبدأ في الأمثلة يبقى the set هذه is a sub ring
+
+166
+00:17:19,320 --> 00:17:29,160
+with unity أربع أربع هو unity لل sub ring لكن ال
+
+167
+00:17:29,160 --> 00:17:33,080
+ring الأصلية ال unity لها بقداشالواحد صحيح وهي
+
+168
+00:17:33,080 --> 00:17:38,000
+الواحد صحيح وهذه ال unity اللي هي اربعة وهي الفرق
+
+169
+00:17:38,000 --> 00:17:42,380
+ما بين العنصرين او جدنا عندك الدرب اربعة في zero
+
+170
+00:17:42,380 --> 00:17:46,680
+في zero اربعة في اتنين باتنين اربعة في اربعة
+
+171
+00:17:46,680 --> 00:17:53,440
+باربعة يبقى هو كل هذا اللي مغلق تحت عملية الدرب
+
+172
+00:17:53,440 --> 00:18:01,640
+يعني تحققت الشروط تلاتة للصدرينالنقطة التالتة أو
+
+173
+00:18:01,640 --> 00:18:16,100
+المثال الثالث for each positive integer n for each
+
+174
+00:18:16,100 --> 00:18:22,020
+positive integer n الـ n زاد اللي عبارة عن zero
+
+175
+00:18:22,020 --> 00:18:32,580
+زاد او ناقص زادأو زاد او ناقص N وزاد او ناقص اتنين
+
+176
+00:18:32,580 --> 00:18:45,400
+N ونظل ماشيين إلى ما شاء الله is a subring of Z
+
+177
+00:18:45,400 --> 00:18:51,920
+because النقطة
+
+178
+00:18:51,920 --> 00:18:52,220
+الأولى
+
+179
+00:18:55,620 --> 00:19:03,480
+أنا أدعي الان ان ال N زد هو حاصل ضرب اي رقم صحيح
+
+180
+00:19:03,480 --> 00:19:07,760
+تمين في الزد سواء كان واحد او اتنين او تلاتة او
+
+181
+00:19:07,760 --> 00:19:12,080
+اربعة او مية وخمسين مين ماكان يكون لو ضربته في زد
+
+182
+00:19:12,080 --> 00:19:15,980
+بدأ يطلع نتيجة Zero زد او نقص N زد او نقص اتنين
+
+183
+00:19:15,980 --> 00:19:20,900
+هنا ليش ان الزد Zero واحد اتنين تلاتة يبقى N زد في
+
+184
+00:19:20,900 --> 00:19:28,380
+Zero في Zero انقولي خمسة مثلايبقى خمسة n خمسة في n
+
+185
+00:19:28,380 --> 00:19:34,000
+و خمسة in اللي بعدها ستة in سبعة in تمانية in
+
+186
+00:19:34,000 --> 00:19:38,100
+بالموجة و بالثانية بنفس الشيء يبقى جولنا zero زيدا
+
+187
+00:19:38,100 --> 00:19:42,620
+أو نقص in لإن ال in ضربت في واحد زيدا أو نقص اتنين
+
+188
+00:19:42,620 --> 00:19:46,920
+in لإن ان ضربت في اتنين لإن ان ضربت في تلاتة لإن
+
+189
+00:19:46,920 --> 00:19:50,800
+ان ضربت في تلاتة يعني حطي عناصر ال z و ضربيهم في n
+
+190
+00:19:50,800 --> 00:19:55,790
+بطلع اللي من ال six اللي قدامناهذه ال 6 انا ادعى
+
+191
+00:19:55,790 --> 00:20:00,010
+انها sub ring من مين؟ من ازرق، يعني اذا حققت
+
+192
+00:20:00,010 --> 00:20:04,770
+الشروط التلاتة، بصير خلاصنا، طب النقطة الأولى، هل
+
+193
+00:20:04,770 --> 00:20:12,110
+ال N زد non-empty ولا ممكن تكون empty؟ خلّع هي
+
+194
+00:20:12,110 --> 00:20:19,050
+قدامك، مليون عناصر، كتير فيها بجميع؟infinity of
+
+195
+00:20:19,050 --> 00:20:23,650
+elements يبقى فيها مالة نهاية من العناصر مش عجب
+
+196
+00:20:23,650 --> 00:20:28,710
+عنصر واحد يبقى non-empty الشرط الأول متحفظ طبيعي
+
+197
+00:20:28,710 --> 00:20:35,410
+الشرط التاني بدي أخد عنصرين موجودات في الـ A and Z
+
+198
+00:20:35,410 --> 00:20:42,450
+يبقى بدي أقول له X وY موجودات في الـ A and Z هذا
+
+199
+00:20:42,450 --> 00:20:45,810
+بدي أعطيك أن X يساوي
+
+200
+00:20:48,340 --> 00:20:57,700
+جدش M في N صح؟ مش هاد ينزل؟ طبعا وقولنا اتنين
+
+201
+00:20:57,700 --> 00:21:03,560
+تلاتة اربعة في انفي كذا مظبوط يبقى الشكل هيكون M
+
+202
+00:21:03,560 --> 00:21:08,340
+في N جدش اللي مش عارف يمكن اتنين ويمكن تلاتة ويمكن
+
+203
+00:21:08,340 --> 00:21:14,240
+عشر ويمكن خمسين ويمكن ستة وسبعين جد ما يكون عشوانو
+
+204
+00:21:14,240 --> 00:21:22,300
+ال Y بدها تساوي K في N تمام؟ يبقى ال X Y اللي
+
+205
+00:21:22,300 --> 00:21:27,080
+موجودة في N Z هيكون شكله شكل العناصر اللي موجودة
+
+206
+00:21:27,080 --> 00:21:32,760
+في N Z يبقى M في N و K في N و ال M و ال K موجودة
+
+207
+00:21:32,760 --> 00:21:41,680
+في Z و ال M و ال K عبارة عن integers أعداد صحية
+
+208
+00:21:42,160 --> 00:21:48,160
+يبقى الان بدي اخد X ناقص Y إذا جدرت أثبت ان ال X
+
+209
+00:21:48,160 --> 00:21:53,320
+ناقص Y موجود في NZ يكون خلصنا ال condition الأول
+
+210
+00:21:53,320 --> 00:21:59,420
+تبع من؟ تبع النظرية بقولوا تماما X ناقص Y بدي
+
+211
+00:21:59,420 --> 00:22:10,240
+يساوي ال M N ناقص E في M ويساوي اللي هو من؟ Mناقص
+
+212
+00:22:10,240 --> 00:22:18,700
+كاف من في ال M وين هذا ولا فارق بين two integers
+
+213
+00:22:18,700 --> 00:22:24,720
+يبقى integer ولا لا يبقى integer مضروب في N يبقى
+
+214
+00:22:24,720 --> 00:22:33,320
+بالفعل هذا موجود في ال NZ لأن ال M ناقص ال K هذا
+
+215
+00:22:33,320 --> 00:22:38,720
+موجود في Z إتصاليبقى تحقق ال condition الأول
+
+216
+00:22:38,720 --> 00:22:42,500
+والثاني ولا لا؟ يبقى انا اروح لل condition التالت
+
+217
+00:22:42,500 --> 00:22:49,360
+ال condition التالت بدأ اخد x في y بدي اثبت انه
+
+218
+00:22:49,360 --> 00:22:57,680
+موجود وين في نز يبقى ال x في y بده يساوي ال mn في
+
+219
+00:22:57,680 --> 00:23:05,580
+مين؟ في ال km الشكل اللي عناه تمام؟ يبقى هذا
+
+220
+00:23:05,580 --> 00:23:16,700
+الكلامبتدرساه بدرساه ال M N K كله في N هذا كله
+
+221
+00:23:16,700 --> 00:23:20,720
+Integer لإن هو حاصل ضرب three integers is an
+
+222
+00:23:20,720 --> 00:23:26,700
+integer يبقى هذا لحالة موجود في Z إذن هذا كله
+
+223
+00:23:26,700 --> 00:23:34,360
+موجود في ال NZ يبقى تحقق الشرطينأو ثلاثة شروط تبعت
+
+224
+00:23:34,360 --> 00:23:39,240
+النظرية يبقى بناء على علينا ان Z is a subgroup
+
+225
+00:23:39,240 --> 00:23:58,460
+from Z يبقى هنا ان Z is a subgroup from Z كويس
+
+226
+00:24:01,280 --> 00:24:08,600
+يبقى هذا هو المثال اللي هو رقم 3 فروح للمثال رقم 4
+
+227
+00:24:41,810 --> 00:24:50,690
+مثال رقم 4 لو جت خدت Z of I اللي هي مين؟ كل
+
+228
+00:24:50,690 --> 00:24:58,850
+العلاسة على صلة A زي الـB I لحيث أن الـA والـB
+
+229
+00:24:58,850 --> 00:25:09,770
+موجودة في مين؟ موجودة في الـZ as a subring as a
+
+230
+00:25:09,770 --> 00:25:10,730
+subring
+
+231
+00:25:17,650 --> 00:25:24,910
+بالـ X عندي بقدرش؟ بـ Zero في مين؟ في الـ Y يبقى
+
+232
+00:25:24,910 --> 00:25:29,370
+Zero في الـ Y بدي يعطيني مين؟ الـ Zero هذا بدي
+
+233
+00:25:29,370 --> 00:25:37,890
+يعطيك إن X و Y موجودة في Sهنا لكل ال X و ال Y اللي
+
+234
+00:25:37,890 --> 00:25:44,410
+موجودة في S وهنا كذلك لكل ال X و ال Y اللي موجودة
+
+235
+00:25:44,410 --> 00:25:55,890
+في S وبالتاني ال S is a subring of A وصلنا
+
+236
+00:25:55,890 --> 00:26:03,170
+إلى exercises أطلاش يبقى exercises على شكتر أطلاش
+
+237
+00:26:03,640 --> 00:26:07,960
+فاكرونا في المسائل المرة القادمة على المرة القادمة
+
+238
+00:26:07,960 --> 00:26:13,600
+حل المسائل هنا و بدنا نشغلكم يكونوا مشتغلين آيو
+
+239
+00:26:13,600 --> 00:26:27,460
+سؤال 8 و 13 و 19 و 23 آه ثم أحط كمان 22 معاه 22 و
+
+240
+00:26:27,460 --> 00:26:38,410
+23و .. و تمانية و عشرين و تلاتين و إتنين و تلاتين
+
+241
+00:26:38,410 --> 00:26:46,410
+و تلاتة و تلاتين و تسعة و تلاتين و واحد و أربعين و
+
+242
+00:26:46,410 --> 00:26:53,850
+ستة و أربعين و خمسين يا أبو عياسل من أول التمرين و
+
+243
+00:26:53,850 --> 00:27:00,040
+من نص التمرين و من آخر التمرينوفترة المرة القادمة
+
+244
+00:27:00,040 --> 00:27:03,620
+نشوف إيش بدفس حلو منها
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..71e9b00eb8937570aa39b9bb667d7505fecffad9
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/9Xc_2-3VhnY_raw.srt
@@ -0,0 +1,980 @@
+1
+00:00:20,890 --> 00:00:26,230
+بسم الله الرحمن الرحيم أحنا المرة الماضية كتبنا
+
+2
+00:00:26,230 --> 00:00:31,690
+آخر نظرية ونظرا لقصر الوقت لم نتمكن من مرهانها وها
+
+3
+00:00:31,690 --> 00:00:37,010
+نحن سنبرهنها في هذا اليوم إن شاء الله نظرية نص
+
+4
+00:00:37,010 --> 00:00:43,330
+ماتتبعك وبيقول A non-empty subset S of A ring R is
+
+5
+00:00:43,330 --> 00:00:48,330
+A sub ring إذا كان الـA ومينوس الـB موجود في الـS
+
+6
+00:00:48,630 --> 00:00:54,850
+لكل ال A والB الموجودة في S وكذلك A في B بدي يكون
+
+7
+00:00:54,850 --> 00:00:59,970
+موجود في subset S إذا كان ال A والB موجود وين في
+
+8
+00:00:59,970 --> 00:01:07,270
+ال S طيب يبقى إحنا عندنا ring A أخدنا subset منها
+
+9
+00:01:07,270 --> 00:01:15,220
+S عندي شرطين هدول موجودين تماموالشرط الأول أن الـ
+
+10
+00:01:15,220 --> 00:01:20,080
+non-empty يبقى ثلاثة شروط في الحقيقة تحت هذه
+
+11
+00:01:20,080 --> 00:01:25,680
+الشروط الثلاثة الاسم لنثبت أنها subring يبقى
+
+12
+00:01:25,680 --> 00:01:29,660
+بالنسبة للنقطة الأولى يبقى بالدرجة أقول له let
+
+13
+00:01:29,660 --> 00:01:40,540
+الاسم be non-empty subset of
+
+14
+00:01:40,540 --> 00:01:42,560
+a ring
+
+15
+00:01:45,920 --> 00:01:51,500
+بعدين الخطوات اللي عندي لكي أثبت أنها رقص خطوات
+
+16
+00:01:51,500 --> 00:01:57,300
+التلاتة اللي عندي بدي أبين أن هم عبارة عن الست
+
+17
+00:01:57,300 --> 00:02:04,020
+نقاط اللي قلنا هدول بيكونوا رمين الرجل الآن بدأجي
+
+18
+00:02:04,020 --> 00:02:08,600
+أخد اللي هو خاصية ال associativity بالنسبة لعملية
+
+19
+00:02:08,600 --> 00:02:14,720
+الجامعة و كذلك خاصية الإبداع يبقى بدأجي أقول له ال
+
+20
+00:02:14,720 --> 00:02:23,830
+leftالـ A والـ B موجود في S ثم الـ A والـ B موجودة
+
+21
+00:02:23,830 --> 00:02:30,650
+في R ولا لأ؟ لأن الـ S هي subset من من؟ من الـ A
+
+22
+00:02:30,650 --> 00:02:38,050
+مدام هيك يبقى الـ A زائد الـ B بدي شاوي الـ B زائد
+
+23
+00:02:38,050 --> 00:02:41,690
+الـ A هل
+
+24
+00:02:41,690 --> 00:02:48,050
+الفلام صحيح؟لكل ال a و ال b اللي موجودة في ال 6S
+
+25
+00:02:48,050 --> 00:02:55,510
+زيادة على درجة لو جيت قول خديل ال a و ال b و ال c
+
+26
+00:02:55,510 --> 00:03:03,190
+موجودة في ال S then ال a و ال b و ال c موجودة في R
+
+27
+00:03:03,190 --> 00:03:09,130
+يبقى هذا معناه ان ال distributive ماله صحيح هذا
+
+28
+00:03:09,130 --> 00:03:12,310
+يعني ان ال distributive
+
+29
+00:03:17,540 --> 00:03:23,140
+law whole وكذلك
+
+30
+00:03:23,140 --> 00:03:33,340
+خاصية الدمج برضه تعتد ضارب صحيحة distributive law
+
+31
+00:03:33,340 --> 00:03:42,360
+whole and ال associativity whole
+
+32
+00:03:43,880 --> 00:03:48,540
+يبقى قانون التوزيع وقانون الدمج اتنين صحيحات لان
+
+33
+00:03:48,540 --> 00:03:56,760
+جميع العناصر اللي عندنا موجودة في A طيب نجب نثبت
+
+34
+00:03:56,760 --> 00:04:04,580
+ان ال zero موجود في A يبقى باجي بقوله since بما ان
+
+35
+00:04:04,580 --> 00:04:12,580
+ال a ناقص ال b موجود في Sلكل ال a و ال b اللي
+
+36
+00:04:12,580 --> 00:04:19,240
+موجود في S لو أخدت
+
+37
+00:04:19,240 --> 00:04:29,020
+ال a في b we have ان ال a ناقص ال a موجود في S
+
+38
+00:04:29,020 --> 00:04:35,480
+طبعا لمن؟ ل ال condition الأول we have هذا من ال
+
+39
+00:04:35,480 --> 00:04:39,940
+first conditionطيب الـ A ناقص اللي هي بتعطينا مين؟
+
+40
+00:04:39,940 --> 00:04:45,540
+الـ Zero يبقى الـ Zero موجودة وين؟ في S يبقى
+
+41
+00:04:45,540 --> 00:04:49,420
+معناها الكلمة من الـ S is non-empty زي ما احنا
+
+42
+00:04:49,420 --> 00:04:56,480
+فرضين قبل وزيادة على ذلك الـ Zero موجود في S يبقى
+
+43
+00:04:56,480 --> 00:05:00,720
+هاي الـ Zero element موجود في S وبالتالي الـ S is
+
+44
+00:05:00,720 --> 00:05:06,490
+non-empty طيب بتجي لنفسي ال conditionمش هغيره،
+
+45
+00:05:06,490 --> 00:05:11,870
+الحين عندي الـ zero موجود في S والـ B موجود في S
+
+46
+00:05:11,870 --> 00:05:24,490
+يبقى إذا بقوله for any B اللي موجود في S from
+
+47
+00:05:24,490 --> 00:05:28,290
+واحد،
+
+48
+00:05:28,290 --> 00:05:33,850
+من واحد ليه النقطة الأولى؟ الـ zero ناقص الـ B
+
+49
+00:05:34,210 --> 00:05:40,770
+موجود في S أخد بي في S و Zero أصلا موجود في S تبقى
+
+50
+00:05:40,770 --> 00:05:45,950
+أخدت الفرق في ما بينهما هذا إيش بده يعطيني بده
+
+51
+00:05:45,950 --> 00:05:51,770
+يعطيني إنه ناقص ال بي موجود في S إذا المعكوس
+
+52
+00:05:51,770 --> 00:05:58,370
+الجمعي لأي عنصر موجود في S بده يكون ماله موجود في
+
+53
+00:05:58,370 --> 00:06:02,440
+S يبقى سالب ال elementموجود في اسم ال
+
+54
+00:06:02,440 --> 00:06:09,080
+conditionالرابع من من من ال conditions تبعات ال
+
+55
+00:06:09,080 --> 00:06:14,020
+ring ممتاز يبقى ال zero موجود في اسم السالب بي
+
+56
+00:06:14,020 --> 00:06:19,820
+موجود في اسم هنا الخاصية الإبدال صحيحة بالنسبة
+
+57
+00:06:19,820 --> 00:06:24,700
+للجامعة وكذلك بالنسبة لل associativity عملية الضرب
+
+58
+00:06:24,700 --> 00:06:28,990
+وخاصية ال distributive كذلكبالنسبة لعملية الجامعة
+
+59
+00:06:28,990 --> 00:06:34,050
+هو الضرب اتنين مع بعض محققة لأن جميع العناصر في ا
+
+60
+00:06:34,050 --> 00:06:40,850
+بايلاند يش بس نثبت احكاية ال binary operation تمام
+
+61
+00:06:40,850 --> 00:06:49,530
+الان from condition from
+
+62
+00:06:49,530 --> 00:06:59,010
+condition two من اتنين ان ال a في bموجودة في S لكل
+
+63
+00:06:59,010 --> 00:07:06,750
+ال A و ال B اللي موجودة في S مدام هذا موجود في S
+
+64
+00:07:06,750 --> 00:07:14,810
+حصل الضرب لكل ال A اللي موجودة في S we have ان ال
+
+65
+00:07:14,810 --> 00:07:20,290
+multiplication multiplication is
+
+66
+00:07:24,230 --> 00:07:29,470
+A binary operation
+
+67
+00:07:29,470 --> 00:07:33,030
+is
+
+68
+00:07:33,030 --> 00:07:42,190
+a binary operation on S بقى البس علينا حاجة واحدة
+
+69
+00:07:42,190 --> 00:07:47,270
+ما هي هذه الحاجة نثبت ان عملية الجماعة كذلك هي
+
+70
+00:07:47,270 --> 00:07:59,990
+binary operation على Sيبقى finally و أخيرا ال سالب
+
+71
+00:07:59,990 --> 00:08:10,730
+بيه موجود في اسم ايه تمام يبقى بداجي اقوله ان from
+
+72
+00:08:10,730 --> 00:08:13,970
+condition
+
+73
+00:08:13,970 --> 00:08:17,450
+to
+
+74
+00:08:17,450 --> 00:08:27,280
+بدى يكون عند مينالـ A سالب سالب B أخدت العنصر A
+
+75
+00:08:27,280 --> 00:08:32,060
+والسالب B واخدت ال condition .. ال condition .. لأ
+
+76
+00:08:32,060 --> 00:08:36,160
+condition one مش condition two condition one يا
+
+77
+00:08:36,160 --> 00:08:41,680
+بني يبقى ال condition one يبقى الأول ناقص الثاني
+
+78
+00:08:41,680 --> 00:08:47,440
+يبقى الأول ناقص الثاني لأخدته مين ناقص ال .. ياشبط
+
+79
+00:08:47,440 --> 00:08:55,680
+الشاويتساوي a زائد b موجود في this ايش يعني يعني
+
+80
+00:08:55,680 --> 00:09:00,480
+closed under addition يبقى هذي strategy binary
+
+81
+00:09:00,480 --> 00:09:10,120
+operation يبقى this means that
+
+82
+00:09:10,120 --> 00:09:15,320
+addition is
+
+83
+00:09:16,840 --> 00:09:21,360
+A binary operation
+
+84
+00:09:21,360 --> 00:09:26,940
+on
+
+85
+00:09:26,940 --> 00:09:35,220
+set S ممتاز
+
+86
+00:09:35,220 --> 00:09:41,640
+يبقى بناء عليه تحققت كل شروط ال sub ring ومن هنا
+
+87
+00:09:41,640 --> 00:09:51,500
+ال S is a sub ring يبقى داصرو هكذا ال S is a sub
+
+88
+00:09:51,500 --> 00:10:00,680
+ring of R اذا هذه النتيجة او اللي بتسميها sub ring
+
+89
+00:10:00,680 --> 00:10:06,940
+تس اختصرتلي اللي هو شروط ال ring الستة و ال two
+
+90
+00:10:06,940 --> 00:10:09,880
+binary operation اللي عليهم يعني بيعتبر تمانية
+
+91
+00:10:09,880 --> 00:10:15,850
+اختصرتهم للقداد لتلاتةالان لو عندى ring واخدت منها
+
+92
+00:10:15,850 --> 00:10:21,810
+subset اذا اثبت انها ال subset هذه non-empty اتنين
+
+93
+00:10:21,810 --> 00:10:25,910
+اخدت عنصرين منها لجد الفرق في بينهم موجود في نفس
+
+94
+00:10:25,910 --> 00:10:30,050
+ال set S اخدت عنصرين من S وضلت لجد انها تجي موجود
+
+95
+00:10:30,050 --> 00:10:34,310
+في S تبقى بناء عليه automatic بحكم على S انها sub
+
+96
+00:10:34,310 --> 00:10:39,990
+ring من مين من ال ring S ممتاز طيب الان بدنا نبدأ
+
+97
+00:10:39,990 --> 00:10:45,980
+ناخد أمثلة مختلفةعالميا على ال sub ring بس جابي
+
+98
+00:10:45,980 --> 00:10:51,560
+المثال لو جابي المبدأ أخد أمثلة لو كانت ال ring
+
+99
+00:10:51,560 --> 00:10:56,760
+فيها unity هل ضروري ال sub ring يكون فيها نفس ال
+
+100
+00:10:56,760 --> 00:11:02,780
+unity؟ لأ لأ ممكن مايكونش هناك بالمرة ويمكن يكون
+
+101
+00:11:02,780 --> 00:11:08,020
+فيها unity غير ال unity تبع ال ring كما سنرى بعد
+
+102
+00:11:08,020 --> 00:11:13,130
+قليل ان شاء الله من خلال بعض الأمثلةيبقى بنا نيجي
+
+103
+00:11:13,130 --> 00:11:22,790
+لأول مثال و بدي أبدأ بأبسط مثال example أول
+
+104
+00:11:22,790 --> 00:11:28,090
+مثال خليني
+
+105
+00:11:28,090 --> 00:11:32,970
+أجعل ال group قليلا ثم نتقل إلى ال ringفي حاجة
+
+106
+00:11:32,970 --> 00:11:36,450
+بيبقى نسميها بنات الـtrivial subgroup مين
+
+107
+00:11:36,450 --> 00:11:40,730
+الـtrivial subgroup؟ اللي فيها بس الـsubgroup اللي
+
+108
+00:11:40,730 --> 00:11:46,650
+فيها مين؟ الـidentity element بس تمام يبقى ال set
+
+109
+00:11:46,650 --> 00:11:50,930
+اللي فيش فيها ال zero هي عبارة عن subgroup كمان
+
+110
+00:11:50,930 --> 00:11:57,950
+سؤال من مبادئ الرياضيات أخدنا any set is a subset
+
+111
+00:11:57,950 --> 00:12:03,730
+of itself تمام كمان هناany ring is a sub ring of
+
+112
+00:12:03,730 --> 00:12:09,490
+itself لأن كل شروط متبقية عليها يبقى هنا ال zero
+
+113
+00:12:09,490 --> 00:12:23,450
+and ال R are sub rings of the ring R
+
+114
+00:12:32,200 --> 00:12:38,260
+etrivial ring etrivial
+
+115
+00:12:38,260 --> 00:12:43,620
+يعني من العربي تافه بس احنا مابقولش تافه يعني أبسط
+
+116
+00:12:43,620 --> 00:12:49,920
+حاجة لل etrivial البديهي يبقى هذه ها بنسميها
+
+117
+00:12:49,920 --> 00:12:55,360
+الحلقة الجزئية البديهية من ال ring الأصلية اللي هي
+
+118
+00:12:55,360 --> 00:13:09,060
+ا مثال اتنين مثال اتنينيقول Z6 Z6 اللي على صراحة
+
+119
+00:13:09,060 --> 00:13:14,020
+اها اللي هو Zero و واحد و اتنين و تلاتة و اربعة و
+
+120
+00:13:14,020 --> 00:13:30,140
+خمسة كلهم هذول is a ring of integers Modulo
+
+121
+00:13:30,140 --> 00:13:47,510
+6modulo 6 with unity 1 with unity 1 that's it لو
+
+122
+00:13:47,510 --> 00:13:56,530
+أخدنا ال 6 التانية يجي 0 2 4 نرجع
+
+123
+00:13:56,530 --> 00:14:03,460
+مرة تانية أنا روحت أخدت ال ring z 6على السرعة يعني
+
+124
+00:14:03,460 --> 00:14:07,640
+من Zero لغاية خمسة طبعا لو روحتوا لبعضا كنتوا ممكن
+
+125
+00:14:07,640 --> 00:14:13,580
+تكتبوش زي ما احنا كتبنا لو تكتب Zero Six واحد سيكس
+
+126
+00:14:13,580 --> 00:14:15,140
+اتنين سيكس اتنين سيكس اتنين سيكس اتنين سيكس اتنين
+
+127
+00:14:15,140 --> 00:14:15,360
+سيكس اتنين سيكس اتنين سيكس اتنين سيكس اتنين سيكس
+
+128
+00:14:15,360 --> 00:14:20,260
+اتنين سيكس اتنين سيكس اتنين سيكس اتنين سيكس اتنين
+
+129
+00:14:20,260 --> 00:14:24,280
+سيكس اتنين
+
+130
+00:14:24,280 --> 00:14:29,440
+سيكس اتنين سيكس اتنين سيكس اتنين سيكس اتنين سيكس
+
+131
+00:14:29,440 --> 00:14:34,130
+اتنين سيكطبعا هذه هي ال unity اللي هو ال identity
+
+132
+00:14:34,130 --> 00:14:39,330
+element أو ال unity بالنسبة ال روحنا أخدنا منها
+
+133
+00:14:39,330 --> 00:14:46,850
+مجموعة جزئية V0 2 4 هل هذه ال sub ring بمعنى non
+
+134
+00:14:46,850 --> 00:14:55,740
+-empty لو طرحت أي اتنين من بعض موجود داخل ال Z6لو
+
+135
+00:14:55,740 --> 00:15:00,320
+ضربت اي اتنين في بعض بده لاجيه موجود داخل ال Z6
+
+136
+00:15:00,320 --> 00:15:07,480
+مثال و ذلك لو قولتك اربعة زائد اتنين جدد؟ زير ايه
+
+137
+00:15:07,480 --> 00:15:14,520
+لو قولتك اربعة ناقص اتنين يسوي جدد؟ اتنين ايه اذا
+
+138
+00:15:14,520 --> 00:15:22,240
+قولتك اتنين ناقص اربعةسالب اتنين اربعة اتنين اربعة
+
+139
+00:15:22,240 --> 00:15:27,280
+اتنين سالب اربعة بسالب اتنين سالب اتنين هذه بسلب
+
+140
+00:15:27,280 --> 00:15:31,320
+ماعنديش سالب اتنين لكن سالب اتنين هو كافة مين ضيف
+
+141
+00:15:31,320 --> 00:15:35,000
+عليها ستة لما ضيف عليها ستة مش ماتلعب اربعة موجودة
+
+142
+00:15:35,000 --> 00:15:39,160
+ولا لا إذا سالب اتنين موجودة بمعنى اربعة مين
+
+143
+00:15:39,160 --> 00:15:47,140
+موجودة لما نقول يا بنات الهام الشهيرإنه اتنين سالف
+
+144
+00:15:47,140 --> 00:15:52,540
+أربعة تساوي سالف اتنين كله modular 6 لو أضفت لها
+
+145
+00:15:52,540 --> 00:15:57,720
+ستة يعني كأنه أضفت صفر بالنسبالها يبقى هذا بدي
+
+146
+00:15:57,720 --> 00:16:05,620
+يعطينا 104 موجودة داخل Z6 إذا السالف اتنين هيالي
+
+147
+00:16:05,620 --> 00:16:15,390
+سالف اتنين تساوي هذا كله موجود داخل Z6هل هذه فيها
+
+148
+00:16:15,390 --> 00:16:20,390
+unity؟ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+149
+00:16:20,390 --> 00:16:20,490
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+150
+00:16:20,490 --> 00:16:23,410
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+151
+00:16:23,410 --> 00:16:24,750
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+152
+00:16:24,750 --> 00:16:25,330
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+153
+00:16:25,330 --> 00:16:25,330
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+154
+00:16:25,330 --> 00:16:34,790
+لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+155
+00:16:34,790 --> 00:16:35,370
+ل
+
+156
+00:16:44,520 --> 00:16:46,800
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+157
+00:16:46,800 --> 00:16:48,480
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+158
+00:16:48,480 --> 00:16:53,200
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+159
+00:16:53,200 --> 00:16:54,820
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+160
+00:16:54,820 --> 00:16:56,580
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+161
+00:16:56,580 --> 00:16:59,040
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+162
+00:16:59,040 --> 00:17:01,660
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،
+
+163
+00:17:01,660 --> 00:17:04,620
+نفس العنصر، نفس العنصر، نفس العنصر، نفس العنصر،هو
+
+164
+00:17:04,620 --> 00:17:07,900
+مالوش علاقة بال unity تبع ال ring الأصلية هذي يلها
+
+165
+00:17:07,900 --> 00:17:12,640
+unity وهذه unity تاني كما أشرتنا إلى ذلك قبل أن
+
+166
+00:17:12,640 --> 00:17:19,320
+نبدأ في الأمثلة يبقى the set هذه is a sub ring
+
+167
+00:17:19,320 --> 00:17:29,160
+with unity أربع أربع هو unity لل sub ring لكن ال
+
+168
+00:17:29,160 --> 00:17:33,080
+ring الأصلية ال unity لها بقداشالواحد صحيح وهي
+
+169
+00:17:33,080 --> 00:17:38,000
+الواحد صحيح وهذه ال unity اللي هي اربعة وهي الفرق
+
+170
+00:17:38,000 --> 00:17:42,380
+ما بين العنصرين او جدنا عندك الدرب اربعة في zero
+
+171
+00:17:42,380 --> 00:17:46,680
+في zero اربعة في اتنين باتنين اربعة في اربعة
+
+172
+00:17:46,680 --> 00:17:53,440
+باربعة يبقى هو كل هذا اللي مغلق تحت عملية الدرب
+
+173
+00:17:53,440 --> 00:18:01,640
+يعني تحققت الشروط تلاتة للصدرينالنقطة التالتة أو
+
+174
+00:18:01,640 --> 00:18:16,100
+المثال الثالث for each positive integer n for each
+
+175
+00:18:16,100 --> 00:18:22,020
+positive integer n الـ n زاد اللي عبارة عن zero
+
+176
+00:18:22,020 --> 00:18:32,580
+زاد او ناقص زادأو زاد او ناقص N وزاد او ناقص اتنين
+
+177
+00:18:32,580 --> 00:18:45,400
+N ونظل ماشيين إلى ما شاء الله is a subring of Z
+
+178
+00:18:45,400 --> 00:18:51,920
+because النقطة
+
+179
+00:18:51,920 --> 00:18:52,220
+الأولى
+
+180
+00:18:55,620 --> 00:19:03,480
+أنا أدعي الان ان ال N زد هو حاصل ضرب اي رقم صحيح
+
+181
+00:19:03,480 --> 00:19:07,760
+تمين في الزد سواء كان واحد او اتنين او تلاتة او
+
+182
+00:19:07,760 --> 00:19:12,080
+اربعة او مية وخمسين مين ماكان يكون لو ضربته في زد
+
+183
+00:19:12,080 --> 00:19:15,980
+بدأ يطلع نتيجة Zero زد او نقص N زد او نقص اتنين
+
+184
+00:19:15,980 --> 00:19:20,900
+هنا ليش ان الزد Zero واحد اتنين تلاتة يبقى N زد في
+
+185
+00:19:20,900 --> 00:19:28,380
+Zero في Zero انقولي خمسة مثلايبقى خمسة n خمسة في n
+
+186
+00:19:28,380 --> 00:19:34,000
+و خمسة in اللي بعدها ستة in سبعة in تمانية in
+
+187
+00:19:34,000 --> 00:19:38,100
+بالموجة و بالثانية بنفس الشيء يبقى جولنا zero زيدا
+
+188
+00:19:38,100 --> 00:19:42,620
+أو نقص in لإن ال in ضربت في واحد زيدا أو نقص اتنين
+
+189
+00:19:42,620 --> 00:19:46,920
+in لإن ان ضربت في اتنين لإن ان ضربت في تلاتة لإن
+
+190
+00:19:46,920 --> 00:19:50,800
+ان ضربت في تلاتة يعني حطي عناصر ال z و ضربيهم في n
+
+191
+00:19:50,800 --> 00:19:55,790
+بطلع اللي من ال six اللي قدامناهذه ال 6 انا ادعى
+
+192
+00:19:55,790 --> 00:20:00,010
+انها sub ring من مين؟ من ازرق، يعني اذا حققت
+
+193
+00:20:00,010 --> 00:20:04,770
+الشروط التلاتة، بصير خلاصنا، طب النقطة الأولى، هل
+
+194
+00:20:04,770 --> 00:20:12,110
+ال N زد non-empty ولا ممكن تكون empty؟ خلّع هي
+
+195
+00:20:12,110 --> 00:20:19,050
+قدامك، مليون عناصر، كتير فيها بجميع؟infinity of
+
+196
+00:20:19,050 --> 00:20:23,650
+elements يبقى فيها مالة نهاية من العناصر مش عجب
+
+197
+00:20:23,650 --> 00:20:28,710
+عنصر واحد يبقى non-empty الشرط الأول متحفظ طبيعي
+
+198
+00:20:28,710 --> 00:20:35,410
+الشرط التاني بدي أخد عنصرين موجودات في الـ A and Z
+
+199
+00:20:35,410 --> 00:20:42,450
+يبقى بدي أقول له X وY موجودات في الـ A and Z هذا
+
+200
+00:20:42,450 --> 00:20:45,810
+بدي أعطيك أن X يساوي
+
+201
+00:20:48,340 --> 00:20:57,700
+جدش M في N صح؟ مش هاد ينزل؟ طبعا وقولنا اتنين
+
+202
+00:20:57,700 --> 00:21:03,560
+تلاتة اربعة في انفي كذا مظبوط يبقى الشكل هيكون M
+
+203
+00:21:03,560 --> 00:21:08,340
+في N جدش اللي مش عارف يمكن اتنين ويمكن تلاتة ويمكن
+
+204
+00:21:08,340 --> 00:21:14,240
+عشر ويمكن خمسين ويمكن ستة وسبعين جد ما يكون عشوانو
+
+205
+00:21:14,240 --> 00:21:22,300
+ال Y بدها تساوي K في N تمام؟ يبقى ال X Y اللي
+
+206
+00:21:22,300 --> 00:21:27,080
+موجودة في N Z هيكون شكله شكل العناصر اللي موجودة
+
+207
+00:21:27,080 --> 00:21:32,760
+في N Z يبقى M في N و K في N و ال M و ال K موجودة
+
+208
+00:21:32,760 --> 00:21:41,680
+في Z و ال M و ال K عبارة عن integers أعداد صحية
+
+209
+00:21:42,160 --> 00:21:48,160
+يبقى الان بدي اخد X ناقص Y إذا جدرت أثبت ان ال X
+
+210
+00:21:48,160 --> 00:21:53,320
+ناقص Y موجود في NZ يكون خلصنا ال condition الأول
+
+211
+00:21:53,320 --> 00:21:59,420
+تبع من؟ تبع النظرية بقولوا تماما X ناقص Y بدي
+
+212
+00:21:59,420 --> 00:22:10,240
+يساوي ال M N ناقص E في M ويساوي اللي هو من؟ Mناقص
+
+213
+00:22:10,240 --> 00:22:18,700
+كاف من في ال M وين هذا ولا فارق بين two integers
+
+214
+00:22:18,700 --> 00:22:24,720
+يبقى integer ولا لا يبقى integer مضروب في N يبقى
+
+215
+00:22:24,720 --> 00:22:33,320
+بالفعل هذا موجود في ال NZ لأن ال M ناقص ال K هذا
+
+216
+00:22:33,320 --> 00:22:38,720
+موجود في Z إتصاليبقى تحقق ال condition الأول
+
+217
+00:22:38,720 --> 00:22:42,500
+والثاني ولا لا؟ يبقى انا اروح لل condition التالت
+
+218
+00:22:42,500 --> 00:22:49,360
+ال condition التالت بدأ اخد x في y بدي اثبت انه
+
+219
+00:22:49,360 --> 00:22:57,680
+موجود وين في نز يبقى ال x في y بده يساوي ال mn في
+
+220
+00:22:57,680 --> 00:23:05,580
+مين؟ في ال km الشكل اللي عناه تمام؟ يبقى هذا
+
+221
+00:23:05,580 --> 00:23:16,700
+الكلامبتدرساه بدرساه ال M N K كله في N هذا كله
+
+222
+00:23:16,700 --> 00:23:20,720
+Integer لإن هو حاصل ضرب three integers is an
+
+223
+00:23:20,720 --> 00:23:26,700
+integer يبقى هذا لحالة موجود في Z إذن هذا كله
+
+224
+00:23:26,700 --> 00:23:34,360
+موجود في ال NZ يبقى تحقق الشرطينأو ثلاثة شروط تبعت
+
+225
+00:23:34,360 --> 00:23:39,240
+النظرية يبقى بناء على علينا ان Z is a subgroup
+
+226
+00:23:39,240 --> 00:23:58,460
+from Z يبقى هنا ان Z is a subgroup from Z كويس
+
+227
+00:24:01,280 --> 00:24:08,600
+يبقى هذا هو المثال اللي هو رقم 3 فروح للمثال رقم 4
+
+228
+00:24:41,810 --> 00:24:50,690
+مثال رقم 4 لو جت خدت Z of I اللي هي مين؟ كل
+
+229
+00:24:50,690 --> 00:24:58,850
+العلاسة على صلة A زي الـB I لحيث أن الـA والـB
+
+230
+00:24:58,850 --> 00:25:09,770
+موجودة في مين؟ موجودة في الـZ as a subring as a
+
+231
+00:25:09,770 --> 00:25:10,730
+subring
+
+232
+00:25:17,650 --> 00:25:24,910
+بالـ X عندي بقدرش؟ بـ Zero في مين؟ في الـ Y يبقى
+
+233
+00:25:24,910 --> 00:25:29,370
+Zero في الـ Y بدي يعطيني مين؟ الـ Zero هذا بدي
+
+234
+00:25:29,370 --> 00:25:37,890
+يعطيك إن X و Y موجودة في Sهنا لكل ال X و ال Y اللي
+
+235
+00:25:37,890 --> 00:25:44,410
+موجودة في S وهنا كذلك لكل ال X و ال Y اللي موجودة
+
+236
+00:25:44,410 --> 00:25:55,890
+في S وبالتاني ال S is a subring of A وصلنا
+
+237
+00:25:55,890 --> 00:26:03,170
+إلى exercises أطلاش يبقى exercises على شكتر أطلاش
+
+238
+00:26:03,640 --> 00:26:07,960
+فاكرونا في المسائل المرة القادمة على المرة القادمة
+
+239
+00:26:07,960 --> 00:26:13,600
+حل المسائل هنا و بدنا نشغلكم يكونوا مشتغلين آيو
+
+240
+00:26:13,600 --> 00:26:27,460
+سؤال 8 و 13 و 19 و 23 آه ثم أحط كمان 22 معاه 22 و
+
+241
+00:26:27,460 --> 00:26:38,410
+23و .. و تمانية و عشرين و تلاتين و إتنين و تلاتين
+
+242
+00:26:38,410 --> 00:26:46,410
+و تلاتة و تلاتين و تسعة و تلاتين و واحد و أربعين و
+
+243
+00:26:46,410 --> 00:26:53,850
+ستة و أربعين و خمسين يا أبو عياسل من أول التمرين و
+
+244
+00:26:53,850 --> 00:27:00,040
+من نص التمرين و من آخر التمرينوفترة المرة القادمة
+
+245
+00:27:00,040 --> 00:27:03,620
+نشوف إيش بدفس حلو منها
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..486d1e6a96f1385c7fd21052bad65ff3ccaebbb4
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/E89vr2N7Q3M_raw.srt
@@ -0,0 +1,1572 @@
+1
+00:00:20,690 --> 00:00:25,730
+بسم الله الرحمن الرحيم ننتقل الان الى chapter 17
+
+2
+00:00:25,730 --> 00:00:32,410
+بعد انهينا اللى هو chapter 16 chapter 17 بتتكلم عن
+
+3
+00:00:32,410 --> 00:00:39,190
+ال factorization of polynomial تحليل كثيرات الحدود
+
+4
+00:00:39,190 --> 00:00:45,950
+او تفكيك كثيرات الحدود الى عوامل ممكن نقدر نفككم
+
+5
+00:00:45,950 --> 00:00:52,550
+الى عوامل وممكن مانقدرشكيف ممكن نقدر وكيف ممكن ما
+
+6
+00:00:52,550 --> 00:00:57,910
+نقدرش نفككهم إلى عامل نبدأ بالتعريف الأول يقول لي
+
+7
+00:00:57,910 --> 00:01:03,010
+افترض ان دوي هو عبارة عن integral domain واخدنا
+
+8
+00:01:03,010 --> 00:01:08,850
+كولونوميا ال F of X موجودة في capital F of X مين
+
+9
+00:01:08,850 --> 00:01:14,330
+هو capital F of X هذا بنا؟ ايش العناصر اللي فيه؟
+
+10
+00:01:14,330 --> 00:01:18,250
+ما هو الشكل العنصر اللي موجود في capital F of X
+
+11
+00:01:20,330 --> 00:01:25,330
+Polynomial العواب اللي اتفقتها من وين؟ من الاعلى
+
+12
+00:01:25,330 --> 00:01:33,370
+اه لأ لأ لأ هذه خطأ فهذه D of X يعني هذي دي احنا
+
+13
+00:01:33,370 --> 00:01:38,550
+بنشتغل في Integral لون في D of X وليس في F of X
+
+14
+00:01:38,550 --> 00:01:44,790
+يفجر مين هي D of X؟ هي ال polynomial اللي عناصرها
+
+15
+00:01:44,790 --> 00:01:49,940
+من ال .. مش اللي عناصرهاإن المعاملات تبعاتها
+
+16
+00:01:49,940 --> 00:01:54,580
+ماخودة من الـ integral domain D تمام؟ إذا ال
+
+17
+00:01:54,580 --> 00:01:59,920
+element F of X هو كثيرات حدود معاملات كثيرات
+
+18
+00:01:59,920 --> 00:02:03,940
+الحدود أو كثيرة الحدود هذه ماخودة من مين؟ من ال
+
+19
+00:02:03,940 --> 00:02:09,460
+integral domain D طيب ال F of X هذه بقالها مش
+
+20
+00:02:09,460 --> 00:02:16,200
+Google اللي ليست Zero polynomialيعني ال F of X لا
+
+21
+00:02:16,200 --> 00:02:22,300
+تساوي Zero أي واحدة اتنين nor a unit in D of X
+
+22
+00:02:22,300 --> 00:02:27,480
+يعني هذا ال F of X مالهاش معكوس انه has no
+
+23
+00:02:27,480 --> 00:02:33,040
+invertible element in D of X يبقى ال F of X عليها
+
+24
+00:02:33,040 --> 00:02:39,000
+شرطين ليست كثيرة الحدود الصفرية وليست Polynomial
+
+25
+00:02:39,000 --> 00:02:44,030
+لها معكوس طيب مالها هذه؟هذه ال polynomial بقول
+
+26
+00:02:44,030 --> 00:02:50,810
+عنها irreducible يعني لا يمكن تفكيكها او لا يمكن
+
+27
+00:02:50,810 --> 00:02:56,510
+تحليلها الى حاصل ضرب two polynomials three
+
+28
+00:02:56,510 --> 00:03:00,310
+polynomials اكتر من ذلك يبقى it's called
+
+29
+00:03:00,310 --> 00:03:06,610
+irreducible over the if whenever ان حدث ان ال f of
+
+30
+00:03:06,610 --> 00:03:12,020
+x قدرنا نعكر عنها على حاصل ضربtwo polynomials
+
+31
+00:03:12,020 --> 00:03:18,400
+موجودات في D of X يبقى واحدة من اتنتين بدأت تبقى a
+
+32
+00:03:18,400 --> 00:03:26,040
+unit in D of X مرة تانية بقول انا integral domain
+
+33
+00:03:26,040 --> 00:03:35,320
+D أخدنا F of X هو عنصر غير صفري وليس له معكوس وهذا
+
+34
+00:03:35,320 --> 00:03:41,600
+العنصر موجود في D of X تمامال D of X هذا العنصر ال
+
+35
+00:03:41,600 --> 00:03:49,200
+F of X اللي أخدته عندنا هذا لو جدرت أعبر عنه كحاصل
+
+36
+00:03:49,200 --> 00:03:54,960
+ضرب two chronomials موجودات في ال D of X يبقى واحد
+
+37
+00:03:54,960 --> 00:04:00,220
+فيهم بدي يكون ما هو واحد فيهم بدي يكون is a unit
+
+38
+00:04:00,220 --> 00:04:08,620
+يبقى يا إما ال D of X بيكون unitيا إما ال H of X
+
+39
+00:04:08,620 --> 00:04:13,820
+بدها تكون واحد من الاتنين إن جدرنا نعمل هذه
+
+40
+00:04:13,820 --> 00:04:18,900
+الشغلة، ماجدرناش خلاص، يبقى irreducible، معناته لا
+
+41
+00:04:18,900 --> 00:04:24,820
+يمكن تفكيكها أو لا يمكن تحليلها، إذا كان بقدر الله
+
+42
+00:04:24,820 --> 00:04:31,720
+جدرنا نحللها أو جدرنا نفككها إلى حصل ضربهم صغير،
+
+43
+00:04:31,720 --> 00:04:37,090
+موجود في D of X لازم واحد فيهم يكونionate هذا
+
+44
+00:04:37,090 --> 00:04:41,470
+التعريف الأولى التعريف التاني المرتبط فيه بيقول
+
+45
+00:04:41,470 --> 00:04:48,110
+عندي بلونوميا ليست zero وليست unit لا unit ولا
+
+46
+00:04:48,110 --> 00:04:50,890
+zero اللي هو نفس ال condition اللي في الأول فوق
+
+47
+00:04:50,890 --> 00:04:58,090
+answer f of x موجود في DOS اللي بيكون irreducible
+
+48
+00:04:58,090 --> 00:05:04,320
+بقول عنه ايش? reducibleيبجى هذا العنصر اللى بيكونش
+
+49
+00:05:04,320 --> 00:05:10,460
+irreducible يعني نفي ال irreducible بيعطيني مين؟
+
+50
+00:05:10,460 --> 00:05:15,360
+irreducible يبجى نفي نفي النفي اثبات يبجى
+
+51
+00:05:15,360 --> 00:05:21,680
+irreducible بننفي irreducible ها not reducible
+
+52
+00:05:21,680 --> 00:05:27,120
+يبجى نفي النفي اثبات يبجى بصير irreducible يبجى
+
+53
+00:05:27,120 --> 00:05:34,680
+بقول عن ال F of X هدا irreducibleإذا كان not a
+
+54
+00:05:34,680 --> 00:05:39,480
+radius طب .. طب السؤال اللي بدي أسأله هذا اللي
+
+55
+00:05:39,480 --> 00:05:43,900
+محيرني شوية إذا شوفوا فاهمين زي ما انا فاهم و الله
+
+56
+00:05:43,900 --> 00:05:48,280
+مش فاهمين و الله فاهمكم و غير فاهمين طالع فأول
+
+57
+00:05:48,280 --> 00:05:52,600
+احنا قولنا خد دي integral domain و روحنا حطينا
+
+58
+00:05:52,600 --> 00:05:58,000
+التعريف و ما إلى ذلك و أخدنا يا أخوك سؤالي هو هل
+
+59
+00:05:58,000 --> 00:06:04,360
+كل polynomialبدها تبقى صحيحة هنا؟ يعني لو كانت
+
+60
+00:06:04,360 --> 00:06:08,940
+irreducible على integral domain، بدها تبقى
+
+61
+00:06:08,940 --> 00:06:14,560
+irreducible على كل integral domain؟ مجال الشيء،
+
+62
+00:06:14,560 --> 00:06:19,500
+مجال الشيء، ومش كل element كمان ينطبق عليه هذا
+
+63
+00:06:19,500 --> 00:06:23,800
+التعريف، جال ال element اللي بتاخده، ينطبق عليه
+
+64
+00:06:23,800 --> 00:06:27,320
+هذا التعريف ويقول عنه irreducible، ماينطبقش خلاص،
+
+65
+00:06:27,320 --> 00:06:31,770
+ماقدرش أقول irreducibleيبقى هذا الكلام ال ال
+
+66
+00:06:31,770 --> 00:06:36,470
+polynomial قد تكون irreducible على integral domain
+
+67
+00:06:36,470 --> 00:06:42,210
+وقد تكون reducible على integral domain آخر صح؟
+
+68
+00:06:42,210 --> 00:06:46,030
+يبقى هاي اللي احنا بنقوله والان هنوضح لكذا الكلام
+
+69
+00:06:46,030 --> 00:06:49,750
+بس قبل التوضيح بذاري على two definitions مرة تانية
+
+70
+00:06:49,750 --> 00:06:55,250
+نثبت المعلومة مشان نبدأ نبدأ نبني عليها دي
+
+71
+00:06:55,250 --> 00:06:59,890
+integral domainأخدت عنصر F of X في D of E of X
+
+72
+00:06:59,890 --> 00:07:05,210
+ماله هذا العنصر غير الصفري يعني F of X لا تساوي
+
+73
+00:07:05,210 --> 00:07:11,330
+Zero اتنين فال F of X ليس Unit ماهواش عنصر ماهو
+
+74
+00:07:11,330 --> 00:07:17,450
+معكس تمام يبقى هذا بقول عنه Irreducible فيديو إذا
+
+75
+00:07:17,450 --> 00:07:22,790
+بقدر الله جدرنا نكتب F of X على حاصل ضرب two
+
+76
+00:07:22,790 --> 00:07:27,780
+polynomials موجوداتفى دى يبقى واحدة منهم يبقى unit
+
+77
+00:07:27,780 --> 00:07:34,200
+غير هيك يبعتلنا الله طيب التعريف التانى اللى بتكون
+
+78
+00:07:34,200 --> 00:07:40,640
+ليست zero وليست unit وليست irreducible يبقى
+
+79
+00:07:40,640 --> 00:07:46,360
+irreducible فلأ يبقى نافلة فوق irreducible طيب
+
+80
+00:07:46,360 --> 00:07:52,610
+الملاحظة الأولى قلت لك perhaps ربما ايش ربماالـ F
+
+81
+00:07:52,610 --> 00:07:57,230
+of X تبقى Irreducible على Integral Domain لكنها
+
+82
+00:07:57,230 --> 00:08:02,850
+Reducible على Integral Domain أخر لما قلتش For All
+
+83
+00:08:02,850 --> 00:08:07,430
+Integral Domains أخدت Integral Domain واحد واخدت
+
+84
+00:08:07,430 --> 00:08:11,750
+عنصر موجود فيه تبقى هذا لا ينفذق على كل Integral
+
+85
+00:08:11,750 --> 00:08:17,680
+Domain يعني العنصر اللي بدي أخده F of Xممكن يكون
+
+86
+00:08:17,680 --> 00:08:21,640
+irreducible على integral domain وreducible على
+
+87
+00:08:21,640 --> 00:08:26,260
+integral domain أخر كما ستراهنا من الأمثلة بعد
+
+88
+00:08:26,260 --> 00:08:31,140
+قليل الملاحظة التانية فاطلنا نتكلم على ال F على ال
+
+89
+00:08:31,140 --> 00:08:36,760
+integral domain لنحكي على مين على ال F يبقى لو كان
+
+90
+00:08:36,760 --> 00:08:42,040
+ال F فيه أخدنا non constant polynomial زي ما قلنا
+
+91
+00:08:42,040 --> 00:08:46,430
+فوق non constant polynomialمش قادر اقول non-unit
+
+92
+00:08:46,430 --> 00:08:52,750
+لإن الفيل في كل عمصر غير صفري هو unit تمام؟ بطل
+
+93
+00:08:52,750 --> 00:08:57,630
+نتكلم عن ال unit يبقى non-constant polynomial F of
+
+94
+00:08:57,630 --> 00:09:01,070
+X اللي موجود في ال capital F of X بسميها ال
+
+95
+00:09:01,070 --> 00:09:07,950
+reduceable على F F ال F ماقدرتش اكتبها written as
+
+96
+00:09:07,950 --> 00:09:11,130
+the product of two non-constant polynomials of
+
+97
+00:09:11,130 --> 00:09:17,180
+lower degree ايش يعني؟يعني اللي بقول عنها
+
+98
+00:09:17,180 --> 00:09:24,140
+irreducible إن كانت عنصر غير صفري إتنين ماقدرش
+
+99
+00:09:24,140 --> 00:09:30,040
+أكتبها كحاصل ضرب two polynomials درجة كل واحدة
+
+100
+00:09:30,040 --> 00:09:36,020
+فيهم أقل من درجة ال polynomial الأصلية هي المقصود
+
+101
+00:09:36,020 --> 00:09:42,270
+هنا of lower degree in F of X نوضح الصورة شويةلو
+
+102
+00:09:42,270 --> 00:09:49,330
+قلت اني عندي polynomial f of x تساوي اكسوس خمسة
+
+103
+00:09:49,330 --> 00:09:53,570
+زائد تلاتة اكس تربية زائد اتنين اكس زائد واحد
+
+104
+00:09:53,570 --> 00:09:59,490
+موجودة في field capital F of X تمام ال lower
+
+105
+00:09:59,490 --> 00:10:04,990
+degree ليه اربعة و تلاتة و اتنين و واحد و صفر كمان
+
+106
+00:10:04,990 --> 00:10:08,610
+الصفر ماقدرش اكتب polynomial مع الدرجة الصفرية لان
+
+107
+00:10:08,610 --> 00:10:12,970
+بصي درجة ال polynomial التانيةهي درجة الكلوميا
+
+108
+00:10:12,970 --> 00:10:17,430
+الأصلية هذا قلق لأ of lower degree الدرجة بتكون اي
+
+109
+00:10:17,430 --> 00:10:23,210
+شكل ممكن إن جدرت أحلله واحدة من الدرجة الأولى
+
+110
+00:10:23,210 --> 00:10:27,330
+واحدة من الدرجة الرابعة واحدة من الدرجة التانية
+
+111
+00:10:27,330 --> 00:10:32,890
+واحدة من الدرجة التالتة وهكذا يبقى هذا اسم التحليل
+
+112
+00:10:32,890 --> 00:10:37,590
+of lower degree طيب ال F of X بقول عنها is
+
+113
+00:10:37,590 --> 00:10:43,540
+irreducible إذا ما جدرتشأكتبها على صورة Haselberg
+
+114
+00:10:43,540 --> 00:10:49,000
+two polynomials درجة كل واحدة فيهم أقل من درجة ال
+
+115
+00:10:49,000 --> 00:10:54,380
+polynomial الأصلية هاي اللي بيقولوا لما انتقلنا من
+
+116
+00:10:54,380 --> 00:11:00,120
+integral domain إلى field صار التعريف اللي فوق
+
+117
+00:11:00,120 --> 00:11:05,900
+غيرناه إلى التعريف التالي f of x بتكتب على
+
+118
+00:11:05,900 --> 00:11:10,430
+Haselberg two polynomialsلازم يكون درجة كل واحدة
+
+119
+00:11:10,430 --> 00:11:15,410
+من التنتين اقل من درجة ال polynomial الأصلية، إذا
+
+120
+00:11:15,410 --> 00:11:20,470
+ماقدرناش، يبقى هي irreducible، طب قدرنا؟
+
+121
+00:11:20,470 --> 00:11:25,570
+Irreducible، على طول القدر، يبقى إذا ماقدرناش نكتب
+
+122
+00:11:25,570 --> 00:11:30,050
+ال polynomial الأصلية على صيرة لحاصل ضرب to
+
+123
+00:11:30,050 --> 00:11:34,490
+polynomials of lower degree، يبقى الأصلية
+
+124
+00:11:34,490 --> 00:11:39,420
+irreducible، طب قدرنا؟يبقى بصير رديو سفر. هي اللي
+
+125
+00:11:39,420 --> 00:11:43,340
+بتقوله الملاحظة التانية. قبل أن ندخل إلى الأمثلة،
+
+126
+00:11:43,340 --> 00:11:50,480
+في تساؤل عندكم؟ ندخل في الأمثلة؟ طيب، نبدأ في
+
+127
+00:11:50,480 --> 00:11:56,520
+المثال الأول. المثال الأول بيقول ما يأتي ده
+
+128
+00:11:56,520 --> 00:12:01,080
+polynomial، ده polynomial.
+
+129
+00:12:03,560 --> 00:12:12,230
+F of Xاللي تساوي اتنين X عربية زائد أربعة is
+
+130
+00:12:12,230 --> 00:12:15,670
+irreducible
+
+131
+00:12:15,670 --> 00:12:28,050
+over لكي و but irreducible over
+
+132
+00:12:46,060 --> 00:12:52,420
+أنا أخدت برنامج F of X مزاوية اتنين X تربية زائد
+
+133
+00:12:52,420 --> 00:12:58,480
+أربعة أنا أزعم أن هذه البرنامج is irreducible على
+
+134
+00:12:58,480 --> 00:13:05,680
+الـQ لكنها irreducible على Z طب السؤال هو الـQ
+
+135
+00:13:05,680 --> 00:13:12,580
+انتجرال دومان؟ فهو انتجرال دومان وZ انتجرال دومان؟
+
+136
+00:13:15,110 --> 00:13:19,910
+يبقى اتنين integral domains يبقى هذول اتنتين are
+
+137
+00:13:19,910 --> 00:13:27,730
+integral domains because ال Q and ال Z are
+
+138
+00:13:27,730 --> 00:13:38,330
+integral domains and
+
+139
+00:13:38,330 --> 00:13:47,750
+F of Xبقدر اقول اتنين X تربية زائد اتنين هي بقدر
+
+140
+00:13:47,750 --> 00:13:54,690
+الله حللت ال F of X إلى حاصل ضرمين حاصل ضرم two
+
+141
+00:13:54,690 --> 00:14:00,570
+elements او two factors عاملين هي العامل الأول وهي
+
+142
+00:14:00,570 --> 00:14:07,930
+العامل الثاني حللته عنيش بقول هذه irreducible over
+
+143
+00:14:07,930 --> 00:14:15,590
+Qطب حللتها إلى عاملين تمام بيقول لو طلع واحد فيهم
+
+144
+00:14:15,590 --> 00:14:21,070
+unit تبقى irreducible يبقى انا قلت irreducible
+
+145
+00:14:21,070 --> 00:14:27,070
+ليش؟ على مين؟ على ال EQ لإنه اتنين is a unit في ال
+
+146
+00:14:27,070 --> 00:14:35,730
+EQ مين المعقود سبعة اتنين؟ نص موجود في ال EQ؟ اه
+
+147
+00:14:35,730 --> 00:14:40,160
+موجود في ال EQيبقى هادى because are integral
+
+148
+00:14:40,160 --> 00:14:45,620
+domains and ال F والاتنين
+
+149
+00:14:45,620 --> 00:14:57,580
+and ال X تربية زائد اتنين موجودة في ال Q والاتنين
+
+150
+00:14:57,580 --> 00:15:05,340
+is a unit but ال
+
+151
+00:15:05,340 --> 00:15:13,030
+F of Xتساوي اتنين في X تربيع زائد اتنين is
+
+152
+00:15:13,030 --> 00:15:23,810
+reducible in Z of X هل
+
+153
+00:15:23,810 --> 00:15:32,230
+هذا unit في Z؟ اتنين unit في Z؟ لأن معكوس تبقى و
+
+154
+00:15:32,230 --> 00:15:38,110
+نص، و نص مش موجوديبقى هذا بقول عنها Reducible يبقى
+
+155
+00:15:38,110 --> 00:15:43,610
+جدرنا نحللها إلى two factors وولا واحد فيهم unit
+
+156
+00:15:43,610 --> 00:15:49,230
+لكن في الأول فلكي وطلع واحد فيهم unit ومن هنا قلنا
+
+157
+00:15:49,230 --> 00:15:55,730
+Irreducible يعني جدرنا نحط ال polynomial لأن على
+
+158
+00:15:55,730 --> 00:16:01,510
+حاصل بلاصيرة حاصل ضارب two polynomial بس واحدة
+
+159
+00:16:01,510 --> 00:16:06,130
+فيهموالتانية مانعاش مشكلة بيها ما عليها الشرط
+
+160
+00:16:06,130 --> 00:16:08,950
+المهم واحدة فيهم يكون unit وواحدة فيهم unit يبقى
+
+161
+00:16:08,950 --> 00:16:15,950
+irreducible طيب جدرنا انحللهم بدون مشاكل يبقى هذا
+
+162
+00:16:15,950 --> 00:16:19,850
+strategy اتنين في x تربيه زائد اتنين يبقى
+
+163
+00:16:19,850 --> 00:16:26,370
+reducible على z وirreducible عالميا على ال Q نعطي
+
+164
+00:16:26,370 --> 00:16:27,510
+مثلا اخر
+
+165
+00:16:50,580 --> 00:16:53,160
+يبقى مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+166
+00:16:53,160 --> 00:16:53,360
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+167
+00:16:53,360 --> 00:16:53,760
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+168
+00:16:53,760 --> 00:16:57,860
+مثلًا مثلًا مثلًا مثلًا
+
+169
+00:16:59,300 --> 00:17:09,920
+over a على ال six real numbers but ولكن reducible
+
+170
+00:17:09,920 --> 00:17:19,200
+ولكن reducible over ال six of complex numbers اللي
+
+171
+00:17:19,200 --> 00:17:24,120
+هي main اللي هي C السبب because
+
+172
+00:17:33,940 --> 00:17:38,460
+يبقى نفس ال paranormal غيرت ال integral domains
+
+173
+00:17:38,460 --> 00:17:42,800
+اللي عندى وانتقل من ال integral domains الى main
+
+174
+00:17:42,800 --> 00:17:50,680
+الى field بقول لو كان ال F field هو عندك non
+
+175
+00:17:50,680 --> 00:17:54,360
+constant paranormal يبقى هيها non constant
+
+176
+00:17:54,360 --> 00:17:59,160
+paranormal يبقى هذه بقول عنها ال reduce اذا
+
+177
+00:17:59,160 --> 00:18:04,350
+ماقدرتش اكتبها على شكل productالـ two non constant
+
+178
+00:18:04,350 --> 00:18:10,450
+polynomials of lower degree بقوله كويس يبقى ال
+
+179
+00:18:10,450 --> 00:18:15,430
+polynomial هذه irreducible على R both reducible
+
+180
+00:18:15,430 --> 00:18:27,570
+على C ليه؟ لأن الـ R and الـ C are integral R
+
+181
+00:18:27,570 --> 00:18:28,510
+fields
+
+182
+00:18:33,400 --> 00:18:41,540
+طيب في ال 6th real number بقدر احلل هذه الى حاصر
+
+183
+00:18:41,540 --> 00:18:49,180
+ضرب تعالى نشوف الان بيدادي لل F of X يساوي 2 X
+
+184
+00:18:49,180 --> 00:18:57,340
+تربيع زائد 2 يقولى على الفيل إذا عندك non constant
+
+185
+00:18:57,340 --> 00:19:01,900
+polynomial هيها non constant polynomialis called
+
+186
+00:19:01,900 --> 00:19:07,240
+irreducible if ال if cannot be written as a
+
+187
+00:19:07,240 --> 00:19:13,700
+product of two non-conustant polynomials تقدروا
+
+188
+00:19:13,700 --> 00:19:19,600
+تكتبوا هذه ك product of non-conustant polynomials؟
+
+189
+00:19:19,600 --> 00:19:25,800
+مقدرش يعني مقدرش اتنين هذه أستبدلها ب polynomial
+
+190
+00:19:25,800 --> 00:19:31,600
+تانية ماهياش conustant يبقى هذه إيش؟irreducible
+
+191
+00:19:31,600 --> 00:19:39,200
+يبقى فيه ال F of X هذه is irreducible
+
+192
+00:19:39,200 --> 00:19:49,880
+over R زي ما قلنا irreducible over R لإنها since
+
+193
+00:19:49,880 --> 00:19:55,300
+الإتنين is a constant
+
+194
+00:20:05,840 --> 00:20:13,000
+فولونوميا طيب الآن أنا بقول irreducible على R لكن
+
+195
+00:20:13,000 --> 00:20:21,460
+أزعم أنها irreducible على ال IQ يبقى هنا بعض ولكن
+
+196
+00:20:21,460 --> 00:20:31,480
+ال F of X يساوي 2 في X تربيه زائد 2 الradiusable
+
+197
+00:20:31,480 --> 00:20:43,920
+over set of complex numbers since لإن ال F of X
+
+198
+00:20:43,920 --> 00:20:50,940
+بقدر أكتبها على الشكل تاني نين بدي أكتبها على صيرة
+
+199
+00:20:50,940 --> 00:20:58,900
+حاصل ضرج ل two complex numbers ودرجتهمأقل من درجة
+
+200
+00:20:58,900 --> 00:21:03,740
+القولونوميا الأصلية القولونوميا الأصلية من الدرجة
+
+201
+00:21:03,740 --> 00:21:10,320
+الثانية يبقى بدي أكتب التنتين هذول كحاصل ضرب من
+
+202
+00:21:10,320 --> 00:21:14,820
+الدرجة الأولى ليه أقل من الدرجة الثانية مش هقول
+
+203
+00:21:14,820 --> 00:21:18,740
+واحدة من الدرجة الصفرية وواحدة من الدرجة التانية
+
+204
+00:21:18,740 --> 00:21:21,720
+يبقى لو قلت واحدة من الدرجة التانية صار زي الأصلية
+
+205
+00:21:21,720 --> 00:21:26,500
+يبقى هذا يتناقض مع الكلام اللي احنا قلناه اتنين
+
+206
+00:21:26,780 --> 00:21:31,780
+يتنخذ ان الاتنين constant و هنا قلنا non constant
+
+207
+00:21:31,780 --> 00:21:37,480
+polynomial product of two non constant صارت واحدة
+
+208
+00:21:37,480 --> 00:21:42,580
+constant يبقى هنا في عيبين لو قلنا اللي هو
+
+209
+00:21:42,580 --> 00:21:47,340
+irreducible انه اتنين اللي هو ماهياش non constant
+
+210
+00:21:47,340 --> 00:21:52,480
+صارت constant اتنين الاتنين ماهماش of lower degree
+
+211
+00:21:52,480 --> 00:21:57,690
+صحيح ال constant polynomialال degree تبعها أقل من
+
+212
+00:21:57,690 --> 00:22:01,590
+اتنين لكن التانية لأ ال degree تبعها يسوى اتنين
+
+213
+00:22:01,590 --> 00:22:06,570
+يبقى عيبين موجودين في وين في السواق يبقى هذا بدي
+
+214
+00:22:06,570 --> 00:22:12,090
+أحللها طبعا انتوا أخدتوا complex number بقدر أحلل
+
+215
+00:22:12,090 --> 00:22:19,950
+هذه و أقول ناقص جدر اتنين في I وهذه ال X زائد جدر
+
+216
+00:22:19,950 --> 00:22:28,590
+اتنين في Iصحيه كده؟ تعالى نشوف هذا تحرير الفرق بين
+
+217
+00:22:28,590 --> 00:22:35,710
+المرابعين مظبوط؟ مربع الأولى في X ترابية هيه و هي
+
+218
+00:22:35,710 --> 00:22:41,070
+اتنين اللي برا هي اضاينا برا ناقص مربع التانية جذر
+
+219
+00:22:41,070 --> 00:22:48,130
+اتنين I لكل ترابية باتنين في سالب I وعندي سالب
+
+220
+00:22:48,130 --> 00:22:53,330
+يبقى بصير زائد اتنين يبقى زائد اتنين هيهيبقى
+
+221
+00:22:53,330 --> 00:22:57,510
+تحليلنا سليم مائة بالمائة يبقى هذا ال element
+
+222
+00:22:57,510 --> 00:23:02,810
+irreducible عالى C since ال F of X حلناه إلى حاصل
+
+223
+00:23:02,810 --> 00:23:11,290
+ضرب two polynomials of lower degree and ال X لاطس
+
+224
+00:23:11,290 --> 00:23:21,830
+جذري اتنين I وال X ذاتي جذري اتنين I are of lower
+
+225
+00:23:21,830 --> 00:23:30,800
+degreedegree ده هو degree than F يبقى الدرجة
+
+226
+00:23:30,800 --> 00:23:38,640
+سبعتهم أقل من مين أقل من درجة اللي هو ال ال
+
+227
+00:23:38,640 --> 00:23:44,540
+polynomial الأصلية اللي هي F of A ناخد كمان مثال
+
+228
+00:23:44,540 --> 00:23:50,280
+يبقى هذا مثال رقم 2 مثال رقم 3
+
+229
+00:23:53,800 --> 00:23:58,600
+The polynomial f
+
+230
+00:23:58,600 --> 00:24:10,320
+of x يساوى x ترابيعه ناقص اتنين is irreducible
+
+231
+00:24:10,320 --> 00:24:13,380
+over
+
+232
+00:24:13,380 --> 00:24:20,240
+a cube but irreducible over R
+
+233
+00:24:27,920 --> 00:24:35,780
+معقول؟ طب من هنا نشوف ما هو السبب بيقول إيه؟
+
+234
+00:24:35,780 --> 00:24:41,280
+Irreducible على ليكيوم لكنها irreducible على ..
+
+235
+00:24:41,280 --> 00:24:47,680
+السؤال هو ليكيوم are are fields، مظهر؟ يفجر هنا
+
+236
+00:24:47,680 --> 00:24:58,610
+because ان ليكيوم عندك ال are are fieldsهذه
+
+237
+00:24:58,610 --> 00:25:05,490
+الناحية الأولى الناحية الثانية f of x هي x ترابيع
+
+238
+00:25:05,490 --> 00:25:13,230
+ناقص اتنين بقدر احلل اكس ناقص جدري اتنين في x زائد
+
+239
+00:25:13,230 --> 00:25:18,270
+جدري اتنين اذا قدرت اكتبها على حاصل درج two
+
+240
+00:25:18,270 --> 00:25:23,580
+polynomial الدرجة التي اتبعتهم اقل من 100أقل من
+
+241
+00:25:23,580 --> 00:25:26,480
+ضرر القلعون الملاصية، القلعون الملاصية من الدرجة
+
+242
+00:25:26,480 --> 00:25:29,800
+الثانية هتقول كل واحدة أقل من الدرجة الأولى اللي
+
+243
+00:25:29,800 --> 00:25:35,340
+هي أقل من اتنين طيب هل هذا ال element موجود في ال
+
+244
+00:25:35,340 --> 00:25:42,360
+IQ؟ لأ و هذا و شرط أساسي لازم يكونوا في ال IQ،
+
+245
+00:25:42,360 --> 00:25:47,740
+مظلوم؟ يعني هذا التحليل لا يمكن أن يتم داخل ال IQ
+
+246
+00:25:47,740 --> 00:25:53,570
+لأن جذر اتنين is irrational numberما هو اش عدد
+
+247
+00:25:53,570 --> 00:26:01,850
+نسبي مش موجود في ال EQ يبقى هنا F of X هذا بدي
+
+248
+00:26:01,850 --> 00:26:12,970
+يقين ان ال F of X is irreducible over ال EQ السبب
+
+249
+00:26:12,970 --> 00:26:21,590
+because ان ال X ناقص جدر اتنين وال X زائد جدر
+
+250
+00:26:21,590 --> 00:26:30,780
+اتنينdoes not belong to Q بقى موجودة في R Y بينما
+
+251
+00:26:30,780 --> 00:26:38,860
+Y اللي هو ال X ناقص جذر اتنين وال X زائد جذر اتنين
+
+252
+00:26:38,860 --> 00:26:46,400
+belongs to mean في R موجودة في R and each of them
+
+253
+00:26:46,400 --> 00:26:50,600
+each of them
+
+254
+00:26:53,300 --> 00:27:07,820
+Each of them is of lower degree than the F of X كل
+
+255
+00:27:07,820 --> 00:27:13,560
+واحد فيهم درجته أقل من درجة ال F of X العصرية ال F
+
+256
+00:27:13,560 --> 00:27:19,020
+of X العصرية من الدرجة الثانية كل واحد فيهم من
+
+257
+00:27:19,020 --> 00:27:25,860
+الدرجة الأولىوالـ R is a field بهذا كلامنا صحيح طب
+
+258
+00:27:25,860 --> 00:27:30,680
+احنا اللي هنعطينا بدل المثال تلاتة على integral
+
+259
+00:27:30,680 --> 00:27:37,460
+domino field مشهورة عندنا نتقل شوية مثال رقم أربع
+
+260
+00:27:37,460 --> 00:27:41,500
+مثال
+
+261
+00:27:41,500 --> 00:27:44,200
+رقم أربع بيقول ما تدا polynomial
+
+262
+00:27:49,510 --> 00:27:57,150
+f of x اللي بده يساوي x ترمية زائد واحد is
+
+263
+00:27:57,150 --> 00:28:00,590
+irreducible
+
+264
+00:28:00,590 --> 00:28:10,610
+over z تلاتة but irreducible
+
+265
+00:28:10,610 --> 00:28:15,510
+over
+
+266
+00:28:15,510 --> 00:28:18,330
+z خمسة
+
+267
+00:28:22,770 --> 00:28:32,050
+عقول؟ فبس انا بنسأل هل Z تلاتة فيد؟ او Z خمسة؟
+
+268
+00:28:32,050 --> 00:28:37,730
+يبقى 2 فيد لإن Z P is A فيد where ال P is a prime.
+
+269
+00:28:38,190 --> 00:28:44,730
+يبقى Z تلاتة هو فيد و Z خمسة هو فيد. يبقى ايه؟
+
+270
+00:28:44,730 --> 00:28:58,970
+Because Z تلاتةand Z خمسة are fields and
+
+271
+00:28:58,970 --> 00:29:01,990
+ال
+
+272
+00:29:01,990 --> 00:29:09,330
+F of X بده يساوي X ترابية زي إدوة من وين صار
+
+273
+00:29:09,330 --> 00:29:13,690
+السؤال هذا أصعب من اللي جابله من التحليل اللي بدنا
+
+274
+00:29:13,690 --> 00:29:20,930
+نعمل لو جيت أحلل هذهممكن أقولك اتنين X زائد واحد
+
+275
+00:29:20,930 --> 00:29:27,570
+في تلاتة X زائد واحد معقول التحليل هذا صحيح؟ تعالى
+
+276
+00:29:27,570 --> 00:29:36,730
+نشوف اتنين في تلاتة ستة X ترابيع تمام في Z تلاتة
+
+277
+00:29:36,730 --> 00:29:41,910
+زيرو بطل يصير من الدرجة التانية بالباقي كله من
+
+278
+00:29:41,910 --> 00:29:48,090
+الدرجة الأولىيبقى هذا بالشكل هذا غير موجود في Z3
+
+279
+00:29:48,090 --> 00:29:56,750
+هل موجود في Z5 تعالى نشوف يبقى 2 في 3 ب 6 X تربيع
+
+280
+00:29:56,750 --> 00:30:03,050
+في Z5 X تربيع واحدة مظبوط لإن ما نشيل الخمسة يبقى
+
+281
+00:30:03,050 --> 00:30:08,450
+من ال 6 واحد يبقى X تربيع واحدة هي هو يجعلنا X
+
+282
+00:30:08,450 --> 00:30:17,100
+تربيع نيجي لبعدهنا 2x و 3x و 5x في z خمسة Zero
+
+283
+00:30:17,100 --> 00:30:21,380
+طاري ثرمان طلعنا بس واحد في واحد في واحد في واحد
+
+284
+00:30:21,380 --> 00:30:23,700
+في واحد في واحد في واحد في واحد في واحد في واحد في
+
+285
+00:30:23,700 --> 00:30:24,860
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+286
+00:30:24,860 --> 00:30:25,440
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+287
+00:30:25,440 --> 00:30:26,020
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+288
+00:30:26,020 --> 00:30:26,300
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+289
+00:30:26,300 --> 00:30:27,120
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+290
+00:30:27,120 --> 00:30:27,540
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+291
+00:30:27,540 --> 00:30:28,700
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+292
+00:30:28,700 --> 00:30:28,700
+واحد في واحد في واحد في واحد في واحد في واحد في
+
+293
+00:30:28,700 --> 00:30:34,520
+واحد في واحد في واحد في واحد في واحد في
+
+294
+00:30:34,520 --> 00:30:44,430
+واحد في واحدأنا بدي أسوأ X تربية زائد واحد و اتنين
+
+295
+00:30:44,430 --> 00:30:54,350
+X زائد واحد و تلاتة X زائد واحد اتنين هذول موجودات
+
+296
+00:30:54,350 --> 00:31:00,070
+وين في Z خمسة و كذلك موجودات في Z تلاتة موجودات في
+
+297
+00:31:00,070 --> 00:31:05,630
+الاتنين لكن المهم بدنا مين بقى بس هذا لأ هذا لأ
+
+298
+00:31:05,630 --> 00:31:09,880
+انفعشيبقى فتح مش موجود في زد تلاتة، زد تلاتة Zero
+
+299
+00:31:09,880 --> 00:31:18,320
+واحد واتنين، هذول اتنين موجودات في زد خمسة and
+
+300
+00:31:18,320 --> 00:31:32,080
+each of them is of lower degree than
+
+301
+00:31:36,560 --> 00:31:42,420
+اللي هو main than ال F ال F من الدرجة الثانية وكل
+
+302
+00:31:42,420 --> 00:31:46,540
+واحد من ال اتنين هدول من ال main من الدرجة الو
+
+303
+00:31:46,540 --> 00:31:51,560
+تبقى صلة ال F of X reducible في Z خمسة
+
+304
+00:31:51,560 --> 00:31:55,500
+وirreducible في Z تلت
+
+305
+00:32:11,970 --> 00:32:19,030
+نعطل أول نظرية على هذا الموضوع النظرية بتقول ما
+
+306
+00:32:19,030 --> 00:32:28,950
+يكتر تاريخ ال
+
+307
+00:32:28,950 --> 00:32:35,810
+FDAC لكبت ال FDAC
+
+308
+00:32:42,760 --> 00:32:54,500
+F of X موجودة في كارتة F of X عند ال degree لل F
+
+309
+00:32:54,500 --> 00:33:04,560
+بدأت سوى اتنين او تلاتة say M then ال F then ال F
+
+310
+00:33:04,560 --> 00:33:09,200
+is reducible
+
+311
+00:33:10,690 --> 00:33:19,210
+radius of one لإن ال F is irreducible over capital
+
+312
+00:33:19,210 --> 00:33:32,690
+F F and only F F and only F and F of X has a zero
+
+313
+00:33:32,690 --> 00:33:38,670
+has a zero and no capital F
+
+314
+00:33:53,130 --> 00:34:00,830
+نقرأ النصب ثاني وقبل البرهنة حاول نطرح سؤال ربما
+
+315
+00:34:00,830 --> 00:34:07,150
+هذا السؤال طرق على أذهانكم جال ال A phase أخدت
+
+316
+00:34:07,150 --> 00:34:12,870
+عنصر F of X موجود في capital F of X ضريت ال F of X
+
+317
+00:34:12,870 --> 00:34:17,370
+اتنين ماعندها مشكلة تلاتة ماعندها مشكلة اتنين او
+
+318
+00:34:17,370 --> 00:34:23,940
+تلاتة سيارةبقول ان ال F is reducible على F if and
+
+319
+00:34:23,940 --> 00:34:30,260
+only if ال F of X هي Zero in capital F السؤال اللي
+
+320
+00:34:30,260 --> 00:34:35,580
+بده أطرحه طب لو كان ال degree ل F ل هي اتنين ولا
+
+321
+00:34:35,580 --> 00:34:42,100
+تلت اربعة مثلا خمس ستة ده نظرية صحيحة؟ لا ليس
+
+322
+00:34:42,100 --> 00:34:47,740
+صحيحة وسنثبت هذا الكلام عامليا بمثال ان شاء الله
+
+323
+00:34:47,740 --> 00:34:53,800
+بعد ايه؟بعد أن أثبت هذه النظرية يبقى الـ O يبقى
+
+324
+00:34:53,800 --> 00:35:02,400
+أنا بدي أطلب أنها that ال F of X موجودة في capital
+
+325
+00:35:02,400 --> 00:35:15,300
+F of X with degree لل F هذا سوى 2 أو 3 النظرية كل
+
+326
+00:35:15,300 --> 00:35:20,600
+F عندهم F يبقى القرآن بدي أصير وينالاتجاهية ناخد
+
+327
+00:35:20,600 --> 00:35:25,620
+الاتجاهية لما نوص مذات ثاني ثم العكس يبقى هنا
+
+328
+00:35:25,620 --> 00:35:36,140
+بالداخل اقول اسيوم ذات افترض ان ال F is reducible
+
+329
+00:35:36,140 --> 00:35:39,540
+over
+
+330
+00:35:39,540 --> 00:35:47,160
+F then F
+
+331
+00:35:47,160 --> 00:35:54,970
+of Xهتصير حاصل ضارب ده اللي ده تبقى حاصل ضارب في
+
+332
+00:35:54,970 --> 00:36:06,070
+البرنامج يبقى g of x في h of x where حيث ال g of x
+
+333
+00:36:06,070 --> 00:36:16,370
+و ال h of x هذه موجودة وين؟ في capital F of X and
+
+334
+00:36:16,370 --> 00:36:18,730
+h
+
+335
+00:36:19,560 --> 00:36:30,660
+of ال F و ال H of X او ال G of X and اللي هو ال H
+
+336
+00:36:30,660 --> 00:36:40,300
+of X is of lower degree then
+
+337
+00:36:56,890 --> 00:37:02,670
+يبقى كل من الجيولتش بيكون من الدرجة الأولى لو قلنا
+
+338
+00:37:02,670 --> 00:37:07,250
+تلاتة يبقى على الأقل واحدة فيهم بيكون من وين
+
+339
+00:37:07,250 --> 00:37:12,530
+الدرجة اللي بيبقى على كل الأمرين الواحدة منهم
+
+340
+00:37:12,530 --> 00:37:19,250
+بيكون of the first degree مظبوط؟ يبقى that is
+
+341
+00:37:22,110 --> 00:37:38,150
+I am one of الـG of X or الـH of X has degree one
+
+342
+00:37:38,150 --> 00:37:44,270
+إذا واحدة من التنتين بدأت تكون من الدرجة الأولى لو
+
+343
+00:37:44,270 --> 00:37:48,430
+افترضنا إن الـG هذه من الدرجة الأولى
+
+344
+00:37:51,410 --> 00:38:02,950
+A degree تبع الـG of X او B1 درجة هذه هي من الدرجة
+
+345
+00:38:02,950 --> 00:38:09,230
+الأولى لا يمكنك تدفع شكلها بالأعلى ثم الـG of X
+
+346
+00:38:09,230 --> 00:38:18,830
+بدأ تساوي AX زي B A ممكن تساوي زي ذوالـ B ممكن
+
+347
+00:38:18,830 --> 00:38:23,550
+تسوى Zero فاناش مشكلة لكن الـ A ممنوع تسوى Zero
+
+348
+00:38:23,550 --> 00:38:30,550
+فبحط فاصلة و الـ A does not equal to Zero فلو سوى
+
+349
+00:38:30,550 --> 00:38:34,790
+Zero بتبطل يصير من الدرجة الأولى بيصير constant
+
+350
+00:38:34,790 --> 00:38:46,400
+polynomial طيب كويس ال F of X بنحاصر ضرب تنتينيبقى
+
+351
+00:38:46,400 --> 00:38:54,700
+واحدة فيهم قولنا ax زائد b التانية h of x ال h of
+
+352
+00:38:54,700 --> 00:38:59,360
+x قد تكون من الدرجة الأولى وقد تكون من الدرجة
+
+353
+00:38:59,360 --> 00:39:03,260
+الثانية احنا بنشتغل في integral domain و الله في
+
+354
+00:39:03,260 --> 00:39:10,940
+field في field يبقى كل عمصر له معكوس طبعا طبعا شو
+
+355
+00:39:10,940 --> 00:39:18,560
+رايك لو جيت انا قلت لك letالـ X يساوي ثابت A
+
+356
+00:39:18,560 --> 00:39:25,760
+inverse B مثلا خدي الـ X يساوي N مثلا بدي أشوف شو
+
+357
+00:39:25,760 --> 00:39:35,380
+بده تساوي يعني يبقى N بدنا أخد ال F أُر ثابت A
+
+358
+00:39:35,380 --> 00:39:42,790
+inverse B تمام؟ بده تساوي يا شبنان؟ يبقى Aالـ A
+
+359
+00:39:42,790 --> 00:39:51,130
+inverse B بس بيشارت سالب هاي سالب A inverse B
+
+360
+00:39:51,130 --> 00:39:59,090
+تمام؟ وهذه كلها .. كلها .. أه .. أه طبعا فاهمين؟
+
+361
+00:39:59,090 --> 00:40:07,470
+في زائد B التاني هذه كلها في الـ H of X الـ F
+
+362
+00:40:07,470 --> 00:40:13,630
+inverse of Bشيلت ال X و حطيت قيمتها وهذه بدي
+
+363
+00:40:13,630 --> 00:40:22,470
+احسبها كمان جدار ال H of سالب A inverse B هذه
+
+364
+00:40:22,470 --> 00:40:31,930
+بديها تسوى سالب B زائد B مضربه مين في ال H of سالب
+
+365
+00:40:31,930 --> 00:40:40,960
+A inverse B يعني جدار Zeroيبقى هذه الـ 0 في ماذا؟
+
+366
+00:40:40,960 --> 00:40:47,400
+الـ H أُسالف A inverse B يبقى يساوي 0 بمعنى هذا
+
+367
+00:40:47,400 --> 00:40:52,280
+الكلام، هذا الـ element أيش يمثل بالنسبة للدلة F؟
+
+368
+00:40:52,280 --> 00:41:00,300
+هو الـ 0 الألم يبقى الـ X يساوي أسالف A inverse B
+
+369
+00:41:00,300 --> 00:41:11,010
+هو A 0 forthe function of the polynomial of the
+
+370
+00:41:11,010 --> 00:41:16,150
+polynomial of
+
+371
+00:41:16,150 --> 00:41:24,370
+f of x عظمها المطلوب لفوفيكس هيزيرو انف يبقى اللي
+
+372
+00:41:24,370 --> 00:41:28,850
+هي zero هي أو جمالها اللي هو ال element اللي هو
+
+373
+00:41:28,850 --> 00:41:35,540
+زيرو الان بدنا نمشي معاكس للتجاه المعاكسيجب دلّا
+
+374
+00:41:35,540 --> 00:41:50,260
+conversion conversion
+
+375
+00:41:50,260 --> 00:41:58,060
+assume
+
+376
+00:41:58,060 --> 00:42:16,360
+that ال Earthhas a zero in capital F دلوقت
+
+377
+00:42:16,360 --> 00:42:25,540
+بدي افترض ان ال F has a zero in capital F that is
+
+378
+00:42:25,540 --> 00:42:31,160
+that
+
+379
+00:42:31,160 --> 00:42:45,120
+is قايلة assumeإن ال a is a zero of ال f then ال f
+
+380
+00:42:45,120 --> 00:42:51,800
+of a بدى يسوى قداش بدى يسوى zero مدام هذا zero
+
+381
+00:42:51,800 --> 00:42:57,680
+أخدنا تمين في الشكتر الماضي أنه لو كان في عندي
+
+382
+00:42:57,680 --> 00:43:02,800
+zero لل function f يبقى ال x ناقص هذا الامت هو ال
+
+383
+00:43:02,800 --> 00:43:10,700
+factor لمينلدالة يبقى هنا هذا بدي يعطينا ان ال X
+
+384
+00:43:10,700 --> 00:43:24,340
+ناقص ال A is a factor for the polynomial F
+
+385
+00:43:24,340 --> 00:43:38,220
+of X that is I N ال F of Xيساوي ال X نقص ال A في
+
+386
+00:43:38,220 --> 00:43:46,900
+ال Q of X or sum a
+
+387
+00:43:46,900 --> 00:43:56,520
+Q of X اللي موجودة في مين؟ في كارتن F of X إيش
+
+388
+00:43:56,520 --> 00:44:02,940
+تفسيرك لهذا الكلام؟ كتبته خلصت، يبقى سارتين
+
+389
+00:44:03,350 --> 00:44:09,650
+reducible جدرت أحللها إلى حاصل ضرب two polynomials
+
+390
+00:44:09,650 --> 00:44:21,110
+يرجى this means this means
+
+391
+00:44:21,110 --> 00:44:32,270
+that أن ال F is reducible أو
+
+392
+00:44:32,270 --> 00:44:32,870
+ضرب
+
+393
+00:44:42,260 --> 00:44:50,420
+عطيكم العافية نكمل ان شاء الله المحاضرة القادمة
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GScGwkt4KIA_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GScGwkt4KIA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0dab4845a891605a84c53c2d90e5ade75e00bbdf
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GScGwkt4KIA_raw.srt
@@ -0,0 +1,1772 @@
+1
+00:00:20,700 --> 00:00:25,320
+بالله الرحمن الرحيم نكمل ما ابتدأنا فيه المرة
+
+2
+00:00:25,320 --> 00:00:30,980
+الماضية و آخر مرة مكتوب معاكم هو definition تعريف
+
+3
+00:00:30,980 --> 00:00:36,480
+ال principle ideal domain وقلنا في هذا التعريف ان
+
+4
+00:00:36,480 --> 00:00:42,380
+ال integral domain لو كان كل ideal في ال integral
+
+5
+00:00:42,380 --> 00:00:47,340
+domain هو principle ideal بسميه principle ideal
+
+6
+00:00:47,340 --> 00:00:53,880
+domainهذا آخر تعريف مكتوب معاكم طيب، الآن النظرية
+
+7
+00:00:53,880 --> 00:00:58,140
+على هذه النقطة، على هذا التعريف النظرية بتقول ليه؟
+
+8
+00:00:58,140 --> 00:01:03,780
+ود ال F عبارة عن فيه؟ يبقى ال capital F of X is a
+
+9
+00:01:03,780 --> 00:01:09,520
+principal ideal domain بمعنى كل ideal في capital F
+
+10
+00:01:09,520 --> 00:01:16,490
+of X هو عبارة عن ال principal idealإن أثبتنا هذا
+
+11
+00:01:16,490 --> 00:01:20,670
+الكلام فعلاً يكون capital F of X هو عبارة عن ال
+
+12
+00:01:20,670 --> 00:01:26,710
+principle ideal domain طيب الآن ال F field يبقى
+
+13
+00:01:26,710 --> 00:01:34,450
+هنا فاجب أقول له let ال F دي اي field بنفع يكون
+
+14
+00:01:34,450 --> 00:01:41,190
+integral domain؟ بنفع لأن أي field هو عبارة عن
+
+15
+00:01:41,190 --> 00:01:46,430
+integral domain لكن العكس ليس صحيحايبقى هنا little
+
+16
+00:01:46,430 --> 00:01:59,150
+f با field then ال F is an integral domain لو
+
+17
+00:01:59,150 --> 00:02:04,930
+رجعنا إلى أول نظرية أخذناها في هذا ال chapter قلنا
+
+18
+00:02:04,930 --> 00:02:09,670
+لو كان ال F integral domain يبقى ال capital F of X
+
+19
+00:02:09,670 --> 00:02:16,100
+هو عبارة عن integral domainيبقى باجي بقول by a
+
+20
+00:02:16,100 --> 00:02:28,380
+previous theorem نظرية سابقة capital F of X is an
+
+21
+00:02:28,380 --> 00:02:35,600
+integral domain تمام
+
+22
+00:02:35,600 --> 00:02:45,490
+بتروح أخد ideal في capital F of X يبقى letالـ I be
+
+23
+00:02:45,490 --> 00:02:58,070
+an ideal في اله capital F of X ان هو لا طريقة ال
+
+24
+00:02:58,070 --> 00:03:04,230
+ideal هذا principle ideal بصير capital F of X is a
+
+25
+00:03:04,230 --> 00:03:09,710
+principle ideal domain ال ideal اللي أخدته احتمال
+
+26
+00:03:10,890 --> 00:03:16,330
+الـ ideal هذا يكون بـ zero واحتمال ان لا يكون بـ
+
+27
+00:03:16,330 --> 00:03:22,670
+zero صحيح؟ طيب if ال ideal I بده يساوي zero then
+
+28
+00:03:22,670 --> 00:03:27,670
+ال ideal هو ال principle ال ideal generated by
+
+29
+00:03:27,670 --> 00:03:32,470
+zero مافيش فيه الا العنصر الصفري ال principle ولا
+
+30
+00:03:32,470 --> 00:03:41,730
+لا صح؟ يبقى هذا بده يعطينا ان ال I isa principal
+
+31
+00:03:41,730 --> 00:03:51,750
+ideal لو ماكنش بالزيرو يبقى بداجي اقوله if ال
+
+32
+00:03:51,750 --> 00:04:02,530
+ideal I كان لا يساوي زيرو انتقل في طريقة اني اخد
+
+33
+00:04:02,530 --> 00:04:12,230
+polynomial Geo of X موجودة في I such thatبحيث ان
+
+34
+00:04:12,230 --> 00:04:21,730
+الـG of X is of minimum degree
+
+35
+00:04:21,730 --> 00:04:25,570
+in
+
+36
+00:04:25,570 --> 00:04:31,710
+I ايش قصدك تقولي عنه بالظبط؟ نفهم العبارة يعني
+
+37
+00:04:31,710 --> 00:04:39,590
+يبقى أنا أخدت polynomial موجودة في الـID الـIطبعا
+
+38
+00:04:39,590 --> 00:04:44,750
+في polynomial كتير لإنه لا يسوى ال zero تمام؟ يبقى
+
+39
+00:04:44,750 --> 00:04:50,390
+أخدت واحدة منهم بشرط ان يكون درجة هذه ال
+
+40
+00:04:50,390 --> 00:04:56,010
+polynomial هي أقل درجة ل polynomial موجودة في ال
+
+41
+00:04:56,010 --> 00:05:02,730
+ID ال I يعني لو ال I أقل درجة فيهي الدرجة التالتة
+
+42
+00:05:02,730 --> 00:05:08,130
+مثلا يبقى ال Ge of X من الدرجة التالتةلو كان أقل
+
+43
+00:05:08,130 --> 00:05:14,950
+هي الدرجة التانية يبقى ال polynomial هذي من الدرجة
+
+44
+00:05:14,950 --> 00:05:20,310
+الثانية و هكذا هي المقصود فيها يبقى أخدنها GeoVec
+
+45
+00:05:20,310 --> 00:05:26,590
+هو عنصر موجود في ال I بحيث ال GeoVec of minimum
+
+46
+00:05:26,590 --> 00:05:32,970
+degree in I أقل درجة موجودة ليه؟ موجودة ليه
+
+47
+00:05:32,970 --> 00:05:40,870
+polynomial في ال ideal I؟الحين دي كل .. كل .. كل
+
+48
+00:05:40,870 --> 00:05:47,550
+حاجة بشغلها ، كل شغلة بشغلها. الان أنا أدعي ان ال
+
+49
+00:05:47,550 --> 00:05:52,450
+ideal اللي أخدتها هى هو ال principle، ال ideal
+
+50
+00:05:52,450 --> 00:05:54,430
+generated by Geovics.
+
+51
+00:05:56,550 --> 00:06:02,200
+انا أدعيإن ال ideal I هو ال principle ideal
+
+52
+00:06:02,200 --> 00:06:06,260
+generated by اللي أخدتها minimum degree اللي بتسأل
+
+53
+00:06:06,260 --> 00:06:11,260
+عنها يبقى مش أخدتها بالبلاش لأ أخدتها لهدف بالديام
+
+54
+00:06:11,260 --> 00:06:23,440
+تمام؟ we shall show that بدنا نبين إن ال ideal I
+
+55
+00:06:23,440 --> 00:06:27,840
+هو ال principle ideal generated by ال Geographic
+
+56
+00:06:28,970 --> 00:06:35,350
+إذا قدرنا نثبت صحة هذا الكلام بيكون تمام تماما طيب
+
+57
+00:06:35,350 --> 00:06:42,030
+كويس بدي أجي أقوله let ال F of X موجودة في ال
+
+58
+00:06:42,030 --> 00:06:49,090
+ideal I إذا قدرت أثبت أن ال F of X موجودة هنا بصير
+
+59
+00:06:49,090 --> 00:06:53,410
+ال I subset من ال principle ideal generated by G
+
+60
+00:06:53,410 --> 00:06:59,560
+of X عملت العكس بيحدثي التساوي اللي أنا قاعدبدور
+
+61
+00:06:59,560 --> 00:07:05,460
+عليه وبالتالي ان حدث ذلك بيصير اي Ideal عبارة عن
+
+62
+00:07:05,460 --> 00:07:10,560
+ال principle لأن يساوي zero طالع موجود في I تمام؟
+
+63
+00:07:10,560 --> 00:07:13,440
+لا يساوي zero بدنا نشوف وين بدنا نتوجه معاها
+
+64
+00:07:13,440 --> 00:07:19,480
+الدنيا تمام؟ يبقى بدي احاول اثبت ان ال ideal I هو
+
+65
+00:07:19,480 --> 00:07:24,060
+ال principle ideal generated by geofix حيث ال
+
+66
+00:07:24,060 --> 00:07:30,970
+geofix هيأصغر درجة لقلنوميل او اصغر درجة موجودة في
+
+67
+00:07:30,970 --> 00:07:36,170
+ال I دي ال I بقولك وين خد ال F of X موجودة في ال I
+
+68
+00:07:36,170 --> 00:07:42,850
+اذا بقدر بال division algorithm اكتب F of X بدلالة
+
+69
+00:07:42,850 --> 00:07:53,290
+100 T of X يبقى هنا then by division algorithm
+
+70
+00:07:57,610 --> 00:08:02,470
+we have ان
+
+71
+00:08:02,470 --> 00:08:14,150
+ال F of X بدها تسمى جي جي of X فالي Q of X زائد ال
+
+72
+00:08:14,150 --> 00:08:26,370
+R of X و حيث ال R of X ممكن تكون ب Zero اوالدرجة
+
+73
+00:08:26,370 --> 00:08:34,490
+تبع ال R of X أقل من الدرجة تبع ال G of X بس هو
+
+74
+00:08:34,490 --> 00:08:41,030
+أقل إيش؟ صحيح بس G of X أقل إيش؟ كيف؟ G of X أقل
+
+75
+00:08:41,030 --> 00:08:46,450
+درجة محروفش يقول Minimum degree؟ أقل شرقين من
+
+76
+00:08:46,450 --> 00:08:51,210
+الأول يعني ال F of X أعلى في الدرجة من مين؟من G of
+
+77
+00:08:51,210 --> 00:08:56,130
+X لأنه أنا ماخد G of X of minimum degree in I
+
+78
+00:08:56,130 --> 00:09:01,710
+واخدت ال F of X موجودة في I يبقى أقل ما فينا تكون
+
+79
+00:09:01,710 --> 00:09:05,770
+جدها في الدرجة صح ولا لأ؟ يبقى لو كانت جدها في
+
+80
+00:09:05,770 --> 00:09:09,650
+الدرجة يبقى صير ال remainder ب zero و بصير حاصر
+
+81
+00:09:09,650 --> 00:09:15,810
+الدرجة فده هو اللي بتسوي ال F of X ما علينا يبقى
+
+82
+00:09:15,810 --> 00:09:19,930
+انا كتبتها بال division algorithmحيث R of X يسوي
+
+83
+00:09:19,930 --> 00:09:28,070
+Zero أو درجة R of X أقل من درجة G of X تمام؟ طيب،
+
+84
+00:09:28,070 --> 00:09:33,210
+ماشي الحال، تعالوا نشوف بتخلي الـR of X في ناحية و
+
+85
+00:09:33,210 --> 00:09:38,610
+باقى المعادلة في ناحية ثانية يبقى بناء عليه الـR
+
+86
+00:09:38,610 --> 00:09:46,120
+of X بدي ساوي الـF of X ماقص الـG of Xمضروبة في ال
+
+87
+00:09:46,120 --> 00:09:51,440
+Geo-Vecs السؤال هو كل واحد بيقدر يسوي الشغل هذه
+
+88
+00:09:51,440 --> 00:09:59,460
+هذه موجودة في ال ideal I على فرض ايه هذه موجودة في
+
+89
+00:09:59,460 --> 00:10:05,960
+ال ideal I لإن ال Geo-Vecs موجودة في I و ال I is
+
+90
+00:10:05,960 --> 00:10:10,220
+an idealيبقى الـG of X مضروبة في أي Paranomial
+
+91
+00:10:10,220 --> 00:10:14,480
+أخرى إذا كانت موجودة في الـI دي الـI يبقى هذا
+
+92
+00:10:14,480 --> 00:10:23,500
+موجود في الـI دي الـI السبب because إن الـF of X
+
+93
+00:10:23,500 --> 00:10:34,160
+موجودة في I والـG of X موجودة في I and الـI is an
+
+94
+00:10:34,160 --> 00:10:49,920
+idealالنفجة صار اللي هو R of X موجودة في I طيب
+
+95
+00:10:49,920 --> 00:10:57,580
+احنا اقل درجة في I كانت قدش الـG الهذا درجته اقل
+
+96
+00:10:57,580 --> 00:11:02,040
+من الـG يا اما R of X بدى يساوي Zero ايش
+
+97
+00:11:02,040 --> 00:11:03,180
+بتستنتجوا؟
+
+98
+00:11:05,310 --> 00:11:11,310
+الـ R of X تساوي Zero لأن الـ G of X هي أقل درجة
+
+99
+00:11:11,310 --> 00:11:18,170
+موجودة في I يبقى هذا بدّي يعطينا ان الـ R of X
+
+100
+00:11:18,170 --> 00:11:28,370
+بتساوي Zero السبب because ان الـ G of X is of
+
+101
+00:11:28,370 --> 00:11:38,830
+minimum degree in Iطبعا يبقى ال R of X سوى Zero.
+
+102
+00:11:39,130 --> 00:11:47,610
+إيه صار عندك؟ فال F of X بتسوى ال G of X مضروبة في
+
+103
+00:11:47,610 --> 00:11:53,170
+ال Q of X. هذا العنصر موجود في ال principle؟
+
+104
+00:11:53,170 --> 00:12:00,170
+Generated by Q of X صح؟ يبقى هذا موجود في ال
+
+105
+00:12:00,170 --> 00:12:06,960
+principle ideal generated by G of X.هذا معناته
+
+106
+00:12:06,960 --> 00:12:13,020
+يبقى أنا أخدت ال F of X موجود في I طلع عندي ال F
+
+107
+00:12:13,020 --> 00:12:17,900
+of X موجود في ال principle يبقى هذا يعطينا ان ال
+
+108
+00:12:17,900 --> 00:12:23,820
+ID ال I صابست من مين من ال principle ID generated
+
+109
+00:12:23,820 --> 00:12:31,760
+by X وخليلي هذه المعادلة رقم واحد الآن بدأ امشي
+
+110
+00:12:31,760 --> 00:12:40,050
+للاتجاه الثانيthe other hand من الناحية الأخرى
+
+111
+00:12:40,050 --> 00:12:47,170
+خوديلي ال F of X موجودة في ال principle ideal
+
+112
+00:12:47,170 --> 00:12:57,850
+generated by G of X then ال F of X بدها تساوي ال G
+
+113
+00:12:57,850 --> 00:13:04,810
+of X في function تانية و ليكن مثلا ال Eq of Xfor
+
+114
+00:13:04,810 --> 00:13:16,050
+some Q of X اللي موجودة في مين؟ في capital F of X
+
+115
+00:13:16,050 --> 00:13:19,370
+تمام
+
+116
+00:13:19,370 --> 00:13:27,990
+طيب هذا معناته ال G of X موجود في I ال G of X وهذه
+
+117
+00:13:27,990 --> 00:13:34,890
+Q of X تماميبقى ال F of X مضروبة في G of X في ال Q
+
+118
+00:13:34,890 --> 00:13:39,730
+ال Q of X موجودة وين؟ في I يبقى هذه كلها حصلت ضرب
+
+119
+00:13:39,730 --> 00:13:48,190
+وين موجودة؟ موجودة في I يبقى هنا فال F of X موجود
+
+120
+00:13:48,190 --> 00:13:57,450
+في ال I اسسبب because ان ال G of X موجودة في I and
+
+121
+00:13:57,450 --> 00:14:07,020
+ال I isan ideal is an ideal يبقى بناءً عليه so
+
+122
+00:14:07,020 --> 00:14:12,000
+بدأنا بماذا؟ بدأنا بالprinciple اللي وجدته موجود
+
+123
+00:14:12,000 --> 00:14:17,480
+في I يبقى ال principle ideal generated by g of x
+
+124
+00:14:17,480 --> 00:14:23,800
+صابست من مين؟ من ال I وهذه العلاقة رقم اتنين يبقى
+
+125
+00:14:23,800 --> 00:14:33,120
+بالي بقوله from واحد and اتنينwe have ان ال I هذا
+
+126
+00:14:33,120 --> 00:14:38,900
+هو ال principle ideal generated by g of x يبقاش
+
+127
+00:14:38,900 --> 00:14:46,000
+استنتجنة استنتجنة ان any ideal في capital F of X
+
+128
+00:14:46,000 --> 00:14:53,500
+is a principle ideal صحيح ولا لأ يبقى this means
+
+129
+00:14:53,500 --> 00:15:09,190
+that هذا يعني انAny ideal I in capital F of X is
+
+130
+00:15:09,190 --> 00:15:14,410
+principal يبقى
+
+131
+00:15:14,410 --> 00:15:24,290
+ساعة capital F of X is a principal ideal
+
+132
+00:15:24,290 --> 00:15:24,890
+domain
+
+133
+00:15:30,760 --> 00:15:35,940
+هو المفروض اقول الفكرة مرة تانية لامهالكم مع بعض
+
+134
+00:15:35,940 --> 00:15:40,780
+عشان ترسخ المعلومة عادي عندنا if field بيقول ليه
+
+135
+00:15:40,780 --> 00:15:44,980
+capital F of X هو principal ideal domain يعني كل
+
+136
+00:15:44,980 --> 00:15:49,620
+ideal فيه بيكون principal ideal بيقول لك واحد
+
+137
+00:15:49,620 --> 00:15:54,620
+اخدنا if field يبقى هنا integral domain بأول نظرية
+
+138
+00:15:54,620 --> 00:15:58,220
+في هذا ال chapter capital F of X is an integral
+
+139
+00:15:58,220 --> 00:16:02,410
+domainهذه النقطة الأولى، نقطة تانية أخدنا ID
+
+140
+00:16:02,410 --> 00:16:07,390
+الموجود في capital F of X والله إذا كان هذا هو
+
+141
+00:16:07,390 --> 00:16:13,230
+Zero مافي إلا Zero element يبقى هذا يتولد بواسطة
+
+142
+00:16:13,230 --> 00:16:17,990
+ال Zero يبقى ال ID ال principle ID إذا والله لا
+
+143
+00:16:17,990 --> 00:16:22,570
+يساوي Zero روحت على ال ID ال I اللي مليان Pronomic
+
+144
+00:16:22,570 --> 00:16:27,770
+الخان أصغر واحدة من ال functions من ناحية ال
+
+145
+00:16:27,770 --> 00:16:31,750
+degreeالـ polynomial اللي ال degree تبعتها أصغر
+
+146
+00:16:31,750 --> 00:16:36,730
+واحدة في كل ال polynomials اللي موجودة في I و روحت
+
+147
+00:16:36,730 --> 00:16:41,550
+زعمت ان ال I هذا بدي يسوي ال principle ideal
+
+148
+00:16:41,550 --> 00:16:47,210
+generated by Jehovah أمشي خطوات أثبت هذا الكلام
+
+149
+00:16:47,210 --> 00:16:55,270
+فعلا إذا صار ال non zero ideal هو عبارة عن
+
+150
+00:16:55,270 --> 00:16:59,770
+principle ideal يعني اي non zeroواللي جابله حتى لو
+
+151
+00:16:59,770 --> 00:17:04,310
+كان Zero كمان Principle يبقى أي Ideal في capital F
+
+152
+00:17:04,310 --> 00:17:09,770
+of X هو عبارة عن Principle Ideal Domain يبقى
+
+153
+00:17:09,770 --> 00:17:14,510
+Principle Ideal يبقى Capital F of X is a Principle
+
+154
+00:17:14,510 --> 00:17:20,910
+Ideal Domain تمام؟ طيب، في عنا كمان نظرية تانية
+
+155
+00:17:20,910 --> 00:17:26,920
+متعلقة بيها ومرتبطة بيها تمام؟ حد بتسأل؟مش ممكن
+
+156
+00:17:26,920 --> 00:17:31,620
+أنه أقل درجة لـ GeoVex؟ أه GeoVex كيف GeoVex
+
+157
+00:17:31,620 --> 00:17:37,420
+موجودة في ال ID؟ كيف؟ كيف GeoVex موجودة في ال ID؟
+
+158
+00:17:37,420 --> 00:17:42,400
+ال GeoVex كنت قولت هي ال remainder، وصلنا إلى
+
+159
+00:17:42,400 --> 00:17:48,040
+المعادلة هذه، شايفها؟ هذا فرق بين تولوز، ال ID
+
+160
+00:17:48,040 --> 00:17:52,770
+أصلا subringلو أخدت two elements في ال sub ring و
+
+161
+00:17:52,770 --> 00:17:56,270
+جبت الفرق بينهم موجود في ال sub ring يعني موجود في
+
+162
+00:17:56,270 --> 00:18:02,430
+ال ideal صح أو لا لأ يبقى هذا هذا هذي فرضه في I
+
+163
+00:18:02,430 --> 00:18:09,450
+اتنين ال Geo fix موجود في I و ال I ideal other بأي
+
+164
+00:18:09,450 --> 00:18:13,490
+element من ال ideal لأي element من ال ring موجود
+
+165
+00:18:13,490 --> 00:18:16,950
+في ال ideal مش هذا هو الشرط الأخير من شروط ال
+
+166
+00:18:16,950 --> 00:18:21,050
+idealأه طيب لو ما نجلتش أنا على طرف التاني لو إيش؟
+
+167
+00:18:21,050 --> 00:18:25,970
+يعني لو مااخدتش RX فى طرف الحال مش ال GX لو إيش
+
+168
+00:18:25,970 --> 00:18:31,050
+عيدي تاني؟ لو مااخدتش ال RX فى طرف الحال طيب مش ال
+
+169
+00:18:31,050 --> 00:18:35,690
+GX هي أقل الدرجة؟ ممتاز يعني مافيش أقل منها طيب
+
+170
+00:18:35,690 --> 00:18:40,670
+ماشي شو المشكلة؟ طب حنا سوينا غير هي كان؟ لأ كيف
+
+171
+00:18:40,670 --> 00:18:48,230
+موجودة فى ال I؟هذه polynomial في ال I الفرق بينهم
+
+172
+00:18:48,230 --> 00:18:51,990
+موجود في ال I ولا لا؟ لو مش موجود في ال I، عمره ما
+
+173
+00:18:51,990 --> 00:19:00,810
+كان لا Ideal ولا Subring، مظبوط؟ يا أختي إيه يا
+
+174
+00:19:00,810 --> 00:19:03,950
+حميدة، بتقولي كيف؟ موجود في ال I، صح ولا لا؟ هي
+
+175
+00:19:03,950 --> 00:19:08,350
+سؤالك، إحنا بنقول لما عرفنا ال Subring، ثم روحنا
+
+176
+00:19:08,350 --> 00:19:13,670
+عرفنا اللي هو ال Idealإحدى الشروط إنه لو أخدت two
+
+177
+00:19:13,670 --> 00:19:17,270
+elements من ال ID اللي يبقى الفرق بينهما موجود في
+
+178
+00:19:17,270 --> 00:19:22,550
+ال ID، صحيح ولا لأ؟ طيب، روحنا عند المعادلات،
+
+179
+00:19:22,550 --> 00:19:26,270
+خلّينا ال aerobics في شكل والباقي في ناحيتان،
+
+180
+00:19:26,270 --> 00:19:32,070
+مظبوط؟ هذه ال aerobics هي موجودة في I، وهذه موجودة
+
+181
+00:19:32,070 --> 00:19:35,930
+في I، إذا الفرق بينهما موجود في I، صحيح؟ هو لو
+
+182
+00:19:35,930 --> 00:19:41,020
+فسرت لك ليه؟الـ F of X في I والـ G في I والـ I اي
+
+183
+00:19:41,020 --> 00:19:44,440
+دي يعني لما نقضر الـ G of X في اي Polynomial أخرى،
+
+184
+00:19:44,440 --> 00:19:48,900
+فهو موجود في الـ I، صحيح ولا لا؟ يبقى صار تلقى الـ
+
+185
+00:19:48,900 --> 00:19:53,700
+R of X في الـ I ولا لا؟ طيب، نجي الـ R of X، مشان
+
+186
+00:19:53,700 --> 00:19:57,140
+تبقى في I، بد ال degree تبعها تكون أقل من ال
+
+187
+00:19:57,140 --> 00:20:00,880
+degree of G، إن لم يحدث فالـ R of X بـ Zero
+
+188
+00:20:04,000 --> 00:20:08,020
+أو ال degree لل R أقل من ال degree لل G، صحيح ولا
+
+189
+00:20:08,020 --> 00:20:12,600
+لأ؟ طيب ال degree لل R ليست أقل من ال degree لأن
+
+190
+00:20:12,600 --> 00:20:17,640
+ال G هي ال minimum، تبقى إيش ضال عندي؟ R of X بده
+
+191
+00:20:17,640 --> 00:20:21,580
+يساوي 0، صح ولا لأ؟ مالهاش درجة ال R بيقوم وصحيح؟
+
+192
+00:20:21,580 --> 00:20:24,320
+مالهاش درجة، مش الاقتران الصفر؟ اللي هو مين؟ ال R
+
+193
+00:20:24,320 --> 00:20:28,480
+X بيساوي صفر؟ ماشي، صحيح، معاكي، لكن إحنا بنقول
+
+194
+00:20:28,480 --> 00:20:33,160
+أحد يحتمل أن هي إما هذا أو هذا،هذا سقط لأن Geomext
+
+195
+00:20:33,160 --> 00:20:41,300
+أقل درجة موجودة ايه المشروط اللي عندي Geomext أقل
+
+196
+00:20:41,300 --> 00:20:47,360
+درجة موجودة ايه المشروط اللي عندي Geomext أقل درجة
+
+197
+00:20:47,360 --> 00:20:51,080
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+198
+00:20:51,080 --> 00:20:54,260
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+199
+00:20:54,260 --> 00:20:56,160
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+200
+00:20:56,160 --> 00:20:57,900
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+201
+00:20:57,900 --> 00:20:57,900
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+202
+00:20:57,900 --> 00:20:58,880
+موجودة Geomext أقل درجة موجودة Geomext أقل درجة
+
+203
+00:20:58,880 --> 00:21:02,490
+موجودة Geإذا أصبح ال F of X موجود في الprinciple
+
+204
+00:21:02,490 --> 00:21:08,930
+يبدأ يبقى subset of I subset of B طيب النضرية
+
+205
+00:21:08,930 --> 00:21:16,870
+الثانية بتقول ما يأتي تغيرها بيقول
+
+206
+00:21:16,870 --> 00:21:22,210
+ان انت ال FBA field زي النضرية اللي قبلها FBA
+
+207
+00:21:22,210 --> 00:21:41,370
+field وال Ian ideal of capital F of X and
+
+208
+00:21:41,370 --> 00:21:53,050
+g of x an element of
+
+209
+00:21:53,050 --> 00:22:05,090
+capital F of Xthen ال I هي ال principle ideal
+
+210
+00:22:05,090 --> 00:22:13,750
+generated by G of X if and only if ال G of X is a
+
+211
+00:22:13,750 --> 00:22:23,910
+non-zero polynomial is a non-zero polynomial
+
+212
+00:22:27,080 --> 00:22:38,920
+non-zero polynomial of minimum degree
+
+213
+00:22:38,920 --> 00:22:50,120
+minimum degree in R of اللي
+
+214
+00:22:50,120 --> 00:22:54,100
+هو دفعه
+
+215
+00:22:56,490 --> 00:23:03,110
+as similar to
+
+216
+00:23:03,110 --> 00:23:08,530
+the role
+
+217
+00:23:08,530 --> 00:23:16,690
+of the above hero
+
+218
+00:23:30,820 --> 00:23:36,700
+نفس البرنامج أخدنا G أنه one zero element of
+
+219
+00:23:36,700 --> 00:23:40,960
+minimum degree يبقى من النظرية اللي قبلها أثبتنا
+
+220
+00:23:40,960 --> 00:23:48,800
+أنه يساوي I إلى نفس القصة برضه بده يساوي I إذا كرق
+
+221
+00:23:48,800 --> 00:23:54,140
+ال G of minimum نعطي سؤال أو مثال تنضيحي على ذلك
+
+222
+00:23:54,140 --> 00:23:54,780
+example
+
+223
+00:23:59,940 --> 00:24:11,060
+بقول let Phi من الـ A of X onto a set of complex
+
+224
+00:24:11,060 --> 00:24:17,140
+numbers C given
+
+225
+00:24:17,140 --> 00:24:31,080
+by .. given by اللي هو Phi من الـ F of Xبدا تساوي
+
+226
+00:24:31,080 --> 00:24:42,500
+F of I بـ Homomorphism هذا يعطيني Homomorphism
+
+227
+00:24:42,500 --> 00:24:55,220
+المطلوب الأول شهو ذات بيجيلي شهو ذات ان ال X تربيع
+
+228
+00:24:55,220 --> 00:25:02,740
+زائد الواحدموجود للكيرنال للـ Phi الامر يبين show
+
+229
+00:25:02,740 --> 00:25:15,780
+that .. show that بيّن كذلك إن ال R of X موديلو لـ
+
+230
+00:25:15,780 --> 00:25:20,960
+principle ideal generated by X ترمية زاد واحد
+
+231
+00:25:20,960 --> 00:25:29,750
+isomorphic لل set of complex numbers اللي هو Cمرة
+
+232
+00:25:29,750 --> 00:25:36,970
+تانية عندنا في هموموفيزم من ال R of X إلى ال 6 of
+
+233
+00:25:36,970 --> 00:25:41,410
+complex number مُعطَى بالفي لما تأثر عليه ال
+
+234
+00:25:41,410 --> 00:25:46,370
+polynomial اللي موجودة في R of X بدي يعطينا F of I
+
+235
+00:25:46,370 --> 00:25:52,190
+يعني complex number عدد موجود في C المطموب الأول
+
+236
+00:25:52,190 --> 00:25:56,860
+جاني اثبت ان ال functionأو البرنامج ال X تربية
+
+237
+00:25:56,860 --> 00:26:01,780
+زائد واحد موجودة في ال kernel يقول والله إذا
+
+238
+00:26:01,780 --> 00:26:06,220
+صورتها طلعت ب zero يبقى موجودة في ال kernel ما
+
+239
+00:26:06,220 --> 00:26:10,060
+طلعت ب zero يبقى مش موجودة في ال kernel يبقى عين
+
+240
+00:26:10,060 --> 00:26:17,380
+مقتلولة طيب بشأن هيك بداجة أقوله افترض ان ال F of
+
+241
+00:26:17,380 --> 00:26:21,580
+X بدي سوى ال X تربية زائد واحد then
+
+242
+00:26:23,670 --> 00:26:30,410
+بدي أخد ال F of I كده بده ثالث I ترمية زايد واحد
+
+243
+00:26:30,410 --> 00:26:37,790
+كده I ترمية ثالث واحد يبقى ثالث واحد زايد واحد
+
+244
+00:26:37,790 --> 00:26:46,470
+يسوى كده؟ Zero طب ال F of I مش هي صورة F of X يبقى
+
+245
+00:26:46,470 --> 00:26:55,890
+هنا ال F of I هي Phi لل F of Xيبدو يساوي Zero هذا
+
+246
+00:26:55,890 --> 00:27:02,850
+معناه ان ال F of X يعني X تربيه زائد واحد موجودة
+
+247
+00:27:02,850 --> 00:27:08,370
+للكامل للفاتر خلصنا
+
+248
+00:27:08,370 --> 00:27:14,870
+المطبوخ الأول فهذا المطبوخ التالي نمر هذه بدنا
+
+249
+00:27:14,870 --> 00:27:22,070
+نثبت ان ال R of X Modulo ال X تربيه زائد واحد
+
+250
+00:27:22,370 --> 00:27:29,730
+Isomorphic لمن؟ لـ set of complex numbers تمام طيب
+
+251
+00:27:29,730 --> 00:27:34,710
+مش هنطول كتير مش هروح أعرف function one to one و
+
+252
+00:27:34,710 --> 00:27:40,450
+one to one لأ لأ بدي أاخد جاهز تمام طيب كيف ناخد
+
+253
+00:27:40,450 --> 00:27:45,950
+جاهز؟ اللي بيبين ليه انه هات ال first isomorphism
+
+254
+00:27:45,950 --> 00:27:51,070
+theorem بيقول الارو بيرس موديولون كيرنيت طيب سؤال
+
+255
+00:27:51,600 --> 00:28:00,180
+هذا ال X تربيه زائد واحد موجود في ال kernel موجودة
+
+256
+00:28:00,180 --> 00:28:07,340
+في ال kernel تمام انا ادعي ان ال kernel لل FI هو
+
+257
+00:28:07,340 --> 00:28:11,320
+عبارة عن ال X principal ID generated by X تربيه
+
+258
+00:28:11,320 --> 00:28:16,500
+زائد واحد هم بيقولك هذا الكلام تعالوا نشوفه نجيبه
+
+259
+00:28:16,500 --> 00:28:20,610
+لنا خليني أقولكوا هنا بقىأحنا عندنا الآن ال X
+
+260
+00:28:20,610 --> 00:28:27,290
+تربيها زي الواحد موجودة في الكيرنر طيب سؤال هل
+
+261
+00:28:27,290 --> 00:28:32,610
+هناك polynomial أصغر من ال polynomial هذه في
+
+262
+00:28:32,610 --> 00:28:39,450
+الدرجة الموجودة في الكيرنر؟ تقدر تجيبولي بس واحدة؟
+
+263
+00:28:39,450 --> 00:28:45,330
+مش إمكانية لأنه لما تيجي تعوض ب F of I ليمكن أن
+
+264
+00:28:45,330 --> 00:28:52,210
+تطلع Zero تمام؟يبقى لو جيت قلت له الامر لو أخدت ال
+
+265
+00:28:52,210 --> 00:29:02,450
+G of X يساوي ال A X زائد B وروحت قلت خذي ال G of I
+
+266
+00:29:02,450 --> 00:29:10,830
+يبقى بده يساوي A I زائد B هذه ممكن تساوي Zero؟ لأ
+
+267
+00:29:11,100 --> 00:29:16,020
+لكن لو قلت a و b ب0 يصير 0 يبقى انت مااخدتش ولا
+
+268
+00:29:16,020 --> 00:29:19,500
+حاجة اخدت معناه في الصفر وجهة تضحك علينا لا احنا
+
+269
+00:29:19,500 --> 00:29:25,180
+بدنا polynomial in general يبقى هذه does not
+
+270
+00:29:25,180 --> 00:29:30,180
+belong لprinciple ideal generated by X تربية زائد
+
+271
+00:29:30,180 --> 00:29:35,640
+واحد بمعناته ال X تربية هي ال polynomial of
+
+272
+00:29:35,640 --> 00:29:43,750
+minimum degree in I يبقى هنا ساعةالـ F of X يساوي
+
+273
+00:29:43,750 --> 00:29:57,910
+X تربية زائد واحد is .. is a polynomial of
+
+274
+00:29:57,910 --> 00:30:07,710
+minimum degree in the principle ideal generated by
+
+275
+00:30:07,710 --> 00:30:13,980
+X تربية زائد واحد، هذه أصغر واحدةطب اطلعيلي طب
+
+276
+00:30:13,980 --> 00:30:20,960
+اطلعيلي على نص النظرية رقم اتنين بيقولش اذا g of x
+
+277
+00:30:20,960 --> 00:30:26,400
+non zero polynomial of minimum degree يبدو ال I
+
+278
+00:30:26,400 --> 00:30:34,460
+بدو يساوي مين؟ بدو يساوي ال g of x يبقى by the
+
+279
+00:30:34,460 --> 00:30:36,160
+above
+
+280
+00:30:39,880 --> 00:30:49,100
+Any Ideal I Any Ideal I بده يساوي ال principle
+
+281
+00:30:49,100 --> 00:30:58,260
+Ideal generated by X³±1 طيب
+
+282
+00:30:58,260 --> 00:31:05,760
+السؤال هل الكيرنل الفي هو Ideal؟ صح ولا لا؟ يبقى
+
+283
+00:31:05,760 --> 00:31:10,030
+الكيرنل بديه يساوي مين؟ بديه يساوي هذهيبقى باري
+
+284
+00:31:10,030 --> 00:31:20,370
+بيقوله since بما أن ال kernel للفاي is an ideal R
+
+285
+00:31:20,370 --> 00:31:31,630
+اللي هو capital R of X we have من الاتنين هدول
+
+286
+00:31:31,630 --> 00:31:36,760
+يبقى ال kernel للفايبدي يساوي ال principle ideal
+
+287
+00:31:36,760 --> 00:31:43,120
+generated by X تربية زايد واحد صح؟ سكتش يا عزيزي
+
+288
+00:31:43,120 --> 00:31:52,420
+أي ideal على الشكل هذا مظبوط؟ يبقى أي ideal موجود
+
+289
+00:31:52,420 --> 00:31:57,420
+على الشكل هذا ال kernel لل Phi أثبتناه قبل ذلك أنه
+
+290
+00:31:57,420 --> 00:32:01,820
+ideal صح ولا لا؟ إذا ال kernel على الشكل اللي
+
+291
+00:32:01,820 --> 00:32:06,490
+عندنا هذا بدي يساوي هذاطب ماذا أستفيد من ذلك؟
+
+292
+00:32:06,490 --> 00:32:12,350
+بقوله R by the
+
+293
+00:32:12,350 --> 00:32:18,070
+first isomorphism
+
+294
+00:32:18,070 --> 00:32:29,870
+theorem we have ان ال R of X modulo ال L كيرنل لل
+
+295
+00:32:29,870 --> 00:32:40,410
+Phi isomorphicللـ Phi of R of X يداشى الـ Phi للـ
+
+296
+00:32:40,410 --> 00:32:47,950
+R of X؟ C لإنها on two تمام يبقى هذه بدها ساوي C
+
+297
+00:32:47,950 --> 00:32:58,090
+since Phi is on two فهي هذه صارت مين؟ الـ R of X
+
+298
+00:32:58,790 --> 00:33:03,550
+موديله ال kernel هو ال principle ID ال generated
+
+299
+00:33:03,550 --> 00:33:09,830
+by one يبقى هذا isomorphic لمين؟ لـC عظيم هو
+
+300
+00:33:09,830 --> 00:33:15,590
+المطلوب؟ و هو المطلوب خلاصه حد فيكوا بتسأل أي سؤال
+
+301
+00:33:15,590 --> 00:33:20,990
+هنا؟ ايوة احنا اتفكنا انه مش درجة اقل من اكتر برد
+
+302
+00:33:20,990 --> 00:33:26,690
+واحد ممكن تساوي سفر صح؟ تكون في ال IDيعني الـ X
+
+303
+00:33:26,690 --> 00:33:29,710
+تربية زاد واحد، الدرجة التانية هي أقل الـ
+
+304
+00:33:29,710 --> 00:33:34,970
+polynomial موجودة في هذا الـ ID الـ I دي الـ I
+
+305
+00:33:34,970 --> 00:33:37,590
+اللي هو بدنا نثبت إنه بساوي الكيرنات
+
+306
+00:33:45,200 --> 00:33:50,620
+لأيش؟ لأن ال X تربية زاد واحد أقل degree حققت F of
+
+307
+00:33:50,620 --> 00:33:53,700
+Y سوى Zero بس مش موجودة في ال ID ولا مش موجودة في
+
+308
+00:33:53,700 --> 00:33:59,560
+ال Kernel؟ مش موجودة في ال Kernel طيب ما احنا ال
+
+309
+00:33:59,560 --> 00:34:03,080
+Kernel هتتفنى .. بس احنا بالأسل أول يعني بس ..
+
+310
+00:34:03,080 --> 00:34:08,580
+احنا قلنا هذا هاي اللي أخد G of X سوى هذا G of Y
+
+311
+00:34:08,580 --> 00:34:14,880
+سوى كذا مش موجود في ال X يعني لا يحقق هذه المعادلة
+
+312
+00:34:15,580 --> 00:34:20,480
+وبعد شوية بصير هذا مش موجود في ال I لإن ال I هي ال
+
+313
+00:34:20,480 --> 00:34:24,900
+kernel هي ال principle ideal generated by X تربية
+
+314
+00:34:24,900 --> 00:34:30,160
+زاد واحد هي هي يعني هذه كمان ولا يهمك تقول it does
+
+315
+00:34:30,160 --> 00:34:36,200
+not belong to I برضه موافق هذه و هذه التنتين صح
+
+316
+00:34:36,200 --> 00:34:40,700
+لإن بعد شوية أثبت لك أن هذا هو هذا سواء هذا والله
+
+317
+00:34:40,700 --> 00:34:47,670
+هذا سيئة في أي استفسار أخرطيب، لأت الآن لحل بعض
+
+318
+00:34:47,670 --> 00:34:56,110
+الأسئلة خلاص
+
+319
+00:34:56,110 --> 00:35:01,770
+الشفتة فسي
+
+320
+00:35:01,770 --> 00:35:07,860
+الجبر تلاقي النظر يحبي معروفانوالأسئلة فيها
+
+321
+00:35:07,860 --> 00:35:15,160
+معلومات برضه كتيرة وكأنها جديدة أحيانا. يبقى بنيدي
+
+322
+00:35:15,160 --> 00:35:24,560
+على شبتر ستاشر. فشبتر ستاشر بلد اللي هو الأسئلة
+
+323
+00:35:24,560 --> 00:35:30,640
+بتبعه. يبقى exercises على شبتر ستاشر.
+
+324
+00:35:40,760 --> 00:35:45,280
+السؤال الأول حلناه زيه السؤال التالت عرض مباشر
+
+325
+00:35:45,280 --> 00:35:51,140
+السؤال التالت حلناه شخصيا حلناه السؤال هذا بدنا
+
+326
+00:35:51,140 --> 00:35:59,020
+نروح للسؤال الغرق الغرق بيقول لي if ال a is
+
+327
+00:35:59,020 --> 00:36:09,200
+commutative commutative ring شو
+
+328
+00:36:09,200 --> 00:36:19,050
+دهshow that إن ال characteristics لل R of X بدأت
+
+329
+00:36:19,050 --> 00:36:35,530
+ساوى ال characteristics لمين لل R بحل
+
+330
+00:36:35,530 --> 00:36:41,420
+هذا السؤال نكون حلينا سؤال أربعةو السؤال تمانية و
+
+331
+00:36:41,420 --> 00:36:47,220
+احنا مش ذارين هم بنوريكم كيف نحلهم اتنين مرة واحدة
+
+332
+00:36:47,220 --> 00:36:54,140
+بسؤال اربع بيقول لي لو فات ال R commutative يبقى
+
+333
+00:36:54,140 --> 00:36:59,060
+ال characteristic ل ال R هي نفس ال characteristic
+
+334
+00:36:59,060 --> 00:37:06,620
+لمين؟ R of X بنقول له تماني بدي اروح اجيب صوت ب
+
+335
+00:37:06,620 --> 00:37:11,640
+ring من مين؟من ال ring A من ال polynomial ring A
+
+336
+00:37:11,640 --> 00:37:22,300
+تمام ابادي بقوله ما يأتي led ال S بي the set of
+
+337
+00:37:22,300 --> 00:37:33,540
+all constant polynomials polynomials
+
+338
+00:37:33,540 --> 00:37:47,840
+ofR of X ذات X هذا كلام غريب ده أحطه في صيغة يهضيه
+
+339
+00:37:47,840 --> 00:37:54,540
+لما أحطه في صيغة يهضيه يتجلس كل ال polynomials
+
+340
+00:37:54,540 --> 00:38:03,280
+اللي هو F of X اللي موجودة في capital R of X بحيث
+
+341
+00:38:03,280 --> 00:38:14,390
+أنf of x بده يساوي a و ال a is constant عزيزي
+
+342
+00:38:14,390 --> 00:38:21,970
+شوفنا هذه السيطرة قبل هيك في الأسئلة قبل شترين و
+
+343
+00:38:21,970 --> 00:38:29,290
+أثبتنا إنها صابرين تمام؟ يبقى هذا بده يخلي هذي ي
+
+344
+00:38:29,290 --> 00:38:32,090
+check that
+
+345
+00:38:33,610 --> 00:38:42,530
+الـ S is a subring of
+
+346
+00:38:42,530 --> 00:38:55,530
+X تأكديلي أن هذه هي subring من الـ S تمام الآن سوف
+
+347
+00:38:55,530 --> 00:38:59,190
+أعرف الـ function Define
+
+348
+00:39:01,070 --> 00:39:06,950
+A function على A mapping Phi
+
+349
+00:39:06,950 --> 00:39:19,190
+من الـR للـS by Phi of ال element R يجب أن أضعه في
+
+350
+00:39:19,190 --> 00:39:26,750
+S يعني constant لأن كلهم constant و ليكن R لكل
+
+351
+00:39:26,750 --> 00:39:29,010
+الـR اللي موجودة في الـR
+
+352
+00:39:34,020 --> 00:39:40,640
+متعرف فانكشن فاي من R إلى S By Phi of R بيبقى ساوي
+
+353
+00:39:40,640 --> 00:39:46,380
+R ليش؟ لإن ال S العناصر اللي بيبقى F of X كلها
+
+354
+00:39:46,380 --> 00:39:52,580
+بيبقى ساوي constant مقدار ثابت يبقى المقدار ثابت
+
+355
+00:39:52,580 --> 00:39:57,720
+اللي هو R إلي عندنا إذا أثبت أن Phi هو
+
+356
+00:39:57,720 --> 00:40:02,830
+homomorphism هو one to oneوانتوا تصير في
+
+357
+00:40:02,830 --> 00:40:09,950
+isomorphism ما بين الاتنين سؤال هو واش استفدناه؟
+
+358
+00:40:09,950 --> 00:40:13,910
+يبقى نفس الخواصة الرياضية يعني ال characteristic
+
+359
+00:40:13,910 --> 00:40:20,610
+لل R بصير هو ال characteristic لمين؟ لل S اتنين زي
+
+360
+00:40:20,610 --> 00:40:25,370
+بعض و بعدين بيظل علينا خطوة بنعملها مش مشكلة طيب
+
+361
+00:40:25,810 --> 00:40:33,690
+يبقى بداخل اقول الـ Phi is homomorphic يبقى بداخل
+
+362
+00:40:33,690 --> 00:40:43,710
+Phi of R1 زائد R2 حسب التعريف R1 زائد R2 R1 هي Phi
+
+363
+00:40:43,710 --> 00:40:55,370
+of R1 والتانية Phi of R2 اللي بعدها and Phi of R1
+
+364
+00:40:55,830 --> 00:41:03,930
+R2 هذا الكلام يتساوي R1 R2 طبقا للـ definition الـ
+
+365
+00:41:03,930 --> 00:41:12,650
+R1 هي Phi of R1 و Phi of R2 هذا الكلام صحيح لكل
+
+366
+00:41:12,650 --> 00:41:19,330
+الـ R1 وR2 اللي موجود في الـ R وهذا صحيح لكل الـ
+
+367
+00:41:19,330 --> 00:41:24,770
+R1وR2 اللي موجود في الـR لذلك Phi is a
+
+368
+00:41:24,770 --> 00:41:32,670
+homomorphism Phi is one to one يمكن بالدرجة أقوله
+
+369
+00:41:32,670 --> 00:41:41,390
+افترض ان Phi of R1 بتساوي Phi of R2 عسب ال
+
+370
+00:41:41,390 --> 00:41:48,230
+definition Phi of R1 هي في R1 Phi of R2 هي في R2
+
+371
+00:41:48,470 --> 00:41:54,690
+يبقى أخد صوتين متساويتين لقيت أن أصلهم متساوي لذلك
+
+372
+00:41:54,690 --> 00:42:04,010
+five is one to one بعدين five is on يقعد ياخد
+
+373
+00:42:04,010 --> 00:42:15,210
+element وليكن وي موجود في اسم وي موجود في اسم يبقى
+
+374
+00:42:15,210 --> 00:42:24,190
+هذا بالدنيا قيمةإن Y تساوي مين؟ تساوي F of X اللي
+
+375
+00:42:24,190 --> 00:42:33,130
+هو constant وليكن A لأن عناصر S كله اللي هو دوال
+
+376
+00:42:33,130 --> 00:42:40,310
+ثوابت تمام أليس هذا هو I of A حسب ال definition
+
+377
+00:42:40,310 --> 00:42:48,690
+تمام يبقى Y اللي أخدته في S لجيتله أصلفي من؟ في ال
+
+378
+00:42:48,690 --> 00:42:54,730
+.. في R اللي هو من اللي هو إيه؟ يبقى Phi is under
+
+379
+00:42:54,730 --> 00:43:05,650
+يبقى هنا ف Phi is an isomorphism طيب إيش استفدنا
+
+380
+00:43:05,650 --> 00:43:15,080
+من ذلك؟ استفدنا إن ال characteristic لل-Rيساوي
+
+381
+00:43:15,080 --> 00:43:23,200
+characteristic لمن؟ لل S فبستنى شوية هل في منها
+
+382
+00:43:23,200 --> 00:43:30,500
+فائدة؟ أه في منها فائدة شو الفائدة المرجوة منها؟
+
+383
+00:43:30,500 --> 00:43:34,020
+السؤال
+
+384
+00:43:34,020 --> 00:43:38,980
+هو إيش علاقة ال S ب capital R
+
+385
+00:43:44,390 --> 00:43:55,870
+بما أن ال S صبست من R of X نحن لدينا ان ال
+
+386
+00:43:55,870 --> 00:44:03,190
+characteristic لل S أقل من أو يساوي ال
+
+387
+00:44:03,190 --> 00:44:09,790
+characteristic لمن؟ لل A طب ال characteristic لل S
+
+388
+00:44:09,790 --> 00:44:16,110
+من هو؟هو لو شفت اكتر استك لل R بدي اشيله و اكتب
+
+389
+00:44:16,110 --> 00:44:24,010
+بداله ال characteristic ال characteristic لل R of
+
+390
+00:44:24,010 --> 00:44:29,590
+X هذا بدي اعطيكي ال characteristic لل S هشيلها و
+
+391
+00:44:29,590 --> 00:44:38,210
+اكتب بدالها ال characteristic لل R اقل من او يساوي
+
+392
+00:44:38,210 --> 00:44:44,050
+ال characteristicللـ R of X واتبريلي هذه المعادلة
+
+393
+00:44:44,050 --> 00:44:50,850
+لرقم واحد إذا قدرت أثبت إن ال characteristics للـ
+
+394
+00:44:50,850 --> 00:44:55,710
+R of X أقل من أو يسوء ال characteristics لـ R يبقى
+
+395
+00:44:55,710 --> 00:45:04,790
+بيحدث التساوي تمام؟ يبقى بدالي أقولك للـ
+
+396
+00:45:04,790 --> 00:45:08,730
+R has بي
+
+397
+00:45:11,400 --> 00:45:19,260
+of characteristic k طب ال R ال characteristic L هي
+
+398
+00:45:19,260 --> 00:45:33,380
+يسوى k and let f of x بتسوى a n x n a n minus ال 1
+
+399
+00:45:33,380 --> 00:45:42,330
+x n minus ال 1 زائد a 1 x زائد ال a نوتموجودة وين؟
+
+400
+00:45:42,330 --> 00:45:48,230
+في ال R of X مرة
+
+401
+00:45:48,230 --> 00:45:54,630
+تانية فردت ان ال characteristic ل R يسوي K وفردت
+
+402
+00:45:54,630 --> 00:45:59,590
+ان ال F of X موجودة وين؟ في ال R of X اللي عندنا
+
+403
+00:45:59,590 --> 00:46:07,730
+ايش رأيكم؟ بدي اضرب K في ال F of X و بدي اضرب K في
+
+404
+00:46:07,730 --> 00:46:14,700
+الناحية التانية كلهاهذا سيعطينا k في مين؟ في a in
+
+405
+00:46:14,700 --> 00:46:23,340
+x in a in minus one x in minus one زائد a one x
+
+406
+00:46:23,340 --> 00:46:30,660
+زائد a naught هذا الكلام يساوي k في a in x to the
+
+407
+00:46:30,660 --> 00:46:38,580
+power n k في a in minus one x to the power n minus
+
+408
+00:46:38,580 --> 00:46:47,840
+oneزائد الـK في الـA1X زائد الـK في الـA0 سؤال هو
+
+409
+00:46:47,840 --> 00:46:55,280
+كده هذا؟ Zero لأن الـANPR والـcharacteristic L هي
+
+410
+00:46:55,280 --> 00:47:03,300
+سوى K كده هذا؟ Zero وهذا Zero وهذا Zero وهذا Zero
+
+411
+00:47:03,300 --> 00:47:09,920
+لأن الإيهات كلهم عناصر من عناصر الـRing A تماممدام
+
+412
+00:47:09,920 --> 00:47:17,280
+زيرو يسوى زيرو زائد زيرو زائد زيرو بتسوى زيرو
+
+413
+00:47:17,280 --> 00:47:26,700
+تمام؟ إذا الكابلات ضربته في أحد عناصر اللي هو ال R
+
+414
+00:47:26,700 --> 00:47:31,580
+of X طالع الناتد يسوى زيرو يبقى يا هذا هو ال
+
+415
+00:47:31,580 --> 00:47:37,440
+characteristic يا رقم أصغر منه صح ولا لا؟يعني لما
+
+416
+00:47:37,440 --> 00:47:41,480
+أقول K هو الـ Characteristic اتنين K بيجيب ليه
+
+417
+00:47:41,480 --> 00:47:44,920
+أصفار و تلاتة K بيجيب و مية K بيجيب ليها أصفار
+
+418
+00:47:44,920 --> 00:47:51,040
+كلهم يبقى الـ Characteristic يا K يا إما أقل من K،
+
+419
+00:47:51,040 --> 00:47:58,980
+تمام؟ هاي ضربت الـ K في element من ال R of X يبقى
+
+420
+00:47:58,980 --> 00:48:08,600
+هنا سواء الـ Characteristic للـ R of Xأقل من وقد
+
+421
+00:48:08,600 --> 00:48:17,040
+يساوي K طيب من هو ال K characteristic لها؟ يبقى
+
+422
+00:48:17,040 --> 00:48:25,540
+هذا بده يعطينا ان ال characteristic لل R of X أقل
+
+423
+00:48:25,540 --> 00:48:32,500
+من أو يساوي ال characteristic لمن؟ لل R هو يساوي K
+
+424
+00:48:32,500 --> 00:48:38,730
+هذه العلاقة رقم اتنينطالعيلي في واحد و اثنين في
+
+425
+00:48:38,730 --> 00:48:47,370
+واحد و اثنين اتنين R equal يبقى هنا from واحد and
+
+426
+00:48:47,370 --> 00:48:54,130
+اتنين ال characteristic لcapital
+
+427
+00:48:54,130 --> 00:49:03,210
+R of X هو بالضبط تماما ال characteristic لمين بالR
+
+428
+00:49:04,080 --> 00:49:08,260
+فيها انا طرحت كلمة لكن مش شايفين هو هنا في الشغل
+
+429
+00:49:08,260 --> 00:49:13,260
+شغل كلمة قولناها ده حل سؤال تمانية سؤال تمانية
+
+430
+00:49:13,260 --> 00:49:17,540
+بيقولي خد ال R commutative ring بيجيلي ان ال R of
+
+431
+00:49:17,540 --> 00:49:25,120
+X has a sub ring isomorphic لمين؟ isomorphic ل R،
+
+432
+00:49:25,120 --> 00:49:29,520
+مين هي؟ ال S اللي أخدناها هذه وهي أتبعناها
+
+433
+00:49:29,520 --> 00:49:33,900
+isomorphic ل Rيبقى حلينا سؤال تمانية واحدة مش
+
+434
+00:49:33,900 --> 00:49:42,960
+دارية تمام؟ خديني .. خديني المسائل التالية يبقى
+
+435
+00:49:42,960 --> 00:49:51,080
+هذا ال exercises قلول سؤال أتناشر تجيبوا حلينه
+
+436
+00:49:51,080 --> 00:49:55,080
+إزاي سؤال إحدى عشر اللي جابله طبعا زي إحدى عشر
+
+437
+00:49:55,080 --> 00:49:59,260
+والإحدى عشر جواب عنكوا بالكتابة هذا مش حلول بنا
+
+438
+00:49:59,260 --> 00:50:09,330
+نحلله زيهوغير الـ 12، بدنا سؤال 17، نظرة لأهميته
+
+439
+00:50:09,330 --> 00:50:18,050
+لزملة في ال chapters القادمة، وسؤال 18،
+
+440
+00:50:18,050 --> 00:50:22,550
+سؤال 24،
+
+441
+00:50:22,550 --> 00:50:29,090
+وسؤال 30، وسؤال 36،
+
+442
+00:50:32,600 --> 00:50:41,640
+وسؤال اتنين واربعين. يالا. طيب إذا هنا انتهت هذه
+
+443
+00:50:41,640 --> 00:50:45,360
+المحاضرة و القادة المحاضرة القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..6120ea552b2dad0fd1468b85ab2148dfadc11409
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk_raw.json
@@ -0,0 +1 @@
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96.09, "end": 96.57, "word": " ماخدين", "probability": 0.9564208984375}, {"start": 96.57, "end": 97.79, "word": " بالكوينز", "probability": 0.652734375}, {"start": 97.79, "end": 98.11, "word": " كيف", "probability": 0.834716796875}, {"start": 98.11, "end": 98.55, "word": " موجود", "probability": 0.98388671875}, {"start": 98.55, "end": 98.79, "word": " بين", "probability": 0.908203125}, {"start": 98.79, "end": 99.73, "word": " إيدانا", "probability": 0.74609375}, {"start": 99.73, "end": 100.71, "word": " السؤال", "probability": 0.93994140625}, {"start": 100.71, "end": 101.17, "word": " هو", "probability": 0.9765625}, {"start": 101.17, "end": 102.09, "word": " z", "probability": 0.84716796875}, {"start": 102.09, "end": 102.91, "word": " سبعة", "probability": 0.8836263020833334}, {"start": 102.91, "end": 103.59, "word": " هو", "probability": 0.1298828125}, {"start": 103.59, "end": 104.33, "word": " square", "probability": 0.6513671875}, {"start": 104.33, "end": 104.99, "word": " root", "probability": 0.814453125}, {"start": 104.99, "end": 105.29, "word": " ل", "probability": 0.84521484375}, {"start": 105.29, "end": 105.71, "word": " 3", "probability": 0.41552734375}], "temperature": 1.0}, {"id": 4, "seek": 13563, "start": 106.43, "end": 135.63, "text": "communitative ring with unity و لا لأ ال ZN عموما يبقى هذي communicative ring with unity تمام طيب الآن لو رجعنا إلى المثال رقم أربع اللي شرحناه في المحاضرة الأولى", "tokens": [25451, 14275, 4875, 365, 18205, 4032, 20193, 5296, 10721, 2423, 1176, 45, 6225, 2304, 2407, 15042, 7251, 3555, 4587, 7578, 8032, 8848, 1829, 3363, 1166, 4875, 365, 18205, 46811, 10943, 23032, 1829, 3555, 6024, 48506, 45164, 12602, 7435, 3615, 8315, 30731, 9673, 12984, 6027, 12602, 4587, 2304, 5551, 25513, 3615, 13672, 1829, 13412, 2288, 5016, 8315, 3224, 8978, 9673, 5016, 46958, 25720, 16247, 12610, 7578], "avg_logprob": -0.29450758388548187, "compression_ratio": 1.4606060606060607, "no_speech_prob": 0.0, "words": [{"start": 106.43, "end": 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communicative", "probability": 0.52093505859375}, {"start": 114.03, "end": 116.73, "word": " ring", "probability": 0.81787109375}, {"start": 116.73, "end": 119.95, "word": " with", "probability": 0.916015625}, {"start": 119.95, "end": 122.31, "word": " unity", "probability": 0.97802734375}, {"start": 122.31, "end": 125.69, "word": " تمام", "probability": 0.665771484375}, {"start": 125.69, "end": 127.97, "word": " طيب", "probability": 0.808349609375}, {"start": 127.97, "end": 129.53, "word": " الآن", "probability": 0.6097412109375}, {"start": 129.53, "end": 129.69, "word": " لو", "probability": 0.9833984375}, {"start": 129.69, "end": 130.15, "word": " رجعنا", "probability": 0.9827880859375}, {"start": 130.15, "end": 130.35, "word": " إلى", "probability": 0.425048828125}, {"start": 130.35, "end": 130.91, "word": " المثال", "probability": 0.9059244791666666}, {"start": 130.91, "end": 131.57, "word": " رقم", "probability": 0.8740234375}, {"start": 131.57, "end": 132.17, "word": " أربع", 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يبقى مرتان يبقى قول افترض انكستر بيه تساوي K has no solution in ZP مالهاش حل اللي هو الادعي اللي احنا متدعينه بدنا نثبت ان هذا الكلام is a fail لذلك بروح اقول ماهيأدي خديلي عنصر A زائد B جدر ال K", "tokens": [1829, 3555, 4587, 7578, 28242, 18871, 9381, 2288, 32771, 13546, 20328, 5172, 16572, 46740, 2407, 20449, 4117, 2407, 11622, 7251, 3555, 4587, 7578, 3714, 43500, 7649, 7251, 3555, 4587, 7578, 12174, 12610, 1975, 5172, 2655, 43042, 16472, 4117, 14851, 2288, 4724, 1829, 3224, 6055, 3794, 995, 45865, 591, 575, 572, 3827, 294, 1176, 47, 3714, 6027, 3224, 33599, 11331, 1211, 13672, 1829, 31439, 2423, 18513, 3615, 1829, 13672, 1829, 1975, 5016, 8315, 44650, 3215, 3615, 9957, 3224, 47525, 8315, 8717, 12984, 3555, 2655, 16472, 23758, 2423, 28820, 10943, 307, 257, 3061, 5296, 8848, 23275, 4724, 32887, 5016, 1975, 39648, 19446, 3224, 1829, 10721, 16254, 16490, 16254, 20292, 18871, 9381, 2288, 316, 30767, 16373, 3215, 363, 10874, 3215, 2288, 2423, 591], "avg_logprob": -0.2773760271466468, 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"word": " K", "probability": 0.8046875}], "temperature": 1.0}, {"id": 18, "seek": 54038, "start": 511.36, "end": 540.38, "text": "موجود في ZP of جذر ال K such that بحيث أن ال A زائد B جذر ال K not equal 0 هذا الكلام ما يسوي السفر بالمرة نذهب و نثبت أن هذا العنصر عكوس له English", "tokens": [2304, 29245, 23328, 8978, 1176, 47, 295, 10874, 8848, 2288, 2423, 591, 1270, 300, 4724, 5016, 1829, 12984, 14739, 2423, 316, 30767, 16373, 3215, 363, 10874, 8848, 2288, 2423, 591, 406, 2681, 1958, 23758, 2423, 28820, 10943, 19446, 7251, 3794, 45865, 21136, 5172, 2288, 20666, 2304, 25720, 8717, 24192, 3555, 4032, 8717, 12984, 3555, 2655, 14739, 23758, 18863, 1863, 9381, 2288, 6225, 4117, 2407, 3794, 46740, 3669], "avg_logprob": -0.44163603160311193, "compression_ratio": 1.3550295857988166, "no_speech_prob": 0.0, "words": [{"start": 511.36, "end": 512.46, "word": "موجود", "probability": 0.8341471354166666}, {"start": 512.46, "end": 512.78, "word": " في", "probability": 0.9501953125}, {"start": 512.78, 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زيرو بفترض أنا من عندي إن هذه القيمة لا تساوي زيرو و بدي أروحها بالصحيتة يعني مش تدعي ادعاء دون نسبة لأ بدي أنفقه", "tokens": [28814, 15730, 9122, 29399, 6055, 12984, 3555, 2655, 36145, 3224, 11933, 1211, 2407, 11933, 1863, 4724, 9381, 15040, 14111, 18863, 1863, 9381, 2288, 6225, 8592, 2407, 16373, 1829, 20449, 8315, 47395, 6156, 3615, 15040, 14111, 30767, 1829, 8717, 39648, 5296, 11296, 4724, 28259, 8717, 1829, 7435, 1829, 24976, 5016, 6027, 3660, 6024, 104, 7649, 10632, 13672, 1829, 4724, 1829, 20193, 6055, 3794, 995, 45865, 30767, 13546, 2407, 39182, 19446, 16472, 47395, 1829, 8315, 9154, 21542, 6027, 3660, 4724, 1829, 6055, 3794, 995, 45865, 30767, 13546, 2407, 6156, 1211, 2407, 25961, 2655, 2423, 4724, 1829, 20193, 6055, 3794, 995, 45865, 30767, 13546, 2407, 4724, 5172, 2655, 43042, 41850, 9154, 43242, 1829, 36145, 29538, 25062, 32640, 3660, 20193, 6055, 3794, 995, 45865, 30767, 13546, 2407, 4032, 4724, 16254, 5551, 32887, 5016, 11296, 20666, 9381, 5016, 36081, 3660, 37495, 22653, 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بدي أخد ال ring اللي هي زد أربعة هذا ك characteristic أربعة تمام يبقى هذه إلها ال characteristic اللي هو يساوي مين؟", "tokens": [1211, 10721, 37893, 20328, 5016, 7251, 3555, 4587, 7578, 4724, 16254, 5551, 3215, 13063, 15844, 4875, 2423, 16282, 13672, 1829, 39896, 7251, 3794, 995, 45865, 5551, 25513, 27884, 3714, 9957, 22807, 30767, 3215, 5551, 25513, 27884, 3714, 33599, 1829, 7251, 3555, 4587, 7578, 4724, 16254, 5551, 9778, 3215, 2423, 4875, 13672, 1829, 39896, 30767, 3215, 5551, 25513, 27884, 23758, 9122, 16282, 5551, 25513, 27884, 46811, 10943, 7251, 3555, 4587, 7578, 29538, 11933, 1211, 11296, 2423, 16282, 13672, 1829, 31439, 7251, 3794, 995, 45865, 3714, 9957, 22807], "avg_logprob": -0.2866379351451479, "compression_ratio": 1.9878787878787878, "no_speech_prob": 0.0, "words": [{"start": 2145.32, "end": 2145.86, "word": "لأ", "probability": 0.427947998046875}, {"start": 2145.86, "end": 2146.26, "word": " مش", "probability": 0.54150390625}, {"start": 2146.26, "end": 2146.46, "word": " 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1.0}, {"id": 80, "seek": 231727, "start": 2287.89, "end": 2317.27, "text": "لسؤال 640 بيقول الـ R commutative ring with unity و prime characteristic يبقى السؤال 640 الـ R commutative ring with unity اللي هو الواحد و prime characteristic", "tokens": [1211, 3794, 33604, 6027, 1386, 5254, 4724, 1829, 39648, 2423, 39184, 497, 800, 325, 1166, 4875, 365, 18205, 4032, 5835, 16282, 7251, 3555, 4587, 7578, 21136, 33604, 6027, 1386, 5254, 2423, 39184, 497, 800, 325, 1166, 4875, 365, 18205, 13672, 1829, 31439, 2423, 14407, 24401, 4032, 5835, 16282], "avg_logprob": -0.2672193974864726, "compression_ratio": 1.550387596899225, "no_speech_prob": 0.0, "words": [{"start": 2287.89, "end": 2288.91, "word": "لسؤال", "probability": 0.753173828125}, {"start": 2288.91, "end": 2290.39, "word": " 640", "probability": 0.3818359375}, {"start": 2290.39, "end": 2291.69, "word": " بيقول", "probability": 0.8173828125}, {"start": 2291.69, "end": 2291.97, "word": " الـ", "probability": 0.76171875}, {"start": 2291.97, 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2317.83, "end": 2343.77, "text": "will be prime as the characteristic of R تمام أخد ال A موجودة في R نيل بوتن ال A اللي موجودة في R is Neil Potten", "tokens": [17044, 312, 5835, 382, 264, 16282, 295, 497, 46811, 10943, 5551, 9778, 3215, 2423, 316, 3714, 29245, 23328, 3660, 8978, 497, 8717, 26895, 4724, 35473, 1863, 2423, 316, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 497, 307, 18615, 430, 1521, 268], "avg_logprob": -0.3193824340899785, "compression_ratio": 1.2295081967213115, "no_speech_prob": 0.0, "words": [{"start": 2317.83, "end": 2318.43, "word": "will", "probability": 0.17333984375}, {"start": 2318.43, "end": 2319.25, "word": " be", "probability": 0.9404296875}, {"start": 2319.25, "end": 2321.15, "word": " prime", "probability": 0.6328125}, {"start": 2321.15, "end": 2323.31, "word": " as", "probability": 0.47998046875}, {"start": 2323.31, "end": 2324.39, "word": " the", "probability": 0.81982421875}, {"start": 2324.39, "end": 2327.37, "word": " characteristic", "probability": 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2414.85, "word": " يكون", "probability": 0.96142578125}, {"start": 2414.85, "end": 2415.49, "word": " شكله", "probability": 0.9853515625}, {"start": 2415.49, "end": 2416.23, "word": " يكون", "probability": 0.889892578125}], "temperature": 1.0}, {"id": 84, "seek": 244323, "start": 2416.45, "end": 2443.23, "text": "بدي يا يطلع هذا الكلام يسوى قدر واحد صحيح بنقول الحلقة التالية solution الان ال potent اش يتطلب هذا يتطلب ان ال a to the power n تسوى zero for some positive انتجة", "tokens": [3555, 16254, 35186, 7251, 9566, 1211, 3615, 23758, 2423, 28820, 10943, 7251, 3794, 2407, 7578, 12174, 3215, 2288, 36764, 24401, 20328, 5016, 1829, 5016, 44945, 39648, 21542, 1211, 28671, 16712, 6027, 10632, 3827, 2423, 7649, 2423, 27073, 1975, 8592, 7251, 2655, 9566, 46152, 23758, 7251, 2655, 9566, 46152, 16472, 2423, 257, 281, 264, 1347, 297, 6055, 3794, 2407, 7578, 4018, 337, 512, 3353, 16472, 2655, 7435, 3660], "avg_logprob": -0.30537684217971917, "compression_ratio": 1.4879518072289157, "no_speech_prob": 0.0, "words": [{"start": 2416.45, "end": 2416.93, "word": "بدي", "probability": 0.4202880859375}, {"start": 2416.93, "end": 2417.19, "word": " يا", "probability": 0.1693115234375}, {"start": 2417.19, "end": 2417.61, "word": " يطلع", "probability": 0.9539794921875}, {"start": 2417.61, "end": 2417.83, "word": " هذا", "probability": 0.88037109375}, {"start": 2417.83, "end": 2418.25, "word": " الكلام", "probability": 0.91845703125}, {"start": 2418.25, "end": 2418.61, "word": " يسوى", "probability": 0.78759765625}, {"start": 2418.61, "end": 2419.17, "word": " قدر", "probability": 0.5635986328125}, {"start": 2419.17, "end": 2420.07, "word": " واحد", "probability": 0.785400390625}, {"start": 2420.07, "end": 2420.63, "word": " صحيح", "probability": 0.88525390625}, {"start": 2420.63, "end": 2421.49, "word": " بنقول", "probability": 0.721923828125}, {"start": 2421.49, "end": 2422.35, "word": " الحلقة", "probability": 0.9661458333333334}, {"start": 2422.35, "end": 2423.21, "word": " التالية", "probability": 0.99072265625}, {"start": 2423.21, "end": 2425.01, "word": " solution", "probability": 0.79150390625}, {"start": 2425.01, "end": 2427.69, "word": " الان", "probability": 0.411590576171875}, {"start": 2427.69, "end": 2428.03, "word": " ال", "probability": 0.74072265625}, {"start": 2428.03, "end": 2428.85, "word": " potent", "probability": 0.33203125}, {"start": 2428.85, "end": 2431.01, "word": " اش", "probability": 0.4512939453125}, {"start": 2431.01, "end": 2431.81, "word": " يتطلب", "probability": 0.9769287109375}, {"start": 2431.81, "end": 2432.29, "word": " هذا", "probability": 0.966796875}, {"start": 2432.29, "end": 2433.33, "word": " يتطلب", "probability": 0.90966796875}, {"start": 2433.33, "end": 2433.79, "word": " ان", "probability": 0.88427734375}, {"start": 2433.79, "end": 2434.13, "word": " ال", "probability": 0.92529296875}, {"start": 2434.13, "end": 2434.39, "word": " a", "probability": 0.4033203125}, {"start": 2434.39, "end": 2434.63, "word": " to", "probability": 0.82177734375}, {"start": 2434.63, "end": 2434.89, "word": " the", "probability": 0.921875}, {"start": 2434.89, "end": 2435.29, "word": " power", "probability": 0.88623046875}, {"start": 2435.29, "end": 2435.79, "word": " n", "probability": 0.53564453125}, {"start": 2435.79, "end": 2436.39, "word": " تسوى", "probability": 0.8829345703125}, {"start": 2436.39, "end": 2436.85, "word": " zero", "probability": 0.55908203125}, {"start": 2436.85, "end": 2438.11, "word": " for", "probability": 0.92041015625}, {"start": 2438.11, "end": 2439.29, "word": " some", "probability": 0.888671875}, {"start": 2439.29, "end": 2440.95, "word": " positive", "probability": 0.9208984375}, {"start": 2440.95, "end": 2443.23, "word": " انتجة", "probability": 0.84765625}], "temperature": 1.0}, {"id": 85, "seek": 246806, "start": 2451.12, "end": 2468.06, "text": "أحنا الآن لو خدنا ال prime مثلا تلاتة وال K يساوي عشر مثلا على سبيل المثال يبقى ال P تربيع P تربيع يعني تلاتة تربيع أقل من عشرة", "tokens": [10721, 5016, 8315, 6024, 48506, 45164, 16490, 3215, 8315, 2423, 5835, 50113, 15040, 6055, 1211, 9307, 3660, 16070, 591, 7251, 3794, 995, 45865, 6225, 46309, 50113, 15040, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 7251, 3555, 4587, 7578, 2423, 430, 6055, 2288, 21292, 3615, 430, 6055, 2288, 21292, 3615, 37495, 22653, 6055, 1211, 9307, 3660, 6055, 2288, 21292, 3615, 5551, 4587, 1211, 9154, 6225, 8592, 25720], "avg_logprob": -0.2129197712264844, "compression_ratio": 1.5755395683453237, "no_speech_prob": 0.0, "words": [{"start": 2451.12, "end": 2452.2, "word": "أحنا", "probability": 0.645751953125}, {"start": 2452.2, "end": 2452.6, "word": " الآن", "probability": 0.58221435546875}, {"start": 2452.6, "end": 2452.96, "word": " لو", "probability": 0.92626953125}, {"start": 2452.96, "end": 2453.72, "word": " خدنا", "probability": 0.91748046875}, {"start": 2453.72, "end": 2454.32, "word": " ال", "probability": 0.8994140625}, {"start": 2454.32, "end": 2454.64, "word": " prime", "probability": 0.2099609375}, {"start": 2454.64, "end": 2455.28, "word": " مثلا", "probability": 0.964599609375}, {"start": 2455.28, "end": 2456.08, "word": " تلاتة", "probability": 0.8895263671875}, {"start": 2456.08, "end": 2457.36, "word": " وال", "probability": 0.4580078125}, {"start": 2457.36, "end": 2457.8, "word": " K", "probability": 0.53076171875}, {"start": 2457.8, "end": 2458.74, "word": " يساوي", "probability": 0.82366943359375}, {"start": 2458.74, "end": 2459.22, "word": " عشر", "probability": 0.802734375}, {"start": 2459.22, "end": 2460.38, "word": " مثلا", "probability": 0.830810546875}, {"start": 2460.38, "end": 2460.62, "word": " على", "probability": 0.8134765625}, {"start": 2460.62, "end": 2461.04, "word": " سبيل", "probability": 0.9920247395833334}, {"start": 2461.04, "end": 2461.64, "word": " المثال", "probability": 0.98876953125}, {"start": 2461.64, "end": 2463.22, "word": " يبقى", "probability": 0.962890625}, {"start": 2463.22, "end": 2463.46, "word": " ال", "probability": 0.59716796875}, {"start": 2463.46, "end": 2463.72, "word": " P", "probability": 0.96240234375}, {"start": 2463.72, "end": 2464.64, "word": " تربيع", "probability": 0.8731689453125}, {"start": 2464.64, "end": 2465.3, "word": " P", "probability": 0.329833984375}, {"start": 2465.3, "end": 2465.78, "word": " تربيع", "probability": 0.935791015625}, {"start": 2465.78, "end": 2466.04, "word": " يعني", "probability": 0.8837890625}, {"start": 2466.04, "end": 2466.64, "word": " تلاتة", "probability": 0.97314453125}, {"start": 2466.64, "end": 2466.96, "word": " تربيع", "probability": 0.85400390625}, {"start": 2466.96, "end": 2467.26, "word": " أقل", "probability": 0.9147135416666666}, {"start": 2467.26, "end": 2467.46, "word": " من", "probability": 0.99609375}, {"start": 2467.46, "end": 2468.06, "word": " عشرة", "probability": 0.8263346354166666}], "temperature": 1.0}, {"id": 86, "seek": 249686, "start": 2468.54, "end": 2496.86, "text": "لكن لو أخدنا K تكعيب يعني تلاتة تكعيب بيصير ايه؟ بيصير أكبر من عشر صحيح ولا لأ؟ يبقى أنا بدي أخد L prime لو رفعتها لأس يكون أكبر من مين؟ أكبر من K اللي عندنا، تمام؟ يبقى هنا let P to the power I greater than N", "tokens": [1211, 19452, 45164, 5551, 9778, 3215, 8315, 591, 6055, 4117, 3615, 1829, 3555, 37495, 22653, 6055, 1211, 9307, 3660, 6055, 4117, 3615, 1829, 3555, 4724, 1829, 9381, 13546, 1975, 1829, 3224, 22807, 4724, 1829, 9381, 13546, 5551, 4117, 26890, 9154, 6225, 46309, 20328, 5016, 1829, 5016, 49429, 5296, 10721, 22807, 7251, 3555, 4587, 7578, 41850, 4724, 16254, 5551, 9778, 3215, 441, 5835, 45164, 12602, 5172, 34268, 11296, 5296, 10721, 3794, 7251, 30544, 5551, 4117, 26890, 9154, 3714, 9957, 22807, 5551, 4117, 26890, 9154, 591, 13672, 1829, 43242, 8315, 12399, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 34105, 718, 430, 281, 264, 1347, 286, 5044, 813, 426], "avg_logprob": -0.23145444120202108, "compression_ratio": 1.5896226415094339, "no_speech_prob": 0.0, "words": [{"start": 2468.54, "end": 2468.84, "word": 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"probability": 0.99365234375}, {"start": 2474.02, "end": 2474.46, "word": " عشر", "probability": 0.828857421875}, {"start": 2474.46, "end": 2475.16, "word": " صحيح", "probability": 0.8818359375}, {"start": 2475.16, "end": 2475.36, "word": " ولا", "probability": 0.91650390625}, {"start": 2475.36, "end": 2476.06, "word": " لأ؟", "probability": 0.7249348958333334}, {"start": 2476.06, "end": 2476.56, "word": " يبقى", "probability": 0.9593505859375}, {"start": 2476.56, "end": 2476.98, "word": " أنا", "probability": 0.69384765625}, {"start": 2476.98, "end": 2477.66, "word": " بدي", "probability": 0.794677734375}, {"start": 2477.66, "end": 2478.18, "word": " أخد", "probability": 0.8894856770833334}, {"start": 2478.18, "end": 2478.4, "word": " L", "probability": 0.41357421875}, {"start": 2478.4, "end": 2478.98, "word": " prime", "probability": 0.34228515625}, {"start": 2478.98, "end": 2479.34, "word": " لو", "probability": 0.92431640625}, {"start": 2479.34, "end": 2480.28, "word": " رفعتها", "probability": 0.788909912109375}, {"start": 2480.28, "end": 2480.66, "word": " لأس", "probability": 0.7413736979166666}, {"start": 2480.66, "end": 2481.16, "word": " يكون", "probability": 0.984619140625}, {"start": 2481.16, "end": 2481.78, "word": " أكبر", "probability": 0.9557291666666666}, {"start": 2481.78, "end": 2481.98, "word": " من", "probability": 0.9931640625}, {"start": 2481.98, "end": 2482.7, "word": " مين؟", "probability": 0.88427734375}, {"start": 2482.7, "end": 2483.52, "word": " أكبر", "probability": 0.9695638020833334}, {"start": 2483.52, "end": 2484.48, "word": " من", "probability": 0.99169921875}, {"start": 2484.48, "end": 2485.1, "word": " K", "probability": 0.93017578125}, {"start": 2485.1, "end": 2485.42, "word": " اللي", "probability": 0.973388671875}, {"start": 2485.42, "end": 2486.28, "word": " عندنا،", "probability": 0.77490234375}, {"start": 2486.28, "end": 2487.42, "word": " تمام؟", "probability": 0.9471028645833334}, {"start": 2487.42, "end": 2488.12, "word": " يبقى", "probability": 0.986083984375}, {"start": 2488.12, "end": 2488.66, "word": " هنا", "probability": 0.94970703125}, {"start": 2488.66, "end": 2489.88, "word": " let", "probability": 0.283203125}, {"start": 2489.88, "end": 2492.22, "word": " P", "probability": 0.89697265625}, {"start": 2492.22, "end": 2492.94, "word": " to", "probability": 0.85546875}, {"start": 2492.94, "end": 2493.26, "word": " the", "probability": 0.93310546875}, {"start": 2493.26, "end": 2493.82, "word": " power", "probability": 0.88134765625}, {"start": 2493.82, "end": 2494.38, "word": " I", "probability": 0.74658203125}, {"start": 2494.38, "end": 2495.16, "word": " greater", "probability": 0.46044921875}, {"start": 2495.16, "end": 2496.36, "word": " than", "probability": 0.9541015625}, {"start": 2496.36, "end": 2496.86, "word": " N", "probability": 0.89306640625}], "temperature": 1.0}, {"id": 87, "seek": 252578, "start": 2497.46, "end": 2525.78, "text": "أكبر من N then بتاخد على مين؟ واحد زائد A to the power P أُس I من سؤال خمسة وأربعين يجب أقول واحد to the power P أُس I زائد A to the power P أُس I", "tokens": [10721, 4117, 26890, 9154, 426, 550, 39894, 47283, 3215, 15844, 3714, 9957, 22807, 36764, 24401, 30767, 16373, 3215, 316, 281, 264, 1347, 430, 5551, 10859, 3794, 286, 9154, 8608, 33604, 6027, 16490, 2304, 3794, 3660, 36725, 25513, 3615, 9957, 7251, 7435, 3555, 5551, 39648, 36764, 24401, 281, 264, 1347, 430, 5551, 10859, 3794, 286, 30767, 16373, 3215, 316, 281, 264, 1347, 430, 5551, 10859, 3794, 286], "avg_logprob": -0.2880130712665729, "compression_ratio": 1.5777777777777777, "no_speech_prob": 0.0, "words": [{"start": 2497.46, "end": 2498.26, "word": "أكبر", "probability": 0.7735188802083334}, {"start": 2498.26, "end": 2498.64, "word": " من", "probability": 0.98681640625}, {"start": 2498.64, "end": 2499.08, "word": " N", "probability": 0.3232421875}, {"start": 2499.08, "end": 2501.3, "word": " then", "probability": 0.2216796875}, {"start": 2501.3, "end": 2504.74, "word": " بتاخد", "probability": 0.7791341145833334}, {"start": 2504.74, "end": 2505.0, "word": " على", "probability": 0.10809326171875}, {"start": 2505.0, "end": 2505.7, "word": " مين؟", "probability": 0.8317057291666666}, {"start": 2505.7, "end": 2506.5, "word": " واحد", "probability": 0.829833984375}, {"start": 2506.5, "end": 2507.4, "word": " زائد", "probability": 0.9451497395833334}, {"start": 2507.4, "end": 2507.92, "word": " A", "probability": 0.27783203125}, {"start": 2507.92, "end": 2508.52, "word": " to", "probability": 0.81640625}, {"start": 2508.52, "end": 2508.82, "word": " the", "probability": 0.93115234375}, {"start": 2508.82, "end": 2509.68, "word": " power", "probability": 0.88720703125}, {"start": 2509.68, "end": 2510.46, "word": " P", "probability": 0.6240234375}, {"start": 2510.46, "end": 2511.12, "word": " أُس", "probability": 0.5895182291666666}, {"start": 2511.12, "end": 2511.58, "word": " I", "probability": 0.9814453125}, {"start": 2511.58, "end": 2514.06, "word": " من", "probability": 0.89697265625}, {"start": 2514.06, "end": 2514.38, "word": " سؤال", "probability": 0.89453125}, {"start": 2514.38, "end": 2514.88, "word": " خمسة", "probability": 0.780914306640625}, {"start": 2514.88, "end": 2515.62, "word": " وأربعين", "probability": 0.889404296875}, {"start": 2515.62, "end": 2516.68, "word": " يجب", "probability": 0.5709635416666666}, {"start": 2516.68, "end": 2517.18, "word": " أقول", "probability": 0.6256103515625}, {"start": 2517.18, "end": 2518.02, "word": " واحد", "probability": 0.974609375}, {"start": 2518.02, "end": 2518.26, "word": " to", "probability": 0.90771484375}, {"start": 2518.26, "end": 2518.5, "word": " the", "probability": 0.939453125}, {"start": 2518.5, "end": 2519.12, "word": " power", "probability": 0.90087890625}, {"start": 2519.12, "end": 2519.78, "word": " P", "probability": 0.95849609375}, {"start": 2519.78, "end": 2520.32, "word": " أُس", "probability": 0.9153645833333334}, {"start": 2520.32, "end": 2520.84, "word": " I", 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2851.04, "end": 2851.88, "word": " المحاضرة", "probability": 0.84185791015625}, {"start": 2851.88, "end": 2852.22, "word": " القادمة", "probability": 0.9890950520833334}, {"start": 2852.22, "end": 2852.72, "word": " نبدأ", "probability": 0.737060546875}, {"start": 2852.72, "end": 2852.88, "word": " ال", "probability": 0.2744140625}, {"start": 2852.88, "end": 2853.26, "word": " chapter", "probability": 0.92724609375}, {"start": 2853.26, "end": 2854.46, "word": " الجديد", "probability": 0.9793294270833334}, {"start": 2854.46, "end": 2854.8, "word": " ان", "probability": 0.449951171875}, {"start": 2854.8, "end": 2855.18, "word": " شاء", "probability": 0.967041015625}, {"start": 2855.18, "end": 2855.32, "word": " الله", "probability": 0.94091796875}, {"start": 2855.32, "end": 2855.82, "word": " تعليه", "probability": 0.6185709635416666}, {"start": 2855.82, "end": 2855.96, "word": " ال", "probability": 0.400634765625}, {"start": 2855.96, "end": 2856.7, "word": " ideals", "probability": 0.89697265625}, {"start": 2856.7, "end": 2858.42, "word": " and", "probability": 0.9091796875}, {"start": 2858.42, "end": 2859.62, "word": " quotient", "probability": 0.83837890625}, {"start": 2859.62, "end": 2860.24, "word": " rings", "probability": 0.8720703125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2860.83775, "duration_after_vad": 2769.0293749999896}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a513288a80c1b4a621d812591cb2081f9e699f6b
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/GwZ2s5Lpnkk_raw.srt
@@ -0,0 +1,1580 @@
+1
+00:00:20,740 --> 00:00:25,440
+بسم الله الرحمن الرحيم اليوم إن شاء الله بنكمل حل
+
+2
+00:00:25,440 --> 00:00:29,220
+المسائل تبع هذا ال section المرة اللي بقى تكون
+
+3
+00:00:29,220 --> 00:00:35,580
+حلنا بعض المسائل ووقفنا عند سؤال أربعين طيب سؤال
+
+4
+00:00:35,580 --> 00:00:42,400
+أربعين بيقول لي النقطة الأولى اثبتلي إن زد سبعة أو
+
+5
+00:00:42,400 --> 00:00:48,400
+جذر تلاتة هي عبارة عن فين؟ فسؤال أربعين هو عبارة
+
+6
+00:00:48,400 --> 00:00:58,880
+عن مطلوبينالمطلوب الأول نمره a show that z7 of
+
+7
+00:00:58,880 --> 00:01:06,800
+square root لثلاثة is و لو بحط التعريف تبعه دفع
+
+8
+00:01:06,800 --> 00:01:15,020
+التعريف تبع هذا هو عبارة عن ال a زائد ال g جدر
+
+9
+00:01:15,020 --> 00:01:24,190
+تلاتةبحيث ال a و ال b موجودة في z سبعة is a field
+
+10
+00:01:24,190 --> 00:01:31,850
+هذا اللي بدنا نقوله الحل كانت تالي solution الحل
+
+11
+00:01:31,850 --> 00:01:36,570
+بسيط جدا موجود بين إيداكوا و لو انكم مش ماخدين
+
+12
+00:01:36,570 --> 00:01:43,590
+بالكوينز كيف موجود بين إيدانا السؤال هو z سبعة هو
+
+13
+00:01:43,590 --> 00:01:48,310
+square root ل 3communitative ring with unity و لا
+
+14
+00:01:48,310 --> 00:01:59,950
+لأ ال ZN عموما يبقى هذي communicative ring with
+
+15
+00:01:59,950 --> 00:02:05,690
+unity تمام
+
+16
+00:02:05,690 --> 00:02:13,790
+طيب الآن لو رجعنا إلى المثال رقم أربع اللي شرحناه
+
+17
+00:02:13,790 --> 00:02:19,440
+في المحاضرة الأولىمثال رقم أربع يبقى بقوله هنا
+
+18
+00:02:19,440 --> 00:02:31,080
+from example four بشرحناها سابقا we have we have
+
+19
+00:02:31,080 --> 00:02:40,200
+ان زد P قد جدر تلاتة ولا زد سبعة لإن P احنا عندنا
+
+20
+00:02:40,200 --> 00:02:49,090
+هنا يعني سبعة يبقى زد سبعة و جدر تلاتةis an
+
+21
+00:02:49,090 --> 00:02:56,530
+integral domain تمام؟
+
+22
+00:02:56,530 --> 00:03:01,090
+يبقى هذه integral domain السؤال هو هل هذه ال ring
+
+23
+00:03:01,090 --> 00:03:04,810
+finite ولا infinite؟ و ال integral domain finite
+
+24
+00:03:04,810 --> 00:03:08,770
+ولا infinite؟ finite و احنا خدنا نظرية every
+
+25
+00:03:08,770 --> 00:03:16,490
+finite integral domain is a field يبقى بطء ولكنزد
+
+26
+00:03:16,490 --> 00:03:29,350
+سبعة of جذر تلاتة is finite مادام finite وintegral
+
+27
+00:03:29,350 --> 00:03:40,410
+domain finite and integral domain يبقى هذا بيعطينا
+
+28
+00:03:40,410 --> 00:03:50,290
+ان زد سبعة ofجذر تلاتة is a .. فيه ال .. ده يبقى
+
+29
+00:03:50,290 --> 00:03:54,110
+هذا عبارة عن ايه؟ عبارة عن فيه يبقى هذا المطلوب
+
+30
+00:03:54,110 --> 00:03:58,150
+الأول من السؤال اللي هو المطلوب السهل اللي مافيش
+
+31
+00:03:58,150 --> 00:04:05,290
+فيه مشكلة نمر بيه المشكلة في نمر بيه نمر بيه بيقول
+
+32
+00:04:05,290 --> 00:04:18,490
+لي ما يأتي بيقول لي بدنا find thenecessary and
+
+33
+00:04:18,490 --> 00:04:23,110
+sufficient
+
+34
+00:04:23,110 --> 00:04:32,650
+condition
+
+35
+00:04:32,650 --> 00:04:41,870
+for zp
+
+36
+00:04:42,870 --> 00:04:53,470
+جذر الـ K جذر الـ K ثم بيقفل
+
+37
+00:04:53,470 --> 00:05:01,670
+ثم بيقفل
+
+38
+00:05:01,670 --> 00:05:07,230
+راح
+
+39
+00:05:07,230 --> 00:05:14,290
+أخد K انتجة و أخد P Primeقال هاتلي ال necessary
+
+40
+00:05:14,290 --> 00:05:21,990
+and sufficient condition بحيث يكون ZP of جذر ال K
+
+41
+00:05:21,990 --> 00:05:28,350
+is a field أنا أدعى أن ال necessary and sufficient
+
+42
+00:05:28,350 --> 00:05:36,770
+condition for ZP of K to be a field is ال X تربية
+
+43
+00:05:36,770 --> 00:05:54,150
+تساوي K hasno solution in zp that is in ال
+
+44
+00:05:54,150 --> 00:06:07,490
+x تربيع تساوي k has no solution in zp if and only
+
+45
+00:06:07,490 --> 00:06:22,300
+if zP of January الـ K is A field تمام؟
+
+46
+00:06:22,300 --> 00:06:30,020
+طيب بروح نوضح هذا الكلام نمربي
+
+47
+00:06:30,020 --> 00:06:37,490
+من السؤال بيقول ما هو الشرط الضروري والكافياللي
+
+48
+00:06:37,490 --> 00:06:44,790
+بتتحقق في كل من P وK بحيث انه يطلع ZP of K هو
+
+49
+00:06:44,790 --> 00:06:50,730
+عبارة عن field تصير هذا الكلام سيارة رياضية أنا
+
+50
+00:06:50,730 --> 00:06:57,770
+أدعي أن الشرط هو X تربيع تساوي K has no solution
+
+51
+00:06:57,770 --> 00:07:04,570
+in ZP if and only if ZP of جدر ال K is a field
+
+52
+00:07:05,110 --> 00:07:11,950
+الادعاء هذا لا يكون صحيحا إلا إذا أثبتناه يبقى
+
+53
+00:07:11,950 --> 00:07:18,870
+بقول الحلقة التالية كلمة F انحلي F تعني ان المسار
+
+54
+00:07:18,870 --> 00:07:25,890
+بيسير باتجاهين يبقى بالداجة اقوله افترض ان ال X
+
+55
+00:07:25,890 --> 00:07:38,670
+تربيه تساوي T has no solutionno solution in ZP ايش
+
+56
+00:07:38,670 --> 00:07:45,110
+بدي اثبت بدي اثبت ان ZP of general K is A field
+
+57
+00:07:45,110 --> 00:07:54,370
+يعني كل عنصر غير صفري يكون له ايش بكله في ال field
+
+58
+00:07:54,370 --> 00:08:00,830
+ايش معنى field كل عنصر غير صفري له معكوس
+
+59
+00:08:00,830 --> 00:08:06,300
+multiplicative inverseيبقى كل عنصر غير صفري لهو
+
+60
+00:08:06,300 --> 00:08:10,560
+معكوز يبقى مرتان يبقى قول افترض انكستر بيه تساوي K
+
+61
+00:08:10,560 --> 00:08:16,040
+has no solution in ZP مالهاش حل اللي هو الادعي
+
+62
+00:08:16,040 --> 00:08:21,160
+اللي احنا متدعينه بدنا نثبت ان هذا الكلام is a
+
+63
+00:08:21,160 --> 00:08:29,220
+fail لذلك بروح اقول ماهيأدي خديلي عنصر A زائد B
+
+64
+00:08:29,220 --> 00:08:40,980
+جدر ال Kموجود في ZP of جذر ال K such that بحيث أن
+
+65
+00:08:40,980 --> 00:08:51,120
+ال A زائد B جذر ال K not equal 0 هذا الكلام ما
+
+66
+00:08:51,120 --> 00:08:59,820
+يسوي السفر بالمرة نذهب و نثبت أن هذا العنصر عكوس
+
+67
+00:08:59,820 --> 00:09:04,470
+له Englishإذا كنت تثبت إنه إلو إن بصلاً العنصر
+
+68
+00:09:04,470 --> 00:09:09,270
+عشوائي معناته فعلاً زي نقول لها بدا نيجي للحالة
+
+69
+00:09:09,270 --> 00:09:13,530
+الثانية اللي بي لا تساوي زيرو بعد ما انتهينا من
+
+70
+00:09:13,530 --> 00:09:18,970
+الحالة بي تساوي زيرو فلو كانت ال بي لا تساوي زيرو
+
+71
+00:09:18,970 --> 00:09:23,970
+بفترض أنا من عندي إن هذه القيمة لا تساوي زيرو و
+
+72
+00:09:23,970 --> 00:09:28,150
+بدي أروحها بالصحيتة يعني مش تدعي ادعاء دون نسبة لأ
+
+73
+00:09:28,150 --> 00:09:33,230
+بدي أنفقهفبقى جيب الدئاتة وقلت لو كان يساوي zero
+
+74
+00:09:33,230 --> 00:09:37,090
+إيش اللي بدي يحصل؟ امشي بالشكل اللي انا لقيت K
+
+75
+00:09:37,090 --> 00:09:43,070
+ساوي A ل B تربيع يعني هذه المعادلة X تربيع يساوي K
+
+76
+00:09:43,070 --> 00:09:48,130
+صار لها حل وانا فرض انها مالهاش حل يبقى هذا
+
+77
+00:09:48,130 --> 00:09:53,150
+الإدعاء مش صحيح وعكس اللي هو هذا هو الصحيح إذا ال
+
+78
+00:09:53,150 --> 00:09:58,870
+A تربيع ناقص B تربيع K لا يمكن أن يساويلا يمكن أن
+
+79
+00:09:58,870 --> 00:10:04,450
+يساوي Zero مدام لا يمكن أن يساوي Zero يبقى واحد
+
+80
+00:10:04,450 --> 00:10:09,310
+على هذا المقدار بيصير معرف لأن لو كان المقام يساوي
+
+81
+00:10:09,310 --> 00:10:13,870
+Zero بيصير Infinity مش معرف لكن المقام لا يساوي
+
+82
+00:10:13,870 --> 00:10:17,410
+Zero يبقى واحد على هذا المقدار بيصير معرف روح
+
+83
+00:10:17,410 --> 00:10:23,270
+Symmetry أو A تربيه ناقص B تربيه K كله مرفوع للأس
+
+84
+00:10:23,270 --> 00:10:28,560
+سالك واحدالمهم ده دي ياخد حاصل ضرب القوسين هدول
+
+85
+00:10:28,560 --> 00:10:34,040
+نظره ضربنا القسم صار ضرب المقدار اللي عندنا ده بدي
+
+86
+00:10:34,040 --> 00:10:40,260
+اشوف ليش وصل هدى مع هدى مع السلامة يبقى هدى بدها
+
+87
+00:10:40,260 --> 00:10:52,630
+الساوي ايه تربيع ناقص ناقص بتربيع ككل قسيهذا
+
+88
+00:10:52,630 --> 00:11:01,030
+الكلام بده يساوي A تربيع ناقص B تربيع K B تربيع K
+
+89
+00:11:01,030 --> 00:11:08,730
+كله مضروف في C من C هيها فوق يبقى في A تربيع ناقص
+
+90
+00:11:08,730 --> 00:11:14,950
+B تربيع K أسالي واحد هذا القص مش هذا القص نفسه
+
+91
+00:11:14,950 --> 00:11:21,200
+يبقى هذا عبارة عن الأس Zero يبقى كله في قداشواحد
+
+92
+00:11:21,200 --> 00:11:26,680
+يبقى هذا العمصر له معكس مين معكسه اللي هو ال term
+
+93
+00:11:26,680 --> 00:11:35,040
+اللي عندنا هذا يبقى this means that هذا يعني every
+
+94
+00:11:35,040 --> 00:11:47,960
+none zero element اللي هو ال a زائد b جدر ال k n z
+
+95
+00:11:47,960 --> 00:11:57,070
+pof general K has an inverse يبقاش معنى هذا الكلام
+
+96
+00:11:57,070 --> 00:12:06,290
+ان هذا is a field يبقى صراحة ZP
+
+97
+00:12:06,290 --> 00:12:15,350
+of general K is a field اهو المفهوم نمشي من اتجاه
+
+98
+00:12:15,350 --> 00:12:24,840
+المعاكسيبقى بدأ أقوله conversely Assume that
+
+99
+00:12:24,840 --> 00:12:36,020
+Assume that the theme of gathering cake is a theme
+
+100
+00:12:36,020 --> 00:12:47,030
+one to show one to show بما أروح نبينإن الـ X
+
+101
+00:12:47,030 --> 00:12:57,970
+ترابيع تساوي K، has no solution No
+
+102
+00:12:57,970 --> 00:13:05,190
+solution in ZP أظن أخدته البرهين بالـ
+
+103
+00:13:05,190 --> 00:13:12,330
+Contrapositive مطلوب هذه بدي أفترض عكسها إذا وصلني
+
+104
+00:13:12,330 --> 00:13:18,980
+إلى تناقض يبقى فرضي غلطوعكسه هيوغو الصحي طبعا يعني
+
+105
+00:13:18,980 --> 00:13:28,320
+بيبقى بدي أقوله الآن لك ال X ترابيع تساوي K has a
+
+106
+00:13:28,320 --> 00:13:39,640
+solution in ZP هذا بده يعطينا ان ال A ترابيع تساوي
+
+107
+00:13:39,640 --> 00:13:49,870
+K وال A موجودة في ZPطبعا مرة تانية بقول احنا ما
+
+108
+00:13:49,870 --> 00:13:55,130
+نمشي لاتجاه الاخر، لاتجاه المعاكس، يبقى فرط هذا
+
+109
+00:13:55,130 --> 00:13:59,650
+عبارة عن field، وبدي أحاول أثبت أن المعادل X تساوي
+
+110
+00:13:59,650 --> 00:14:04,890
+و X تربع تساوي كده، مالهاش حل، لإن بروحت فترط إنه
+
+111
+00:14:04,890 --> 00:14:13,930
+إلها حل، هي إلها حل، معناته كل عنصر في Z P
+
+112
+00:14:14,380 --> 00:14:19,840
+بدي ممكن اقول ايه تربيع بدي يسوي مين بدي يسوي كي
+
+113
+00:14:19,840 --> 00:14:26,780
+هذا كلام صحيح بدي افترضه تمام وخديلي هال عنصرين و
+
+114
+00:14:26,780 --> 00:14:33,740
+تعالى يشوف لوين بدهم يوصلوا فبقى اجيب و بقوله F LX
+
+115
+00:14:33,740 --> 00:14:45,110
+يسوي A زي P ناقص واحد في جدر الكيك موجودفي الـ Z P
+
+116
+00:14:45,110 --> 00:14:54,030
+وفي جذر ال K ولا لا؟ لأن هذا رقم صح؟ والـ Y بدل
+
+117
+00:14:54,030 --> 00:15:03,750
+سوى A زائد جذر ال K، ذلك. بدي أخد ال X في ال Y،
+
+118
+00:15:03,750 --> 00:15:10,310
+هشوف إيش تعطيك. لوين بدي أتواصل؟ أخدت عنصرين بقدر
+
+119
+00:15:10,310 --> 00:15:18,180
+اللهسميت الأول a زي ال P نقص واحد في K وسميت
+
+120
+00:15:18,180 --> 00:15:25,340
+التاني A زي جذر ال K وبدأت أضغطهم في بعض A في A ب
+
+121
+00:15:25,340 --> 00:15:38,490
+A ترابيع ايه في جذر ال K ب A في جذر ال Kهيضربنا ال
+
+122
+00:15:38,490 --> 00:15:46,990
+a في كل الطرف المضاجي اضربه هنا P K في A تمام يبقى
+
+123
+00:15:46,990 --> 00:16:00,350
+زائد P P A في جزر ال P هيضربنا P في جزر ال K في A
+
+124
+00:16:00,350 --> 00:16:10,150
+اللي قاعدة ناقص A في جزر ال Kناقص A في جذر ال K
+
+125
+00:16:10,150 --> 00:16:20,750
+ضايل عندنا اخر حاجة يبقى ضايل P في K يبقى زائد P
+
+126
+00:16:20,750 --> 00:16:29,290
+في K ضايل عندنا بس ناقص اللي هو جذر ال K في جذر ال
+
+127
+00:16:29,290 --> 00:16:37,690
+K يبقى ناقص K يبقى تكيت ال XYيبقى بصير عندنا ال X
+
+128
+00:16:37,690 --> 00:16:46,290
+Y يساوي كداش ال A تربيها يا بنات؟ كيه؟ يبقى بقدر
+
+129
+00:16:46,290 --> 00:16:51,270
+أشيلها و أحط مكانها كيه؟ يبقى هذا الكلام يساوي
+
+130
+00:16:51,270 --> 00:17:00,990
+كيه؟ طيب زائد AK و ناقص AK مع السلامة طيب هذا ال P
+
+131
+00:17:00,990 --> 00:17:03,810
+AK كداش؟
+
+132
+00:17:06,070 --> 00:17:13,230
+مضاعفات اللي هو العناصر في Z ب P قد إيش؟ مضاعفات
+
+133
+00:17:13,230 --> 00:17:17,530
+إذا هي P ب Zero صح ولا لا؟ Zero تضربي في أي حاجة ب
+
+134
+00:17:17,530 --> 00:17:25,270
+Zero نفق الطار هذا ب Zero وهذا كمان راح ب Zero صح؟
+
+135
+00:17:25,270 --> 00:17:33,870
+مظبوط؟ إيش ضل عندنا؟ ضل عندنا سالب K نفق هذا سالب
+
+136
+00:17:33,870 --> 00:17:45,260
+Kيساوي Zero مظبوط يبقى صار عندنا ال X ه and او ال
+
+137
+00:17:45,260 --> 00:17:56,020
+X and ال Y are Zero divisors مظبوط يبقى بنفع يكون
+
+138
+00:17:56,020 --> 00:18:02,700
+Integral domain وبالتالي بنفع يكون فيل لأ يبقى هذا
+
+139
+00:18:02,700 --> 00:18:12,100
+معناههذا بدي يعطينا ان الـ Z P of general K of
+
+140
+00:18:12,100 --> 00:18:25,400
+general K is not an integral domain لأنه ما هوش
+
+141
+00:18:25,400 --> 00:18:31,440
+integral domain هذا كمان بدي يعطينا ان النقط فيه
+
+142
+00:18:34,250 --> 00:18:40,090
+طيب وصلنا للتناقض ليش هنفرض من الأساس فيه؟ يبقى
+
+143
+00:18:40,090 --> 00:18:48,850
+هذا بده يعطينا مين؟ contradiction يبقى
+
+144
+00:18:48,850 --> 00:18:54,850
+هذا تناقض يبقى الفرض اللي أنا فرضته has a solution
+
+145
+00:18:54,850 --> 00:19:00,830
+غلط وعكسه هو مين الصح يبقى بروح بقوله
+
+146
+00:19:17,150 --> 00:19:23,070
+يبقى this is contradiction يبقى shown X تربيه تسوي
+
+147
+00:19:23,070 --> 00:19:34,610
+K has no solution in Z بقى يبقى بناء عليه صار
+
+148
+00:19:34,610 --> 00:19:38,950
+الشرط الضروري والكافي ل Z P of جدري ال Kالـ cone
+
+149
+00:19:38,950 --> 00:19:43,790
+field هو مربع أي عنصر من عناصرها لا يمكن أن يساوي
+
+150
+00:19:43,790 --> 00:19:48,630
+100 لا يمكن أن يساوي 50 الشطرة الثانية يعتبر صعبة
+
+151
+00:19:48,630 --> 00:19:53,810
+جدا بالنسبة لكم لكن الشطرة الأولية يعتبر مباشرة من
+
+152
+00:19:53,810 --> 00:20:00,570
+سؤال أربعين نجي لسؤال أتنين وأربعين بقول افترض ال
+
+153
+00:20:00,570 --> 00:20:07,350
+A و B موجودات في ring commutative ring Rوكان ال A
+
+154
+00:20:07,350 --> 00:20:12,490
+B Zero Divisor يبقى نبين أنه يا إما ال A Zero
+
+155
+00:20:12,490 --> 00:20:20,510
+Divisor يا إما ال B هو عبارة عن Zero Divisor يبقى
+
+156
+00:20:20,510 --> 00:20:24,970
+السؤال 42 بيقول
+
+157
+00:20:24,970 --> 00:20:33,990
+ما يدى أن ال A B is A Zero Divisor
+
+158
+00:20:40,090 --> 00:20:46,330
+in a commutative
+
+159
+00:20:46,330 --> 00:20:51,830
+ring تمام؟
+
+160
+00:20:51,830 --> 00:21:03,350
+بدنا نثبت ان هذا بده يعطينا يا MLARBSA0
+
+161
+00:21:03,350 --> 00:21:14,710
+divisorالقصة بسيطة جدا solution ال a,b is a zero
+
+162
+00:21:14,710 --> 00:21:23,130
+divisor هذا ايش معناه؟ معناته ان there exist
+
+163
+00:21:23,130 --> 00:21:31,750
+element c موجود في الارض وحيث ال c لا يساوي zero
+
+164
+00:21:31,750 --> 00:21:33,310
+such that
+
+165
+00:21:35,850 --> 00:21:46,670
+ساعدش ذات ال A B في C بده يساوي Z تمام ال ring
+
+166
+00:21:46,670 --> 00:21:50,950
+عندنا commutative قاللي بدك تثبتلي يا إما ال A
+
+167
+00:21:50,950 --> 00:21:56,870
+Zero divisor يا إما ال B Zero divisor بقوله تمام
+
+168
+00:21:56,870 --> 00:22:04,430
+من خاصية ال associativity بقدر أقول هذا عبارة عن A
+
+169
+00:22:05,610 --> 00:22:14,470
+C8 في الـ B بده يساوي 0 صح؟ إيش معنى هذا الكلام؟
+
+170
+00:22:14,470 --> 00:22:20,950
+إن الـ B is zero divisible يبقى هذا بده يعطينا إن
+
+171
+00:22:20,950 --> 00:22:28,810
+الـ B is A zero divisible طيب
+
+172
+00:22:28,810 --> 00:22:41,100
+في حتمة أخر يبقى هنا أخدناإن ال F ال A C بده يساوي
+
+173
+00:22:41,100 --> 00:22:47,680
+Zero عشان مايصيرش شكك ولا حاجة F A C بده يساوي
+
+174
+00:22:47,680 --> 00:22:53,220
+Zero وهذا بده يساوي Zero يبقى ال B is A Zero
+
+175
+00:22:53,220 --> 00:22:59,300
+Divisor لايمكن أن تساوي Zero يبقى A Zero Divisor
+
+176
+00:22:59,300 --> 00:23:05,990
+طب لو كانتال AC لا يساوي زيرو لأ اللي فوق AC لا
+
+177
+00:23:05,990 --> 00:23:11,810
+يساوي زيرو لو كان ال AC بده يساوي زيرو زيرو في بيه
+
+178
+00:23:11,810 --> 00:23:13,250
+زيرو في بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+179
+00:23:13,250 --> 00:23:13,650
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+180
+00:23:13,650 --> 00:23:14,310
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+181
+00:23:14,310 --> 00:23:18,250
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+182
+00:23:18,250 --> 00:23:25,250
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه ب
+
+183
+00:23:30,850 --> 00:23:35,350
+هذه لو كان ال A C لا تساوي زيرو فجبه B يكون زيرو
+
+184
+00:23:35,350 --> 00:23:46,990
+تمام بدنا نيجي ناخد الحالة التالتة if ال A C تساوي
+
+185
+00:23:46,990 --> 00:23:58,470
+زيرو then احنا هنا مين A B C A B C بتساوي زيرو
+
+186
+00:23:58,470 --> 00:24:07,480
+impliesبقدر اقول هذه مين بقدر اقول a في b في c
+
+187
+00:24:07,480 --> 00:24:18,640
+مظبوط تساوي بقدر اعملها على الشكل التالي تساوي a b
+
+188
+00:24:18,640 --> 00:24:27,180
+في c ال a بيبقى داشر ب zero يبقى هذا بتعطيك zero
+
+189
+00:24:27,180 --> 00:24:32,200
+في c يساوي كده؟ Zeroيبقى معناه هذا الكلام انه ايش
+
+190
+00:24:32,200 --> 00:24:40,220
+ال a is a zero divisor يبقى هذا بيعطيك ان ال a is
+
+191
+00:24:40,220 --> 00:24:50,420
+a zero divisor تمام طيب يبقى هنا يا اما ال a zero
+
+192
+00:24:50,420 --> 00:24:55,840
+divisor يا اما ال b zero divisor هذه واحدة منهم
+
+193
+00:24:55,840 --> 00:25:02,800
+فقط طيب هذا سؤال جداسؤال اللي هو اتنين واربعين
+
+194
+00:25:02,800 --> 00:25:08,020
+الان سؤال ستة واربعين لا يمكن حله إذا حلنا سؤال
+
+195
+00:25:08,020 --> 00:25:12,960
+خمسة واربعين لأن سؤال ستة واربعين يعتمد على سؤال
+
+196
+00:25:12,960 --> 00:25:19,000
+خمسة واربعين إذا بدنا نروح لسؤال خمسة واربعين في
+
+197
+00:25:19,000 --> 00:25:27,550
+الأول وإذا حلنا بصير خمسة واربعين تحصيل حاصلخمسة
+
+198
+00:25:27,550 --> 00:25:32,610
+واربعين بيقول ما يعطي بيقول X وY موجودة في
+
+199
+00:25:32,610 --> 00:25:37,930
+commutative ring with prime characteristic X وY
+
+200
+00:25:37,930 --> 00:25:44,750
+موجودة في الأرض كمام
+
+201
+00:25:44,750 --> 00:25:51,290
+ليه في commutative ring with prime characteristic
+
+202
+00:25:51,910 --> 00:26:01,270
+وال characteristic إلها prime وليكن P. خلصنا؟ طيب،
+
+203
+00:26:01,270 --> 00:26:09,950
+الآن المطلوب الأول Show that بيّلي إن ال X زائد ال
+
+204
+00:26:09,950 --> 00:26:18,490
+Y to the power P يساوي X أوس P زائد Y أوس P. نمرى
+
+205
+00:26:18,490 --> 00:26:25,520
+بيه.بقول لمرة بيقول show that for all positive
+
+206
+00:26:25,520 --> 00:26:36,400
+integer n ال X زائد Y مرفوعة لمين لل P أُس N يزاوى
+
+207
+00:26:36,400 --> 00:26:47,140
+ال X أُس P N زائد ال Y أُس P N لمرة C لمرة C بيقول
+
+208
+00:26:47,140 --> 00:27:02,840
+هتلف عينعنصرين x و y find عنصرين x و y in R و ال
+
+209
+00:27:02,840 --> 00:27:09,640
+characteristic ل R بده يساوي أربعة و ال
+
+210
+00:27:09,640 --> 00:27:15,900
+characteristic ل R بده يساوي أربعة بحيث انه such
+
+211
+00:27:15,900 --> 00:27:16,560
+that
+
+212
+00:27:20,770 --> 00:27:29,950
+ال X زائد ال Y قص أربعة لا يساوي ال X قص أربعة
+
+213
+00:27:29,950 --> 00:27:38,430
+زائد ال Y قص أربعة بسبب ال prime طيب في السؤال
+
+214
+00:27:38,430 --> 00:27:42,750
+اللي جابني ايش دخل A C تساوي ستر؟ السؤال اللي
+
+215
+00:27:42,750 --> 00:27:45,470
+جابني انا مستفدتش في الحلقة التانية من الفرض ان A
+
+216
+00:27:45,470 --> 00:27:52,050
+C تساوي ستر هذا؟ اه وين هو؟أنا ما استخدمته مش هذا؟
+
+217
+00:27:52,050 --> 00:27:55,750
+اه طب احنا دخلنا A C لا يساوي Zero إذا استخدمي B
+
+218
+00:27:55,750 --> 00:28:00,490
+Zero دي بجر طبعا اللي بعد لو كان A C يساوي Zero
+
+219
+00:28:00,490 --> 00:28:06,310
+طلعت ال A لحال شايفة طلعت ال A لحال اللي أنا بديها
+
+220
+00:28:06,310 --> 00:28:13,390
+طبعا يبقى ما هو السبب اللي خل هذا Zero ال B ال ..
+
+221
+00:28:13,390 --> 00:28:20,270
+ال .. ال .. ال ..طلعت ال a و ال b لحالة اللي أصلاً
+
+222
+00:28:20,270 --> 00:28:25,050
+zero يبقى جدير الأستثمار أن ال a في هذا هو ال zero
+
+223
+00:28:25,050 --> 00:28:32,130
+صح ولا لأ؟ أنا بدي a لحالها، أنا بدي a أو b
+
+224
+00:28:32,930 --> 00:28:35,830
+بيطلعناها من المعادلة الأولى، صح؟ طيب، أنا قاعدة
+
+225
+00:28:35,830 --> 00:28:39,310
+يفهمها بدج يطلع أيه من المعادلة التانية طب انا
+
+226
+00:28:39,310 --> 00:28:42,210
+مستفدتش من انه نرمى، حكيت ان انت A, C تساوي صفر
+
+227
+00:28:42,210 --> 00:28:45,470
+ايه؟ مستفدناش من ايه اش؟ من انه A, C تساوي صفر، ما
+
+228
+00:28:45,470 --> 00:28:49,090
+استخدمنهاش، يعني احنا بس استخدمنا خاصية التجميع،
+
+229
+00:28:49,090 --> 00:28:52,130
+في الحلقة التانية بس، يعني لو رفعنا A, C تساوي
+
+230
+00:28:52,130 --> 00:28:56,610
+صفر، مش حاسس، مش حاجة يا ست مش مشكلة، بنقول أرسل،
+
+231
+00:28:56,610 --> 00:29:01,990
+بدل هذه، بنرايحك منها، و بنقولك أرسلطيب يا دكتور
+
+232
+00:29:01,990 --> 00:29:05,570
+طيب لو ماتساوي لو ساوات صفر طيب؟ كيف لو ايه؟
+
+233
+00:29:05,570 --> 00:29:06,930
+اتسانى شوية واحدة واحدة اتسانى شوية واحدة واحدة
+
+234
+00:29:06,930 --> 00:29:06,930
+اتسانى شوية واحدة اتسانى شوية واحدة اتسانى شوية
+
+235
+00:29:06,930 --> 00:29:07,150
+واحدة اتسانى شوية واحدة اتسانى شوية واحدة اتسانى
+
+236
+00:29:07,150 --> 00:29:14,370
+شوية واحدة اتسانى شوية واحدة اتسانى شوية
+
+237
+00:29:14,370 --> 00:29:18,150
+واحدة اتسانى شوية واحدة اتسانى شوية واحدة اتسانى
+
+238
+00:29:18,150 --> 00:29:20,590
+شوية واحدة اتسانى شوية واحدة اتسانى شوية واحدة
+
+239
+00:29:20,590 --> 00:29:25,370
+اتسانى شوية واحدة اتسانى ش
+
+240
+00:29:31,200 --> 00:29:38,120
+فى B فى C او هي A فى B فى C يساوي Zero هو الأصل
+
+241
+00:29:38,120 --> 00:29:45,400
+مظبوط قدرت أطلع منه A لحاله فى B فى C هذا الكلام
+
+242
+00:29:45,400 --> 00:29:49,000
+بده يساوي Zero بده يساوي Zero ليش؟ لأن ال A فى ال
+
+243
+00:29:49,000 --> 00:29:54,100
+B أصلا أنا فرضها في Zero صح ولا لا؟ يبقى هنا صارت
+
+244
+00:29:54,100 --> 00:29:57,860
+هذه النتيجة تساوي Zero يبقى ال A زي Zero دلوقتي
+
+245
+00:29:57,860 --> 00:30:03,740
+أسهلعنا A C في B بتساوي Zero، لو ماكانش A C بتساوي
+
+246
+00:30:03,740 --> 00:30:06,960
+Zero، هاجدوا عنا B .. حط في دماغك في الأول .. بس
+
+247
+00:30:06,960 --> 00:30:11,120
+اسمع .. انت خليك تكمل .. حط في دماغي في الأول ان
+
+248
+00:30:11,120 --> 00:30:15,120
+ال A في B بدو ساوي Zero، و بدنا نشتغل عليها، يبقى
+
+249
+00:30:15,120 --> 00:30:21,000
+بنروح نجيب Element من ال Ring و نضربه فيها، لإنها
+
+250
+00:30:21,000 --> 00:30:25,020
+Zero Divisor، يبقى بدنا ناجي عنصر لا يساوي الصغر
+
+251
+00:30:25,020 --> 00:30:30,310
+مثل C، حصل ضربه فيهم، بدو ساوي Zero، صح؟يبقى هذه
+
+252
+00:30:30,310 --> 00:30:33,590
+هي المعادلة الأساسية مرة بدي أطلع منها ايه و مرة
+
+253
+00:30:33,590 --> 00:30:39,630
+بدي أطلع منها بيه بالبلد هيه ماشي ايه طلعنا منها
+
+254
+00:30:39,630 --> 00:30:43,770
+مرة ايه طلعنا منها بيه صار و هو المطلوب يجيب أحدهم
+
+255
+00:30:43,770 --> 00:30:48,890
+بدي يكون هو zero divisor يا إما الـA يا إما الـB
+
+256
+00:30:48,890 --> 00:30:54,570
+يا إما الـA يا إما الـB طيب نجي للسؤال اللي عنا
+
+257
+00:30:54,570 --> 00:30:58,590
+هذا غناط اللي وصار خمسة واربعين قبل أن ندخل إلى
+
+258
+00:30:58,590 --> 00:31:25,460
+السؤال640 طيب
+
+259
+00:31:25,460 --> 00:31:27,640
+بدنا النقطة الأولى
+
+260
+00:31:33,130 --> 00:31:37,170
+علمًا بأن الـ X زائد Y to the power of P يسمى X to
+
+261
+00:31:37,170 --> 00:31:42,230
+the power of P زائد Y to the power of P علمًا بأن
+
+262
+00:31:42,230 --> 00:31:46,810
+الـ characteristic لا الرنج اللي عندنا هو P هو رنج
+
+263
+00:31:46,810 --> 00:31:51,450
+commutative فبروح و بقولوا معناتي احنا عندنا X
+
+264
+00:31:51,450 --> 00:31:58,040
+زائد Y كله to the power of Pهذا خطوة نظرية ذات
+
+265
+00:31:58,040 --> 00:32:04,480
+الحدين في الاحتمالات وكذلك في الثانوية برحبتها في
+
+266
+00:32:04,480 --> 00:32:11,500
+الكلمة فبقول هذه X to the power P زائد توافق P من
+
+267
+00:32:11,500 --> 00:32:18,520
+الأشياء مأخوذة واحد واحد X أُس P ناقص واحد Y زائد
+
+268
+00:32:18,520 --> 00:32:25,960
+توافق P من الأشياء مأخوذة متنا متناXP ناقص اتنين
+
+269
+00:32:25,960 --> 00:32:32,620
+في الـY تربيع ونظل مستمرين لغاية ما نوصل للـY أُس
+
+270
+00:32:32,620 --> 00:32:41,480
+P هذا الكلام يساوي XP هذا الآن يحتوي على P ولا لا؟
+
+271
+00:32:41,480 --> 00:32:50,100
+خلّيني أذكركم الآن بجينا نقول توفي قنون من الأشياء
+
+272
+00:32:50,100 --> 00:32:57,780
+مأخوذة راء راءبجينا نقول N factorial على R
+
+273
+00:32:57,780 --> 00:33:06,780
+factorial N ناقص R factorial تذكرين العلاقة هذه في
+
+274
+00:33:06,780 --> 00:33:13,960
+التوافق والتباديل تمام أو في توزيع ذات الحدد الآن
+
+275
+00:33:13,960 --> 00:33:19,580
+هذا العمصر دائما و أبدا يحتوي على العمصر N
+
+276
+00:33:19,580 --> 00:33:25,570
+وبالتاليهذا عندنا دائما يعتمد على علم موجود في
+
+277
+00:33:25,570 --> 00:33:33,330
+عنصر P P مضروب في شغلة تمام؟ وهذا P مضروب في شغلة
+
+278
+00:33:33,330 --> 00:33:39,650
+وهذا P مضروب في شغلة فبالسؤال هو هذا مش عنصر موجود
+
+279
+00:33:39,650 --> 00:33:44,330
+في الريم ومضروب في P وال characteristic اللي
+
+280
+00:33:44,330 --> 00:33:50,500
+هيساوي P يبقى كده شهدة المقدار؟ Zeroيبقى هذا هو 1
+
+281
+00:33:50,500 --> 00:33:56,620
+زائد Zero والثاني زائد Zero والتالت زائد Zero زائد
+
+282
+00:33:56,620 --> 00:34:01,480
+Y فيه كل العناصر معدل الأنصر الأول والأنصر الأخير
+
+283
+00:34:01,480 --> 00:34:06,380
+كلها موجودة فيها الرقم P ال P هو ال characteristic
+
+284
+00:34:06,380 --> 00:34:10,920
+لل ring بتقدروا في جميع عناصر ال ring يعطيني Zero
+
+285
+00:34:10,920 --> 00:34:16,170
+يبقى كل العناصر في النص بتروح ب Zeroيبقى يصير هذا
+
+286
+00:34:16,170 --> 00:34:23,810
+X أُس P زائد Y أُس P وهو المطموب الأول المطموب
+
+287
+00:34:23,810 --> 00:34:30,490
+التام نمرأ به نمرأ به بإنه نثبت ان X زايد Y مرفوع
+
+288
+00:34:30,490 --> 00:34:39,910
+للأس P أُس N يساوي X أُس P N وY أُس P N هذا إلك by
+
+289
+00:34:39,910 --> 00:34:42,390
+induction
+
+290
+00:34:45,730 --> 00:34:50,390
+يبقى هذا بالاستنتاج الرياضي أو الاستقرار الرياضي
+
+291
+00:34:50,390 --> 00:34:55,590
+لو حطيت N بواحد عشان تطلع الحالة الأولى يبقى
+
+292
+00:34:55,590 --> 00:35:00,290
+الحالة الأولى يبقى بدأ أفترض أن هذه صحيحة عند N
+
+293
+00:35:00,290 --> 00:35:07,690
+تساوي M و أثبت صحتها عند N تساوي M زي 1 أظن سهلة
+
+294
+00:35:07,690 --> 00:35:11,750
+ويوم سويته زيها في مبادئ الرياضية يبقى هذه سهلة
+
+295
+00:35:11,750 --> 00:35:19,040
+طيب نمر ال C نمر ال Cبيقول لها لـ ring و فيها
+
+296
+00:35:19,040 --> 00:35:24,320
+عنصرين و ال characteristic إلها بيسوي أربعة و هذه
+
+297
+00:35:24,320 --> 00:35:32,040
+العلاقة ماهياش صحيحة طلع ندور على ring ال
+
+298
+00:35:32,040 --> 00:35:38,400
+characteristic إلها أربعة و العلاقة هذه مش صحيحة
+
+299
+00:35:38,400 --> 00:35:44,040
+احنا أثبتنا صحتها لما كان ال P prime لكن هل
+
+300
+00:35:44,040 --> 00:35:48,400
+الأربعة تانيةلأ مش صح يبقى بدي أدور على ring ال
+
+301
+00:35:48,400 --> 00:35:54,360
+characteristic اللي هي يساوي أربعة مين؟ زد أربعة
+
+302
+00:35:54,360 --> 00:36:04,340
+ماشي يبقى بدي أخد ال ring اللي هي زد أربعة هذا ك
+
+303
+00:36:04,340 --> 00:36:12,100
+characteristic أربعة تمام يبقى هذه إلها ال
+
+304
+00:36:12,100 --> 00:36:17,400
+characteristic اللي هو يساوي مين؟يساوي أربعة تدور
+
+305
+00:36:17,400 --> 00:36:23,620
+على عنصرين فيها لا يحققني هذه العلاقة عناصر زد
+
+306
+00:36:23,620 --> 00:36:27,800
+اربعة Zero واحد واتنين وتلاتة اربع عناصر بس مش
+
+307
+00:36:27,800 --> 00:36:33,460
+غيرهم خليني نجرب اي رقمين فيهم وليكن مثلا واحد
+
+308
+00:36:33,460 --> 00:36:40,580
+وثلاثة لو أخد X بواحد و Y تساوي تلاتة بهذا الشكل
+
+309
+00:36:40,580 --> 00:36:49,250
+تمام؟ وبتاجر أقولهذا يريد أن يعطينا ان الـ x زائد
+
+310
+00:36:49,250 --> 00:36:59,090
+y to the power 4 يساوي 1 زائد 3 to the power 4
+
+311
+00:36:59,090 --> 00:37:09,310
+فبتشوف كده يساوي هذا كده 1 زائد 3 فزيت 4 صفر صفر
+
+312
+00:37:09,310 --> 00:37:17,140
+هذا بزيتبتادي واخد واحد أُص أربعة ثلاثة أُص أربعة
+
+313
+00:37:17,140 --> 00:37:29,700
+واحد أُص أربعة أبواحد ثلاثة أُص أربعة واحد أكيد
+
+314
+00:37:29,700 --> 00:37:35,380
+ثلاثة تربية تسعة مشيل منها أربعتين بيظل واحد
+
+315
+00:37:35,380 --> 00:37:40,860
+والتاني بيظل واحد في واحد أبواحدأو تسعة فى تسعة
+
+316
+00:37:40,860 --> 00:37:45,480
+بواحد و تمانين التمانين بتقسمها لاربعه مانشيلها
+
+317
+00:37:45,480 --> 00:37:50,440
+بيظهر الواحد هذي والله هذي سيان واحد يبقى النتج
+
+318
+00:37:50,440 --> 00:37:56,640
+يسوى ايش اتنين هذا بدي أكيد ان واحد زائد تلاته أُص
+
+319
+00:37:56,640 --> 00:38:02,720
+أربعه لا يساوي واحد أُص أربعه زائد تلاته أُص أربعه
+
+320
+00:38:02,720 --> 00:38:08,910
+وهو المطلوب هذا سؤال خمسة واربعين بروحي الآنلسؤال
+
+321
+00:38:08,910 --> 00:38:15,430
+640 بيقول الـ R commutative ring with unity و
+
+322
+00:38:15,430 --> 00:38:24,030
+prime characteristic يبقى السؤال 640 الـ R
+
+323
+00:38:24,030 --> 00:38:36,130
+commutative ring with unity اللي هو الواحد و prime
+
+324
+00:38:36,130 --> 00:38:47,370
+characteristicwill be prime as the characteristic
+
+325
+00:38:47,370 --> 00:38:58,650
+of R تمام أخد ال A موجودة في R نيل بوتن ال A اللي
+
+326
+00:38:58,650 --> 00:39:06,750
+موجودة في R is Neil Pottenما هو المطلوب بعد هذه
+
+327
+00:39:06,750 --> 00:39:12,790
+المعلومات بيقول ان ال botan prove there is a
+
+328
+00:39:12,790 --> 00:39:21,030
+positive integer k such that اثبت ان في عندك
+
+329
+00:39:21,030 --> 00:39:27,410
+positive integer k بحيث واحد زائد a to the power k
+
+330
+00:39:27,410 --> 00:39:30,830
+يساوي واحد صحيح
+
+331
+00:39:51,250 --> 00:39:56,670
+أحنا الآن عندنا R commutative with unity واحد و ال
+
+332
+00:39:56,670 --> 00:40:01,170
+P prime هو ال characteristic لل ring اللي عندنا R
+
+333
+00:40:01,170 --> 00:40:09,270
+ال A هو لبوتن بداية من واحد زاد اتو رفعته كوصل ل
+
+334
+00:40:09,270 --> 00:40:13,810
+positive integer P منه المهم يجيبلي positive
+
+335
+00:40:13,810 --> 00:40:17,830
+integer أيش ما يكون شكله يكونبدي يا يطلع هذا
+
+336
+00:40:17,830 --> 00:40:23,210
+الكلام يسوى قدر واحد صحيح بنقول الحلقة التالية
+
+337
+00:40:23,210 --> 00:40:34,390
+solution الان ال potent اش يتطلب هذا يتطلب ان ال a
+
+338
+00:40:34,390 --> 00:40:43,230
+to the power n تسوى zero for some positive انتجة
+
+339
+00:40:51,120 --> 00:40:58,740
+أحنا الآن لو خدنا ال prime مثلا تلاتة وال K يساوي
+
+340
+00:40:58,740 --> 00:41:05,780
+عشر مثلا على سبيل المثال يبقى ال P تربيع P تربيع
+
+341
+00:41:05,780 --> 00:41:10,500
+يعني تلاتة تربيع أقل من عشرةلكن لو أخدنا K تكعيب
+
+342
+00:41:10,500 --> 00:41:15,160
+يعني تلاتة تكعيب بيصير ايه؟ بيصير أكبر من عشر صحيح
+
+343
+00:41:15,160 --> 00:41:20,660
+ولا لأ؟ يبقى أنا بدي أخد L prime لو رفعتها لأس
+
+344
+00:41:20,660 --> 00:41:28,120
+يكون أكبر من مين؟ أكبر من K اللي عندنا، تمام؟ يبقى
+
+345
+00:41:28,120 --> 00:41:39,080
+هنا let P to the power I greater than Nأكبر من N
+
+346
+00:41:39,080 --> 00:41:44,740
+then بتاخد
+
+347
+00:41:44,740 --> 00:41:54,380
+على مين؟ واحد زائد A to the power P أُس I من سؤال
+
+348
+00:41:54,380 --> 00:42:00,840
+خمسة وأربعين يجب أقول واحد to the power P أُس I
+
+349
+00:42:00,840 --> 00:42:10,990
+زائد A to the power P أُس Iطبعا ؟ طيب هذا الكلام
+
+350
+00:42:10,990 --> 00:42:15,990
+بقدر اكتره على صيغة هذا كله جداشا مناهي يبقى هذا
+
+351
+00:42:15,990 --> 00:42:23,250
+الكلام from exercises خمسة و أربعين مش عشوائي يعني
+
+352
+00:42:23,250 --> 00:42:30,790
+هذا الكلام يسوى واحد زائد هذه a to the power inf
+
+353
+00:42:30,790 --> 00:42:37,700
+of a to the power of P أُص I ناقص Mبقدر اكتب هذا
+
+354
+00:42:37,700 --> 00:42:45,020
+اكثر صح ليش لأن ال P و PY أكبر من ال N وبالتالي
+
+355
+00:42:45,020 --> 00:42:50,740
+بقدر اخد هذه منها طيب هذه كلها بقدر ايش؟ نشيب Zero
+
+356
+00:42:50,740 --> 00:42:55,840
+من ال Quotient هيبقى لكم ب Zero يبقى صارت النتيجة
+
+357
+00:42:55,840 --> 00:43:00,180
+واحد زائد Zero يسوى كده يعني يسوى واحد يبدأ يعني
+
+358
+00:43:00,180 --> 00:43:07,690
+قدرت هجيبله رقم Kرفعته لل أُس هذا طلع النتج يساوي
+
+359
+00:43:07,690 --> 00:43:15,910
+قدر واحد يبقى ساعة الـ K تساوي P أُس I قال جيبلي
+
+360
+00:43:15,910 --> 00:43:22,590
+any positive integer K يحقق مين؟ يحقق هذه المعادلة
+
+361
+00:43:22,590 --> 00:43:29,130
+إذا كنت هنا من ستة واربعين وصلنا لاتنين وخمسين
+
+362
+00:43:29,130 --> 00:43:36,420
+ولسة ضالة أربعة أسئلةطيب لأن لو جينا لسؤال 52 جالي
+
+363
+00:43:36,420 --> 00:43:42,460
+find all solutions سؤال
+
+364
+00:43:42,460 --> 00:43:50,340
+52 جالي هاتلي ال solutions للمعادلة x تربيع ماقص x
+
+365
+00:43:50,340 --> 00:43:58,780
+زائد 2 يسوى 0 ان هذا
+
+366
+00:43:59,570 --> 00:44:12,350
+ن زد تلاتة I ن زد تلاتة I يبني
+
+367
+00:44:12,350 --> 00:44:16,950
+احنا عندنا معادلة والمعادلة هذه طلب الحلول لها
+
+368
+00:44:16,950 --> 00:44:22,930
+تمين في زد تلاتة I عظم زد تلاتة I كتبنا عناصرها
+
+369
+00:44:22,930 --> 00:44:29,800
+قبل هيك كم عنصر فيها تسعة عناصرلو جيت للعناصر هذي
+
+370
+00:44:29,800 --> 00:44:35,120
+الدمسك كل عنصر معوض في المعادلة تمام؟ طبعا زي
+
+371
+00:44:35,120 --> 00:44:39,220
+التلاتة عتمت ب zero واحد و اتنين ولا واحد فيهم
+
+372
+00:44:39,220 --> 00:44:47,300
+بيحقق المعادلة لكن لو جيتي اتنين زائد I اندي اتنين
+
+373
+00:44:47,300 --> 00:44:57,220
+زائد اتنين I هذول satisfy the above equation
+
+374
+00:44:58,880 --> 00:45:07,960
+موليكي واحدة فيهم ناخد هذه تربيع يبقى I أربعة زائد
+
+375
+00:45:07,960 --> 00:45:17,740
+أربعة I ناقص واحد ناقص X يبقى ناقص اتنين ناقص I
+
+376
+00:45:17,740 --> 00:45:26,900
+زائد اتنين ويسبب هدول قداش ناقص ثلاثة وزائد اتنين
+
+377
+00:45:27,250 --> 00:45:33,430
+بظل ناقص واحد وعندك أربعة بظل تلاتة تلاتة بزد
+
+378
+00:45:33,430 --> 00:45:40,190
+تلاتة بزيرو يبقى الأرقام كلها بزيرو تمام الأربعة I
+
+379
+00:45:40,190 --> 00:45:46,910
+بدي أشيل منها تلاتة بظل I واحدة I واحدة و سالف I
+
+380
+00:45:46,910 --> 00:45:53,330
+كله راح بزيرو يبقى هالي حققتها طويلة والتالي نفسه
+
+381
+00:45:53,330 --> 00:45:58,620
+بالصبابةنفس الرقم اللي هو عند هذا ال complex بشرة
+
+382
+00:45:58,620 --> 00:46:03,820
+سالف زي الاتنين بتلاقي zero يبقى هدول فقط هم اللي
+
+383
+00:46:03,820 --> 00:46:08,760
+بحلوا المعادلة السؤال اللي بعده إزاي؟ بس اللي بعده
+
+384
+00:46:08,760 --> 00:46:13,600
+أربع مطالب لإن كل واحدة فيهم شكل يعطيك معادلة
+
+385
+00:46:13,600 --> 00:46:23,180
+ويعطيك ring تانية تلترها بحط عناصرها وبجيب عوضوحدة
+
+386
+00:46:23,180 --> 00:46:27,760
+منهم هتلاقي فيها حلين وحدة بتلاقي فيها ثلاثة حلول
+
+387
+00:46:27,760 --> 00:46:34,940
+وحدة مثلا أربعة حلول إلى آخرين فمثلا فمثلا لو جيتي
+
+388
+00:46:34,940 --> 00:46:47,660
+لسؤال 53 سؤال 53 سؤال 53 بتلاقي عندك نمرة A نمرة A
+
+389
+00:46:47,660 --> 00:46:56,380
+الحل تبعه اللي هو عبارة عنالـ X يساوي 2 و 3 ونمره
+
+390
+00:46:56,380 --> 00:47:09,100
+B الحل تبعه نمره B الحل تبعه كمان 2 و 3 ونمره C
+
+391
+00:47:09,100 --> 00:47:21,140
+ونمره C الحل تبعه 2 و 3 و 6 و 11 ونمره D الحل تبعه
+
+392
+00:47:21,380 --> 00:47:28,400
+إتنين و تلاتة و تسعة و عشرة لإن كل واحدة فيهم ring
+
+393
+00:47:28,400 --> 00:47:32,880
+شكله بتختلف عن التانية المحاضرة القادمة نبدأ ال
+
+394
+00:47:32,880 --> 00:47:38,420
+chapter الجديد ان شاء الله تعليه ال ideals and
+
+395
+00:47:38,420 --> 00:47:40,240
+quotient rings
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/K1zwu7gTN7M.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/K1zwu7gTN7M.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ac8332da3e6a595d30951e3aca6e58344870f12d
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/K1zwu7gTN7M.srt
@@ -0,0 +1,1379 @@
+1
+00:00:20,860 --> 00:00:25,640
+بسم الله الرحمن الرحيم نكمل ما ابتدأنا به في المرة
+
+2
+00:00:25,640 --> 00:00:30,860
+الماضية في نهاية المحاضرة الماضية كتبنا الـ remark
+
+3
+00:00:30,860 --> 00:00:36,140
+التالية أنه لو كان عندي function من Z كله لـ square
+
+4
+00:00:36,140 --> 00:00:42,300
+root لـ D لـ Z plus معرفة N of A زائد B لـ square
+
+5
+00:00:42,300 --> 00:00:47,120
+root لـ D بتساوي الـ absolute value لـ A تربيع نقص
+
+6
+00:00:47,120 --> 00:00:54,800
+الـ D بيه تربيع. النقطة الأولى والثانية برهنّاهم المرة
+
+7
+00:00:54,800 --> 00:01:00,200
+الماضية، ووصلنا إلى النقطة الثالثة والرابعة. إذا كلا
+
+8
+00:01:00,200 --> 00:01:07,280
+كتر، بدنا نيجي لنمرة الـC. نمرة الـC قال X is a unit
+
+9
+00:01:07,280 --> 00:01:14,220
+if and only if الـ N X يساوي 101. هذا العشري نسبته الـ
+
+10
+00:01:14,220 --> 00:01:18,660
+1000. يبقى أبراد الـ N أكثر
+
+11
+00:01:21,070 --> 00:01:26,790
+الـ X هو الذي موجودة هذه في
+
+12
+00:01:26,790 --> 00:01:32,770
+ذات الاسم. وعود لـ D هي كمعنى هذا الكلام، التي هي N
+
+13
+00:01:32,770 --> 00:01:40,990
+of A زائد B جذر الـ D بدها تساوي 1 if and only if
+
+14
+00:01:40,990 --> 00:01:47,290
+وده بيجيبنا، نستخدم التعريف، نشيل هذا ونحط التعريف
+
+15
+00:01:47,290 --> 00:01:54,570
+الذي نحن حاطينه، اللي هم A تربيع ناقص D B تربيع.
+
+16
+00:01:54,570 --> 00:02:05,450
+كل هذا الكلام بدّه يساوي واحدة if and only if يبقى
+
+17
+00:02:05,450 --> 00:02:11,630
+الـ A تربيع ناقص D B تربيع يساوي زائد أو ناقص
+
+18
+00:02:11,630 --> 00:02:17,070
+واحدة. نشيل الـ absolute value حطيناه للـ element
+
+19
+00:02:17,070 --> 00:02:21,990
+واحد زائد أو ناقص واحد. هذا ممكن أحلّله كفرق بين
+
+20
+00:02:21,990 --> 00:02:29,090
+المربعين. يبقى هذا الكلام صحيح إذا كان الـ A ناقص B
+
+21
+00:02:29,090 --> 00:02:37,150
+في جذر الـ D في الـ A زائد B جذر الـ D بيكون زائد أو
+
+22
+00:02:37,150 --> 00:02:46,840
+ناقص واحد. if and only if هذا صحيح لو كانّه مدام
+
+23
+00:02:46,840 --> 00:02:51,980
+واحد واحد هو الـ unity مظبوط ولا لا؟ يبقى بناء عليه
+
+24
+00:02:51,980 --> 00:02:58,100
+هذا الكلام صحيح لو كان هذا unit يبقى if and only
+
+25
+00:02:58,100 --> 00:03:07,800
+if الـ X التي تساوي الـ A زائد B جذر الـ D is a unit
+
+26
+00:03:07,800 --> 00:03:17,270
+وهو المفروض، حيث نبرهن النمرة دي بتاعتي، أقول له assume
+
+27
+00:03:17,270 --> 00:03:27,130
+افترض أن الـ N of X is a prime. أيش
+
+28
+00:03:27,130 --> 00:03:35,310
+بدنا نثبت؟ أيش بدنا نثبت يا بنات؟ أيش بدنا نثبت؟
+
+29
+00:03:35,310 --> 00:03:40,330
+أن الـ X is irreducible. المرة التي فاتت عرفنا الـ
+
+30
+00:03:40,330 --> 00:03:45,380
+prime وعرفنا الـ irreducible. يبقى الـ element A بقول
+
+31
+00:03:45,380 --> 00:03:53,460
+عنه irreducible إذا حقق شرطين. الشرط الأول أن الـ A
+
+32
+00:03:53,460 --> 00:03:58,900
+is non unit. الشرط الثاني لو قدرت أكتبه على صيغة
+
+33
+00:03:58,900 --> 00:04:04,520
+حاصل ضرب عنصرين، يبقى واحد منهم يكون unit. يعني لو
+
+34
+00:04:04,520 --> 00:04:09,920
+كان الـ A كتبته على شكل B في C، يبقى الـ A is unit أو
+
+35
+00:04:09,920 --> 00:04:15,320
+الـ B is unit. هذا الـ irreducible. طيب ليه prime؟ الشرط
+
+36
+00:04:15,320 --> 00:04:20,720
+الأولاني هو الشرط نفسه. أن الـ A بقول عنه prime إذا
+
+37
+00:04:20,720 --> 00:04:26,180
+كان الـ A non unit. اتنين، مش كان يساوي حاصل ضرب بـ two
+
+38
+00:04:26,180 --> 00:04:31,220
+elements، لأ كان الـ A بيقسم الـ B في C، إذا الـ A
+
+39
+00:04:31,220 --> 00:04:34,560
+بيقسم الـ B or الـ B بيقسم الـ C. هذا الـ two
+
+40
+00:04:34,560 --> 00:04:39,940
+definitions التي معكم في بداية المحاضرة الماضية.
+
+41
+00:04:39,940 --> 00:04:45,810
+طيب نمشي هنا. إن نحن افترضنا أن الـ N of X is a
+
+42
+00:04:45,810 --> 00:04:54,170
+prime. مطلوب نثبت أن الـ X is a reducer. ممتاز جداً. طب
+
+43
+00:04:54,170 --> 00:05:00,790
+لما أقول N of X is a prime تمام، يبقى الـ N of X
+
+44
+00:05:00,790 --> 00:05:07,370
+ممكن تكون unit، ممكن
+
+45
+00:05:07,370 --> 00:05:18,590
+تكون واحدة. يبقى ذلك، الـ n of x does not equal to one.
+
+46
+00:05:18,590 --> 00:05:25,110
+مش ممكن تكون واحد. طب لو ما كانتش واحد، يبقى أيش بدها
+
+47
+00:05:25,110 --> 00:05:33,150
+... بدها تكون ... لأ، من unit تمام؟ يبقى هذا بدي أقرر
+
+48
+00:05:33,150 --> 00:05:38,090
+أن الـ n of x is من unit.
+
+49
+00:05:40,330 --> 00:05:47,050
+استغلّني شوية بس. يبقى هذا الـ ... الـ ... الـ X is non
+
+50
+00:05:47,050 --> 00:05:53,590
+-unit تمام؟ طيب نحن الآن افترضنا أن الـ N ... آه
+
+51
+00:05:53,590 --> 00:05:59,450
+وين افترضنا؟ طيب افترضنا أن الـ N of X is prime و
+
+52
+00:05:59,450 --> 00:06:06,590
+الـ N of X قلنا ممنوع تساوي واحد. يبقى الـ ... يبقى الـ
+
+53
+00:06:06,590 --> 00:06:13,480
+N of X is non-unit. طبعاً. طيب ممتاز جداً. يبقى بدي أروح
+
+54
+00:06:13,480 --> 00:06:21,220
+افترض أن عندي الذي هو الـ element الذي عندنا هذا.
+
+55
+00:06:21,220 --> 00:06:34,040
+هههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+56
+00:06:39,520 --> 00:06:47,480
+بتساوي A في B. افترض أن الـ X يساوي حاصل ضرب A في B.
+
+57
+00:06:47,480 --> 00:06:55,540
+الـ X هذا، مشان يكون عندي irreducible، بيكون واحد من
+
+58
+00:06:55,540 --> 00:07:01,580
+هذول عبارة عن unit. صحيح ولا لأ؟ طيب تعال نشوف الآن.
+
+59
+00:07:01,580 --> 00:07:08,520
+لو أخذنا تأثير الـ function N على X، مش يساوي تأثير الـ
+
+60
+00:07:08,520 --> 00:07:16,610
+N على الـ A في الـ B. صحيح؟ طيب هذا الكلام يعني أن الـ
+
+61
+00:07:16,610 --> 00:07:27,790
+N of X يساوي الـ N of A في الـ N of B. طب الـ N of X
+
+62
+00:07:27,790 --> 00:07:36,070
+is a prime. أيش معناه؟ ومعناه أن الـ N of X يساوي حاصل
+
+63
+00:07:36,070 --> 00:07:41,840
+ضرب هذين العددين. يبقى واحد منهم بده يساوي واحد على
+
+64
+00:07:41,840 --> 00:07:51,000
+الأقل. صحيح؟ يبقى بجي بقول since الـ N of X is a
+
+65
+00:07:51,000 --> 00:08:01,780
+prime we have يبقى
+
+66
+00:08:01,780 --> 00:08:11,560
+we have أن الـ N of A بده يساوي واحد أو الـ N of B
+
+67
+00:08:11,560 --> 00:08:23,100
+يساوي واحد. مظبوط؟ طيب هذا مظبوط. تعال، أيش الـ
+
+68
+00:08:23,100 --> 00:08:29,180
+N of A يساوي واحد؟ معناته الـ A is unit. هذا يساوي واحد
+
+69
+00:08:29,180 --> 00:08:36,260
+لأن معناته الـ B is unit. يبقى ضروري أقوله by part C
+
+70
+00:08:39,430 --> 00:08:51,170
+أن الـ A is a unit أو الـ B is a unit. إذا واحد
+
+71
+00:08:51,170 --> 00:08:59,090
+منهم unit. فبإيش صار عندي؟ الـ X is irreducible.
+
+72
+00:08:59,090 --> 00:09:06,350
+صحيح؟ لأن الـ X هي فرضناها حاصل ضرب اتنين طلع واحد
+
+73
+00:09:06,350 --> 00:09:17,370
+فيهم unit. يبقى this means that أن الـ X is
+
+74
+00:09:17,370 --> 00:09:26,670
+irreducible over ... irreducible
+
+75
+00:09:26,670 --> 00:09:33,270
+over Z of the square root of D.
+
+76
+00:09:39,100 --> 00:09:47,880
+طيب ننتقل الآن إلى أول نظرية على هذا الموضوع، نقل
+
+77
+00:09:47,880 --> 00:09:54,600
+integral
+
+78
+00:09:54,600 --> 00:10:00,280
+domain. integral
+
+79
+00:10:00,280 --> 00:10:02,500
+domain.
+
+80
+00:10:06,600 --> 00:10:17,900
+every prime is a reducer. every prime is a reducer.
+
+81
+00:10:17,900 --> 00:10:29,380
+every prime is a reducer. افترض
+
+82
+00:10:29,380 --> 00:10:33,820
+يجب
+
+83
+00:10:33,820 --> 00:10:38,980
+أن افترض إنه في عندي integral domain الذي أجيء إليه هنا.
+
+84
+00:10:38,980 --> 00:10:51,280
+فأقول له let D be an integral domain. طبعاً
+
+85
+00:10:51,280 --> 00:10:57,960
+أي prime بده يكون الـ reducer. إذا بدي آخذ
+
+86
+00:10:57,960 --> 00:11:03,260
+element وأفترضه أنه prime وأروح أثبّت له أنه reducer.
+
+87
+00:11:03,890 --> 00:11:12,950
+يرجع هنا فجأة بيقولوا let A الذي موجود في D بـ
+
+88
+00:11:12,950 --> 00:11:22,830
+A prime. وأنت شارف أن
+
+89
+00:11:22,830 --> 00:11:31,950
+نحاول نثبت أن الـ A is irreducible. يبقى
+
+90
+00:11:31,950 --> 00:11:38,270
+كل شغلنا منصبّ على التعريفات تبعات المحاضرة الماضية.
+
+91
+00:11:38,270 --> 00:11:45,430
+طيب الآن فرضنا أن A is a prime. الـ A معناته ممكن
+
+92
+00:11:45,430 --> 00:11:55,910
+يكون unit؟ لأ. يبقى هنا بجي بقول since الـ A since الـ
+
+93
+00:11:55,910 --> 00:12:06,820
+A is a prime، الـ A is not a unit. يجيء الشرط الأول من شرط
+
+94
+00:12:06,820 --> 00:12:12,800
+الـ irreducible يتحقق. بدنا نيجي لمين؟ للشرط الثاني.
+
+95
+00:12:12,800 --> 00:12:20,560
+الشرط الثاني، بدي أثبت irreducible. يعني آه، بس في
+
+96
+00:12:20,560 --> 00:12:28,060
+عندك. بدنا نستفيد من مين؟ نستفيد من مين؟ من
+
+97
+00:12:28,060 --> 00:12:33,330
+المعطيات. الـ A is a prime. ماذا يعني الـ prime؟ لو كان
+
+98
+00:12:33,330 --> 00:12:38,330
+الـ A بيقسم حاصل الضرب، يبقى الـ A بيقسم واحد فيه،
+
+99
+00:12:38,330 --> 00:12:51,630
+مظبوط؟ يبقى الـ A and if الـ A بيقسم الـ B، C، then
+
+100
+00:12:51,630 --> 00:12:57,750
+الـ A بيقسم الـ B or الـ A بيقسم الـ C.
+
+101
+00:13:00,820 --> 00:13:08,220
+بدأ آخذ. لو كان الـ A بيقسم الـ B، أيش اللي بده
+
+102
+00:13:08,220 --> 00:13:17,580
+يحدث؟ مشان نثبتها irreducible، يبقى none، zero، و
+
+103
+00:13:17,580 --> 00:13:22,660
+بدي أكتبها علاقة، ما كتبناش على شكل حاصل ضرب. نكتبها
+
+104
+00:13:22,660 --> 00:13:25,100
+على شكل حاصل ضرب.
+
+105
+00:13:31,120 --> 00:13:39,820
+الـ A بدها تساوي الـ B في C، مشان
+
+106
+00:13:39,820 --> 00:13:43,760
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+107
+00:13:43,760 --> 00:13:44,260
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+108
+00:13:44,260 --> 00:13:44,720
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+109
+00:13:44,720 --> 00:13:45,220
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+110
+00:13:45,220 --> 00:13:46,600
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+111
+00:13:46,600 --> 00:13:46,800
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+112
+00:13:46,800 --> 00:13:50,820
+أنا أنا أنا أنا أنا
+
+113
+00:13:50,820 --> 00:13:50,900
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+114
+00:13:50,900 --> 00:13:58,360
+أنا أنا
+
+115
+00:13:58,360 --> 00:14:04,600
+أنا الـ A non-unit، فالـ A تقسم الـ C. فالفرضية إن
+
+116
+00:14:04,600 --> 00:14:13,780
+الـ A بده يساوي مين؟ B في C. الآن since الـ A بتقسم
+
+117
+00:14:13,780 --> 00:14:22,640
+الـ BC، أكيد ما هي الـ A تساوي مين؟ الـ B في C. يعني
+
+118
+00:14:22,640 --> 00:14:28,440
+الـ A بتقسم نفسها، صح ولا لأ؟ يبقى الـ A بتقسم الـ B في
+
+119
+00:14:28,440 --> 00:14:40,430
+C. يبقى we have أن الـ A تقسم الـ B أو الـ A تقسم الـ C.
+
+120
+00:14:40,430 --> 00:14:51,010
+ليش؟ لأن الـ A is a prime because الـ
+
+121
+00:14:51,010 --> 00:14:55,790
+A is a prime. فهي تمام.
+
+122
+00:15:00,870 --> 00:15:06,490
+نحن نثبت يا إما الـ B unit يا إما الـ C unit.
+
+123
+00:15:06,490 --> 00:15:18,410
+مظبوط؟ طيب الآن لو جئتُ قلت لك الـ A أو if الـ A
+
+124
+00:15:18,410 --> 00:15:28,570
+بتقسم، تقسم الـ B، then الـ B تساوي A في T مثلاً.
+
+125
+00:15:31,780 --> 00:15:42,220
+وهو some T الذي موجود في D. طب
+
+126
+00:15:42,220 --> 00:15:50,440
+لو جأنا للعنصر B وضربته في واحد، ضربته في واحد، يبقى
+
+127
+00:15:50,440 --> 00:15:57,900
+هذا مش هو عبارة عن الـ B. تمام؟ طب و الـ B هو عبارة عن
+
+128
+00:15:57,900 --> 00:16:08,470
+مين؟ A في T. صح؟ ما هي الـ A تساوي؟ B في C. يبقى هنا B
+
+129
+00:16:08,470 --> 00:16:19,850
+في C في T. تمام؟ طيب هذا قد يعطيني الـ B في C في T. الآن
+
+130
+00:16:19,850 --> 00:16:23,290
+نحن نشتغل أين؟ في ring ولا في integral domain؟
+
+131
+00:16:23,290 --> 00:16:27,850
+الـ integral domain. أخذنا علاقة بتقول لي لو عندك
+
+132
+00:16:27,850 --> 00:16:32,320
+integral domain و A في B بده يساوي A في C، بقى بالـ
+
+133
+00:16:32,320 --> 00:16:36,280
+left cancellation. الـ B بده يساوي مين؟ بده يساوي C.
+
+134
+00:16:36,280 --> 00:16:48,340
+يجيء By left cancellation. لأ.
+
+135
+00:16:48,340 --> 00:16:56,540
+We have بده يصير الواحد بده يساوي C في T. أيش معنى
+
+136
+00:16:56,540 --> 00:17:03,210
+هذا الكلام؟ أن الـ C is a unit. يبقى هذا معناته أن
+
+137
+00:17:03,210 --> 00:17:11,490
+الـ C is a unit. طبعاً؟ طب الـ irreducible قلنا يا إما
+
+138
+00:17:11,490 --> 00:17:15,570
+الـ B unit يا إما الـ C unit. يبقى لما طلعت الـ C unit
+
+139
+00:17:15,570 --> 00:17:20,790
+أروح أدوّر على B، ما في داعي. يبقى معنى هذا الكلام
+
+140
+00:17:20,790 --> 00:17:31,050
+يبقى this means that هذا يعني أن الـ A is
+
+141
+00:17:31,050 --> 00:17:36,970
+irreducible over
+
+142
+00:17:36,970 --> 00:17:46,270
+الذي هو Z over
+
+143
+00:17:46,270 --> 00:17:51,230
+D. على
+
+144
+00:17:51,230 --> 00:17:52,530
+D فقط. لإيه؟
+
+145
+00:18:15,190 --> 00:18:20,550
+طيب النظرية هذه كان بيقول في الـ integral domain لو
+
+146
+00:18:20,550 --> 00:18:26,370
+عندي A prime بصير irreducible. السؤال هو طب لو كان الـ A
+
+147
+00:18:26,370 --> 00:18:33,190
+irreducible، بصير A prime؟ قد يكون وقد لا يكون. إذا
+
+148
+00:18:33,190 --> 00:18:39,290
+العكس، النظرية ليس بالضرورة صحيحة. تبقى بنا نكتب
+
+149
+00:18:39,290 --> 00:18:42,790
+هذه الملاحظة في Gary Mark.
+
+150
+00:18:47,180 --> 00:18:56,240
+the converse of
+
+151
+00:18:56,240 --> 00:19:01,560
+the
+
+152
+00:19:01,560 --> 00:19:16,400
+above theorem. نظريتي على 100، 100 متر.
+
+153
+00:19:17,300 --> 00:19:28,580
+ليس بالضرورة صحيحاً. that is, I am الـ
+
+154
+00:19:28,580 --> 00:19:43,460
+A is a radio source لا يعني أن الـ A is prime.
+
+155
+00:19:45,570 --> 00:19:54,750
+بنعطي مثال على ذلك. طبعاً
+
+156
+00:19:54,750 --> 00:20:02,930
+الكتاب أعطاني المثال في الأول، ثم النظرية، ثم الـ
+
+157
+00:20:02,930 --> 00:20:08,350
+remark. تمام. فالترتيب مش دقيق. نحن أعطينا النظرية
+
+158
+00:20:08,350 --> 00:20:13,170
+ثم أعطينا الـ remark، ثم بدنا نجيب counter example
+
+159
+00:20:13,170 --> 00:20:17,820
+يثبت مين؟ يثبت هذه الـ remark. يبقى أنا بدأ آخذ
+
+160
+00:20:17,820 --> 00:20:21,920
+integral domain وأثبت أنه على الـ integral domain
+
+161
+00:20:21,920 --> 00:20:26,540
+هنا في عندي element irreducible لكنه في الحقيقة
+
+162
+00:20:26,540 --> 00:20:34,180
+ليس prime. تمام؟ for example بيقول ما يأتي: consider
+
+163
+00:20:34,180 --> 00:20:41,880
+the integral domain. consider the integral
+
+164
+00:20:44,920 --> 00:20:51,340
+domain. افترض أنه عندك integral domain الذي هو D
+
+165
+00:20:51,340 --> 00:21:03,620
+يساوي Z of الجذر التربيعي لسالب ثلاثة.
+
+166
+00:21:03,620 --> 00:21:09,220
+يبقى
+
+167
+00:21:09,220 --> 00:21:15,040
+أنا بروح آخذ element في هذا الـ integral domain و
+
+168
+00:21:15,040 --> 00:21:19,720
+أثبت أن هذا الـ element في الأول is irreducible.
+
+169
+00:21:19,720 --> 00:21:25,020
+يعني في الحل أنا همشي خطوتين. مش أنا قلت لك خلاص
+
+170
+00:21:25,020 --> 00:21:29,260
+خذ هذا الـ element is irreducible؟ لأ. بدي أثبت أن في
+
+171
+00:21:29,260 --> 00:21:33,880
+عندي element irreducible وفي الحقيقة هذا الـ
+
+172
+00:21:33,880 --> 00:21:38,080
+element ليس a prime. يبقى خطوات الحل بيكون على
+
+
+223
+00:27:08,380 --> 00:27:19,240
+السؤال هو: ممكن ألاقي A و B في Z يحقق هذه المعادلة؟
+
+224
+00:27:19,240 --> 00:27:23,160
+ممكن ألاقي أنت؟ مش مهم، سالم موجة بصفر اللي بدك
+
+225
+00:27:23,160 --> 00:27:29,420
+إياه، ممكن ألاقي؟ ولا واحد تمام؟ يعني هذا كلام
+
+226
+00:27:29,420 --> 00:27:35,290
+ممكن؟ this is impossible، يبدأ هنا، بروح بقول له this
+
+227
+00:27:35,290 --> 00:27:45,230
+is impossible because there
+
+228
+00:27:45,230 --> 00:27:56,110
+are no integers أو
+
+229
+00:27:56,110 --> 00:27:59,410
+no integers
+
+230
+00:27:59,410 --> 00:28:07,740
+a and the B satisfied the
+
+231
+00:28:07,740 --> 00:28:14,580
+equation، المعادلة اللي هي A تربيع زائد ثلاثة B
+
+232
+00:28:14,580 --> 00:28:21,820
+تربيع يساوي اثنين. إذن، فيه شغل غلط. هي اللي وصلتني
+
+233
+00:28:21,820 --> 00:28:29,420
+إلى نتيجة غلط. هذول اثنين منهم إيش؟ not units، معناته
+
+234
+00:28:29,420 --> 00:28:39,220
+واحدة منهم unit أو 1، يبقى هذا contradiction، تناقض
+
+235
+00:28:39,220 --> 00:28:49,520
+مادام تناقض، هذا يعطينا أن الـ X is a unit أو الـ Y
+
+236
+00:28:49,520 --> 00:28:57,200
+is a unit، طبعًا هذا تعريف مين؟ طبعًا هي في الـ
+
+237
+00:28:57,200 --> 00:29:05,200
+irreducibility، يبقى هنا ساق الـ X is ايه الـ... مش الـ
+
+238
+00:29:05,200 --> 00:29:13,020
+X، الـ element اللي عندنا واحد زائد جذر ناقص ثلاثة
+
+239
+00:29:13,020 --> 00:29:19,940
+is irreducible of
+
+240
+00:29:19,940 --> 00:29:24,180
+الجذر
+
+241
+00:29:24,180 --> 00:29:25,740
+اللي سالب ثلاثة
+
+242
+00:29:33,440 --> 00:29:38,620
+لكن لو كانت reducible، ده يعني إن إيه؟ إذا بتعرف؟
+
+243
+00:29:38,620 --> 00:29:47,060
+إذا بتعرف لو كانت إيه؟ reducible، بس إيش رأيك
+
+244
+00:29:47,060 --> 00:29:52,560
+تصبري علينا شوية، النظرية اللي جاية مربوطة بالنظرية
+
+245
+00:29:52,560 --> 00:29:57,780
+الأولانية، إيه؟ بل تجمع النظرية الاولانية أو
+
+246
+00:29:57,780 --> 00:30:01,900
+النظرية اللي جاية، نص النظرية الأولى ونص النظرية
+
+247
+00:30:01,900 --> 00:30:07,720
+التالية. يكون أجوبنا على سؤالك إن شاء الله، يبقى الـ
+
+248
+00:30:07,720 --> 00:30:12,720
+element هذه مرة يا بنات is irreducible، يبقى احنا
+
+249
+00:30:12,720 --> 00:30:19,860
+حققنا مين؟ حققنا الأمر الأول من الـ remark اللي كنا
+
+250
+00:30:19,860 --> 00:30:24,280
+كاتبينه هنا، إن لو كان الـ element is irreducible
+
+251
+00:30:24,280 --> 00:30:30,280
+ليس بالضرورة أن يكون prime، يبقى الآن بدنا نثبت أنه
+
+252
+00:30:30,280 --> 00:30:36,510
+ليس بالضرورة يكون إيه؟ يكون prime. طيب، شوفين يا شغل
+
+253
+00:30:36,510 --> 00:30:44,930
+غيرك. لو جيتِ قلتِ لي consider واحد زائد جذر ناقص
+
+254
+00:30:44,930 --> 00:30:52,130
+ثلاثة في واحد ناقص جذر لناقص ثلاثة. يعني كأننا
+
+255
+00:30:52,130 --> 00:31:00,730
+حللنا فرق بين مربعين. أليس هذا هو واحد زائد
+
+256
+00:31:00,730 --> 00:31:08,690
+ثلاثة؟ اللي هو أربعة، اللي هو بده يساوي كمان اثنين
+
+257
+00:31:08,690 --> 00:31:13,370
+في اثنين، يعني
+
+258
+00:31:13,370 --> 00:31:17,930
+معناته إن الـ element هذا بده يساوي اثنين في اثنين
+
+259
+00:31:17,930 --> 00:31:24,870
+صح؟ اللي حاصل ضربه يساوي أربعة، إذا بده يساوي، و
+
+260
+00:31:24,870 --> 00:31:29,330
+الأربعة كتبتها اثنين في اثنين، يبقى هذا بده يقينا
+
+261
+00:31:29,330 --> 00:31:36,600
+إيش؟ بدي يعطينا أن واحد زائد جذر ناقص ثلاثة divides
+
+262
+00:31:36,600 --> 00:31:44,540
+اثنين في اثنين، لو كان الـ prime بدي يقسم اثنين، صح
+
+263
+00:31:44,540 --> 00:31:51,300
+ولا لا، يبقى أبدًا نشوفه هل هو بيقسم ولا بيقسمش، طيب
+
+264
+00:31:51,300 --> 00:32:01,410
+if الواحد زائد جذر ناقص ثلاثة يقسم الاثنين، إذا لازم
+
+265
+00:32:01,410 --> 00:32:07,190
+ألاقي رقم ثاني أو عنصر ثاني أضربه فيه، طبعًا أنّه
+
+266
+00:32:07,190 --> 00:32:18,450
+يجب أن نجد، صح ولا لا؟ يبقى هنا يساوي اثنين، then for الـ
+
+267
+00:32:18,450 --> 00:32:26,090
+A والـ B اللي موجودين في Z، we have for some، مش الكل
+
+268
+00:32:26,090 --> 00:32:34,650
+يعني for some، الـ A والـ B اللي موجودين في Z، We
+
+269
+00:32:34,650 --> 00:32:44,470
+have أن الواحد زائد جذر ناقص ثلاثة في A زائد B جذر
+
+270
+00:32:44,470 --> 00:32:52,050
+ناقص ثلاثة يساوي اثنين، بظبط يعني؟ هذا بيقسم اثنين
+
+271
+00:32:52,050 --> 00:32:57,670
+يبقى لازم ألاقي عنصر أضربه في هذا يطلع اثنين، بدي
+
+272
+00:32:57,670 --> 00:33:03,710
+أشوف هذا وين بيوصل، طب بدفك القوس، الأول دي عنها يبقى
+
+273
+00:33:03,710 --> 00:33:12,850
+هذا A ناقص ثلاثة B زائد
+
+274
+00:33:12,850 --> 00:33:20,930
+B جذر هذا في هذا بـ A، هذا في هذا بـ A، وهذا في هذا
+
+275
+00:33:20,930 --> 00:33:30,430
+بـ B، يبقى A زائد B في جذر ناقص ثلاثة يساوي، يساوي
+
+276
+00:33:30,430 --> 00:33:34,310
+اثنين، طيب
+
+277
+00:33:34,310 --> 00:33:40,950
+هذه ممكن أكون منها معادلتين، المعادلة الأولى A ناقص
+
+278
+00:33:40,950 --> 00:33:45,870
+ثلاثة B يساوي اثنين، والمعادلة الثانية A زائد B
+
+279
+00:33:45,870 --> 00:33:50,390
+يساوي صفر، مظبوط
+
+280
+00:33:50,990 --> 00:33:56,190
+طيب إيش رأيك؟ بتحلي المعادلتين هذول مع بعض، يبقى A
+
+281
+00:33:56,190 --> 00:34:01,510
+ناقص ثلاثة B يساوي اثنين، وهذه بتضربيها بسالب واحد، يبقى سالب A
+
+282
+00:34:01,510 --> 00:34:08,650
+سالب B يساوي صفر، لو جمعنا يبقى هذول مع السلامة هذا
+
+283
+00:34:08,650 --> 00:34:14,570
+بده يعطيني سالب أربعة B يساوي اثنين، يبقى B بده
+
+284
+00:34:14,570 --> 00:34:21,910
+يساوي قداش؟ سالب نصف، موجود في Z؟ إذًا فيه تناقض،
+
+285
+00:34:21,910 --> 00:34:28,030
+مظبوط؟ طيب، التناقض هذا جابه شلة، شو الشلة؟ قلت إن
+
+286
+00:34:28,030 --> 00:34:36,270
+هذا بيقسم، مظبوط؟ يبقى هنا سواء الواحد زائد الجذر
+
+287
+00:34:36,270 --> 00:34:41,450
+ناقص ثلاثة does not divide اثنين، لا يمكن نقسم
+
+288
+00:34:41,450 --> 00:34:48,140
+اثنين، لما فرضت نقسم اثنين وصلت إلى تناقض، وصلت إلى
+
+289
+00:34:48,140 --> 00:34:52,960
+عنصر مش موجود، وان في Z، يبقى هذا لا يمكن أن
+
+290
+00:34:52,960 --> 00:34:58,260
+يحدث، يعني لا يمكن لواحد زائد جذر ناقص ثلاثة أن يقسم
+
+291
+00:34:58,260 --> 00:35:04,220
+الاثنين، يبقى ممكن يكون هذا try، لا، يبقى هذا بده
+
+292
+00:35:04,220 --> 00:35:10,740
+يعطينا إيه؟ أن الواحد زائد جذر ناقص ثلاثة is not a
+
+293
+00:35:10,740 --> 00:35:20,350
+prime، يبقى هذا ليس بالضرورة أولي، يبقى هذا مثال يوضح أن لو
+
+294
+00:35:20,350 --> 00:35:25,490
+كان عندي عنصر، وعنصر irreducible على integral
+
+295
+00:35:25,490 --> 00:35:30,450
+domain، يبقى ليس بالضرورة أن يكون هذا العنصر prime
+
+296
+00:35:30,610 --> 00:35:36,030
+يعني عكس النظرية، إذا عكس النظرية ليس صحيحًا إلا أن
+
+297
+00:35:36,030 --> 00:35:43,290
+فيه نظرية تجمع النظرية الأولى وبتجيب لي كمان نص
+
+298
+00:35:43,290 --> 00:35:46,550
+نظرية جديدة، إيش بتقول النظرية
+
+299
+00:35:51,040 --> 00:35:58,580
+بتقول النظرية، من آياتك، أو يا ريكو، In
+
+300
+00:35:58,580 --> 00:36:06,600
+a principal ideal domain، In a principal ideal
+
+301
+00:36:06,600 --> 00:36:09,800
+domain
+
+302
+00:36:09,800 --> 00:36:15,780
+اللي هأختصرها يا بنات إلى PID، Principal Ideal
+
+303
+00:36:15,780 --> 00:36:18,160
+Domain، An element
+
+304
+00:36:21,630 --> 00:36:32,090
+an element is irreducible if
+
+305
+00:36:32,090 --> 00:36:45,310
+and only if it is prime، لو كان لو
+
+306
+00:36:45,310 --> 00:36:46,630
+كان الـ prime
+
+307
+00:36:52,400 --> 00:37:03,400
+الـ proof تبقى
+
+308
+00:37:03,400 --> 00:37:11,540
+بدلًا، هأقول له let D be a principal ideal domain
+
+309
+00:37:11,540 --> 00:37:14,800
+بتأكد
+
+310
+00:37:14,800 --> 00:37:21,660
+أنه عندي element، والـ element هذا is irreducible
+
+311
+00:37:22,150 --> 00:37:27,210
+أها، بتفترض أنه is a prime، في الأول، ناخد الأسهم
+
+312
+00:37:27,210 --> 00:37:38,970
+يبقى هنا، لـ A، B، A prime in D
+
+313
+00:37:38,970 --> 00:37:42,190
+النظرية
+
+314
+00:37:42,190 --> 00:37:49,430
+السابقة، النظرية السابقة، يبقى الـ A is irreducible
+
+315
+00:37:49,430 --> 00:37:55,580
+وهو المطلوب، المطلوب الأول، يبقى هنا تلعبِ A prime in
+
+316
+00:37:55,580 --> 00:38:08,320
+D، by the above theorem، النظرية الأعلى، الـ A is
+
+317
+00:38:08,320 --> 00:38:18,280
+irreducible in D، هذا
+
+318
+00:38:18,280 --> 00:38:40,290
+الاتجاه الأول، بنروح من الاتجاه الثاني، consider
+
+319
+00:38:40,290 --> 00:38:46,370
+إحنا
+
+320
+00:38:46,370 --> 00:38:56,260
+أخذنا هنا A، بدنا ناخد الـ A irreducible، assume that
+
+321
+00:38:56,260 --> 00:39:08,020
+أن الـ A is irreducible، one
+
+322
+00:39:08,020 --> 00:39:19,900
+to show that، one to show that، إن الـ A is a prime
+
+323
+00:39:19,900 --> 00:39:26,300
+إيش
+
+324
+00:39:26,300 --> 00:39:31,640
+يعني الـ A is a prime؟ يعني لو كان الـ A بيقسم الـ B
+
+325
+00:39:31,640 --> 00:39:44,260
+في C، يقسم الـ B أو يقسم الـ C، تفهم؟ يعني that is if الـ
+
+326
+00:39:44,260 --> 00:39:51,120
+A بيقسم الـ BC، then
+
+327
+00:39:51,120 --> 00:40:03,260
+الـ A بيقسم الـ B أو الـ A بيقسم الـ C
+
+328
+00:40:03,260 --> 00:40:11,240
+تجاهنا بفترض أن الـ A بيقسم الـ BC، هذا بيكون معطى
+
+329
+00:40:11,240 --> 00:40:16,490
+وهذا اللي إحنا عايزينه، يعني عايزين نثبت، يبقى باجي
+
+330
+00:40:16,490 --> 00:40:21,690
+بقول له هنا، الـ CEO إن
+
+331
+00:40:21,690 --> 00:40:28,230
+الـ A بيقسم الـ BC، طيب
+
+332
+00:40:28,230 --> 00:40:42,370
+بدي أجي أقول له define an ideal I، وبده يساوي AX زائد
+
+333
+00:40:42,370 --> 00:40:47,600
+BY، حيث الـ X والـ Y موجودة في D.
+
+334
+00:40:50,680 --> 00:40:55,900
+طيب، وإحنا مليش نظرية يا بنات؟
+
+335
+00:40:55,900 --> 00:41:00,220
+الـ principal ideal domain، دماغية؟ يبقى أي ideal يبقى
+
+336
+00:41:00,220 --> 00:41:08,140
+inside، صح؟ يبقى ده الـ
+
+337
+00:41:08,140 --> 00:41:14,750
+I هذا بده يساوي D، يعني هو الـ principal ideal
+
+338
+00:41:14,750 --> 00:41:21,430
+generated by D، تمام؟ بنقول له، كويسة. الآن السؤال هو
+
+339
+00:41:21,430 --> 00:41:30,770
+هل الـ A موجود في الـ I؟ موجود
+
+340
+00:41:30,770 --> 00:41:38,470
+ليش؟ لأن الـ A بقدر أكتبه A في واحد، زي الـ B في صفر
+
+341
+00:41:41,580 --> 00:41:45,560
+على الصيغة اللي موجودة، يبقى هذا صفر، وA في واحد في
+
+342
+00:41:45,560 --> 00:41:54,500
+أي مصدر، إيه ابتدأ، يبقى هذه، عارفين اللي هي، شملات الـ
+
+343
+00:41:54,500 --> 00:41:58,600
+I يساوي D؟ principal I، دي إيه؟ لأن principal I دي
+
+344
+00:41:58,600 --> 00:42:08,620
+domain، تمام، كويس، طيب الآن، then الـ A موجود وين؟
+
+345
+00:42:09,070 --> 00:42:13,930
+موجود في الـ principal ideal generated by D، يعني
+
+346
+00:42:13,930 --> 00:42:26,630
+بقدر أكتب، إن الـ A بده يساوي D في A، for some A اللي
+
+347
+00:42:26,630 --> 00:42:27,890
+موجودة في D
+
+348
+00:42:40,170 --> 00:42:46,910
+الآن... الآن أنا بقول إن الـ A تساوي الـ، يعني دي R
+
+349
+00:42:46,910 --> 00:42:55,510
+وإحنا إيش فرضنا؟ إن الـ A is reducible، مظبوط؟ أنا من
+
+350
+00:42:55,510 --> 00:43:05,470
+هنا باجي بقول له since، بما أن الـ A is irreducible، we
+
+351
+00:43:05,470 --> 00:43:13,270
+have، هذه irreducible وقدرنا نكتبها على الشكل
+
+352
+00:43:13,270 --> 00:43:20,010
+حاصل ضرب two elements، يبقى واحد unit، مظبوط، we
+
+353
+00:43:20,010 --> 00:43:32,230
+have أن الـ D is a unit or الـ R is a unit، طيب
+
+354
+00:43:32,230 --> 00:43:39,620
+بتاخذيها واحدة واحدة وشوفي وين بتوصلِ، الـ D is a
+
+355
+00:43:39,620 --> 00:43:40,120
+unit.
+
+356
+00:43:42,840 --> 00:43:50,360
+Then، بدك تكتبيها العبارة، شفويًا صحيحة ولا لأ. يبقى
+
+357
+00:43:50,360 --> 00:43:55,880
+الواحد موجود في الـ principal ideal generated from
+
+358
+00:43:55,880 --> 00:44:03,820
+D، لأنه D unit، مظبوط؟ طيب، مدام الواحد موجود في D
+
+359
+00:44:04,310 --> 00:44:09,370
+لو كان الـ unity موجود في الـ ideal، اللي بيبقى الـ ideal
+
+360
+00:44:09,370 --> 00:44:15,690
+بتساوي إيه؟ الـ ring كلها، مظبوط، إن هذا يرجع، there
+
+361
+00:44:15,690 --> 00:44:27,950
+أو هذا بيبقى موجود هنا implies that إن الـ D هذا
+
+362
+00:44:27,950 --> 00:44:30,930
+كله بيبقى يساوي كل الـ
+
+363
+00:44:34,840 --> 00:44:42,240
+طيب، الواحد موجود في D، الآن هل الواحد موجود في A
+
+364
+00:44:42,240 --> 00:44:46,960
+ماهو
+
+365
+00:44:46,960 --> 00:44:55,960
+I،  ∈ D، صح ولا لأ؟ الـ ∈ هذه R، تمام؟ إذًا هذا بدي
+
+366
+00:44:55,960 --> 00:45:03,130
+يعطينا، يعني  موجود في I، يبقى الواحد، بدي أساوي
+
+367
+00:45:03,130 --> 00:45:09,670
+AX زائد BY، مظبوط
+
+368
+00:45:09,670 --> 00:45:18,690
+اضرب كلّه في C، إذا ضربنا كلّه في C، بيصير C بيساوي AC
+
+369
+00:45:18,690 --> 00:45:27,030
+X زائد BCY، ده
+
+370
+00:45:27,030 --> 00:45:31,090
+جيبوا النظر معايا، هل A تقسم هذا term
+
+371
+00:45:34,160 --> 00:45:43,560
+هل الـ A تقسم هذا الـ term؟ مظبوط؟ يبقى فاجب يقول له
+
+372
+00:45:43,560 --> 00:45:55,520
+now، الـ A تقسم الـ ACX، هذه واحدة، and الـ A تقسم الـ
+
+373
+00:45:55,520 --> 00:46:08,490
+BCY، because الـ A تقسم الـ BC، هذا يتطلب أن الـ A
+
+374
+00:46:08,490 --> 00:46:17,930
+تقسم الـ ACX زائد الـ BCY، طيب هذه مين هي؟ C، هذا
+
+375
+00:46:17,930 --> 00:46:24,630
+معناته إن الـ A تقسم الـ C، هتجيبها، المطلب الأول
+
+376
+00:46:32,190 --> 00:46:39,030
+خلصنا، نمشي مرة ثانية، إحنا أخذنا لو كانت الـ R unit
+
+377
+00:46:39,030 --> 00:46:44,930
+طلعنا منها إن، إذا تقسم الـ C، الآن لو كانت الـ R is
+
+378
+00:46:44,930 --> 00:47:01,580
+a unit، if الـ R is a unit، then إحنا أخذنا الـ A بدأ
+
+379
+00:47:01,580 --> 00:47:08,120
+تساوي الـ DR، صح؟ أخذنا الـ A بدأ تساوي الـ DR،
+
+380
+00:47:08,120 --> 00:47:14,320
+والـ R هذا unit، يعني إيه؟ معكوس، لو ضربنا في
+
+381
+00:47:14,320 --> 00:47:23,940
+المعكوس، إيش بده يصير؟ AR inverse بده يساوي D، سكت
+
+382
+00:47:23,940 --> 00:47:32,820
+الشعر، لأنها A تساوي DR، أيها فوق بدي أضربها في R
+
+383
+00:47:32,820 --> 00:47:38,800
+inverse، كيف؟ يبقى بصير AR inverse بده يساوي D، طيب،
+
+384
+00:47:38,800 --> 00:47:47,700
+مين هو هذا بنا؟ تعريف مين؟ مش كل العناصر على الشكل
+
+385
+00:47:47,700 --> 00:47:54,020
+هذا، element A في element من R وفي element من D، مش
+
+386
+00:47:54,020 --> 00:48:00,400
+بشكل الـ ideal generated by A، صح ولا لأ؟ يبقى
+
+387
+00:48:00,400 --> 00:48:05,120
+هذا معناه إن الـ principal ideal generated by إيه؟
+
+388
+00:48:05,120 --> 00:48:13,940
+هو الـ principal ideal generated by D، صحيح ولا لأ؟
+
+389
+00:48:13,940 --> 00:48:21,580
+أنا سكت ولا اشتغل؟ مظبوط ولا لأ؟ هذه العبارة اللي
+
+390
+00:48:21,580 --> 00:48:27,460
+عندك، هذه مش العنصر هذا هو العنصر هذا، يبقى الـ ideal
+
+391
+00:48:27,460 --> 00:48:31,440
+اللي يولد بهذا العنصر هو الـ ideal اللي يولد بهذا
+
+392
+00:48:31,440 --> 00:48:35,140
+العنصر، الـ principal ideal، مظبوط؟ هذا الـ principal
+
+393
+00:48:35,140 --> 00:48:39,640
+ideal تبع الـ D، هذا لو جيت أعرف الـ principal ideal
+
+394
+00:48:39,640 --> 00:48:44,980
+generated by A، مش هو كل العناصر A في R حيث R
+
+395
+00:48:44,980 --> 00:48:4
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/K1zwu7gTN7M_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/K1zwu7gTN7M_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8b8dd29670b7319994e81626b8cfbbed301925b9
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/K1zwu7gTN7M_raw.srt
@@ -0,0 +1,1708 @@
+1
+00:00:20,860 --> 00:00:25,640
+بسم الله الرحمن الرحيم نكمل ما ابتدأنا به في المرة
+
+2
+00:00:25,640 --> 00:00:30,860
+الماضية في نهاية المحاضرة الماضية كتبنا ال remark
+
+3
+00:00:30,860 --> 00:00:36,140
+التالية أنه لو كان عندي function من Z كله ل square
+
+4
+00:00:36,140 --> 00:00:42,300
+root ل D ل Z plus معرفة N of A زائد B ل square
+
+5
+00:00:42,300 --> 00:00:47,120
+root ل D بتساوي ال absolute value لل A ترابية نقص
+
+6
+00:00:47,120 --> 00:00:54,800
+ال D بيه ترابيةالنقطة الأولى والثانية برهنهم المرة
+
+7
+00:00:54,800 --> 00:01:00,200
+الماضية ووصلنا الى النقطة الثالثة والرابعة إذا كلا
+
+8
+00:01:00,200 --> 00:01:07,280
+كتر بدنا نيجي لنمرى الـC نمرى الـC قال X is a unit
+
+9
+00:01:07,280 --> 00:01:14,220
+if and only if ال N X يسوى 101 هذا العشري نسبته ال
+
+10
+00:01:14,220 --> 00:01:18,660
+1000 يبقى أبراد ال N أكتر
+
+11
+00:01:21,070 --> 00:01:26,790
+الـ X هو اللي موجودة هذه في
+
+12
+00:01:26,790 --> 00:01:32,770
+ذات الاسم وعود لـ D هي كمعنى هذا الكلام اللي هي N
+
+13
+00:01:32,770 --> 00:01:40,990
+of A زائد B جادر الـ D بديه سوى 1 if and only if
+
+14
+00:01:40,990 --> 00:01:47,290
+وده يجيب روح نستخدم التعريف نشيل هذا ونحط التعريف
+
+15
+00:01:47,290 --> 00:01:54,570
+اللي احنا حاطينااللي همين a تربيع ناقص d بي تربيع
+
+16
+00:01:54,570 --> 00:02:05,450
+كل هذا الكلام بدي يساوي واحدة if and only if يبقى
+
+17
+00:02:05,450 --> 00:02:11,630
+ال a تربيع ناقص d بي تربيع يساوي زائد او ناقص
+
+18
+00:02:11,630 --> 00:02:17,070
+واحدة يشيلنا ال absolute valueحطينا لل element
+
+19
+00:02:17,070 --> 00:02:21,990
+واحد زايد او ناقص واحد هذا ممكن احلله كفارق بين
+
+20
+00:02:21,990 --> 00:02:29,090
+المرابعين يبقى هذا الكلام صحيح اذا كان ال a ناقص b
+
+21
+00:02:29,090 --> 00:02:37,150
+في جذر ال D في ال a زايد b جذر ال D بيكون زايد او
+
+22
+00:02:37,150 --> 00:02:46,840
+ناقص واحد if and only if هذا صحيح لو كانهه مدام
+
+23
+00:02:46,840 --> 00:02:51,980
+واحد واحد هو ال unity مظبوط ولا لا يبقى بناء عليه
+
+24
+00:02:51,980 --> 00:02:58,100
+هذا الكلام صحيح لو كان هداش unit يبقى if and only
+
+25
+00:02:58,100 --> 00:03:07,800
+if ال X اللي تساوي ال A زائد B جذر ال D is a unit
+
+26
+00:03:07,800 --> 00:03:17,270
+وهو المفروض حيث نبردالنمرة دي بتاعي أقول له assume
+
+27
+00:03:17,270 --> 00:03:27,130
+افترض ان ال N of X is a prime ايش
+
+28
+00:03:27,130 --> 00:03:35,310
+بدنا نثبت؟ ايش بدنا نثبت يا بنات؟ ايش بدنا نثبت؟
+
+29
+00:03:35,310 --> 00:03:40,330
+ان ال X is irreducible المرة اللي فاتت عرفنا ال
+
+30
+00:03:40,330 --> 00:03:45,380
+prime وعرفنا ال irreducibleيبقى ال element a بقول
+
+31
+00:03:45,380 --> 00:03:53,460
+عنه irreducible إذا حقق شرطين الشرط الأول أن ال a
+
+32
+00:03:53,460 --> 00:03:58,900
+is non unit الشرط التاني لو جدرت أكتبه على صيغة
+
+33
+00:03:58,900 --> 00:04:04,520
+حصل ضرب عنصرين يبقى واحد فيهم يكون unit يعني لو
+
+34
+00:04:04,520 --> 00:04:09,920
+كان ال a كتبته على شكل b في c يبقى ال a is unit أو
+
+35
+00:04:09,920 --> 00:04:15,320
+ال b is unit هذا ال irreducibleطيب ليه prime الشرط
+
+36
+00:04:15,320 --> 00:04:20,720
+الأولاني هو الشرط نفسه ان ال a بقول عنه prime إذا
+
+37
+00:04:20,720 --> 00:04:26,180
+كان ال a non unit اتنين مش كان يسوى حصر ضرب ب two
+
+38
+00:04:26,180 --> 00:04:31,220
+elements لأ كان ال a بيقسم ال b في c إذا ال a
+
+39
+00:04:31,220 --> 00:04:34,560
+بيقسم ال b or ال b بيقسم ال c هذا ال two
+
+40
+00:04:34,560 --> 00:04:39,940
+definitions اللي معاكم في بداية المحاضرة الماضية
+
+41
+00:04:39,940 --> 00:04:45,810
+طيب نمشي هناان احنا افترضنا ان ال N of X is a
+
+42
+00:04:45,810 --> 00:04:54,170
+prime مطلوب يثبت ان ال X is a reducer ممتاز جدا طب
+
+43
+00:04:54,170 --> 00:05:00,790
+لما اقول N of X is a prime تمام يبقى ال N of X
+
+44
+00:05:00,790 --> 00:05:07,370
+ممكن تكون unit ممكن
+
+45
+00:05:07,370 --> 00:05:18,590
+تكون واحديبقى ذلك ال n of x does not equal to one
+
+46
+00:05:18,590 --> 00:05:25,110
+مش ممكن تكون واحد طب لو ماكنتش واحد يبقى إيش بدها
+
+47
+00:05:25,110 --> 00:05:33,150
+.. بدها تكون .. لأ من unit تمام؟ يبقى هذا بدي أقين
+
+48
+00:05:33,150 --> 00:05:38,090
+أن ال n of x is من unit
+
+49
+00:05:40,330 --> 00:05:47,050
+استغلني شوية بس يبقى هذا ال .. ال .. ال X is non
+
+50
+00:05:47,050 --> 00:05:53,590
+-unit تمام؟ طيب احنا الآن افترضنا ان ال N .. اه
+
+51
+00:05:53,590 --> 00:05:59,450
+وين افترضنا؟ طيب افترضنا ان ال N of X is prime و
+
+52
+00:05:59,450 --> 00:06:06,590
+ال N of X قلنا ممنوع تساوي واحد يبقى ال .. يبقى ال
+
+53
+00:06:06,590 --> 00:06:13,480
+N of X is non-unitطبعا طيب ممتاز جدا يبقى بدي اقعد
+
+54
+00:06:13,480 --> 00:06:21,220
+افترض ان عندي اللي هو ال element اللي عندنا هذا
+
+55
+00:06:21,220 --> 00:06:34,040
+ههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههههه
+
+56
+00:06:39,520 --> 00:06:47,480
+بتساوي A في B افترض ان ال X بيساوي حاصل ضرب A في B
+
+57
+00:06:47,480 --> 00:06:55,540
+ال X هذا مشان يكون عندي irreducible بيكون واحد من
+
+58
+00:06:55,540 --> 00:07:01,580
+هذول عبارة عن unit صحيح ولا لأ طيب تعالى نشوف الان
+
+59
+00:07:01,580 --> 00:07:08,520
+لو أخد تأثير ال function N على X مش يساوي تأثير ال
+
+60
+00:07:08,520 --> 00:07:16,610
+Nعلى ال A في ال B صحيح؟ طيب هذا الكلام يعني ان ال
+
+61
+00:07:16,610 --> 00:07:27,790
+N of X يساوي ال N of A في ال N of B طب ال N of X
+
+62
+00:07:27,790 --> 00:07:36,070
+is a prime ايش معناه؟ ونجاه ان ال N of X يساوي حصل
+
+63
+00:07:36,070 --> 00:07:41,840
+ضرب الاتنين هدوليبقى واحد فيهم بده يسوى واحد على
+
+64
+00:07:41,840 --> 00:07:51,000
+الأقل صحيح يبقى بجي بقول since ال N of X is a
+
+65
+00:07:51,000 --> 00:08:01,780
+prime we have يبقى
+
+66
+00:08:01,780 --> 00:08:11,560
+we have ان ال N of A بده يسوى واحداو ال N of B
+
+67
+00:08:11,560 --> 00:08:23,100
+يسوى واحد مظبوط ؟ طيب هذا مظبوط تعالى ايه ال
+
+68
+00:08:23,100 --> 00:08:29,180
+N of A يسوى واحد معناته ال A is unit هذا يسوى واحد
+
+69
+00:08:29,180 --> 00:08:36,260
+لأن معناته ال B is unit يبقى ضروري اقوله by part C
+
+70
+00:08:39,430 --> 00:08:51,170
+إن الـ A is A unit أو الـ B is A unit إذا واحد
+
+71
+00:08:51,170 --> 00:08:59,090
+منهم unit فبإيش صار عندي؟ ال X is irreducible
+
+72
+00:08:59,090 --> 00:09:06,350
+صحيح؟ لإن ال X هي فرضناها حاصل ضرب اتنين طالع واحد
+
+73
+00:09:06,350 --> 00:09:17,370
+فيهم unit يبقى thismeans that ان ال X is
+
+74
+00:09:17,370 --> 00:09:26,670
+irreducible over .. irreducible
+
+75
+00:09:26,670 --> 00:09:33,270
+over Z of the square root of D
+
+76
+00:09:39,100 --> 00:09:47,880
+طيب ننتقل الآن الى الأول نظرية على هذا الموضوع نقل
+
+77
+00:09:47,880 --> 00:09:54,600
+integral
+
+78
+00:09:54,600 --> 00:10:00,280
+domain integral
+
+79
+00:10:00,280 --> 00:10:02,500
+domain
+
+80
+00:10:06,600 --> 00:10:17,900
+every prime is a reducer every prime is a reducer
+
+81
+00:10:17,900 --> 00:10:29,380
+every prime is a reducer افترض
+
+82
+00:10:29,380 --> 00:10:33,820
+يجب
+
+83
+00:10:33,820 --> 00:10:38,980
+ان افترضإنه في عندي integral domain اللي بجيه هنا
+
+84
+00:10:38,980 --> 00:10:51,280
+فده اقول له left دي be an integral domain طبعا
+
+85
+00:10:51,280 --> 00:10:57,960
+جالس اي prime بده يكون ال reducer إذا بده اخد
+
+86
+00:10:57,960 --> 00:11:03,260
+element و اثرضه انه prime وروح اثبتله انه reducer
+
+87
+00:11:03,890 --> 00:11:12,950
+يرجع هنا فجأة بيقولوا let ال A اللي موجودة في D ب
+
+88
+00:11:12,950 --> 00:11:22,830
+A prime وانت شارف ان
+
+89
+00:11:22,830 --> 00:11:31,950
+نحاول نثبت ان ال A is irreducible يبقى
+
+90
+00:11:31,950 --> 00:11:38,270
+كل شغلنا منصفعلى التعريفات تبعات المحاضرة الماضية
+
+91
+00:11:38,270 --> 00:11:45,430
+طيب الان فرضنا ان a is a prime ال a معناته ممكن
+
+92
+00:11:45,430 --> 00:11:55,910
+يكون unit لأ يبقى هنا باجي بقول send ال a since ال
+
+93
+00:11:55,910 --> 00:12:06,820
+a is a prime ال a is my unitيجي الشرط الأول من شرط
+
+94
+00:12:06,820 --> 00:12:12,800
+ال irreducible يتحقق بدنا نيجي لمين للشرط الثاني
+
+95
+00:12:12,800 --> 00:12:20,560
+الشرط الثاني بد أثبت irreducible يعني اه بس في
+
+96
+00:12:20,560 --> 00:12:28,060
+عندك بدنا نستفيد من مين نستفيد من مين من
+
+97
+00:12:28,060 --> 00:12:33,330
+المعطيات ال A is a primeماذا يعني الـ Time؟ لو كان
+
+98
+00:12:33,330 --> 00:12:38,330
+الـ A بيقسم حاصل الضرب يبقى فانت بيقسم واحد فيه،
+
+99
+00:12:38,330 --> 00:12:51,630
+مظبوط؟ يبقى الـ A and if ال A بيقسم ال B، C then
+
+100
+00:12:51,630 --> 00:12:57,750
+ال A بيقسم ال B or ال A بيقسم ال C
+
+101
+00:13:00,820 --> 00:13:08,220
+بدأ أخد لو كان الـ A بيقسم الـ B إيش اللي بده
+
+102
+00:13:08,220 --> 00:13:17,580
+يحصل؟ مشان نثبتها Irreducible يبقى None، Zero و
+
+103
+00:13:17,580 --> 00:13:22,660
+بده كتبتها علاقة ما كتبناش على شكل حاصل ضرب نكتبها
+
+104
+00:13:22,660 --> 00:13:25,100
+على شكل حاصل ضرب
+
+105
+00:13:31,120 --> 00:13:39,820
+الـ A بدها تساوي الـ B في C مشان
+
+106
+00:13:39,820 --> 00:13:43,760
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+107
+00:13:43,760 --> 00:13:44,260
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+108
+00:13:44,260 --> 00:13:44,720
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+109
+00:13:44,720 --> 00:13:45,220
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+110
+00:13:45,220 --> 00:13:46,600
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+111
+00:13:46,600 --> 00:13:46,800
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+112
+00:13:46,800 --> 00:13:50,820
+انا انا انا انا انا
+
+113
+00:13:50,820 --> 00:13:50,820
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+114
+00:13:50,820 --> 00:13:50,900
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+115
+00:13:50,900 --> 00:13:58,360
+انا انا
+
+116
+00:13:58,360 --> 00:14:04,600
+اناالـ A non-unit فالـ A تقسم الـ C فالترضيه ان
+
+117
+00:14:04,600 --> 00:14:13,780
+الـ A بده يساوي مين؟ P في C الان since ال A بتقسم
+
+118
+00:14:13,780 --> 00:14:22,640
+ال بي سي أكيد ما هي ال A تساوي مين؟ ال P في C يعني
+
+119
+00:14:22,640 --> 00:14:28,440
+ال A بتقسم نفسها صح ولا لأ يبقى ال A بتقسم ال P في
+
+120
+00:14:28,440 --> 00:14:40,430
+C يبقىwe have ان ال A تقسم ال B او ال A تقسم ال C
+
+121
+00:14:40,430 --> 00:14:51,010
+لش؟ لأن ال A is a prime because ال
+
+122
+00:14:51,010 --> 00:14:55,790
+A is a prime فهي تمام
+
+123
+00:15:00,870 --> 00:15:06,490
+احنا بنثبت يا اما ال B unit يا اما ال C unit
+
+124
+00:15:06,490 --> 00:15:18,410
+مظبوط؟ طيب الان لو جيت قولتلك ال A او F ال A
+
+125
+00:15:18,410 --> 00:15:28,570
+بتقسمين تقسمي ال B then ال B تساوي A في T مثلا
+
+126
+00:15:31,780 --> 00:15:42,220
+وهو sum T اللي موجودة في دي طب
+
+127
+00:15:42,220 --> 00:15:50,440
+لو جتنا العنصر B وضربته في واحد ضربته في واحد يبقى
+
+128
+00:15:50,440 --> 00:15:57,900
+هذا مش هو عبارة عن ال B تمام طب و ال B هو عبارة عن
+
+129
+00:15:57,900 --> 00:16:08,470
+مين A FTصح؟ مافجدش ال ايه تساوي؟ P في C يبقى هنا P
+
+130
+00:16:08,470 --> 00:16:19,850
+في C في T تمام؟ طيب هذا قد يعطيني ال P في C T الان
+
+131
+00:16:19,850 --> 00:16:23,290
+احنا بنشتغل وين؟ في ring ولا في integral domain؟
+
+132
+00:16:23,290 --> 00:16:27,850
+ال integral domain أخدنا علاقة بتقولي لو عندك
+
+133
+00:16:27,850 --> 00:16:32,320
+integral domainو A في B بده يسوي A في C بقى بال
+
+134
+00:16:32,320 --> 00:16:36,280
+left cancellation ال B بده يسوي مين؟ بده يسوي C
+
+135
+00:16:36,280 --> 00:16:48,340
+يجينا By left cancellation لأ
+
+136
+00:16:48,340 --> 00:16:56,540
+We have بده يصير الواحد بده يسوي C في T إيش معنى
+
+137
+00:16:56,540 --> 00:17:03,210
+هذا الكلام؟إن الـC is a unit يبقى هذا معناته إن
+
+138
+00:17:03,210 --> 00:17:11,490
+الـC is a unit طبعا؟ طب ال irreducible قلنا يا إما
+
+139
+00:17:11,490 --> 00:17:15,570
+الـB unit يا إما الـC unit يبقى لما طلعت الـC unit
+
+140
+00:17:15,570 --> 00:17:20,790
+أروح أدور على B مافيش داعي يبقى معنى هذا الكلام
+
+141
+00:17:20,790 --> 00:17:31,050
+يبقى this means thatهذا يعني ان ال A is
+
+142
+00:17:31,050 --> 00:17:36,970
+irreducible over
+
+143
+00:17:36,970 --> 00:17:46,270
+اللي هو Z over
+
+144
+00:17:46,270 --> 00:17:51,230
+D على
+
+145
+00:17:51,230 --> 00:17:52,530
+D فقط لإيه
+
+146
+00:18:15,190 --> 00:18:20,550
+طيب النظرية هذه كان بيقول في ال integral domain لو
+
+147
+00:18:20,550 --> 00:18:26,370
+عندي A' بصير irreducible السؤال هو طب لو كان ال A
+
+148
+00:18:26,370 --> 00:18:33,190
+irreducible بصير A' قد يكون و قد لا يكون، إذا
+
+149
+00:18:33,190 --> 00:18:39,290
+العكس النظرية ليس بالضرورة صحيحة، تبقى بنا نكتب
+
+150
+00:18:39,290 --> 00:18:42,790
+هذه الملاحظة في Gary Mark
+
+151
+00:18:47,180 --> 00:18:56,240
+the converse of
+
+152
+00:18:56,240 --> 00:19:01,560
+the
+
+153
+00:19:01,560 --> 00:19:16,400
+above theorem نظريتي على 100.100 مرتر
+
+154
+00:19:17,300 --> 00:19:28,580
+ليس بالضرورة صحيحا that is I am ال
+
+155
+00:19:28,580 --> 00:19:43,460
+A is a radio source لا يعني ان ال A is right
+
+156
+00:19:45,570 --> 00:19:54,750
+بنعطي مثال على ذلك طبعا
+
+157
+00:19:54,750 --> 00:20:02,930
+الكتاب أعطاني المثال في الأول ثم النظرية ثم ال
+
+158
+00:20:02,930 --> 00:20:08,350
+remark تمام فالترتيب مش دقيق احنا أعطينا النظرية
+
+159
+00:20:08,350 --> 00:20:13,170
+ثم أعطينا ال remark ثم بدنا نجيب counter example
+
+160
+00:20:13,170 --> 00:20:17,820
+يثبت مينيثبت هذه الـ remark يبقى أنا بدأ أخد
+
+161
+00:20:17,820 --> 00:20:21,920
+integral domain و أثبت أنه على ال integral domain
+
+162
+00:20:21,920 --> 00:20:26,540
+هنا في عندي element irreducible لكنه في الحقيقة
+
+163
+00:20:26,540 --> 00:20:34,180
+ليس prime تمام؟ for example بيقول ما يأتي consider
+
+164
+00:20:34,180 --> 00:20:41,880
+the integral domain consider the integral
+
+165
+00:20:44,920 --> 00:20:51,340
+domain افترض انه عندك integral domain اللى هو D
+
+166
+00:20:51,340 --> 00:21:03,620
+يساوي Z of الجدرق الترابيعى اللى سارب تلاتة
+
+167
+00:21:03,620 --> 00:21:09,220
+يبقى
+
+168
+00:21:09,220 --> 00:21:15,040
+انا بروح اخد elementفي هذا الـ integral domain و
+
+169
+00:21:15,040 --> 00:21:19,720
+أثبت ان هذا ال element في الأول is irreducible
+
+170
+00:21:19,720 --> 00:21:25,020
+يعني في الحل انا همشي خطواتين مش انا قولت لك خلاص
+
+171
+00:21:25,020 --> 00:21:29,260
+خد هال element is irreducible لأ بدي أثبت ان في
+
+172
+00:21:29,260 --> 00:21:33,880
+عندي element irreducible وفي الحقيقة هذا ال
+
+173
+00:21:33,880 --> 00:21:38,080
+element ليس a prime يبقى الخطوة الحل بيكون على
+
+174
+00:21:38,080 --> 00:21:47,050
+مرحلتينإيش بدالي أقوله الواحد زائد جدد سالب تلاتة
+
+175
+00:21:47,050 --> 00:21:59,050
+belong to z of the square root لسالبين بعدين
+
+176
+00:21:59,050 --> 00:22:09,210
+بدالي أقول له assume افترض ان there exist x و y
+
+177
+00:22:09,660 --> 00:22:20,100
+موجودة في Z of الجذر السالب تلاتة such that وبحيث
+
+178
+00:22:20,100 --> 00:22:28,520
+ان ال X في ال Y يساوي الواحد زائد الجذر السالب
+
+179
+00:22:28,520 --> 00:22:50,890
+تلاتة with ال X and ال Y arenot units يبقى
+
+180
+00:22:50,890 --> 00:22:55,730
+احنا ايش سوينا هنا اخدنا element في ال integral
+
+181
+00:22:55,730 --> 00:23:01,350
+domain اللي عندنا وجينا افترضنا انه في عندي عمصرين
+
+182
+00:23:01,350 --> 00:23:05,850
+حاصل ضربه ما يساوي هذا ال element و ال two
+
+183
+00:23:05,850 --> 00:23:10,500
+elements هدول are not unitsطيب و لا واحد فيهم
+
+184
+00:23:10,500 --> 00:23:17,580
+عبارة عن ايش عن units تمام تمام طيب تشوف حالي هل
+
+185
+00:23:17,580 --> 00:23:23,720
+بوصل لتناقض و لا بوصلش لتناقض من هذا الكلام نرجع
+
+186
+00:23:23,720 --> 00:23:30,540
+مرة تانية احنا أخدنا قبل قليل ال function من z of
+
+187
+00:23:30,540 --> 00:23:31,980
+z of z of z of z of z of z of z of z of z of z of
+
+188
+00:23:31,980 --> 00:23:33,480
+z of z of z of z of z of z of z of z of z of z of
+
+189
+00:23:33,480 --> 00:23:33,660
+z of z of z of z of z of z of z of z of z of z of
+
+190
+00:23:33,660 --> 00:23:33,760
+z of z of z of z of z of z of z of z of z of z of
+
+191
+00:23:33,760 --> 00:23:33,860
+z of z of z of z of z of z of z of z of z of z of
+
+192
+00:23:33,860 --> 00:23:33,860
+z of z of z of z of z of z of z of z of z of z of
+
+193
+00:23:33,860 --> 00:23:33,860
+z of z of z of z of z of z of z of z of z of z of
+
+194
+00:23:33,860 --> 00:23:33,860
+z
+
+195
+00:23:37,230 --> 00:23:44,630
+تخليها تأثر على XY تأثير ال N على 1 زائد جدر ناقص
+
+196
+00:23:44,630 --> 00:23:49,230
+تلاتة الخاصية
+
+197
+00:23:49,230 --> 00:23:57,170
+التانية هذه معناها ايش ان ال N X في ال N Y يساوي
+
+198
+00:23:57,170 --> 00:24:05,510
+هذه من التعريف مربع الأول زائد ناقص تلاتة في مربع
+
+199
+00:24:05,510 --> 00:24:09,390
+التاني الأول بواحدوالمعامل اللي جيبنا الجذر جداش
+
+200
+00:24:09,390 --> 00:24:16,310
+واحد يبقى هذه واحد تربيع بواحد ناقص دي اللي يبقى
+
+201
+00:24:16,310 --> 00:24:24,130
+ناقص ثلاثة في واحد يبقى ناتج جداش أربع تمام الأربع
+
+202
+00:24:24,130 --> 00:24:29,810
+هذه لها تحليلين التحليل الأول اتنين في اتنين
+
+203
+00:24:29,810 --> 00:24:37,940
+والتحليل التاني واحد في أربع يعني ممكن تكونواحدة
+
+204
+00:24:37,940 --> 00:24:44,360
+منهم واحد وواحدة منهم أربعة بصوصهم شوية لو استفعدت
+
+205
+00:24:44,360 --> 00:24:50,100
+الواحد بظهر فيه إمكانية للأربعة؟ لأ طيب أنا الأن
+
+206
+00:24:50,100 --> 00:25:00,340
+أدعي أن ال N of X بده ساوين اتنين ليش؟ because
+
+207
+00:25:00,340 --> 00:25:05,520
+طالعش
+
+208
+00:25:05,520 --> 00:25:06,800
+كاتب هنا؟
+
+209
+00:25:09,320 --> 00:25:16,320
+ال X and Y are not units مظبوط يبقى لو قلت ال N of
+
+210
+00:25:16,320 --> 00:25:22,620
+X يساوي واحد مع انتهي X unit صحيح ولا لا يبقى لما
+
+211
+00:25:22,620 --> 00:25:26,700
+أقول ال N of X لا تساوي واحد معناته ال X is not a
+
+212
+00:25:26,700 --> 00:25:33,480
+unit مظبوط يبقى because ان ال N of X يساوي اتنين
+
+213
+00:25:33,480 --> 00:25:42,550
+because ال N of X لا تساوي واحدsince x is not a
+
+214
+00:25:42,550 --> 00:25:48,730
+unit يبقى حكايته باربع حطيها على الشكل بظل مين؟
+
+215
+00:25:48,730 --> 00:25:55,810
+بظل عندى اتنين و اتنين يبقى ندل ال N of X ال N of
+
+216
+00:25:55,810 --> 00:26:03,790
+X يا بناه أليست هي N of A زائد B generally سالب
+
+217
+00:26:03,790 --> 00:26:11,780
+تلاتة يساوي اتنين؟ بظبططيب هذا الكلام بدي أروح
+
+218
+00:26:11,780 --> 00:26:19,400
+أستخدم تعريف ال N يبقى A ترابية absolute value
+
+219
+00:26:19,400 --> 00:26:26,700
+ناقص ال D اللي هي بناقص تلاتة في ال B ترابية يساوي
+
+220
+00:26:26,700 --> 00:26:36,140
+اتنين طيب هذا معناه ان ال A ترابية زائد تلاتة B
+
+221
+00:26:36,140 --> 00:26:40,960
+ترابيةيساوى اتنى، احط ال absolute value، مافيش
+
+222
+00:26:40,960 --> 00:26:45,680
+داعي لها، مافيش داعي لها، لإن الكمية مربعة اتنين
+
+223
+00:26:45,680 --> 00:26:51,280
+بالموجة، طيب هذا الكلام يساوي اتنى، طب ال A و ال B
+
+224
+00:26:51,280 --> 00:26:58,680
+وين موجودة هذه؟ في Z، صح ولا لأ؟ يبقى هنا لو جلنا
+
+225
+00:26:58,680 --> 00:27:05,140
+جنب هذي، و ال A و ال B belong to Zبعد اتنين حطيلي
+
+226
+00:27:05,140 --> 00:27:08,380
+فاصفة و أقولي الـA و الـB موجودة وين في الـZ
+
+227
+00:27:08,380 --> 00:27:19,240
+السؤال هو ممكن ألاقي A و B في Z يحقق هذه المعاملة؟
+
+228
+00:27:19,240 --> 00:27:23,160
+ممكن ألاقي انت؟ مش مهم سالم موجة بصفر اللي بدك
+
+229
+00:27:23,160 --> 00:27:29,420
+إياه ممكن ألاقي؟ ولا واحد تمام؟ يعني هذا كلام
+
+230
+00:27:29,420 --> 00:27:35,290
+ممكن؟ this is impossibleيبدأ هنا فروح بقول له this
+
+231
+00:27:35,290 --> 00:27:45,230
+is impossible because there
+
+232
+00:27:45,230 --> 00:27:56,110
+is no integers او
+
+233
+00:27:56,110 --> 00:27:59,410
+no integers
+
+234
+00:27:59,410 --> 00:28:07,740
+a andالـ B satisfied the
+
+235
+00:28:07,740 --> 00:28:14,580
+equation المعادلة اللي هو A ترابية زائد تلاتة B
+
+236
+00:28:14,580 --> 00:28:21,820
+ترابية يساوية نكت. إذن في شغل غلط. هي اللي وصلتني
+
+237
+00:28:21,820 --> 00:28:29,420
+إلى نتيجة غلط. هذول فرطب انهم ايش؟not units معناته
+
+238
+00:28:29,420 --> 00:28:39,220
+واحدة منهم unit أو 10 يبقى هذا contradiction تناقض
+
+239
+00:28:39,220 --> 00:28:49,520
+مادام تناقض هذا يعطينا ان ال X is a unit او ال Y
+
+240
+00:28:49,520 --> 00:28:57,200
+is a unit طبعا هذا تعريف مين؟طبعا هي في ال
+
+241
+00:28:57,200 --> 00:29:05,200
+reducibility يبقى هنا ساق ال X is ايه ال .. مش ال
+
+242
+00:29:05,200 --> 00:29:13,020
+X ال element اللي عندنا الواحد زائد جدر ناقص تلاتة
+
+243
+00:29:13,020 --> 00:29:19,940
+is irreducible of
+
+244
+00:29:19,940 --> 00:29:24,180
+الجدر
+
+245
+00:29:24,180 --> 00:29:25,740
+اللي سالب تلاتة
+
+246
+00:29:33,440 --> 00:29:38,620
+لكن لو كانت Reduceable ده يعني ان ايه اذا بتعرف؟
+
+247
+00:29:38,620 --> 00:29:47,060
+اذا بتعرف لو كانت ايه؟ Reduceable بس ايش رايك
+
+248
+00:29:47,060 --> 00:29:52,560
+تصبري علينا شوية النظرية اللى جاية مربوطة بالنظرية
+
+249
+00:29:52,560 --> 00:29:57,780
+الاولانية ايه؟ بلب تجمع النظرية الاولانية او
+
+250
+00:29:57,780 --> 00:30:01,900
+النظرية اللى جاية نص النظرية الاولى ونص النظرية
+
+251
+00:30:01,900 --> 00:30:07,720
+التاليةيكون أجوبنا على سؤالك ان شاء الله يبقى ال
+
+252
+00:30:07,720 --> 00:30:12,720
+element هذه مرة يا بنات is irreducible يبقى احنا
+
+253
+00:30:12,720 --> 00:30:19,860
+حققنا مين؟ حققنا الأمر الأول من ال remark اللي كنا
+
+254
+00:30:19,860 --> 00:30:24,280
+كاتبينه هنا ان لو كان ال element is irreducible
+
+255
+00:30:24,280 --> 00:30:30,280
+ليس بالضرورة ان يكون fine يبقى الآن بدنا نثبت انه
+
+256
+00:30:30,280 --> 00:30:36,510
+ليس بالضرورة يكون ايهيكون افعال.طيب، شوفين يا شغل
+
+257
+00:30:36,510 --> 00:30:44,930
+غيرك. لو جيتني قولتلي consider واحد زائد جذر ناقص
+
+258
+00:30:44,930 --> 00:30:52,130
+تلاتة في واحد ناقص جذر لناقص تلاتة.يعني كأننا
+
+259
+00:30:52,130 --> 00:31:00,730
+حللنا فرق بين المربعين.أليس هذا هو واحد زائد
+
+260
+00:31:00,730 --> 00:31:08,690
+تلاتة؟اللي هو أربعة اللي هو بده يساوي كمان اتنين
+
+261
+00:31:08,690 --> 00:31:13,370
+في اتنين يعني
+
+262
+00:31:13,370 --> 00:31:17,930
+معناته ان ال element هذا بده يجسم اتنين في اتنين
+
+263
+00:31:17,930 --> 00:31:24,870
+صح؟ اللي حاصل ضربه مايساوي أربعة إذا بده يجسم و
+
+264
+00:31:24,870 --> 00:31:29,330
+الأربعة كتبتها اتنين في اتنين يبقى هذا بده يقينا
+
+265
+00:31:29,330 --> 00:31:36,600
+إيشبدي يعطينا ان واحد زي الجذر ناقص تلاتة divides
+
+266
+00:31:36,600 --> 00:31:44,540
+اتنين في اتنين لو كان ال prime بدي يقسم اتنين صح
+
+267
+00:31:44,540 --> 00:31:51,300
+ولا لا يبقى ابدا نشوفه هل هو بيقسم ولا بيقسمش طيب
+
+268
+00:31:51,300 --> 00:32:01,410
+if الواحد زي الجذر ناقص تلاتة يقسم لإتنينإذا لازم
+
+269
+00:32:01,410 --> 00:32:07,190
+ألاقي رقم تاني أو عنصر تاني أضرب فيه طبعا أنها
+
+270
+00:32:07,190 --> 00:32:18,450
+تجتنيه صح ولا لا يبقى هنا يساوي اتنين then for ال
+
+271
+00:32:18,450 --> 00:32:26,090
+a و ال b اللي موجود في z we have for some مش الكل
+
+272
+00:32:26,090 --> 00:32:34,650
+يعني for someالـ A و الـ B اللي موجودة في ذلك We
+
+273
+00:32:34,650 --> 00:32:44,470
+have ان الواحد زائد جذر ناقص تلاتة في A زائد B جذر
+
+274
+00:32:44,470 --> 00:32:52,050
+ناقص تلاتة يساوي اتنين بظبط يعنى؟ هذه بيقسم اتنين
+
+275
+00:32:52,050 --> 00:32:57,670
+يبقى لازم ألاقي عنصر أضربه في هذا يطلع اتنين بدي
+
+276
+00:32:57,670 --> 00:33:03,710
+أشوف هذه وين بتوصلطب بدفك القوس الأول دي عنها يبقى
+
+277
+00:33:03,710 --> 00:33:12,850
+هذا A ناقص تلاتة B زائد
+
+278
+00:33:12,850 --> 00:33:20,930
+بيجي نظر هذا في هذا ب A هذا في هذا ب A وهذا في هذا
+
+279
+00:33:20,930 --> 00:33:30,430
+ب B يبقى A زائد B في جدر ناقص تلاتة يسوى جداريساوي
+
+280
+00:33:30,430 --> 00:33:34,310
+اتنين طيب
+
+281
+00:33:34,310 --> 00:33:40,950
+هذه ممكن اكوّن منها معادلتين المعادلة الأولى A نقص
+
+282
+00:33:40,950 --> 00:33:45,870
+ثلاثة B يساوي اتنين والمعادلة التانية A زائد B
+
+283
+00:33:45,870 --> 00:33:50,390
+يساوي زين مصبوط
+
+284
+00:33:50,990 --> 00:33:56,190
+طيب إيش رايك؟ بتحلي المعادلتين هذول مع بعض يبقى a
+
+285
+00:33:56,190 --> 00:34:01,510
+ناقص ثلاثة بيه وهذه بتضربك بسالب واحد يبقى سالب a
+
+286
+00:34:01,510 --> 00:34:08,650
+سالب بيه ساوي زير لو جمعنا يبقى هذول مع السلام هذا
+
+287
+00:34:08,650 --> 00:34:14,570
+بده يعطيني سالب أربعة بيه ساوي اتنين يبقى بيه بده
+
+288
+00:34:14,570 --> 00:34:21,910
+يساوي قداش سالب نص موجود في ذلك؟إذا صار فيه تناقض،
+
+289
+00:34:21,910 --> 00:34:28,030
+مظبوط؟ طب التناقض هذا جابه شلة، شو الشلة؟ قلت إن
+
+290
+00:34:28,030 --> 00:34:36,270
+هذا بيقسم، مظبوط؟ يبقى هنا سواء الواحد زي الجذر
+
+291
+00:34:36,270 --> 00:34:41,450
+ناقص ثلاثة does not divide اتنين، لا يمكن نقسم
+
+292
+00:34:41,450 --> 00:34:48,140
+اتنين لما فرضت نقسم اتنين وصلت إلى تناقضوصلت إلى
+
+293
+00:34:48,140 --> 00:34:52,960
+عنصر مش موجود وان في الذات يبقى هذا لا يمكن ان
+
+294
+00:34:52,960 --> 00:34:58,260
+يحدث يعني لا يمكن لواحد ناقص جذر تلاتة انه يقسم
+
+295
+00:34:58,260 --> 00:35:04,220
+لاتنين يبقى ممكن يكون هذا try لا يبقى هذا بده
+
+296
+00:35:04,220 --> 00:35:10,740
+يعطينا آية ان الواحد زي جذر ناقص تلاتة is not a
+
+297
+00:35:10,740 --> 00:35:20,350
+try يبقى هذا ليس عادة أوليايبقى هذا مثل يوضح ان لو
+
+298
+00:35:20,350 --> 00:35:25,490
+كان عندى عنصر وعنصر irreducible على integral
+
+299
+00:35:25,490 --> 00:35:30,450
+domain يبقى ليس بالضرورة ان يكون هذا العنصر A'
+
+300
+00:35:30,610 --> 00:35:36,030
+يعني عكس النظرية اذا عكس النظرية ليس صحيحا الا ان
+
+301
+00:35:36,030 --> 00:35:43,290
+في نظرية تجمع النظرية الأولى و بتجيبلي كمان نص
+
+302
+00:35:43,290 --> 00:35:46,550
+نظرية جديدة ايش بتقول النظرية
+
+303
+00:35:51,040 --> 00:35:58,580
+بتقول النظرية من آياتك، او يا ريكو In
+
+304
+00:35:58,580 --> 00:36:06,600
+a principal ideal domain In a principal ideal
+
+305
+00:36:06,600 --> 00:36:09,800
+domain
+
+306
+00:36:09,800 --> 00:36:15,780
+اللي هاختصرها يا بنات إلى PID Principal Ideal
+
+307
+00:36:15,780 --> 00:36:18,160
+Domain An element
+
+308
+00:36:21,630 --> 00:36:32,090
+an element is irreducible is
+
+309
+00:36:32,090 --> 00:36:45,310
+irreducible if and only if it is prime لو كان لو
+
+310
+00:36:45,310 --> 00:36:46,630
+كان ال prime
+
+311
+00:36:52,400 --> 00:37:03,400
+الـ Pro تبقى
+
+312
+00:37:03,400 --> 00:37:11,540
+بدالي هقوله let D be a principal ideal domain
+
+313
+00:37:11,540 --> 00:37:14,800
+بتقفرك
+
+314
+00:37:14,800 --> 00:37:21,660
+انه عندي element و ال element هذا is irreducible
+
+315
+00:37:22,150 --> 00:37:27,210
+أها بتفترض انه is a prime في الأول ناخد الأسهم
+
+316
+00:37:27,210 --> 00:37:38,970
+يبقى هنا ل ال A B A prime D
+
+317
+00:37:38,970 --> 00:37:42,190
+النظرية
+
+318
+00:37:42,190 --> 00:37:49,430
+السابقة النظرية السابقة يبقى ال A is irreducible
+
+319
+00:37:49,430 --> 00:37:55,580
+وهو المطلوب المطلوب الأوليبقى هنا تلعبى A prime in
+
+320
+00:37:55,580 --> 00:38:08,320
+D by the above theorem النظرية الأعلى ال A is
+
+321
+00:38:08,320 --> 00:38:18,280
+irreducible in D هذا
+
+322
+00:38:18,280 --> 00:38:40,290
+الاتجاه الأولبنروح من اتجاه الثاني كونزر
+
+323
+00:38:40,290 --> 00:38:46,370
+احنا
+
+324
+00:38:46,370 --> 00:38:56,260
+اخدنا هنا A'بدنا ناخد ال a irreducible assume that
+
+325
+00:38:56,260 --> 00:39:08,020
+ان ال a is irreducible one
+
+326
+00:39:08,020 --> 00:39:19,900
+to show that one to show thatإن ال A is a prime
+
+327
+00:39:19,900 --> 00:39:26,300
+إيش
+
+328
+00:39:26,300 --> 00:39:31,640
+يعني ال A is a prime؟ يعني لو كان ال A بيقسم ال B
+
+329
+00:39:31,640 --> 00:39:44,260
+C يقسم ال B أو يقسم ال C تفهم؟ يعني that is if ال
+
+330
+00:39:44,260 --> 00:39:51,120
+Aبيقسم ال بي سي then
+
+331
+00:39:51,120 --> 00:40:03,260
+ال A بيقسم ال بي او ال A بيقسم ال بي سي
+
+332
+00:40:03,260 --> 00:40:11,240
+تجاهنا بفترض ان ال A بيقسم ال بي سي هذا بيكون معطى
+
+333
+00:40:11,240 --> 00:40:16,490
+وهذا اللي احنا عايزينه يعني عايزين نفريبقى باجي
+
+334
+00:40:16,490 --> 00:40:21,690
+بقوله هنا ال CEO ان
+
+335
+00:40:21,690 --> 00:40:28,230
+ال A بيقسم ال VC طيب
+
+336
+00:40:28,230 --> 00:40:42,370
+بدي أجي أقوله define an idea I و بده يساوي Ax زي
+
+337
+00:40:42,370 --> 00:40:47,600
+بي ورح بحيث الـ X والـ Y موجودة في دي.
+
+338
+00:40:50,680 --> 00:40:55,900
+طب واحنا مليش نرانا يا بنات؟
+
+339
+00:40:55,900 --> 00:41:00,220
+ال principle of ideal دماغيه؟ يبقى أي ideal يبقى
+
+340
+00:41:00,220 --> 00:41:08,140
+inside، صح؟ يبقى ده الـ
+
+341
+00:41:08,140 --> 00:41:14,750
+I هذا بدي ساوي دييعني هو ال principle idea
+
+342
+00:41:14,750 --> 00:41:21,430
+generated by D تمام؟ بنقوله كويسة. الآن السؤال هو
+
+343
+00:41:21,430 --> 00:41:30,770
+هل ال A موجود في ال I؟ موجود
+
+344
+00:41:30,770 --> 00:41:38,470
+ليش؟ لأن ال A بقدر أكتبه A في واحد زي ال B في Zero
+
+345
+00:41:41,580 --> 00:41:45,560
+على الصيغة اللى موجودة يبقى هذا Zero و F واحد في
+
+346
+00:41:45,560 --> 00:41:54,500
+اي مصدر ايه ابتدأ يبقى هذه عارفين اللي هي شملات ال
+
+347
+00:41:54,500 --> 00:41:58,600
+I يساوي دي؟ principle I دي ايه لإن principle I دي
+
+348
+00:41:58,600 --> 00:42:08,620
+domain تمام كويس طيب الآن then ال A موجود وين؟
+
+349
+00:42:09,070 --> 00:42:13,930
+موجود في ال principle ideal generated by D يعني
+
+350
+00:42:13,930 --> 00:42:26,630
+بقدر اكتره ان ال A بدر ساوي D في A for some A اللي
+
+351
+00:42:26,630 --> 00:42:27,890
+موجودة في D
+
+352
+00:42:40,170 --> 00:42:46,910
+الان ..الان انا بقول ان ال A تسوى ال mean دي R
+
+353
+00:42:46,910 --> 00:42:55,510
+واحنا ايش فرضنا ان ال A is reducible مظبوط؟ انا من
+
+354
+00:42:55,510 --> 00:43:05,470
+جباجي بقوله since بما ان ال A is irreducible we
+
+355
+00:43:05,470 --> 00:43:13,270
+have هاهذه irreducible وقدرنا نكتبها على الشكل
+
+356
+00:43:13,270 --> 00:43:20,010
+الحاصل تضارب two elements يبقى واحد unit مظبوط we
+
+357
+00:43:20,010 --> 00:43:32,230
+have ان ال D is a unit or ال R is a unit طيب
+
+358
+00:43:32,230 --> 00:43:39,620
+بتاخدهم واحدة واحدة وشوف لون بتوصلنا Fالـ D is a
+
+359
+00:43:39,620 --> 00:43:40,120
+unit.
+
+360
+00:43:42,840 --> 00:43:50,360
+Then بدك تكتبها العبارة شفوانة صحيحة ولا لأ. يبقى
+
+361
+00:43:50,360 --> 00:43:55,880
+الواحد موجود في ال principle idea generated from
+
+362
+00:43:55,880 --> 00:44:03,820
+D. لأنه D unit. مظبوط؟ طيب، مدام الواحد موجود في D
+
+363
+00:44:04,310 --> 00:44:09,370
+لو كان ال unity موجود في ال id اللي بيبقى ال id
+
+364
+00:44:09,370 --> 00:44:15,690
+بتسوى ميه؟ ال ring كلها، مظبوط ان هذا يرجع there
+
+365
+00:44:15,690 --> 00:44:27,950
+او هذا بيبقى موجود هنا implies that ان ال D هذا
+
+366
+00:44:27,950 --> 00:44:30,930
+كله بيبقى يسوى كل ال
+
+367
+00:44:34,840 --> 00:44:42,240
+طيب الواحد موجود في D الان هل الواحد موجود في A
+
+368
+00:44:42,240 --> 00:44:46,960
+ماهي
+
+369
+00:44:46,960 --> 00:44:55,960
+I E D صح ولا لأ ال E هذي R تمام؟ اذا هذا بدي
+
+370
+00:44:55,960 --> 00:45:03,130
+يعطينا معين مدينة موجود في I يبقى الواحدبدي ساول
+
+371
+00:45:03,130 --> 00:45:09,670
+ax زائد b مصبوط
+
+372
+00:45:09,670 --> 00:45:18,690
+اضرب كله في c إذا ضربنا كله في c بصير c بيساوي a c
+
+373
+00:45:18,690 --> 00:45:27,030
+x زائد b c y ده
+
+374
+00:45:27,030 --> 00:45:31,090
+جيبوا النظر معايا هل a تقسم هذا term
+
+375
+00:45:34,160 --> 00:45:43,560
+هل ال A تقسم هذا ال term؟ مظبوط؟ يبقى فاجب يقوله
+
+376
+00:45:43,560 --> 00:45:55,520
+now ال A تقسم ال A C X هذه واحدة and ال A تقسم ال
+
+377
+00:45:55,520 --> 00:46:08,490
+B C Y becauseال A تقسم ال B C هذا يتطلب ان ال A
+
+378
+00:46:08,490 --> 00:46:17,930
+تقسم ال A C X زائد ال B C Y طب هذي مين هي؟ C هذا
+
+379
+00:46:17,930 --> 00:46:24,630
+معناته ان ال A تقسم ال C هتجيبها المطلب الأول
+
+380
+00:46:32,190 --> 00:46:39,030
+خلصنا نمشي مرة تانية احنا اخدنا لو كانت ال E unit
+
+381
+00:46:39,030 --> 00:46:44,930
+طلعنا منها ان اذا تقسم ال C الان لو كانت ال R is
+
+382
+00:46:44,930 --> 00:47:01,580
+unit if ال R is unit then احنا اخدنا الالـ A بدأ
+
+383
+00:47:01,580 --> 00:47:08,120
+تساوي الـ D A صح؟ أخدنا الـ A بدأ تساوي الـ D R M
+
+384
+00:47:08,120 --> 00:47:14,320
+I الـ R هدا unit يعني إيه معكوس لو ضربنا في
+
+385
+00:47:14,320 --> 00:47:23,940
+المعكوس إيش بده يصير؟ A R inverse بده يساوي D سكت
+
+386
+00:47:23,940 --> 00:47:32,820
+الشعر لإنها A تساوي D Aأيها فوق بدي أضربها في R
+
+387
+00:47:32,820 --> 00:47:38,800
+inverse كيف يبقى بصير A R inverse بدي أساوي D طيب،
+
+388
+00:47:38,800 --> 00:47:47,700
+مين هو هذا بنا؟ تعريف مين؟ مش كل العناصر على الشكل
+
+389
+00:47:47,700 --> 00:47:54,020
+هذا element A في element من R وفي element من D مش
+
+390
+00:47:54,020 --> 00:48:00,400
+بشكل الisomal ideal generated by A صح ولا لأ؟يفقى
+
+391
+00:48:00,400 --> 00:48:05,120
+هذا معناه ان ال principle ideal generated by ايه؟
+
+392
+00:48:05,120 --> 00:48:13,940
+هو ال principle ideal generated by دي صحيح ولا لأ؟
+
+393
+00:48:13,940 --> 00:48:21,580
+انا سكت ولا اشتغل؟ مظبوط ولا لأ؟ هذه العبارة اللي
+
+394
+00:48:21,580 --> 00:48:27,460
+عندك هذه مش العنصر هذا هو العنصر هذا يبقىال ideal
+
+395
+00:48:27,460 --> 00:48:31,440
+اللي يولد بهذا العمصر هو ال ideal اللي يولد بهذا
+
+396
+00:48:31,440 --> 00:48:35,140
+العمصر ال principle ideal، مظبوط؟ هذا ال principle
+
+397
+00:48:35,140 --> 00:48:39,640
+ideal تبع ال D هذا لو جيت أعرف ال principle ideal
+
+398
+00:48:39,640 --> 00:48:44,980
+generated by A، مش هو كل العلاصر A في R حيث R
+
+399
+00:48:44,980 --> 00:48:49,340
+موجودة في R أو R موجودة في D اللي عندنا هنا؟ R
+
+400
+00:48:49,340 --> 00:48:53,060
+والله Rين بس، بس هو ليه شدله معكس؟ يبقى هو ولا مش
+
+401
+00:48:53,060 --> 00:48:57,380
+هومش غير ان العنصر او المعكس يولد نفس ال subgroup
+
+402
+00:48:57,380 --> 00:49:02,560
+زمان نفس القسم يبقى صار هذا ال principle هو هذا ال
+
+403
+00:49:02,560 --> 00:49:08,260
+principle طيب بدأ أسألكوا سؤال هل ال B موجود في ال
+
+404
+00:49:08,260 --> 00:49:12,200
+I؟
+
+405
+00:49:12,200 --> 00:49:21,200
+ممكن أخد X ب Zero و Y ب أحد صح؟ يبقى ال B موجود في
+
+406
+00:49:21,200 --> 00:49:29,290
+ال Iطيب ال I هذه مش هي ال D صح ولا لأ؟ هي ال A
+
+407
+00:49:29,290 --> 00:49:36,310
+يبقى implies ان ال B موجودة في ال principle I D
+
+408
+00:49:36,310 --> 00:49:43,050
+generated by A يبقى هذا معناه ان ال B بدها تسوي
+
+409
+00:49:43,050 --> 00:49:55,550
+مثلا AT for some Tاللي موجودة في دي طب ايش تفسيرك
+
+410
+00:49:55,550 --> 00:50:06,470
+لهذا العبارة؟ ان ال A بتقسمين تقسمين B يبقى هذا
+
+411
+00:50:06,470 --> 00:50:13,570
+بده يعطينا ان ال A تقسم ال B اتطلعيلي هنا هاي واحد
+
+412
+00:50:13,570 --> 00:50:20,410
+وهي اتنين يبقى Trump واحد
+
+413
+00:50:20,930 --> 00:50:33,830
+أمس اتنين we have ان ال a تقسم ال b or ال a تقسم
+
+414
+00:50:33,830 --> 00:50:41,450
+ال c يبقى تفسير من تفسير من ال prime يبقى هذا بدي
+
+415
+00:50:41,450 --> 00:50:51,690
+يعطينا انه وان بدأنا ان ال a is a primeوهو اتبعه
+
+416
+00:50:51,690 --> 00:50:57,370
+طبعا
+
+417
+00:50:57,370 --> 00:51:03,590
+طبعا الى هنا نكتفي بهذا القدر من هذا ال section
+
+418
+00:51:03,590 --> 00:51:08,490
+لان عندكم امتحانات تبدأ من الغد فمشان هيك نقول ان
+
+419
+00:51:08,490 --> 00:51:14,270
+يكفينا ما أخدناه حتى هذه اللحظة واتمنى ان تكونوا
+
+420
+00:51:14,270 --> 00:51:20,290
+قد استمتعتم بهذا المساق خلال الدراسة في هذا الفصل
+
+421
+00:51:20,700 --> 00:51:26,740
+ولن يستمتع الطالب إلا إذا اشتغل بدينه، مش بس رسم
+
+422
+00:51:26,740 --> 00:51:31,200
+من على الصبح لو خلصناه. وهدفي كل مسرح كان سواء كان
+
+423
+00:51:31,200 --> 00:51:37,280
+جبر أو غيره على أي حال نتمنى لكم التوفيق والنجاح
+
+424
+00:51:37,280 --> 00:51:42,240
+في هذا المساء وفي جميع المساقات الأخرى. وتمنى لكم
+
+425
+00:51:42,240 --> 00:51:48,360
+التوفيق والنجاح في حياتكننا إلى أن يأتي الأجالي
+
+426
+00:51:48,360 --> 00:51:54,620
+المحتوملكل واحدة منكنا ولكل واحد مننا بارك الله
+
+427
+00:51:54,620 --> 00:51:59,580
+فيكم وشكر لكم و السلام عليكم ورحمة الله وبركته
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ea308b20ce597f681d17422dd7dc02d492c67a1a
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ_postprocess.srt
@@ -0,0 +1,1660 @@
+1
+00:00:21,600 --> 00:00:26,440
+رحمان الله الرحيم احنا انتهينا المرة الماضية من
+
+2
+00:00:26,440 --> 00:00:31,420
+chapter ال ideas and factoring وبدأنا في حل
+
+3
+00:00:31,420 --> 00:00:35,560
+الأسئلة في نصف التانية من المحاضرة واليوم ان شاء
+
+4
+00:00:35,560 --> 00:00:41,780
+الله نكمل حل الأسئلة اللي كلفناها بحلها في البيت
+
+5
+00:00:41,780 --> 00:00:48,120
+طبعا اخر سؤال مرة اتعرضنا له هو سؤال 17 اليوم سؤال
+
+6
+00:00:48,120 --> 00:00:54,390
+17يقول لو كان الـ I هو ID المنازل و هذا الـ ID
+
+7
+00:00:54,390 --> 00:00:59,570
+الاحتواء unit بدا نثبت ان الـ I بدي ساوي R يبقى
+
+8
+00:00:59,570 --> 00:01:13,670
+السؤال 17 كان I ID of R و الـ I contains a unit
+
+9
+00:01:13,670 --> 00:01:20,260
+هذا الكلام بدي يعطينا ان الـ ID الـ Rبدو يساوي
+
+10
+00:01:20,260 --> 00:01:27,160
+الـRing R itself.مشان نحل هذا السؤال، بنرجع
+
+11
+00:01:27,160 --> 00:01:32,400
+بمعلوماتنا قليلا إلى الأوراق. الـ Set Theory،
+
+12
+00:01:32,400 --> 00:01:36,520
+بجينا نثبت أن الـ two sets are equal و بنثبت أن
+
+13
+00:01:36,520 --> 00:01:40,440
+الأولى صبست من التانية و التانية صبست من الأولى،
+
+14
+00:01:40,440 --> 00:01:45,100
+إن حدث ذلك، بقول يبقى الـ two sets are equal، بأن
+
+15
+00:01:45,100 --> 00:01:50,770
+نفسي نمشي نفسي التفتيق.الأن يا بنات I هو ideal من
+
+16
+00:01:50,770 --> 00:01:57,410
+R يبقى .. يبقى هذا يجد الـ R أقل منه صح ولا لأ؟
+
+17
+00:01:57,410 --> 00:02:04,010
+يعني صدست من الـ R وقد يساويها يبقى in a sense بما
+
+18
+00:02:04,010 --> 00:02:16,710
+أن ال I is an ideal of R we have أنهالـ I سادسة من
+
+19
+00:02:16,710 --> 00:02:22,470
+الـ A وسمّيلي هذه العلاقة رقم واحد بعد هيك بدنا
+
+20
+00:02:22,470 --> 00:02:34,850
+نيجي نقول افترضي ان A is a unit in A in X in
+
+21
+00:02:34,850 --> 00:02:40,590
+I يبقى بنفترض ان العمصر A هو unit و ال unit هذا
+
+22
+00:02:40,590 --> 00:02:42,270
+موجود في I زي انه قال
+
+23
+00:02:46,200 --> 00:02:55,940
+لأثبت أن الـR صبست من الـI يبقى لو أخدت الآن الـR
+
+24
+00:02:55,940 --> 00:03:01,640
+موجودة في R لو قدرت أثبت أن الـR اسمه الهادي
+
+25
+00:03:01,640 --> 00:03:09,360
+موجودة في I بتمام المطلوب يبقى then الـR هادي بقدر
+
+26
+00:03:09,360 --> 00:03:16,610
+أكتبها على شكل الـR في A inverse Aلأن الـinity
+
+27
+00:03:16,610 --> 00:03:23,250
+يعني معكوث العنصر exist هذا كله الـR يسوى R في A
+
+28
+00:03:23,250 --> 00:03:30,190
+اللي بقدر أقول هو عبارة عن R A inverse في مين في
+
+29
+00:03:30,190 --> 00:03:40,130
+الـA هذا الآن موجود في I صح؟ و هذا موجود وين؟ في R
+
+30
+00:03:40,130 --> 00:03:46,440
+يبقى و الـI ID اللي يبقى حاصر ضربه مين موجودفي I
+
+31
+00:03:46,440 --> 00:03:57,820
+يبقى هذا موجود في I since لإن ال I is an ID لإن ال
+
+32
+00:03:57,820 --> 00:04:04,180
+I ideally يبقى هذا موجود فيها تمام يبقى أخدنا عنصر
+
+33
+00:04:04,180 --> 00:04:10,880
+R موجود في R أثبتنا إنه موجود وين؟ موجود في I يبقى
+
+34
+00:04:10,880 --> 00:04:17,080
+ساق ال R subset من مين؟من I و هذه العلاقة رقم
+
+35
+00:04:17,080 --> 00:04:26,640
+اتنين بروح بقول from واحد and اتنين we have ان ال
+
+36
+00:04:26,640 --> 00:04:34,900
+ideal R تسوى ال ring R كله إذا حتى الآن استمعنا
+
+37
+00:04:34,900 --> 00:04:40,020
+يعني حصلنا على معلومتين مهماتالمعلومة الأولى
+
+38
+00:04:40,020 --> 00:04:44,440
+قلتلناها سابقا والمعلومة الثانية هي بيننا الآن
+
+39
+00:04:44,440 --> 00:04:48,420
+المعلومة السابقة بجينا نقول إذا ال ID اللي احتوى
+
+40
+00:04:48,420 --> 00:04:53,160
+على ال unity على عنصر الوحدة يبقى ال ID اللي بدي
+
+41
+00:04:53,160 --> 00:04:57,420
+أسوأ مين في ال ring itself وهنا نقول لو ال ID اللي
+
+42
+00:04:57,420 --> 00:05:02,600
+احتوى على unit واحدة يبقى ال ID اللي هذا بدي أسوأ
+
+43
+00:05:02,600 --> 00:05:08,870
+مين بيسوء ال ring R يبقى من الأن أساعداهذا أخدنا
+
+44
+00:05:08,870 --> 00:05:13,270
+ideal من ال ring و لجأت فيه ال unity أو لجأت فيه
+
+45
+00:05:13,270 --> 00:05:17,790
+unit يبقى على كل الخط ال ideal هذا بده يساوي مين؟
+
+46
+00:05:17,790 --> 00:05:23,690
+بده يساوي نفس ال ring هذا كان سؤال سبعتاشر بعد ذلك
+
+47
+00:05:23,690 --> 00:05:29,190
+معانا سؤال اتنين و عشرين جال يخد لل ideal و ال
+
+48
+00:05:29,190 --> 00:05:35,550
+principle ideal generated by اتنين يبقى سؤال اتنين
+
+49
+00:05:35,550 --> 00:05:40,790
+و عشرينالـ I هو الـ principle IG generated by
+
+50
+00:05:40,790 --> 00:05:50,110
+إتنين ومعطيني بعد ذلك I of X وإن I of X is not
+
+51
+00:05:50,110 --> 00:05:56,890
+maximal ideal في Z even though I is maximal يبقى
+
+52
+00:05:56,890 --> 00:06:04,830
+هنا sure إن I of X is not
+
+53
+00:06:07,860 --> 00:06:19,740
+maximum in z of x الرغم ان ال principle ideal
+
+54
+00:06:19,740 --> 00:06:25,660
+generated by a هو عبارة عن maximum من مين في z
+
+55
+00:06:25,660 --> 00:06:30,840
+وعندنا ال principle ideal generated by a هو
+
+56
+00:06:30,840 --> 00:06:40,370
+maximum in zيعني برغم ان هذا ال ideal maximal في Z
+
+57
+00:06:40,370 --> 00:06:46,510
+لكن I of X ماهياش maximal في ماين في Z of X يبقى
+
+58
+00:06:46,510 --> 00:06:54,490
+خلوم شده اظهر ال principle ideal generated by
+
+59
+00:06:54,490 --> 00:07:01,270
+اتنين هذا معروف بالنسبة ايه؟ اللي همين ال zero
+
+60
+00:07:01,270 --> 00:07:03,990
+وزاد او ناقص اتنين
+
+61
+00:07:09,670 --> 00:07:17,830
+طب ال I of X مين
+
+62
+00:07:17,830 --> 00:07:23,610
+ال I of X؟ مين ال Z of X؟ كثيرات الحدود إلى
+
+63
+00:07:23,610 --> 00:07:29,830
+المعاملة تبعها تعدد صحيح صح ولا لأ؟ قياسا عليها ال
+
+64
+00:07:29,830 --> 00:07:39,400
+I of X هو كثيرات الحدود لمعاملتهاإنها عدالة زوجية
+
+65
+00:07:39,400 --> 00:07:44,760
+2 4 6 8 إلى أخرى صح؟ نعم لأن هاي ال principle
+
+66
+00:07:44,760 --> 00:07:48,680
+ideal generated by اتنين اتنين اربع ستة كلها عدالة
+
+67
+00:07:48,680 --> 00:07:56,340
+زوجية تمام يبقى I of X هو عبارة عن كل ال functions
+
+68
+00:07:56,340 --> 00:08:05,480
+F of X such that ال F of X has
+
+69
+00:08:07,160 --> 00:08:11,420
+even او
+
+70
+00:08:11,420 --> 00:08:21,500
+has even coefficients او كولونوميال او
+
+71
+00:08:21,500 --> 00:08:29,640
+كولونوميال with even
+
+72
+00:08:29,640 --> 00:08:32,320
+coefficients
+
+73
+00:08:42,410 --> 00:08:48,450
+كل كثيرات الحدود اللي المعاملات تبعتها أعداد زوجية
+
+74
+00:08:48,450 --> 00:08:54,810
+even إنتجاه يبقى أعداد زوجية، منطقية، هيها من
+
+75
+00:08:54,810 --> 00:08:59,250
+أربعة، ستة، تمانية، بالسالف أو في الموجة عرفنا
+
+76
+00:08:59,250 --> 00:09:04,950
+الـI of X، قال لي أثبت إنه هذه الماكسيمال، لو
+
+77
+00:09:04,950 --> 00:09:10,090
+رجعنا لتعريف الماكسيمال idealبنقول ال ideal بقول
+
+78
+00:09:10,090 --> 00:09:15,250
+عنه maximum لو جدت و لاقي ideal تاني بعيط هذا ال
+
+79
+00:09:15,250 --> 00:09:21,050
+ideal subset منه و لا يساويه و هذا ال ideal إذا
+
+80
+00:09:21,050 --> 00:09:25,970
+كان بيسويش يبقى بيساوي 100 بيساوي ال R itself إن
+
+81
+00:09:25,970 --> 00:09:30,010
+حدث ذلك يبقى بيقول هذا ال ideal ما له maximal
+
+82
+00:09:30,010 --> 00:09:37,510
+ideal طيب احنا لو قدرنا نجيب ideal تاني بحيث ال I
+
+83
+00:09:37,510 --> 00:09:43,970
+of Xهو لا يساويه و ال ideal التاني الصبصت من ال
+
+84
+00:09:43,970 --> 00:09:50,250
+ring هو لا يساويها يبقاش من السنة تانية ماقوم على
+
+85
+00:09:50,250 --> 00:09:55,450
+طول الخط مش هنجيب من المريخ ال ideal لأ لأ لأ من
+
+86
+00:09:55,450 --> 00:10:00,090
+اللي أخدناه أخدنا فيه principle ideal generated by
+
+87
+00:10:00,090 --> 00:10:10,180
+X و 2 تذكروا ال polynomialاللي كل ال .. كل العدد
+
+88
+00:10:10,180 --> 00:10:15,940
+الأخير أو العدد الثابت هو عدد زوجي، مظبوط؟ يفجأة
+
+89
+00:10:15,940 --> 00:10:22,340
+بدنا نروح نطبق صحة هذا الكلام، فبعدين بيقول أخدنا
+
+90
+00:10:22,340 --> 00:10:29,340
+part ولكن اللي هو seminary principle ideal
+
+91
+00:10:29,340 --> 00:10:33,720
+generated by X و 2
+
+92
+00:10:37,970 --> 00:10:46,710
+بحيث أن ال F of X تسادي X في G of X زائد اتنين H
+
+93
+00:10:46,710 --> 00:10:55,210
+of X صح؟ طيب تعالوا ندقق النظر في الأتنين هدولة ال
+
+94
+00:10:55,210 --> 00:11:01,470
+I of X كل ال F of X كتيرات الحدود اللي المعاملات
+
+95
+00:11:01,470 --> 00:11:09,900
+تبعتها أعداد زوجية صح؟ هذا مهمهذا كل العناصر اللي
+
+96
+00:11:09,900 --> 00:11:16,920
+الحد الأخير فيها بيكون عدد زوجي، تمام؟ ممتاز جدا،
+
+97
+00:11:16,920 --> 00:11:22,140
+طيب هل الأولى صبست من التانية و الله التانى صبست
+
+98
+00:11:22,140 --> 00:11:26,240
+من التانية؟ لأن
+
+99
+00:11:26,240 --> 00:11:32,140
+الأولى كلهم عدد زوجية، هذا العدد الزوجي هو مين؟
+
+100
+00:11:32,140 --> 00:11:36,550
+العدد الأخير و قبل هيكفردي والله زوجي مابتفرقش عنا
+
+101
+00:11:36,550 --> 00:11:45,790
+لما بروح بقوله هنا clearly واضح انه ال I or X
+
+102
+00:11:45,790 --> 00:11:53,730
+subset من ال principle ideal generated by X ذأ و
+
+103
+00:11:53,730 --> 00:12:01,350
+اتنين ولا يساوي طيب السؤال and ال principle ideal
+
+104
+00:12:04,170 --> 00:12:10,570
+subset من ال R ولا لا؟ يساويها؟ لأ لأن الحد اللي
+
+105
+00:12:10,570 --> 00:12:16,030
+قد يكون زوجي و قد يكون صفر و قد يكونه فرديا يبقى
+
+106
+00:12:16,030 --> 00:12:23,010
+subset منها ولا تساويه يبقى جبت ideal موجود ما بين
+
+107
+00:12:23,010 --> 00:12:29,330
+ال ring و ما بين ال ideal و proper شرط أساسي وقدرت
+
+108
+00:12:29,330 --> 00:12:33,990
+أثبت أن ال ideal عندي ما هواشأي لا يساوي و اللي
+
+109
+00:12:33,990 --> 00:12:37,830
+جبناه لا يساوي ال R، يبقى ال I دي لديه maximum؟
+
+110
+00:12:37,830 --> 00:12:52,790
+لأ، if this means that ان ال I of X is not maximum
+
+111
+00:12:52,790 --> 00:12:56,670
+in Z
+
+112
+00:13:01,380 --> 00:13:06,780
+أدا كان سؤال اللي هو الأتنين وعشرين رغم انه ال
+
+113
+00:13:06,780 --> 00:13:09,980
+principle ideal generated by اتنين هو maximum
+
+114
+00:13:09,980 --> 00:13:16,840
+ideal في Z وهو أعلى ideal ممكن أخده من مين أخده من
+
+115
+00:13:16,840 --> 00:13:21,860
+الـ Z بعد اتنين وعشرين عندنا أربعة وعشرين جالي هات
+
+116
+00:13:21,860 --> 00:13:26,680
+مثال a commutative ring that has maximal ideal
+
+117
+00:13:26,680 --> 00:13:34,170
+that is not a prime idealيبقى اربعة و عشرين بدنا
+
+118
+00:13:34,170 --> 00:13:46,470
+مثال لكميوتاتيف رينج كوميوتاتيف رينج كوميوتاتيف
+
+119
+00:13:46,470 --> 00:13:51,970
+رينج that has maximal ما هو عشان five و has
+
+120
+00:13:51,970 --> 00:13:58,650
+maximal idea but
+
+121
+00:14:14,840 --> 00:14:25,120
+الحمد لله لو جينا وقلنا set of integers community
+
+122
+00:14:25,120 --> 00:14:26,260
+of ring و لا لأ
+
+123
+00:14:29,460 --> 00:14:35,760
+zev and usual
+
+124
+00:14:35,760 --> 00:14:44,560
+addition يعني تحت عملية الجمعين العادية and
+
+125
+00:14:44,560 --> 00:14:47,600
+multiplication
+
+126
+00:14:47,600 --> 00:14:52,480
+defined
+
+127
+00:14:52,480 --> 00:14:58,460
+by الملء
+
+128
+00:15:21,490 --> 00:15:30,880
+معروف؟ أي سؤال يحتاج إلى إجابة هو أحنا لكي نثبتإن
+
+129
+00:15:30,880 --> 00:15:36,700
+ال six strings تحت ال two operations اللي عليها مش
+
+130
+00:15:36,700 --> 00:15:41,560
+لازم نثبت ال six conditions تمام؟ طيب لما بقولنا
+
+131
+00:15:41,560 --> 00:15:46,000
+ال usual addition الجامعة العادى يعني الأول أربعة
+
+132
+00:15:46,000 --> 00:15:52,200
+الشروط محققة صح ولا لأ اللي اختلفوا مين؟ أخر شرطين
+
+133
+00:15:52,200 --> 00:15:57,640
+أخر شرطين هم اللي مين؟ هم اللي اختلفوا ليش؟ ليش
+
+134
+00:15:57,640 --> 00:16:03,990
+اختلفوا؟لأن هدول مش عملية الضرب العادية، عملية ضرب
+
+135
+00:16:03,990 --> 00:16:08,250
+خاصة، يمسك، يعطلهم جرم ويسويهم بالصبر، هي أتعرف
+
+136
+00:16:08,250 --> 00:16:14,010
+عملية الضرب، بدى أثبتله إن هذه ال ring و كذلك
+
+137
+00:16:14,010 --> 00:16:19,610
+كميوتة ال ring، يبقى أول أربعة شهور محققة لعملية
+
+138
+00:16:19,610 --> 00:16:23,890
+الجمع العالمي، دول شرطين، الشرط الأول خاصية ال
+
+139
+00:16:23,890 --> 00:16:29,180
+accessibility، الخاصية التانية هي خاصيةالتوزيع
+
+140
+00:16:29,180 --> 00:16:33,380
+Distributive law طيب نجرى الخاصية دي ال
+
+141
+00:16:33,380 --> 00:16:42,460
+sociability بقى بقى بقى بقول that if four
+
+142
+00:16:42,460 --> 00:16:48,700
+conditions of
+
+143
+00:16:48,700 --> 00:16:53,240
+a ring are satisfied
+
+144
+00:16:58,670 --> 00:17:02,470
+نقلت ما عملى فى الجامعة العادية نيجى للتانى ال
+
+145
+00:17:02,470 --> 00:17:07,650
+associativity فبداية أقوله لفت ال a و ال b و ال c
+
+146
+00:17:07,650 --> 00:17:17,690
+مويزة فى z لأن لو أخدت ال a فى ال b و ال z هميزة
+
+147
+00:17:17,690 --> 00:17:25,910
+هي a فى zero عصر ضرب اتنين فدي سوى z أحوالنا
+
+148
+00:17:28,750 --> 00:17:39,330
+يساوي الـ Z يعني لو أخدت ال A وB كلها في الـ C بدي
+
+149
+00:17:39,330 --> 00:17:45,430
+أساوي Zero في الـ C يساوي الـ D معناه هذا الكلام
+
+150
+00:17:45,430 --> 00:17:53,630
+أن ال A وB في الـ C بدي أساوي KB في الـ C لكل الـ
+
+151
+00:17:53,630 --> 00:17:56,390
+A وB وC الموجودة
+
+152
+00:17:59,260 --> 00:18:05,220
+distributive law صحيحة طيب الآن هذه الخاصية
+
+153
+00:18:05,220 --> 00:18:10,760
+التانية الخالصة الخاصية السادسة بدنا distributive
+
+154
+00:18:10,760 --> 00:18:23,260
+law داخل ال a ال b زائد ال c تمام هذا الكلام بده
+
+155
+00:18:23,260 --> 00:18:24,100
+يساوي
+
+156
+00:18:28,500 --> 00:18:33,280
+لأن هذا كله يعتبر element وهذا element تاني وكان
+
+157
+00:18:33,280 --> 00:18:36,880
+اللي حاصد الطريق يساوي zero لأي two elements
+
+158
+00:18:36,880 --> 00:18:46,040
+موجودة فيها امين لو أخدت ال A P زي ان ال A C Zero
+
+159
+00:18:46,040 --> 00:18:53,060
+زاخد Zero اللي هو يساوي Zero فإتبعنا هذا الكلام أن
+
+160
+00:18:53,060 --> 00:19:03,160
+ال A ال Bزايد الـ C يساوي بـ A B زايد بـ A C و
+
+161
+00:19:03,160 --> 00:19:09,880
+بنفس الطريقة Similarly بنفس
+
+162
+00:19:09,880 --> 00:19:20,080
+الطريقة الـ B زايد الـ C كل K يساوي بـ A زايد C A
+
+163
+00:19:20,080 --> 00:19:32,530
+Plus وهكذا الـ Zis A غير B عملية
+
+164
+00:19:32,530 --> 00:19:41,490
+مين؟ commutative الأن ال A في B كده تسوية منها حسب
+
+165
+00:19:41,490 --> 00:19:48,150
+ال definition طيب و ال B في A؟ Zero يبقى معنا هذا
+
+166
+00:19:48,150 --> 00:19:56,960
+الكلام أن ال A بيلكل الـ A و الـ B موجودة في نزل
+
+167
+00:19:56,960 --> 00:20:04,300
+هذا اللي هو commutative point
+
+168
+00:20:04,300 --> 00:20:11,960
+لما احنا جبنا مثل لـ commutative ring ها يبدو
+
+169
+00:20:11,960 --> 00:20:15,720
+commutative ring جبنا له commutative ring هذا
+
+170
+00:20:15,720 --> 00:20:22,140
+maximum ideal باطناطي الفعل السؤال هو لما نزل
+
+171
+00:20:24,840 --> 00:20:33,640
+maximum ideal انزل، صحيح ولا لا؟ طيب السؤال هو هل
+
+172
+00:20:33,640 --> 00:20:42,260
+هذا هو prime؟ بنقول آه، إذا بتاخد رقم حاسم ضرهم
+
+173
+00:20:42,260 --> 00:20:45,340
+موجود في هذا ال ideal
+
+174
+00:20:49,630 --> 00:20:56,450
+موجود في هذا ID، إن حدث ذلك، بقول هذا هو prime ID،
+
+175
+00:20:56,450 --> 00:21:02,450
+ماحدثش، يبقى هو نقطة prime ID، طيب، لو جاءت
+
+176
+00:21:02,450 --> 00:21:11,430
+conflict، مثلا، قد يلي ثلاثة في سبعة، ثلاثة في
+
+177
+00:21:11,430 --> 00:21:12,490
+سبعة، كم سنة؟
+
+178
+00:21:17,840 --> 00:21:23,420
+في الشغل العادى، لأن 3×7 يساوي 0، لماذا؟ لأن 3
+
+179
+00:21:23,420 --> 00:21:28,820
+موجود في الـ Z وال7 موجود في الـ Z، وعملية الضرب
+
+180
+00:21:28,820 --> 00:21:33,840
+علي حصة الضرب أي اتنين يساوي 0، طيب، هذا الكلام
+
+181
+00:21:33,840 --> 00:21:38,660
+يساوي 0، طيب، هل الـ Zero موجودة في اتنين Z ولا
+
+182
+00:21:38,660 --> 00:21:45,820
+لا؟ هل موجودة في اتنين Z؟اللي هو مين؟ اللي فيه الـ
+
+183
+00:21:45,820 --> 00:21:51,400
+Zero وزاد أو نقص اتنين وزاد أو نقص اربع وانا مجرد
+
+184
+00:21:51,400 --> 00:21:57,980
+موجودة في هذه الـ Zero، بطل ولكن هذه التلاتة
+
+185
+00:21:57,980 --> 00:22:05,500
+موجودة في اتنين زرد؟ لأ، مش موجودة أنزل السبعة مش
+
+186
+00:22:05,500 --> 00:22:11,860
+موجودة في اتنين زرد كذلك صحيح ولا لأ؟يبقى صرحد ما
+
+187
+00:22:11,860 --> 00:22:23,440
+هواش بيه إسرائيل، يبقى هنا ساعة ننزل الناس إسرائيل
+
+188
+00:22:23,440 --> 00:22:30,400
+قاعدين الزجاج
+
+189
+00:22:30,400 --> 00:22:33,760
+فالرياضات
+
+190
+00:22:33,760 --> 00:22:39,200
+عموما، كما يقولك برهم، أسهر اللي يقولك تاتي مثال
+
+191
+00:22:40,440 --> 00:22:47,440
+تكون عملية جالب المثال صعبة، لكن الورهان أسهل من
+
+192
+00:22:47,440 --> 00:22:53,000
+مفروض البراجين الرياضيات معروفة تلاتة طرق، طرق
+
+193
+00:22:53,000 --> 00:22:58,320
+تاعتها بنقدر عليها و بنحاول نحقق السؤال، ابتعدوا.
+
+194
+00:22:58,840 --> 00:23:04,200
+هذا كان سؤال أربع وعشرين، ثم سؤال تلاتين.
+
+195
+00:23:06,340 --> 00:23:17,340
+سؤال تلاتين بيقولأعفر مطالب مطلوب الأول شراء ذات
+
+196
+00:23:17,340 --> 00:23:26,220
+ما يلغ أنه لقيت يساوي كل الأزواج المغتلة تلاتة x و
+
+197
+00:23:26,220 --> 00:23:33,880
+y بحيث ال x و ال y موجودة في z شراء ذات is a
+
+198
+00:23:33,880 --> 00:23:39,640
+maximal idea is a maximal
+
+199
+00:23:41,760 --> 00:23:52,760
+Ideal أن زرق ضايق صنع زرق المطلوب
+
+200
+00:23:52,760 --> 00:24:05,140
+التالي مربي بنرع لايك عم المطلوب التالي what
+
+201
+00:24:05,140 --> 00:24:15,580
+happen شو اللي بده يحصلwhen تلاتة
+
+202
+00:24:15,580 --> 00:24:21,220
+X replace باربع
+
+203
+00:24:21,220 --> 00:24:30,740
+X، شو اللي بده يحصل؟ D generalized،
+
+204
+00:24:30,740 --> 00:24:31,780
+برضه عامل
+
+205
+00:24:46,380 --> 00:24:55,060
+هذا فيكو أثبتت أن هذا ID لبنات بس؟ كيف؟ لأ
+
+206
+00:24:55,060 --> 00:25:00,820
+هو هذا، هل تثبت أنه ID؟ لأ، هو قال أثبت أنه
+
+207
+00:25:00,820 --> 00:25:04,240
+maximal ID، لم يمرش علينا قبل الليلة أثبتنا أنه
+
+208
+00:25:04,240 --> 00:25:08,380
+ID، يبقى الخبرة ويبقى الابنانية، بيثبت أنه ID، ثم
+
+209
+00:25:08,380 --> 00:25:12,960
+نذهب إلى ال максимالين، كتير ID ولا حد يعمل فيش؟
+
+210
+00:25:13,750 --> 00:25:18,330
+مده ما مرش علينا قبل هير كمان لازم نكفت أولا إنه
+
+211
+00:25:18,330 --> 00:25:24,930
+ideal ثم نذهب نبحث عن ماكسيمالي أه حد عارف أولا
+
+212
+00:25:24,930 --> 00:25:30,090
+إنه ideal؟ طب عارف هذا الفيلم لازم تتكتر أنه ideal
+
+213
+00:25:30,090 --> 00:25:34,430
+أولا ثم بقعد أدرك أن هو تتكتر أنه maximum ideal
+
+214
+00:25:34,430 --> 00:25:41,490
+نفنجي الأول بدنا نكفت أنه ideal كيف جبالي بيقولونه
+
+215
+00:25:41,490 --> 00:25:49,650
+نمرأيهمبتجد النقطة الأولى بدي أكتر من M يبقى الـ A
+
+216
+00:25:49,650 --> 00:26:02,470
+أزمن M because الـ Zero و Zero موجود في .. اللي هو
+
+217
+00:26:02,470 --> 00:26:09,130
+المسافر تلاتة مضروف في Zero و Zero صار على الصيلة
+
+218
+00:26:09,130 --> 00:26:13,950
+هذهما جاليش الـ Nox بتسوي و لا بتسوي حرب خد زي ما
+
+219
+00:26:13,950 --> 00:26:22,030
+بدها يبقى A موجودة في A يبقى بشأن هاتمان M يبقى
+
+220
+00:26:22,030 --> 00:26:26,790
+تحقق ال condition الأول ال condition التاني فتروح
+
+221
+00:26:26,790 --> 00:26:35,350
+أخد عنصرين موجودات في A يبقى net A و B موجودة في A
+
+222
+00:26:35,350 --> 00:26:42,960
+then شكل ال A إيش بدي يكون؟يبقى بيكون ثلاثة x one
+
+223
+00:26:42,960 --> 00:26:54,540
+و y one and شكل ال b ثلاثة x two و y two تمام؟ كل
+
+224
+00:26:54,540 --> 00:26:59,440
+عنصر على شكل or ضارف a مزود مرتب زي ما انتوا
+
+225
+00:26:59,440 --> 00:27:06,460
+شايفينه الاند ده ياخد ال a ماعقرس ال bيبقى هذا
+
+226
+00:27:06,460 --> 00:27:13,960
+الكلام بالدرسان تلاتة x one و y one ناقص تلاتة x
+
+227
+00:27:13,960 --> 00:27:20,300
+two و y two الطرح أو الجمع component twice يبقى
+
+228
+00:27:20,300 --> 00:27:27,540
+هذا الكلام بالدرسان تلاتة x one ناقص x two و y one
+
+229
+00:27:27,540 --> 00:27:35,070
+ناقص y two هل هذا على الشكل اللي عندنا؟ صح؟الـ C
+
+230
+00:27:35,070 --> 00:27:39,390
+موجود في الـ A خلاصة من ال condition الثالث،
+
+231
+00:27:39,390 --> 00:27:45,110
+الثاني، ضالان ال condition الثالث والأخير، إذا
+
+232
+00:27:45,110 --> 00:27:51,410
+ناخد element من ال ring الأصلية، و ناخد element من
+
+233
+00:27:51,410 --> 00:27:58,610
+هنا، يبقى بالتالي أقول للـ L، الـ C و الـ D موجودة
+
+234
+00:27:58,610 --> 00:28:02,870
+في الـ Z-direct صمع Z، and
+
+235
+00:28:05,290 --> 00:28:13,070
+الـ A اللي بدها تساوي تلاتة X1 و Y1 موجودة في الـ
+
+236
+00:28:13,070 --> 00:28:20,750
+A ثم بدي أشوف حاصل ضاربهم إذا موجود في A، بيكون
+
+237
+00:28:20,750 --> 00:28:25,090
+صار الـ A عفر عن الـ Ideal سواء ما كان ضارب من
+
+238
+00:28:25,090 --> 00:28:33,170
+اليمين أو من الشمال يبقى الأواخر C وD مضروب في من؟
+
+239
+00:28:33,170 --> 00:28:44,630
+في الـ Aبتي ساوى C و D LLي تلاتة X one و Y one هذا
+
+240
+00:28:44,630 --> 00:28:58,370
+الكلام يساوى تلاتة C X one و هذا D Y one موجود؟
+
+241
+00:29:00,380 --> 00:29:08,700
+يبقى هذا موجود في A Similarي بنفس الطريقة اللي هو
+
+242
+00:29:08,700 --> 00:29:18,020
+A في C وD موجود في الـ A يبقى الـ A معلوم is
+
+243
+00:29:18,020 --> 00:29:24,780
+unideal سواء الـ A is unideal
+
+244
+00:29:29,710 --> 00:29:35,630
+خلصنا؟ لما قلتوا إلى أين؟ إلى أين خلصت؟ انت كل
+
+245
+00:29:35,630 --> 00:29:43,170
+اللي اتبعته انه ideal فقط بقى عليك تثبت انه ايش؟
+
+246
+00:29:43,170 --> 00:29:50,790
+not maximum ماهواش maximum ideal لك maximum؟ اه
+
+247
+00:29:50,790 --> 00:29:56,050
+هذا صحييني كويس طيب كليتوا صحيين معانا ماشي الآن
+
+248
+00:29:56,050 --> 00:30:02,410
+طيبيبقى المطموع أن نثبت أن هذا هو عبارة عن maximum
+
+249
+00:30:02,410 --> 00:30:09,750
+ايدين لذلك قدامي بدأت بطريقة اثنين طريقة ثانية
+
+250
+00:30:09,750 --> 00:30:15,090
+يعني ناخد ا او طريقة اثنين يعني طريقة التعريف هي
+
+251
+00:30:15,090 --> 00:30:19,610
+طريقة النظرية ليست النظرية اللي هو تقول لو كان
+
+252
+00:30:19,610 --> 00:30:24,370
+عندي range commutative with unity يبقى ال a module
+
+253
+00:30:24,370 --> 00:30:30,030
+is a في ال F عنده دقة is maximumيعني لو كان ارهد
+
+254
+00:30:30,030 --> 00:30:34,390
+يقوله ايه كانت فيه يبقى لإيه maximum أو على
+
+255
+00:30:34,390 --> 00:30:39,210
+التعريض، قبل شوية احنا أثبتنا ذلك بواسطة التعريض،
+
+256
+00:30:39,210 --> 00:30:44,670
+المثبتنا الماكسيماليتي، ده استخدمنا التعريض، هنا،
+
+257
+00:30:44,670 --> 00:30:49,410
+ده استخدمنا ضغيط، وشو المشكلة؟ بلاش، اه، فاستنى
+
+258
+00:30:49,410 --> 00:30:52,270
+شوية، وين تبقى التعريض؟
+
+259
+00:31:01,270 --> 00:31:08,510
+السؤال هو هل هذه commutative؟ أكيد
+
+260
+00:31:08,510 --> 00:31:12,390
+ميل ميل، لأن الـZ أصلاً commutative فلما يكون حاصل
+
+261
+00:31:12,390 --> 00:31:15,990
+ضرب عنصرين في الـZ، يقل بيهم أو بداية الـZ، يبقى
+
+262
+00:31:15,990 --> 00:31:23,170
+commutative و الـUnity لهم إيه؟ واحد و واحد، يبقى
+
+263
+00:31:23,170 --> 00:31:23,570
+الـUnity
+
+264
+00:31:28,040 --> 00:31:38,200
+Is plus is plus is plus is plus is plus is plus is
+
+265
+00:31:38,200 --> 00:31:39,640
+plus is plus is plus is plus is plus is plus is
+
+266
+00:31:39,640 --> 00:31:41,360
+plus is plus is plus is plus is plus is plus is
+
+267
+00:31:41,360 --> 00:31:46,460
+plus is plus is plus is plus is plus is plus is
+
+268
+00:31:46,460 --> 00:31:46,760
+plus is plus is plus is plus is plus is plus is
+
+269
+00:31:46,760 --> 00:31:47,040
+plus is plus is plus is plus is plus is plus is
+
+270
+00:31:47,040 --> 00:31:47,140
+plus is plus is plus is plus is plus is plus is
+
+271
+00:31:47,140 --> 00:31:47,180
+plus is plus is plus is plus is plus is plus is
+
+272
+00:31:47,180 --> 00:31:47,200
+plus is plus is plus is plus is plus is plus is
+
+273
+00:31:47,200 --> 00:31:50,760
+plus is plus
+
+274
+00:31:50,760 --> 00:31:58,930
+is plus is plusيبقى بس بايلة علينا لو نثبت أن الـ
+
+275
+00:31:58,930 --> 00:32:05,270
+direct sum بينه زي وزي مدهوله إيه لفتنا إنها فيه
+
+276
+00:32:05,270 --> 00:32:10,710
+اللي بيكون خلصنا فالسؤال هو أكم عنصر في ال direct
+
+277
+00:32:10,710 --> 00:32:22,250
+sum تبع زي plus زي مدهوله إيه؟ أكم عنصر؟ كده؟ مدني
+
+278
+00:32:22,250 --> 00:32:29,680
+هذا العناصر؟لا؟ علمية مثلا؟ بقى حسب ايه؟ قداش
+
+279
+00:32:29,680 --> 00:32:33,920
+متجدر يعني قيمة ايه؟ قيمة ايه؟ اه وين قيمة ايه؟
+
+280
+00:32:33,920 --> 00:32:39,860
+ايه ال R & D؟ ايه ال R & D؟ فى عناصر كتير ثلاثة
+
+281
+00:32:39,860 --> 00:32:44,860
+ثلاثة عناصر؟ لأ، عدد العناصر زد، زد ايه؟ عدد عناصر
+
+282
+00:32:44,860 --> 00:32:49,980
+زد؟ زد فيها ملنهاد من العناصر يعني ممكن يكون فيها
+
+283
+00:32:49,980 --> 00:32:51,780
+ملنهاد من العناصر؟
+
+284
+00:32:58,770 --> 00:33:07,170
+أنا أزعم أنه لا يوجد ثلاثة تعارفين عشان وجود
+
+285
+00:33:07,170 --> 00:33:13,970
+الثلاثة مهاجورة، قبل نهيئة الثلاثة بتلعب؟ صحيح؟
+
+286
+00:33:13,970 --> 00:33:18,650
+وليش؟ ثلاثة؟ وليش؟ كمان، مش يا ثلاثة أي أخ قطر
+
+287
+00:33:18,650 --> 00:33:19,730
+يبقى هناك، لأ
+
+288
+00:33:27,330 --> 00:33:39,630
+يبقى F وE شادة إذا قدرنا نظبر إنه دائرة صغيرة ما
+
+289
+00:33:39,630 --> 00:33:43,610
+بين الـ Z و الـ Z موديولة A
+
+290
+00:33:52,850 --> 00:34:01,190
+We have a prison يعني
+
+291
+00:34:01,190 --> 00:34:05,530
+بالاسم هذه فيه نجيبه و نقول ايه is maximum و نقول
+
+292
+00:34:05,530 --> 00:34:15,070
+فلسطين I am الهدف الباريكي الصاممي بين الذنب و
+
+293
+00:34:15,070 --> 00:34:18,550
+الذنب مُتي قُدر فيه الازر
+
+294
+00:34:33,700 --> 00:34:42,420
+بس تلاتة انصار؟ اه بس التلاتة هذول؟ اه بس التلاتة
+
+295
+00:34:42,420 --> 00:34:47,960
+هذول، مش لذا طيب واحد هذول قبخل لكل انصار وشوفوا
+
+296
+00:34:47,960 --> 00:34:52,740
+من التلاتة هذول ولايلا هاتيلي عمصر جاله على بانه و
+
+297
+00:34:52,740 --> 00:34:56,800
+القره و خنيه كبيرة شوية مش يعني اتنين او اتنين
+
+298
+00:34:56,800 --> 00:34:59,140
+اتنين خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+299
+00:34:59,140 --> 00:35:00,280
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+300
+00:35:00,280 --> 00:35:02,580
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+301
+00:35:02,580 --> 00:35:02,860
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+302
+00:35:02,860 --> 00:35:15,900
+خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص خلاص
+
+303
+00:35:15,900 --> 00:35:18,000
+خل
+
+304
+00:35:21,050 --> 00:35:25,430
+كيف؟ يبقى الـ God ما يطرحش، يبقى واحد وصفر كما
+
+305
+00:35:25,430 --> 00:35:32,670
+تقول، زي ما جالس، لأن لو
+
+306
+00:35:32,670 --> 00:35:36,910
+أخدنا خمسة وعشرين وانت، أن أحدث واحد ثالث وواحد
+
+307
+00:35:36,910 --> 00:35:45,020
+ثالث، تمام؟ هذا الكلام زي الـ 2007بادر أبوتي واحد
+
+308
+00:35:45,020 --> 00:35:53,400
+وزير زائد اربعة وعشرين واتنين زائد الاية هذا
+
+309
+00:35:53,400 --> 00:36:01,180
+الكلام يساوي واحد وزير زائد اربعة وعشرين تلاتة في
+
+310
+00:36:01,180 --> 00:36:06,820
+تمانية واتنين زائد الايةهذا موجود في ايه ولا لا؟
+
+311
+00:36:06,820 --> 00:36:10,120
+اه موجود في ايه، صح؟ اه، اه، اه، اه، اه، اه، اه،
+
+312
+00:36:10,120 --> 00:36:14,160
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+313
+00:36:14,160 --> 00:36:15,180
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+314
+00:36:15,180 --> 00:36:16,680
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+315
+00:36:16,680 --> 00:36:20,780
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+316
+00:36:20,780 --> 00:36:32,860
+اه، اه، اه، اه، اه، اه، اه، اه، اه، اه، اه،
+
+317
+00:36:32,860 --> 00:36:42,810
+اعشرين واربع عشرين واربع عشرين واربع زائد الان
+
+318
+00:36:42,810 --> 00:36:51,650
+العشرين بقدر اكسبها اتنين وزيرو زائد تمانبعشر
+
+319
+00:36:51,650 --> 00:36:58,170
+واربع زائد الان تمام؟
+
+320
+00:36:58,170 --> 00:37:00,150
+هللي بردودة دي ولا ده؟
+
+321
+00:37:03,140 --> 00:37:12,300
+يبقى هنا اتنين وزيرو زائد ثلاثة في ستة وأربعة زائد
+
+322
+00:37:12,300 --> 00:37:18,000
+الـA هذه الموجودة في الـA يبقى اتنين وزيرو زائد
+
+323
+00:37:18,000 --> 00:37:18,660
+الـA
+
+324
+00:37:23,530 --> 00:37:28,270
+الحين لو جبت مضاعفات، الرقم الأول مضاعفات التلاتة،
+
+325
+00:37:28,270 --> 00:37:35,510
+بيطلع الـ00، بيطلع الـ100، بيطلع الـ100، بيطلع
+
+326
+00:37:35,510 --> 00:37:35,550
+بيطلع الـ100، بيطلع الـ100، بيطلع الـ100، بيطلع
+
+327
+00:37:35,550 --> 00:37:35,650
+الـ100، بيطلع الـ100، بيطلع الـ100، بيطلع الـ100،
+
+328
+00:37:35,650 --> 00:37:36,350
+بيطلع الـ100، بيطلع الـ100، بيطلع الـ100، بيطلع
+
+329
+00:37:36,350 --> 00:37:44,550
+الـ100، بيطلع الـ100، بيطلع الـ100، بيطلع الـ100،
+
+330
+00:37:44,550 --> 00:37:50,050
+بيطلع
+
+331
+00:37:50,050 --> 00:37:52,610
+الـ
+
+332
+00:37:53,630 --> 00:37:58,050
+أه و البقى كله روتينيا، فهذا شغال روتيني، هذا صورة
+
+333
+00:37:58,050 --> 00:38:01,850
+واحدة في تجابتك، تبقى الإفرار هذا، و كله قدامي في
+
+334
+00:38:01,850 --> 00:38:09,050
+طريقين، يا جيبي ايديل ثاني، يا اما على النظرية،
+
+335
+00:38:09,050 --> 00:38:13,770
+فإذا بتقدر يبقى أنا ممتن وانشغل، كنت يبقى أضافتي
+
+336
+00:38:13,770 --> 00:38:18,630
+للمعلومات اللي كمان معلومة، فيبقى أنا بفكر
+
+337
+00:38:18,630 --> 00:38:23,590
+بالطريقة اللي هي اسم ناسبني،وكل واحد فكر في الأول
+
+338
+00:38:23,590 --> 00:38:28,090
+ممكن احنا اتنين نقصد والتفكير ممكن نقصد النتيجة
+
+339
+00:38:28,090 --> 00:38:31,970
+يعني ليس صعب نروح ندور على عيون تاريو ونقول هذا
+
+340
+00:38:31,970 --> 00:38:37,050
+صرصت منه وهذا صرصت منها ونثبت أن هذا كذا إلى آخرية
+
+341
+00:38:37,050 --> 00:38:43,750
+طيب على أي حال صار عندنا Factoring جديدة وهذا ليس
+
+342
+00:38:43,750 --> 00:38:51,690
+بالجديدة لأن مضوانا كان Ideals and Factoring تمام؟
+
+343
+00:38:51,790 --> 00:38:58,190
+هل هدفي الـshattering
+
+344
+00:38:58,190 --> 00:39:02,610
+فيها ال unity؟
+
+345
+00:39:02,610 --> 00:39:10,190
+واحد وزيره زي ده هو ال unity قضوه فيه هدفي هذا
+
+346
+00:39:10,190 --> 00:39:16,470
+الحاجة ده وزيره زي ده ده لما ملهمي ان هو يشمل نفس
+
+347
+00:39:16,470 --> 00:39:26,430
+الشيء يبقى هدفي هو ال unityيرجع هذه هما هذه كلمة
+
+348
+00:39:26,430 --> 00:39:39,570
+فاكتور رينج فاكتور رينج وال unity اللي هو واحد و
+
+349
+00:39:39,570 --> 00:39:44,810
+zero ذات ال two السؤال،
+
+350
+00:39:44,810 --> 00:39:52,270
+هل هذه field؟يعني هل every non-zero element is a
+
+351
+00:39:52,270 --> 00:39:59,010
+unit؟ هذا unity يبقى unit، بل هذا، لو ضربته في
+
+352
+00:39:59,010 --> 00:40:06,910
+هذا، يبقى unity؟ طبعا لا، طب لو ضربته في نفسه؟
+
+353
+00:40:06,910 --> 00:40:12,910
+طبعا ال unity هو ال unity، يبقى صح unity ولا لا؟
+
+354
+00:40:12,910 --> 00:40:20,910
+يبقى هنا، ماروح بامرناالواحد وزيره زائد ال a is a
+
+355
+00:40:20,910 --> 00:40:32,030
+unit and الإتنين وزيره زائد ال a is unit السبب
+
+356
+00:40:32,030 --> 00:40:35,950
+because إنه
+
+357
+00:40:35,950 --> 00:40:44,270
+الإتنين وزيره زائد ال a لو طردتوا إتنين وزيره زائد
+
+358
+00:40:44,270 --> 00:40:51,200
+ال a بتشيربساوي اتنين وزيرا اتنين وزيرا زائد ال a
+
+359
+00:40:51,200 --> 00:40:59,180
+يعني اربعة وزيرا زائد ال a يعني واحد وزيرا زائد
+
+360
+00:40:59,180 --> 00:41:05,400
+تلاتة وزيرا زائد ال a هذا موجود في ال a يبقى بيبقى
+
+361
+00:41:05,400 --> 00:41:12,320
+بيساوي واحد وزيرا زائد ال L و ال unity مظلوم؟ يبقى
+
+362
+00:41:12,320 --> 00:41:19,600
+صح هذا is a unitطيب مادة unit يبقى every non zero
+
+363
+00:41:19,600 --> 00:41:28,260
+is a unit تبقى صرفيت ولا لأ طيب شاهد تيب every non
+
+364
+00:41:28,260 --> 00:41:44,200
+zero is a unit
+
+365
+00:42:05,700 --> 00:42:11,080
+طيب يبقى صار هذا هو عبارة عن maximal ideal هذا
+
+366
+00:42:11,080 --> 00:42:16,510
+المقبول الأول من السؤالقال لي بيجيلي إن هذا
+
+367
+00:42:16,510 --> 00:42:23,090
+maximum و بعدين كني generalized لذالي لملة التلاتة
+
+368
+00:42:23,090 --> 00:42:29,890
+يا بنات prime ولا لا؟ أو لو سبدلته بخمسة أو لو
+
+369
+00:42:29,890 --> 00:42:36,410
+سبدلته باتنين أو لو سبدلته بسبعة، احداشر، تلتاشر،
+
+370
+00:42:36,410 --> 00:42:42,790
+سبعتاشر كله كانت الكلام صحيح و هذا maximum يبقى
+
+371
+00:42:43,990 --> 00:42:58,330
+the ideal اللي هو A بدرساه P X وY such that X وY
+
+372
+00:42:58,330 --> 00:43:13,330
+موجودة في ذلك I ال P is prime is maximum طيب
+
+373
+00:43:13,770 --> 00:43:17,310
+نمر الـ C طب ليش بقى يا أستاذ باقي الأرقام مقتنعة؟
+
+374
+00:43:17,310 --> 00:43:24,050
+باقي الأرقام؟ أنا جايك لباقي الأرقام، أطلعت، فخلص،
+
+375
+00:43:24,050 --> 00:43:30,370
+مخلصش، قال لي هنا عامة، بقوله لو كان الرقم بدل ما
+
+376
+00:43:30,370 --> 00:43:34,370
+هو التلاتة، أي track ideal، بيكون ال ideal
+
+377
+00:43:34,370 --> 00:43:39,790
+maximum، طب لو جينا لأرقام، نمر ال Cقال إيش بيحصل
+
+378
+00:43:39,790 --> 00:43:46,170
+لو شيلت التلاتة X وحطيت مكانها أربعة X بقوله بسيطة
+
+379
+00:43:46,170 --> 00:43:54,730
+بدي أخد ال A تساوي كل الأربعة X وY بحيث ال X وY
+
+380
+00:43:54,730 --> 00:44:03,070
+موجودة في Z قال هذا maximum ideal هذا ideal في
+
+381
+00:44:03,070 --> 00:44:14,920
+الأول يبقى هذا isID غير هيك ال ring commutative
+
+382
+00:44:14,920 --> 00:44:24,640
+with unity أخذناها من الأول و ال Z بس Z is
+
+383
+00:44:24,640 --> 00:44:29,900
+commutative with
+
+384
+00:44:29,900 --> 00:44:32,120
+unity
+
+385
+00:44:36,880 --> 00:44:43,760
+الأن نشوف هل هي field و لا ماهياش field أنا أزعم
+
+386
+00:44:43,760 --> 00:44:55,840
+أن زر دارف صمم مع زر موديول A هي الـ A و مين؟ واحد
+
+387
+00:44:55,840 --> 00:45:08,600
+و Zero زائد الـ A نين و Zero زائد الـ Aزائد MA
+
+388
+00:45:08,600 --> 00:45:19,100
+ثلاثة و Zero زائد A فلو بدلنا ثلاثة X باربع X بصير
+
+389
+00:45:19,100 --> 00:45:24,820
+بدل ما كان فيها هنا تلات عناصر بس بصير عندى جداش
+
+390
+00:45:24,820 --> 00:45:30,940
+اربع اذا لو بدلتها بخمسة خمسة ستة ستة عناصر و هكذا
+
+391
+00:45:30,940 --> 00:45:36,060
+كل ما تغير رقمبيزداد عدد العناصر في الـ factor،
+
+392
+00:45:36,060 --> 00:45:40,440
+الـ group، الـ unit. طيب، هدول ثلاثة، السؤال هو،
+
+393
+00:45:40,440 --> 00:45:44,780
+هل هذا field؟
+
+394
+00:45:44,780 --> 00:45:51,340
+في ال field، كل عنصر غير الصفر يبقى unit، هذا
+
+395
+00:45:51,340 --> 00:45:57,500
+unit، وهذا unit، لأن تلاتة بتلاتة، تسعة، اثنين،
+
+396
+00:45:57,500 --> 00:46:01,820
+اربعتين، بضلين ال unit اللي بيبقى unit، هل هذا
+
+397
+00:46:01,820 --> 00:46:08,280
+unit؟لأن هذا الـ Potent Element لو ضربته في نفسه
+
+398
+00:46:08,280 --> 00:46:29,720
+بتظهر الـ Zero و Zero تمام؟ إذن باجي بقوله باجي
+
+399
+00:46:29,720 --> 00:46:39,050
+بقوله الآن اتنينوزيره زائد ال a في اتنين وزيره
+
+400
+00:46:39,050 --> 00:46:47,470
+زائد ال a يساوي اربعة وزيره زائد ال a اللي هو قد
+
+401
+00:46:47,470 --> 00:46:54,610
+يساوي ال a itself يبقى هنا ساعة اتنين وزيره زائد
+
+402
+00:46:54,610 --> 00:47:09,430
+ال a is a من الportent من الportentEleven المفروض
+
+403
+00:47:09,430 --> 00:47:19,070
+ليش؟ لأنه مربع أعطاني Zero But Not Unit يبقى قدرت
+
+404
+00:47:19,070 --> 00:47:26,150
+أجيب عنصر واحد مالوش معكوس يبقى هل هذا فيه؟ يبقى
+
+405
+00:47:26,150 --> 00:47:32,940
+هنا هذا بدي يعطينا أن ال direct sum ما عزيزيموديول
+
+406
+00:47:32,940 --> 00:47:43,100
+A is not A فيه هذا بيعطينا ان ال A is not maximum
+
+407
+00:47:43,100 --> 00:47:46,660
+طيب
+
+408
+00:47:46,660 --> 00:47:52,780
+الآن اخر حاجة اللي امر دي بقولي عن مم يبقى باجي
+
+409
+00:47:52,780 --> 00:48:05,090
+بقوله الان ال A بتساوي N X و Ysuch that ال X و ال
+
+410
+00:48:05,090 --> 00:48:14,590
+Y موجودة في Z and ال N هذه not a prime يبقى and ال
+
+411
+00:48:14,590 --> 00:48:30,310
+M is not a prime is not maximum طبعا
+
+412
+00:48:30,310 --> 00:48:40,200
+مثالشكله بسيط كإثبات إنه أرضيل ولكن .. ولكن بده
+
+413
+00:48:40,200 --> 00:48:46,240
+شغل كتير طبعا المرة القادمة إن شاء الله سناخد حل
+
+414
+00:48:46,240 --> 00:48:50,640
+بقية الأسلة مش هنخش في الشكرة اللي بعد إلا لما
+
+415
+00:48:50,640 --> 00:48:53,300
+نخلص هذا إن شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..56cc628077032e0fc3671e0dfae470a8544f93b9
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/M-hAySk0SyQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4868, "start": 21.6, "end": 48.68, "text": "رحمان الله الرحيم احنا انتهينا المرة الماضية من chapter ال ideas and factoring وبدأنا في حل الأسئلة في نصف التانية من المحاضرة واليوم ان شاء الله نكمل حل الأسئلة اللي كلفناها بحلها في البيت طبعا اخر سؤال مرة اتعرضنا له هو سؤال 17 اليوم سؤال 17", "tokens": [2288, 35571, 7649, 21984, 34892, 5016, 32640, 1975, 5016, 8315, 16472, 47395, 1829, 8315, 9673, 25720, 9673, 46958, 10632, 9154, 7187, 2423, 3487, 293, 1186, 3662, 4032, 44510, 10721, 8315, 8978, 11331, 1211, 16247, 3794, 19986, 37977, 8978, 8717, 9381, 5172, 16712, 7649, 10632, 9154, 9673, 5016, 46958, 25720, 4032, 6027, 1829, 20498, 16472, 13412, 16606, 21984, 8717, 24793, 1211, 11331, 1211, 16247, 3794, 19986, 37977, 13672, 1829, 28242, 5172, 8315, 11296, 4724, 5016, 1211, 11296, 8978, 2423, 21292, 2655, 23032, 3555, 3615, 995, 1975, 34740, 8608, 33604, 6027, 3714, 25720, 1975, 2655, 3615, 43042, 8315, 46740, 31439, 8608, 33604, 6027, 3282, 45595, 20498, 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"هذا أخدنا ideal من ال ring و لجأت فيه ال unity أو لجأت فيه unit يبقى على كل الخط ال ideal هذا بده يساوي مين؟ بده يساوي نفس ال ring هذا كان سؤال سبعتاشر بعد ذلك معانا سؤال اتنين و عشرين جال يخد لل ideal و ال principle ideal generated by اتنين يبقى سؤال اتنين و عشرين", "tokens": [3224, 15730, 5551, 9778, 3215, 8315, 7157, 9154, 2423, 4875, 4032, 5296, 7435, 10721, 2655, 8978, 3224, 2423, 18205, 34051, 5296, 7435, 10721, 2655, 8978, 3224, 4985, 7251, 3555, 4587, 7578, 15844, 28242, 33962, 9566, 2423, 7157, 23758, 47525, 3224, 7251, 3794, 995, 45865, 3714, 9957, 22807, 47525, 3224, 7251, 3794, 995, 45865, 8717, 36178, 2423, 4875, 23758, 25961, 8608, 33604, 6027, 8608, 3555, 34268, 33599, 2288, 39182, 29910, 23275, 20449, 7649, 995, 8608, 33604, 6027, 1975, 2655, 1863, 9957, 4032, 6225, 46309, 9957, 10874, 6027, 7251, 9778, 3215, 24976, 7157, 4032, 2423, 8665, 7157, 10833, 538, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 8608, 33604, 6027, 1975, 2655, 1863, 9957, 4032, 6225, 46309, 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"text": "طيب يبقى صار هذا هو عبارة عن maximal ideal هذا المقبول الأول من السؤال", "tokens": [9566, 1829, 3555, 7251, 3555, 4587, 7578, 20328, 9640, 23758, 31439, 6225, 3555, 9640, 3660, 18871, 49336, 7157, 23758, 9673, 4587, 3555, 12610, 16247, 12610, 9154, 21136, 33604, 6027], "avg_logprob": -0.28203123609224956, "compression_ratio": 1.2105263157894737, "no_speech_prob": 0.0, "words": [{"start": 2525.7, "end": 2526.68, "word": "طيب", "probability": 0.6569010416666666}, {"start": 2526.68, "end": 2527.66, "word": " يبقى", "probability": 0.828125}, {"start": 2527.66, "end": 2528.1, "word": " صار", "probability": 0.85400390625}, {"start": 2528.1, "end": 2528.54, "word": " هذا", "probability": 0.81494140625}, {"start": 2528.54, "end": 2528.84, "word": " هو", "probability": 0.483642578125}, {"start": 2528.84, "end": 2529.32, "word": " عبارة", "probability": 0.937255859375}, {"start": 2529.32, "end": 2529.5, "word": " عن", "probability": 0.9873046875}, {"start": 2529.5, "end": 2529.96, 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ال direct sum ما عزيزي", "tokens": [36, 306, 553, 9673, 5172, 32887, 11242, 32239, 8592, 22807, 5296, 33456, 3224, 3714, 25513, 3615, 5551, 3615, 9566, 7649, 1829, 17182, 583, 1726, 27894, 7251, 3555, 4587, 7578, 12174, 3215, 43500, 5551, 7435, 1829, 3555, 18871, 9381, 2288, 36764, 24401, 3714, 6027, 2407, 8592, 20449, 4117, 41779, 7251, 3555, 4587, 7578, 8032, 1211, 23758, 8978, 3224, 22807, 7251, 3555, 4587, 7578, 34105, 23758, 4724, 16254, 37495, 9566, 1829, 8315, 14739, 2423, 2047, 2408, 19446, 6225, 11622, 1829, 11622, 1829], "avg_logprob": -0.33449072896698373, "compression_ratio": 1.3989071038251366, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2823.59, "end": 2824.37, "word": "Eleven", "probability": 0.525390625}, {"start": 2824.37, "end": 2829.43, "word": " المفروض", "probability": 0.62957763671875}, {"start": 2829.43, "end": 2830.19, "word": " ليش؟", "probability": 0.7014973958333334}, {"start": 2830.19, "end": 2830.63, "word": " لأنه", "probability": 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"probability": 0.9814453125}, {"start": 2870.12, "end": 2871.22, "word": " مم", "probability": 0.593994140625}, {"start": 2871.22, "end": 2872.32, "word": " يبقى", "probability": 0.944091796875}, {"start": 2872.32, "end": 2872.78, "word": " باجي", "probability": 0.81298828125}, {"start": 2872.78, "end": 2873.56, "word": " بقوله", "probability": 0.85302734375}, {"start": 2873.56, "end": 2876.04, "word": " الان", "probability": 0.73193359375}, {"start": 2876.04, "end": 2876.72, "word": " ال", "probability": 0.32666015625}, {"start": 2876.72, "end": 2877.24, "word": " A", "probability": 0.939453125}, {"start": 2877.24, "end": 2878.8, "word": " بتساوي", "probability": 0.635986328125}, {"start": 2878.8, "end": 2879.44, "word": " N", "probability": 0.54150390625}, {"start": 2879.44, "end": 2880.3, "word": " X", "probability": 0.6201171875}, {"start": 2880.3, "end": 2881.22, "word": " و", "probability": 0.958984375}, {"start": 2881.22, "end": 2881.74, "word": " Y", "probability": 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"end": 2885.09, "word": " ال", "probability": 0.457763671875}, {"start": 2885.09, "end": 2885.51, "word": " Y", "probability": 0.98583984375}, {"start": 2885.51, "end": 2886.79, "word": " موجودة", "probability": 0.9801025390625}, {"start": 2886.79, "end": 2887.01, "word": " في", "probability": 0.958984375}, {"start": 2887.01, "end": 2887.51, "word": " Z", "probability": 0.273681640625}, {"start": 2887.51, "end": 2888.27, "word": " and", "probability": 0.65576171875}, {"start": 2888.27, "end": 2889.65, "word": " ال", "probability": 0.822265625}, {"start": 2889.65, "end": 2889.99, "word": " N", "probability": 0.82666015625}, {"start": 2889.99, "end": 2890.67, "word": " هذه", "probability": 0.59765625}, {"start": 2890.67, "end": 2890.93, "word": " not", "probability": 0.54443359375}, {"start": 2890.93, "end": 2892.03, "word": " a", "probability": 0.68359375}, {"start": 2892.03, "end": 2892.49, "word": " prime", "probability": 0.88818359375}, {"start": 2892.49, "end": 2893.75, "word": " يبقى", "probability": 0.7994384765625}, {"start": 2893.75, "end": 2894.25, "word": " and", "probability": 0.87939453125}, {"start": 2894.25, "end": 2894.59, "word": " ال", "probability": 0.85791015625}, {"start": 2894.59, "end": 2895.07, "word": " M", "probability": 0.52880859375}, {"start": 2895.07, "end": 2895.81, "word": " is", "probability": 0.88720703125}, {"start": 2895.81, "end": 2897.21, "word": " not", "probability": 0.95263671875}, {"start": 2897.21, "end": 2898.19, "word": " a", "probability": 0.9765625}, {"start": 2898.19, "end": 2898.99, "word": " prime", "probability": 0.92578125}, {"start": 2898.99, "end": 2900.97, "word": " is", "probability": 0.6494140625}, {"start": 2900.97, "end": 2902.35, "word": " not", "probability": 0.9619140625}, {"start": 2902.35, "end": 2903.75, "word": " maximum", "probability": 0.64013671875}, {"start": 2903.75, "end": 2910.31, "word": " طبعا", "probability": 0.943359375}, {"start": 2910.31, "end": 2911.23, "word": " مثال", "probability": 0.804443359375}], "temperature": 1.0}, {"id": 101, "seek": 293330, "start": 2911.54, "end": 2933.3, "text": "شكله بسيط كإثبات إنه أرضيل ولكن .. ولكن بده شغل كتير طبعا المرة القادمة إن شاء الله سناخد حل بقية الأسلة مش هنخش في الشكرة اللي بعد إلا لما نخلص هذا إن شاء الله تعالى", "tokens": [8592, 28820, 3224, 4724, 3794, 1829, 9566, 9122, 28814, 12984, 3555, 9307, 36145, 3224, 5551, 43042, 26895, 35525, 19452, 4386, 35525, 19452, 47525, 3224, 13412, 17082, 1211, 9122, 2655, 13546, 23032, 3555, 3615, 995, 9673, 25720, 25062, 18513, 46007, 36145, 13412, 16606, 21984, 8608, 1863, 47283, 3215, 11331, 1211, 4724, 4587, 10632, 16247, 3794, 37977, 37893, 8032, 1863, 9778, 8592, 8978, 25124, 4117, 25720, 13672, 1829, 39182, 11933, 15040, 5296, 15042, 8717, 9778, 1211, 9381, 23758, 36145, 13412, 16606, 21984, 37279, 6027, 7578], "avg_logprob": -0.2075892784410999, "compression_ratio": 1.7309941520467835, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 2911.54, "end": 2912.24, "word": "شكله", "probability": 0.962890625}, {"start": 2912.24, "end": 2912.96, "word": " بسيط", "probability": 0.98486328125}, {"start": 2912.96, "end": 2914.04, "word": " كإثبات", "probability": 0.91435546875}, {"start": 2914.04, "end": 2914.46, "word": " إنه", "probability": 0.696533203125}, {"start": 2914.46, "end": 2915.12, "word": " أرضيل", "probability": 0.4193522135416667}, {"start": 2915.12, "end": 2917.38, "word": " ولكن", "probability": 0.721923828125}, {"start": 2917.38, "end": 2918.0, "word": " ..", "probability": 0.5546875}, {"start": 2918.0, "end": 2918.82, "word": " ولكن", "probability": 0.900390625}, {"start": 2918.82, "end": 2920.2, "word": " بده", "probability": 0.6500244140625}, {"start": 2920.2, "end": 2920.64, "word": " شغل", "probability": 0.9923502604166666}, {"start": 2920.64, "end": 2921.22, "word": " كتير", "probability": 0.6756998697916666}, {"start": 2921.22, "end": 2922.18, "word": " طبعا", "probability": 0.951904296875}, {"start": 2922.18, "end": 2922.82, "word": " المرة", "probability": 0.9267578125}, {"start": 2922.82, "end": 2923.4, "word": " القادمة", "probability": 0.9889322916666666}, {"start": 2923.4, "end": 2923.66, "word": " إن", "probability": 0.442626953125}, {"start": 2923.66, "end": 2923.94, "word": " شاء", "probability": 0.941162109375}, {"start": 2923.94, "end": 2924.28, "word": " الله", "probability": 0.95849609375}, {"start": 2924.28, "end": 2925.68, "word": " سناخد", "probability": 0.9307861328125}, {"start": 2925.68, "end": 2926.24, "word": " حل", "probability": 0.968017578125}, {"start": 2926.24, "end": 2927.12, "word": " بقية", "probability": 0.8875325520833334}, {"start": 2927.12, "end": 2928.04, "word": " الأسلة", "probability": 0.6681315104166666}, {"start": 2928.04, "end": 2928.54, "word": " مش", "probability": 0.732421875}, {"start": 2928.54, "end": 2929.04, "word": " هنخش", "probability": 0.93505859375}, {"start": 2929.04, "end": 2929.18, "word": " في", "probability": 0.9169921875}, {"start": 2929.18, "end": 2929.66, "word": " الشكرة", "probability": 0.6055094401041666}, {"start": 2929.66, "end": 2929.84, "word": " اللي", "probability": 0.946044921875}, {"start": 2929.84, "end": 2930.08, "word": " بعد", "probability": 0.5673828125}, {"start": 2930.08, "end": 2930.4, "word": " إلا", "probability": 0.8837890625}, {"start": 2930.4, "end": 2930.64, "word": " لما", "probability": 0.917724609375}, {"start": 2930.64, "end": 2931.24, "word": " نخلص", "probability": 0.990966796875}, {"start": 2931.24, "end": 2931.62, "word": " هذا", "probability": 0.91943359375}, {"start": 2931.62, "end": 2932.26, "word": " إن", "probability": 0.84375}, {"start": 2932.26, "end": 2932.54, "word": " شاء", "probability": 0.975830078125}, {"start": 2932.54, "end": 2932.78, "word": " الله", "probability": 0.95703125}, {"start": 2932.78, "end": 2933.3, "word": " تعالى", "probability": 0.8907877604166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2933.562625, "duration_after_vad": 2797.510624999993}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/N-D4GQAtXSk.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/N-D4GQAtXSk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0746de1d4c36949e59fe44d779531815c0a77ea8
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/N-D4GQAtXSk.srt
@@ -0,0 +1,1357 @@
+1
+00:00:20,990 --> 00:00:24,710
+بسم الله الرحمن الرحيم اليوم إن شاء الله هنناقش في
+
+2
+00:00:24,710 --> 00:00:27,790
+ال Chapter الثاني اللي هو الـ Integral Domains بس
+
+3
+00:00:27,790 --> 00:00:32,210
+باقي من المرة الماضية ثلاثة أسئلة بدنا نشرحها
+
+4
+00:00:32,210 --> 00:00:37,350
+أو بدنا نعطي الحل تبعها، ثم نبدأ في الـ Chapter
+
+5
+00:00:37,350 --> 00:00:41,390
+الجديد اللي هو Chapter 13 الـ Integral Domains
+
+6
+00:00:41,390 --> 00:00:46,610
+وصلنا إلى سؤال واحد وأربعين بيقول Prove or Disprove
+
+7
+00:00:47,180 --> 00:00:53,820
+الـ 6R التي تساوي كل المصفوفات لنظام 2x2 واللي
+
+8
+00:00:53,820 --> 00:00:58,420
+على الشكل اللي قدامنا هذا الـ A والـ B والعنصر
+
+9
+00:00:58,420 --> 00:01:04,800
+هذا هو نفس العنصر هذا، وهو الفرق بين هذين العنصرين
+
+10
+00:01:04,800 --> 00:01:17,250
+يبقى A، A-B، A-B نفس العنصر B بحيث الـ A والـ B هل هو
+
+11
+00:01:17,250 --> 00:01:21,110
+Subring من
+
+12
+00:01:21,110 --> 00:01:29,090
+الـ Ring الـ M₂(ℤ)  M₂(ℤ) هي عبارة عن مجموعة كل
+
+13
+00:01:29,090 --> 00:01:35,310
+المصفوفات اللي أرقامها
+
+14
+00:01:35,310 --> 00:01:41,420
+تبعها تبقى أعداد صحيحة. يبقى نشوف Prove or
+
+15
+00:01:41,420 --> 00:01:45,980
+Disprove يعني شوف حالك إنك تقدر تثبت إنها Sub
+
+16
+00:01:45,980 --> 00:01:51,060
+ring ولا لأ. إن قدرت تثبت إنها Subring ما كانش يبقى
+
+17
+00:01:51,060 --> 00:01:57,460
+ممكن تكون ماهي Subring. إذًا احنا هنبتدي نشوف هل
+
+18
+00:01:57,460 --> 00:02:03,240
+ثلاثة شروط تبعات الـ Subring بنقدر نطبقهم على هذه
+
+19
+00:02:03,240 --> 00:02:09,370
+المجموعة ولا لأ. لو جد يا بنات قلنا النقطة الأولى بدي
+
+20
+00:02:09,370 --> 00:02:15,450
+أثبت إن الـ A هذه is non-empty. حط لي شروط على A وB
+
+21
+00:02:15,450 --> 00:02:20,690
+غير إنهم أصفار. لأ، إذًا ممكن يكونوا أصفار، بحيث ولا
+
+22
+00:02:20,690 --> 00:02:27,730
+لأ، إذًا بدي أقول If الـ A تساوي الـ B تساوي الـ 0
+
+23
+00:02:27,730 --> 00:02:37,220
+Then الآن الـ element 0 0 ناقص 0 0 ناقص 0 و 0 اللي
+
+24
+00:02:37,220 --> 00:02:44,340
+هو عبارة عن 0 0 0. إذًا موجود في R. هذا بيجي
+
+25
+00:02:44,340 --> 00:02:53,960
+يقينًا إن الـ R is non-empty. يبقى تحقق الشرط الأول
+
+26
+00:02:53,960 --> 00:03:01,700
+من شروط الـ Subring. بتروح للشرط الثاني، بتاخد عنصرين
+
+27
+00:03:01,700 --> 00:03:07,830
+مختلفين، وأثبت إن الفرق فيما بينهم موجود. هنا إن
+
+28
+00:03:07,830 --> 00:03:12,530
+قدرت أهتم بالشرط الثالث ما قدرت، بكون كفى الله
+
+29
+00:03:12,530 --> 00:03:18,290
+المؤمنين وقاتلهم. يبقى أنا لو جيت قلت ذيت الـ A والـ
+
+30
+00:03:18,290 --> 00:03:24,950
+B مصفوفتين موجودتين في الـ set R اللي عندنا، يبقى
+
+31
+00:03:24,950 --> 00:03:34,740
+Then المصفوفة A بدها تساوي A A ناقص الـ BA ناقص الـ
+
+32
+00:03:34,740 --> 00:03:44,720
+B وB والمصفوفة B بدها تكون C وهنا D وهنا C ناقص D
+
+33
+00:03:44,720 --> 00:03:52,220
+وهنا C ناقص D بالشكل اللي عندها. بدي آجي أطرح الـ A
+
+34
+00:03:52,220 --> 00:03:57,480
+ناقص الـ B، بيطلع مصفوفة على الشكل اللي عندها ده.
+
+35
+00:03:57,480 --> 00:04:03,370
+بيكون الفرق فيما بينهما موجود. يبقى هذا الكلام بدّه
+
+36
+00:04:03,370 --> 00:04:11,630
+يساعدني، بنطرح كل عنصر مع نظيره، يبقى هنا A ناقص
+
+37
+00:04:11,630 --> 00:04:21,250
+الـ C، هنا الـ A ناقص الـ B ناقص الـ C زائد الـ D، هنا الـ
+
+38
+00:04:21,250 --> 00:04:32,990
+A ناقص الـ B ناقص الـ C زائد الـ D، هنا الـ B ناقص الـ D
+
+39
+00:04:32,990 --> 00:04:40,290
+طيب هي عنصرين مختلفين، وهي هذا الفرق ما بين العنصرين
+
+40
+00:04:40,290 --> 00:04:47,250
+هذا، لإنه A ناقص C هي الـ A ناقص الـ C، وB ناقص D يعني
+
+41
+00:04:47,250 --> 00:04:53,710
+بقدر أكتب هذه على الشكل التالي اللي هو الـ A ناقص
+
+42
+00:04:53,710 --> 00:05:01,190
+الـ C، وهذه الـ A ناقص الـ C كلها مع بعض، ضال الـ B والـ
+
+43
+00:05:01,190 --> 00:05:09,710
+D، بقدر آخذ ناقص عامل مشترك لـ B ناقص الـ D، هنا بنفس
+
+44
+00:05:09,710 --> 00:05:19,510
+الطريقة A ناقص الـ C ناقص الـ B ناقص الـ D، تمام؟ و
+
+45
+00:05:19,510 --> 00:05:27,670
+هذه الـ B ناقص الـ D بالشكل اللي أنا طلعته، هاي عنصر،
+
+46
+00:05:27,670 --> 00:05:32,750
+هاي عنصر مختلف، هذا هو الفرق فيما بينهما، وهذا هو
+
+47
+00:05:32,750 --> 00:05:36,950
+الفرق فيما بينهما، إذًا الشكل هذا على الشكل اللي
+
+48
+00:05:36,950 --> 00:05:42,610
+فوق، يبقى هذه موجودة وين؟ موجودة في الـ set اللي فوق اللي
+
+49
+00:05:42,610 --> 00:05:47,450
+عندنا، إذًا أنت حققت الـ condition الثاني، بتروح لمين؟
+
+50
+00:05:47,450 --> 00:05:52,250
+للـ condition الثالث، الـ condition الثالث والأخير
+
+51
+00:05:52,250 --> 00:05:59,440
+إذا طلع حاصل ضرب الـ two matrices الـ A في الـ B على
+
+52
+00:05:59,440 --> 00:06:03,580
+الشكل اللي عندنا هذا، بنقوله خلاص ما كده، وبالتالي
+
+53
+00:06:03,580 --> 00:06:09,280
+بيصير Subring. الـ condition هذا لم يتحقق، بقوله يبقى
+
+54
+00:06:09,280 --> 00:06:15,940
+الـ R ماهي Subring. يبقى بدي أروح آخذ الـ A في الـ
+
+55
+00:06:15,940 --> 00:06:21,700
+B، يبقى المصفوفة اللي عندنا A ناقص الـ B
+
+56
+00:06:41,530 --> 00:06:48,110
+الصف الأول في العمود الأول، ونجمع، بيعطينا العنصر
+
+57
+00:06:48,110 --> 00:06:55,810
+الأول من مصفوفة حاصل الضرب. يبقى باجي بقول A في C، A
+
+58
+00:06:55,810 --> 00:07:04,470
+في C هذول بنضربهم في بعض زائد A ناقص الـ B، فاهمين؟
+
+59
+00:07:04,470 --> 00:07:11,470
+الـ A ناقص الـ B في الـ C ناقص الـ D. هاي بنضرب كل عنصر
+
+60
+00:07:11,470 --> 00:07:18,310
+مع نظيره، ونجمع، أعطاني مين؟ العنصر الأول. نيجي الصف
+
+61
+00:07:18,310 --> 00:07:28,060
+الأول في العمود الثاني. يبقى A في C ناقص الـ D زائد
+
+62
+00:07:28,060 --> 00:07:36,280
+اللي هو الـ A ناقص الـ B في الـ D، شكل عنصر عندنا
+
+63
+00:07:36,280 --> 00:07:42,420
+خلصنا الصف الأول، نروح للصف الثاني، يبقى الصف الثاني
+
+64
+00:07:42,420 --> 00:07:49,500
+في العمود الأول، يبقى الـ C، أو خليها مرتبة زي ما هي.
+
+65
+00:07:50,070 --> 00:07:58,610
+الـ A ناقص الـ B كلها في C، آه answer في نظيره B
+
+66
+00:07:58,610 --> 00:08:07,210
+يبقى زائد B في C ناقص الـ D. أي خلصنا الصف الأول في
+
+67
+00:08:07,210 --> 00:08:10,690
+العمود الأول، بدنا نيجي الصف الثاني في العمود الأول.
+
+68
+00:08:10,690 --> 00:08:18,230
+نيجي الصف الثاني في العمود الأول، يبقى A ناقص الـ B
+
+69
+00:08:18,230 --> 00:08:29,700
+في الـ C ناقص الـ D، وبعده زائد BD. يبقى زائد BD، بيحصل
+
+70
+00:08:29,700 --> 00:08:35,480
+نشوف شكل المصفوفة هذا وين وصلنا. يبقى هذا الكلام
+
+71
+00:08:35,480 --> 00:08:44,020
+يبدو يساوي AC وهنا زائد AC، يبقى بيصير قد إيش
+
+72
+00:08:44,020 --> 00:08:51,130
+عندي اثنين AC، مرة ثانية هذه AC. بدي أضرب A في C
+
+73
+00:08:51,130 --> 00:09:01,890
+بتطلع AC وعندي AC، بتصير 2AC ناقص AD ناقص AD
+
+74
+00:09:01,890 --> 00:09:11,890
+ناقص BC زائد BD. هي خلصنا العنصر اللي عندنا هنا. نيجي
+
+75
+00:09:11,890 --> 00:09:26,400
+لهذا 2AC، زي ما هو. يفجأ هذا 2AC ناقص AD ناقص AD زائد
+
+76
+00:09:26,400 --> 00:09:35,560
+AD وناقص AD مع السلامة طبعًا، هاي مرة ثانية هاي ناقص
+
+77
+00:09:35,560 --> 00:09:44,220
+AD، وعندك هنا زائد AD مع السلامة. بيظهر إن هي ناقص
+
+78
+00:09:44,220 --> 00:09:52,670
+BD ناقص BD. طيب
+
+79
+00:09:52,670 --> 00:10:00,710
+هنا ممكن يصير اختصارات، المهم، طيب هذه 2AC ناقص BD
+
+80
+00:10:00,710 --> 00:10:11,030
+خلصناها. نيجي لهذه، هذه اللي هو AC. يبقى هذه AC، تمام؟
+
+81
+00:10:11,030 --> 00:10:21,220
+هذه A في C ناقص BC زائد BC، وروحوا مع السلامة ويبقى
+
+82
+00:10:21,220 --> 00:10:30,640
+ناقص BD يبقى ناقص BD. ندخل لهذا العنصر، هذا العنصر
+
+83
+00:10:30,640 --> 00:10:45,460
+بيصير عندنا AC ناقص AD ناقص BC زائد BD زائد BD
+
+84
+00:10:45,460 --> 00:10:54,500
+زائد اثنين BD، وهي خلصنا. طيب هل هذه يعني الشكل اللي
+
+85
+00:10:54,500 --> 00:10:59,220
+فوق ولا لأ؟ بنقول الله هو أعلى. طلع لي الـ element
+
+86
+00:10:59,220 --> 00:11:04,900
+هذا، هو الـ element هذا بالضبط؟ طيب تمام، يبقى صار
+
+87
+00:11:04,900 --> 00:11:12,360
+العنصر هذا هو العنصر هذا. الآن، طب خليني أجرب الاثنين
+
+88
+00:11:12,360 --> 00:11:18,960
+هذول لو طرحتهم من بعض، طلع هذا بيكون مئة بالمئة مرة
+
+89
+00:11:18,960 --> 00:11:24,940
+ثانية العنصر هذا هو العنصر هذا. لو طرحت هذول من بعض
+
+90
+00:11:24,940 --> 00:11:30,600
+بدّه يطلع مين؟ اللي هو العنصر هذا. ليه؟ هاي و هذول
+
+91
+00:11:30,600 --> 00:11:34,660
+طرحهم من بعض بدّه يطلع... الآن طلعوا الاثنين هذول من
+
+92
+00:11:34,660 --> 00:11:39,580
+بعض زي بعض بالضبط. إذًا بدي أطرح هذا ناقص هذا بدّه
+
+93
+00:11:39,580 --> 00:11:44,470
+يعطيني... إن شاء الله، في الهامش، مش هيك، نطرحهم من
+
+94
+00:11:44,470 --> 00:11:51,110
+بعض. يبقى لو جيت في الهامش، مش هيك، قلت هذا ما يعني
+
+95
+00:11:51,110 --> 00:12:05,270
+هاي اثنين AC، اثنين AC ناقص AD وناقص BC وزائد BD
+
+96
+00:12:05,270 --> 00:12:12,760
+و هذول بدي أكتبهم بإشارة ناقص، لأن A ناقص الـ B
+
+97
+00:12:12,760 --> 00:12:21,240
+يبقى هذول بالناقص، بتصير ناقص AC، هذا بيصير زائد AD
+
+98
+00:12:21,240 --> 00:12:31,820
+وهذا زائد BC وهذا ناقص اثنين BD. أظن هذول مع بعض بيضل
+
+99
+00:12:31,820 --> 00:12:40,390
+قد إيش؟ AC وهذول مع السلامة، بظل ناقص BD، والـ
+
+100
+00:12:40,390 --> 00:12:48,090
+element هذا. يبقى على طول الخط بس بيثبت إن هذا الـ A
+
+101
+00:12:48,090 --> 00:12:55,390
+في B موجود وين؟ موجود في الـ R. من هنا تحققت الشروط
+
+102
+00:12:55,390 --> 00:13:03,210
+الثلاثة. يبقى الـ R is a Subring. هذا بدي يقين إن الـ R
+
+103
+00:13:03,720 --> 00:13:16,660
+is a Subring of
+
+104
+00:13:16,660 --> 00:13:21,000
+M₂(ℤ)
+
+105
+00:13:21,000 --> 00:13:24,500
+هذا
+
+106
+00:13:24,500 --> 00:13:29,640
+كان طبعًا في عندك كمان سؤالين، زي سؤال أربعين وسؤال
+
+107
+00:13:29,640 --> 00:13:34,510
+اثنين وأربعين، بنفس الفكرة. سؤال أربعين بدل الناقص
+
+108
+00:13:34,510 --> 00:13:40,530
+زائد. هذا الناقص لأربعة عناصر منفصلة عن بعض. طيب
+
+109
+00:13:40,530 --> 00:13:49,150
+نيجي لسؤال ستة وأربعين، يبقى هنا شوف بيقول لي إن اثنين
+
+110
+00:13:49,150 --> 00:13:58,790
+ℤ اتحاد ثلاثة ℤ is not a Subring
+
+111
+00:14:02,210 --> 00:14:11,970
+is not Subring of ℤ. مشان
+
+112
+00:14:11,970 --> 00:14:15,550
+أثبت الـ Subring بيقول لنا، بنروح بنثبت الشروط
+
+113
+00:14:15,550 --> 00:14:20,490
+الثلاثة. أول شيء اثنين ℤ non-empty، وثلاثة ℤ non-
+
+114
+00:14:20,490 --> 00:14:24,790
+empty، يبقى الاثنين non-empty. حطها على شجرة
+
+115
+00:14:24,790 --> 00:14:31,430
+وقال لي أثبت إن هذا ماهو Subring. إذًا هذا متحقق
+
+116
+00:14:31,430 --> 00:14:39,050
+.الثنين تعالَ نجرب الطرح. طب السؤال هل اثنين موجودة في
+
+117
+00:14:39,050 --> 00:14:43,030
+الـ subset اللي عندها هذه؟ في الـ union. طب والثلاثة
+
+118
+00:14:43,030 --> 00:14:49,370
+موجودة. تمام، يعني لو احنا كتبنا اثنين ℤ وكتبنا
+
+119
+00:14:49,370 --> 00:14:53,450
+ثلاثة ℤ وجبنا الـ union، بيكون عناصر الـ union هي
+
+120
+00:14:53,450 --> 00:14:58,490
+عناصر اثنين ℤ وكذلك عناصر ثلاثة ℤ. يبقى باجي
+
+121
+00:14:58,490 --> 00:15:06,250
+بقوله إن الحال كالتالي: احنا عندنا اللي هو الاثنين
+
+122
+00:15:06,250 --> 00:15:16,550
+وثلاثة موجودة في اثنين ℤ اتحاد ثلاثة ℤ، تمام؟
+
+123
+00:15:16,550 --> 00:15:23,270
+بطء، ولكن لو جيت تقول ثلاثة ناقص اثنين، الفرق بين
+
+124
+00:15:23,270 --> 00:15:32,380
+هذين العنصرين، هل الواحد موجود هنا؟ لأ. يبقى الواحد
+
+125
+00:15:32,380 --> 00:15:40,040
+does not belong لـ اثنين ℤ اتحاد ثلاثة ℤ. معناه إن الـ
+
+126
+00:15:40,040 --> 00:15:44,740
+condition الثاني من الـ Subring is not satisfied.
+
+127
+00:15:44,740 --> 00:15:55,720
+يبقى هنا Sir اثنين ℤ Union ثلاثة ℤ is not a
+
+128
+00:15:55,720 --> 00:15:59,920
+Subring of ℤ
+
+129
+00:16:03,020 --> 00:16:08,980
+طيب سؤال خمسين، سؤال
+
+130
+00:16:08,980 --> 00:16:15,640
+خمسين، الحقيقة مشهور في كل كتب الجبر، أي كتاب جبر
+
+131
+00:16:15,640 --> 00:16:20,280
+دور في الهامش اللي في الآخر، في الـ index، على كلمة
+
+132
+00:16:20,280 --> 00:16:24,900
+Boolean Ring، بقول لك موجودة وين في الصفحة الفلانية.
+
+133
+00:16:24,900 --> 00:16:30,840
+لذلك، الـ A is
+
+134
+00:16:34,830 --> 00:16:41,870
+الـ A تربيع، الـ A، لكل الـ A الموجودة في R
+
+135
+00:16:41,870 --> 00:16:49,590
+الـ Ring اللي فيها هذه الخاصية، بسميها
+
+136
+00:16:49,590 --> 00:16:56,170
+Boolean Ring نسبة لاكتشافها، يفجأها باسمها، بنات.
+
+137
+00:16:56,170 --> 00:16:59,070
+Boolean Ring
+
+138
+00:17:01,580 --> 00:17:07,000
+السؤال بيقول لي Show... طبعًا هذه لكل اللي موجودة في
+
+139
+00:17:07,000 --> 00:17:17,160
+الـ Ring، بيقول لي Show that any Boolean Ring
+
+140
+00:17:17,160 --> 00:17:21,860
+is commutative
+
+141
+00:17:35,380 --> 00:17:41,520
+يبقى أنا في عندي Ring، الـ Ring فيها خاصية إن مربع
+
+142
+00:17:41,520 --> 00:17:47,820
+أي عنصر فيها بيعطيني مين؟ نفس العنصر. تمام، بقول كويس
+
+143
+00:17:47,820 --> 00:17:53,640
+إن حدث ذلك، هذا الـ Ring بسميها Boolean Ring. السؤال
+
+144
+00:17:53,640 --> 00:17:59,540
+بيقول أثبت إن أي Boolean Ring is commutative، يعني
+
+145
+00:17:59,540 --> 00:18:04,980
+لو أخذت عنصرين فيها A وB، بدي أثبت إن الـ A في B بدي
+
+146
+00:18:04,980 --> 00:18:10,160
+يساوي B في A، لكل الـ A والـ B اللي موجودة في الـ Ring
+
+147
+00:18:10,160 --> 00:18:16,080
+A، بحكي إن A تنتمي للـ R وB تنتمي للـ R، يعني AB
+
+148
+00:18:16,080 --> 00:18:22,260
+تنتمي للـ R، AB تربيع تساوي AB. إذا قدرت أثبت إنه
+
+149
+00:18:22,260 --> 00:18:28,300
+يساوي BA، بكون تمام، اشتغل شوية احنا بروحنا في
+
+150
+00:18:28,300 --> 00:18:35,090
+طريق إن عندنا مصفوفة، وين موجودة في R؟ يبقى باجي بقوله If
+
+151
+00:18:35,090 --> 00:18:42,350
+الـ A والـ B belongs to R، then الـ A تربيع بدها تساوي
+
+152
+00:18:42,350 --> 00:18:48,550
+الـ A، and الـ B تربيع بدها تساوي B. هيك بدنا بداية
+
+153
+00:18:48,550 --> 00:18:57,890
+صحيحة. طيب، الآن الـ A والـ B موجودة في R، هل هذا يعني
+
+154
+00:18:58,280 --> 00:19:07,940
+إن الـ A زائد الـ B موجودة في R؟ صح؟
+
+155
+00:19:07,940 --> 00:19:14,620
+مش العملية الجمع وعملية الضرب على الـ Ring. A، اثنين
+
+156
+00:19:14,620 --> 00:19:20,400
+R، إيش بنسميها؟ binary operation، binary operation
+
+157
+00:19:20,400 --> 00:19:24,960
+يعني إن جمعت والضرب، بدي يكون الناتج موجود في R
+
+158
+00:19:24,960 --> 00:19:29,110
+itself. يعني closed under addition and closed under
+
+159
+00:19:29,110 --> 00:19:34,290
+multiplication. يبقى إن حدث ذلك، بقول يبقى الـ A زائد
+
+160
+00:19:34,290 --> 00:19:41,150
+B، يبقى ينطبق عليها الخاصية اللي عندنا. يبقى هذا
+
+161
+00:19:41,150 --> 00:19:49,110
+معناه إن الـ A زائد الـ B بدها تساوي الـ A زائد الـ B
+
+162
+00:19:49,110 --> 00:19:56,720
+الكل تربيع، ليش؟ since إن الـ A بتساوي الـ A تربيع، لكل
+
+163
+00:19:56,720 --> 00:20:03,380
+الـ A اللي موجودة فيها. يبقى نظرًا لأن مربع العنصر
+
+164
+00:20:03,380 --> 00:20:08,540
+بيعطينا العنصر نفسه، فمربع هذا العنصر بيعطينا من؟
+
+165
+00:20:08,540 --> 00:20:14,360
+العنصر نفسه. يبقى صار عندنا مين؟ الـ A زي الـ B، بتفك
+
+166
+00:20:14,360
+
+223
+00:27:31,080 --> 00:27:36,080
+ولا واحد فيهم يكون مياه زيه، نوضح لك الفكرة for
+
+224
+00:27:36,080 --> 00:27:45,140
+example مثلاً for example in
+
+225
+00:27:45,140 --> 00:27:54,730
+مثلاً there Ring Z6 Z6، ما هي العناصر التابعة لها؟ Zero، واحد
+
+226
+00:27:54,730 --> 00:28:01,110
+اثنين، ثلاثة، أربعة، خمسة. أول شيء نقول يا زيكي بتصف
+
+227
+00:28:01,110 --> 00:28:06,910
+على شجرة، ما لك دعوة، بدي أمسك الواحد، هل أقدر أجيء
+
+228
+00:28:06,910 --> 00:28:11,170
+أو آخذ أي عنصر من العناصر التي أنا أضربه في واحد
+
+229
+00:28:11,170 --> 00:28:17,980
+يطلع الناتج صفر؟ مش ممكن، يبقى الواحد is not easy هو
+
+230
+00:28:17,980 --> 00:28:24,520
+the advisor طيب، سؤال: لو ضربت الواحد في نفسه، يعني
+
+231
+00:28:24,520 --> 00:28:33,280
+ماذا يعني هذا الكلام؟ أن الواحد عبارة عن unit، تمام؟
+
+232
+00:28:33,280 --> 00:28:37,820
+الـ unity هنا الواحد، يبقى الواحد is a unit. هل هناك
+
+233
+00:28:37,820 --> 00:28:41,840
+unit أخرى؟ لا، بالمرة.
+
+234
+00:28:44,050 --> 00:28:50,150
+طب الخمسة في خمسة يبقى ماذا؟ خمسة، وأيضاً ستة في واحد
+
+235
+00:28:50,150 --> 00:28:53,950
+يبقى الواحد
+
+236
+00:28:53,950 --> 00:28:59,470
+والخمسة are units. يبقى هنا طبعاً هذا ليس دوماً في
+
+237
+00:28:59,470 --> 00:29:06,110
+الإجابة، بس مجرد معلومة. يبقى الواحد والخمسة are
+
+238
+00:29:06,110 --> 00:29:13,610
+units. ما هو السبب؟ since إن واحد تربيع بده يساوي واحد، خمسة تربيع بده يساوي واحد. طيب، نأخذ اثنين، لو ضربتها في
+
+239
+00:29:13,610 --> 00:29:18,990
+ثلاثة، كم الناتج؟ لا، اثنين في صفر، ولا ثلاثة في
+
+240
+00:29:18,990 --> 00:29:23,830
+صفر. يبقى zero divisor ولا لا؟ طب، ثلاثة في أربعة
+
+241
+00:29:23,830 --> 00:29:29,070
+ماشي، يعني ستة، اثنين في ثلاثة يبقى صفر، يبقى كمان zero
+
+242
+00:29:29,070 --> 00:29:34,830
+divisor، يبقى صار اثنان وثلاثة وأربعة أيضاً are
+
+243
+00:29:34,830 --> 00:29:41,480
+zero divisors. يبقى هنا اثنان وثلاثة وأربعة أها
+
+244
+00:29:41,480 --> 00:29:50,680
+zero divisors. لماذا؟ since إن اثنين في ثلاثة بده
+
+245
+00:29:50,680 --> 00:30:01,000
+يساوي صفر، والثلاثة في الأربعة بده تساوي أيضاً صفر.
+
+246
+00:30:01,000 --> 00:30:08,100
+كل مودي له ستة دراهم، كل مودي له ستة، يبقى هؤلاء صاروا
+
+247
+00:30:08,100 --> 00:30:13,160
+zero divisors. يبقى هناك Ring بسيطة، لقينا بعض
+
+248
+00:30:13,160 --> 00:30:18,080
+العناصر فيها units والبعض الآخر zero divisors. طيب،
+
+249
+00:30:18,080 --> 00:30:25,190
+الآن بدنا نروح نعطي أمثلة توضيحية، بس الأمثلة
+
+250
+00:30:25,190 --> 00:30:30,390
+التوضيحية، قبل ما نعطي أمثلة، بدنا نعرف إيش الـ
+
+251
+00:30:30,390 --> 00:30:33,570
+integral domain.  احنا عرفنا zero divisors، تمام؟ الـ
+
+252
+00:30:33,570 --> 00:30:39,130
+integral domain بسيطة جداً، commutative ring فيهاش
+
+253
+00:30:39,130 --> 00:30:43,330
+zero divisors. بس ماذا يعني Zero Divisor؟ يعني لو
+
+254
+00:30:43,330 --> 00:30:49,230
+وجدت عنصرين حاصل ضربهما بده يساوي صفر، يبقى واحد
+
+255
+00:30:49,230 --> 00:30:53,770
+فيهم على الأقل بده يساوي صفر، أي معناه طبعاً يبقى
+
+256
+00:30:53,770 --> 00:30:59,070
+روح نقطة في تعريف الـ integral domain، يبقى definition
+
+257
+00:30:59,070 --> 00:31:04,070
+an
+
+258
+00:31:04,070 --> 00:31:08,650
+integral domain
+
+259
+00:31:08,650 --> 00:31:10,010
+integral domain
+
+260
+00:31:17,430 --> 00:31:20,950
+an integral domain is a commutative ring with
+
+261
+00:31:20,950 --> 00:31:35,550
+unity.  Is a commutative ring with unity, commutative
+
+262
+00:31:35,550 --> 00:31:43,910
+ring with unity and no zero divisors. and no zero
+
+263
+00:31:43,910 --> 00:31:45,770
+divisors
+
+264
+00:31:49,250 --> 00:31:58,930
+this means that توضيح ليس إلا this means that هذا
+
+265
+00:31:58,930 --> 00:32:15,090
+يعني أن الـ integral domain الـ a
+
+266
+00:32:15,090 --> 00:32:25,820
+في b بده يساوي صفر only يحصل when الـ a تساوي صفر or
+
+267
+00:32:25,820 --> 00:32:34,880
+الـ b تساوي صفر. for
+
+268
+00:32:34,880 --> 00:32:39,040
+example كتوضيح
+
+269
+00:32:39,040 --> 00:32:45,200
+بمثال بسيط، زي ما وضحنا في المثال البسيط، لو المثال
+
+270
+00:32:45,200 --> 00:32:51,120
+البسيط الأول،  قال لنا أن بعض العناصر units وبعضهم له
+
+271
+00:32:51,120 --> 00:33:01,860
+zero divisors. الآن لو جئت لـ Z سبعة، هنا أخذنا Z ستة،
+
+272
+00:33:01,860 --> 00:33:09,300
+تكون هنا Z سبعة، أها، عناصرها صفر، واحد، اثنين، ثلاثة،
+
+273
+00:33:09,300 --> 00:33:20,300
+أربعة، خمسة، ستة. سؤال: هو في أي رقم من هؤلاء أضربه في
+
+274
+00:33:20,300 --> 00:33:27,720
+نفسه يطلع صفر أو أضربه في رقم ثاني يطلع صفر؟ هاي
+
+275
+00:33:27,720 --> 00:33:37,380
+من أمامك كله؟ فيه؟ ولا واحد. طيب، هل الواحد is a
+
+276
+00:33:37,380 --> 00:33:44,480
+unit؟  الـ three، هل هو unit؟ اثنان، هل هو unit؟ لماذا؟ اثنان
+
+277
+00:33:44,480 --> 00:33:51,720
+في أربعة بكم؟ يعني unit، صح؟ واثنين في أربعة، بعد
+
+278
+00:33:51,720 --> 00:33:59,620
+هذا الثلاثة؟ ثلاثة في خمسة، كم الناتج؟ واحد، يبقى كمان
+
+279
+00:33:59,620 --> 00:34:06,040
+هؤلاء units، انتهينا؟  لماذا لم نأخذه؟  لأن ستة في ستة
+
+280
+00:34:06,040 --> 00:34:09,040
+ستة، بدنا سبعة.
+
+281
+00:34:22,050 --> 00:34:27,250
+لو جئنا لخمسة، وما فيه إلا سبعة، ستة في خمسة في
+
+282
+00:34:27,250 --> 00:34:30,350
+ثلاثين، وأربعة في سبعة، اثنان وعشرين. لا، ستة في
+
+283
+00:34:30,350 --> 00:34:34,170
+أربعة، أربعة وعشرين. لا، ستة في ثلاثة، ثمانية عشر،
+
+284
+00:34:34,170 --> 00:34:37,950
+ستة في ستة، ستة وثلاثين، ستة في ستة، ثلاثون،
+
+285
+00:34:37,950 --> 00:34:41,450
+ستة في ستة، ثلاثون، ستة في ستة، ثلاثون، ستة في
+
+286
+00:34:41,450 --> 00:34:44,130
+ثلاثين، ستة في ثلاثين، ستة في ثلاثين، ستة في
+
+287
+00:34:44,130 --> 00:34:44,510
+ثلاثين، ستة في ثلاثين، ستة في ثلاثين، ستة في
+
+288
+00:34:44,510 --> 00:34:50,890
+ثلاثين، ستة
+
+289
+00:34:50,890 --> 00:35:03,270
+في ثلاثين، ستة في تلintegral domain because
+
+290
+00:35:03,270 --> 00:35:07,990
+أن
+
+291
+00:35:07,990 --> 00:35:13,210
+الـ Z7 is commutative
+
+292
+00:35:13,210 --> 00:35:19,490
+ring
+
+293
+00:35:19,490 --> 00:35:21,990
+with unity
+
+294
+00:35:25,980 --> 00:35:31,800
+الذي هو one and no
+
+295
+00:35:31,800 --> 00:35:46,080
+zero divisors. يبقى
+
+296
+00:35:46,080 --> 00:35:50,060
+تحققت الشروط الثلاثة للـ Integral domain وهي
+
+297
+00:35:50,060 --> 00:35:54,380
+commutative ring، والـ unit، الشرط الثاني، وما فيه
+
+298
+00:35:54,380 --> 00:35:58,750
+فيها zero divisor. إذا هذه كلها بتكون ماذا؟ بتكون
+
+299
+00:35:58,750 --> 00:36:03,050
+integral domain. نبدأ نأخذ أمثلة مختلفة عن الـ
+
+300
+00:36:03,050 --> 00:36:12,390
+integral domain.  نبدأ بـ examples. أول مثال يقول the
+
+301
+00:36:12,390 --> 00:36:22,030
+ring of integers that ring of integers that
+
+302
+00:36:24,150 --> 00:36:33,850
+مجموعة الأعداد الصحيحة is an integral domain is an integral domain
+
+303
+00:36:33,850 --> 00:36:44,450
+طيب، لماذا؟  السؤال: فيها unity؟  الذي هو الواحد
+
+304
+00:36:44,450 --> 00:36:45,950
+والواحد والواحد والواحد والواحد والواحد والـ
+
+305
+00:36:45,950 --> 00:36:46,170
+والواحد والواحد والواحد والواحد والواحد والـ
+
+306
+00:36:46,170 --> 00:36:47,650
+والواحد والواحد والواحد والواحد والواحد والـ
+
+307
+00:36:47,650 --> 00:36:47,830
+والواحد والواحد والواحد والواحد والواحد والـ
+
+308
+00:36:47,830 --> 00:36:47,910
+والواحد والواحد والواحد والواحد والواحد والـ
+
+309
+00:36:47,910 --> 00:36:48,430
+والواحد والواحد والواحد والواحد والواحد والـ
+
+310
+00:36:48,430 --> 00:36:55,820
+والواحد والواحد والواحِد، يبقى commutative ring with
+
+311
+00:36:55,820 --> 00:37:04,960
+unity. يبقى هنا integral domain because Z is a
+
+312
+00:37:04,960 --> 00:37:17,840
+commutative ring with unity، والـ unity هو الواحد
+
+313
+00:37:17,840 --> 00:37:18,700
+الصحيح.
+
+314
+00:37:21,360 --> 00:37:28,380
+تعالَ نَسأل السؤال التالي: عمرك شوفت عددين صحيحين
+
+315
+00:37:28,380 --> 00:37:35,080
+غير صفريين ضربتهم في بعض، الناتج يساوي صفر؟ ما فيش.
+
+316
+00:37:35,080 --> 00:37:46,380
+يبقى هنا also الـ الـ الـ Z has
+
+317
+00:37:48,120 --> 00:37:57,960
+no zero divisors because if
+
+318
+00:37:57,960 --> 00:38:09,200
+الـ a والـ b موجودة في Z، then a في b بده يساوي صفر
+
+319
+00:38:09,200 --> 00:38:18,810
+implies أن الـ a تساوي صفر أو الـ b تساوي صفر. هذا
+
+320
+00:38:18,810 --> 00:38:24,310
+الكلام في الأعداد الصحيحة. لا يوجد عددين صحيحين
+
+321
+00:38:24,310 --> 00:38:30,110
+حاصل ضربهما يساوي صفر، ما عنديش بالمرة في الأعداد
+
+322
+00:38:30,110 --> 00:38:34,310
+الصحيحة. لو حدث أن يكونوا يساوي صفر، يبقى هذا لن
+
+323
+00:38:34,310 --> 00:38:40,690
+يحدث إلا إذا كان أحدهما أو كلاهما يساوي صفر. واحنا
+
+324
+00:38:40,690 --> 00:38:45,030
+Zero Divisor قلنا ممنوع، الصفة. إيه non-zero
+
+325
+00:38:45,030 --> 00:38:49,620
+element طبق للـ definition؟ وبدي ألاقي non-zero، قلب
+
+326
+00:38:49,620 --> 00:39:02,460
+يبقى thus Z is an integral domain. لماذا؟ لأنها حققت
+
+327
+00:39:02,460 --> 00:39:08,020
+الشروط الثلاثة. طب، خلينا نسأل سؤال آخر: الـ set of
+
+328
+00:39:08,020 --> 00:39:13,740
+rational numbers، مجموعة الأعداد النسبية تحت عملية
+
+329
+00:39:13,740 --> 00:39:16,040
+الجمع والضرب العادية،
+
+330
+00:39:18,490 --> 00:39:25,510
+فيها zero divisor؟ طيب، الـ set of real numbers، عمرك
+
+331
+00:39:25,510 --> 00:39:31,490
+شفت عددين حقيقيين ضربتهم في بعض، يطلع الناتج صفر
+
+332
+00:39:31,490 --> 00:39:37,130
+وممكن يكون واحد فيهم هو صفر؟ عمراً ما حصل في التاريخ.
+
+333
+00:39:37,130 --> 00:39:42,190
+طيب، الـ set of complex numbers، set of complex
+
+334
+00:39:42,190 --> 00:39:47,960
+numbers، نفس الشيء. يبقى هؤلاء الثلاثة rings are
+
+335
+00:39:47,960 --> 00:39:52,480
+commutative with unity with no zero divisors. يبقى
+
+336
+00:39:52,480 --> 00:39:58,420
+هنا هؤلاء integral domains.  دلوقت يبقى similarly بنفس
+
+337
+00:39:58,420 --> 00:40:05,160
+الطريقة، الـ set of rational numbers Q، والـ set of
+
+338
+00:40:05,160 --> 00:40:11,580
+real numbers R، والـ set of complex numbers التي
+
+339
+00:40:11,580 --> 00:40:19,060
+هي C are integral domains.
+
+340
+00:40:19,060 --> 00:40:35,820
+طيب، هذا المثال الأول، المثال الثاني: the ring of
+
+341
+00:40:35,820 --> 00:40:45,400
+Gaussian integers. The ring of Gaussian integers، التي
+
+342
+00:40:45,400 --> 00:40:53,860
+هي من؟ Z of I، العدد التخيلي، قيمته تساوي سالب
+
+343
+00:40:53,860 --> 00:41:00,520
+واحد، التي على الصيغة a + bi، بحيث الـ a والـ b
+
+344
+00:41:00,520 --> 00:41:07,560
+اعداد صحيحة. هل
+
+345
+00:41:07,560 --> 00:41:16,460
+هذا integral domain؟ دعونا نشوف. يبقى هذا is an
+
+346
+00:41:16,460 --> 00:41:24,260
+integral domain. أظن
+
+347
+00:41:24,260 --> 00:41:30,420
+هذه أثبتناها قبل ذلك، أنها commutative with unity.
+
+348
+00:41:30,420 --> 00:41:34,860
+أنت ما تظل علينا إلا حكاية الـ zero divisor، هذه ما
+
+349
+00:41:34,860 --> 00:41:38,060
+أثبتناها. يبقى هنا because
+
+350
+00:41:42,190 --> 00:41:53,990
+الذي هو Z of I is a commutative ring
+
+351
+00:41:53,990 --> 00:41:57,010
+with
+
+352
+00:41:57,010 --> 00:42:02,490
+unity الذي
+
+353
+00:42:02,490 --> 00:42:08,350
+هو واحد، الذي بده يساوي واحد زائد صفر في I الذي
+
+354
+00:42:08,350 --> 00:42:20,350
+موجودة في Z of I. إيش ضايل علينا؟ لإثبات أنه ما عنديش
+
+355
+00:42:20,350 --> 00:42:26,410
+Zero Divisor. أو لو فرضت أنه عندي عددين حاصل ضربهما
+
+356
+00:42:26,410 --> 00:42:32,010
+بده يساوي صفر، بدي أثبت أنه العددين هؤلاء على الأقل
+
+357
+00:42:32,010 --> 00:42:38,800
+واحد فيهم بده يساوي من؟  بديهية سهلة، مش هي subset
+
+358
+00:42:38,800 --> 00:42:42,720
+من الـ complex numbers، خصائصها نفس خصائص الـ complex
+
+359
+00:42:42,720 --> 00:42:45,240
+والـ complex هي integers، دوماً ما فيها zero
+
+360
+00:42:45,240 --> 00:42:47,980
+divisors. يعني كان نفس الشيء. طب، مش عرفنا أن الـ
+
+361
+00:42:47,980 --> 00:42:53,420
+complex مش فيها zero divisors؟ أنا كل شيء من أغلب
+
+362
+00:42:53,420 --> 00:42:58,540
+أنا في عملية، أنا اشتغلت في عملية، كما اشتغلت هذا
+
+363
+00:42:58,540 --> 00:43:04,390
+لكن احنا بنوضح هذا الكلام رياضياً، يعني احنا من هنا
+
+364
+00:43:04,390 --> 00:43:08,210
+اتكلمنا عن خطوتين: commutative with unity، ضايل
+
+365
+00:43:08,210 --> 00:43:15,590
+علينا الخطوة الثانية، فبدي آخذ عددين أو عنصرين
+
+366
+00:43:15,590 --> 00:43:21,230
+موجودين في هذه الـ set، هذين، وأفترض أن حاصل ضربهما
+
+367
+00:43:21,230 --> 00:43:28,250
+ما يساوي صفر، وأثبت أن هذين الاثنين، الـ zero حصل لأن
+
+368
+00:43:28,250 --> 00:43:33,840
+واحد فيهم صفر أو كلاهما كان بصفر، تمام؟ يبقى
+
+369
+00:43:33,840 --> 00:43:43,440
+بيانات إضافية، كله، افترض أن الـ a + bi والـ c
+
+370
+00:43:43,440 --> 00:43:55,200
++ di موجودة في Z of I، و الاثنان لا يساويان بعض، والـ
+
+371
+00:43:55,200 --> 00:44:09,460
+a + bi لا يساوي c + di، والـ a + bi
+
+372
+00:44:09,460 --> 00:44:18,000
+في c + di بده يساوي صفر، يبقى
+
+373
+00:44:18,000 --> 00:44:25,300
+أنا أخذت عنصرين موجودين في ZI، وهؤلاء لا يساويان بعض، و
+
+374
+00:44:25,300 --> 00:44:31,040
+افترضت أن حاصل ضربهما بده يساوي 100، بده يساوي صفر،
+
+375
+00:44:32,090 --> 00:44:36,310
+بدي أروح أضرب هذا، فجأة، لو ضربته، ماذا يحدث يا فنان؟
+
+376
+00:44:36,310 --> 00:44:45,450
+الـ c هذا، الجزء الحقيقي، الـ bi في الـ di بيصير bd
+
+377
+00:44:45,450 --> 00:44:52,170
+في سالب واحد، لأن الـ i تربيع سالب واحد. فجأة ناقص bd
+
+378
+00:44:52,170 --> 00:44:59,710
+ناقص bd، هذا الـ term الأول، أو الجزء الأول
+
+379
+00:44:59,710 --> 00:45:05,570
+من العدد المركب، أو الجزء الحقيقي من العدد
+
+380
+00:45:05,570 --> 00:45:09,150
+المركب.  إننا نجيء للجزء التخيّلي من العدد
+
+381
+00:45:09,150 --> 00:45:22,490
+المركب، زائد ad + bc في i، زائد ad + bc
+
+382
+00:45:22,490 --> 00:45:29,670
+كله في i، هذا الكلام يساوي صفر. من الأعداد التخيّلية
+
+383
+00:45:29,670 --> 00:45:35,670
+إذا عندي عدد تخيّلي بصفر، يبقى الجزء الحقيقي بـ
+
+384
+00:45:35,670 --> 00:45:42,210
+صفر، وجزء التخيّلي بصفر، يبقى هذا بده يعطينا أن
+
+385
+00:45:42,210 --> 00:45:52,810
+الـ ac ناقص bd بده يساوي صفر، والـ ad زائد bc بده
+
+386
+00:45:52,810 --> 00:46:01,130
+يساوي صفر، تمام؟ طيب، ماذا تقول؟ من المعادلة هذه بقدر
+
+387
+00:46:01,130 --> 00:46:12,430
+أقول أن d تساوي ناقص bc على a من المعادلة
+
+388
+00:46:12,430 --> 00:46:18,190
+الثانية، صح؟ طب، ماذا تقول؟ بدي أمسك هذه وأعوّضها في
+
+389
+00:46:18,190 --> 00:46:23,330
+المعادلة الثانية، وأشوف ماذا بده يعطينا هذا. يبقى
+
+390
+00:46:23,330 --> 00:46:31,430
+بتشير المعادلة الثانية ac ناقص b في d، d التي هي
+
+391
+00:46:31,430 --> 00:46:40,110
+ناقص bc على a، كله بده يساوي صفر. بدي أضرب الطرفين
+
+392
+00:46:40,110 --> 00:46:50,890
+في a، هذا الكلام بده يعطينا a تربيع c ناقص
+
+393
+00:46:51,200 --> 00:46:58,920
+زائد b تربيع c بده يساوي صفر، من الـ
+
+394
+00:46:58,920 --> 00:47:05,120
+Distributive Law. يبقى a تربيع زائد b
+
+395
+00:47:05,120 --> 00:47:12,620
+تربيع، كل هذا في c بده يساوي صفر. هذا ماذا
+
+396
+00:47:12,620 --> 00:47:20,2
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/PwNJfpTE50I_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/PwNJfpTE50I_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9004af5e14bc735843069cd261d35f506456b30b
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/PwNJfpTE50I_raw.srt
@@ -0,0 +1,1764 @@
+1
+00:00:21,280 --> 00:00:25,160
+بسم الله الرحمن الرحيم المرة اللي فاتت بدأنا
+
+2
+00:00:25,160 --> 00:00:29,260
+بموضوع ال integral domain اللي هو chapter 14
+
+3
+00:00:29,260 --> 00:00:34,340
+chapter 13 وعطينا تعريف ال integral domain وقلنا
+
+4
+00:00:34,340 --> 00:00:38,440
+ال integral domain هو عبارة عن communicative ring
+
+5
+00:00:38,440 --> 00:00:44,500
+with unity وهذه ال ring مافيهاش zero divisors
+
+6
+00:00:44,500 --> 00:00:49,340
+تمام؟ يبقى هذا كان تعريف ال integral domain وعطينا
+
+7
+00:00:49,340 --> 00:00:55,480
+على ذلك مثلينوهذا هو المثال الثالث إذا نقول للرمز
+
+8
+00:00:55,480 --> 00:01:01,540
+Z of X of polynomial with integer coefficients is
+
+9
+00:01:01,540 --> 00:01:09,500
+an integral domain because يبقى مجموعة الدوال كل
+
+10
+00:01:09,500 --> 00:01:16,700
+كلده على شكل كثيرة حدود والمعاملات هي أعداد صحيحة
+
+11
+00:01:16,700 --> 00:01:22,770
+هو عبارة عن integral domain ليش؟طبعا ال Z of X
+
+12
+00:01:22,770 --> 00:01:29,190
+هدفناها قبل ذلك أنها ring with unity و ال unity
+
+13
+00:01:29,190 --> 00:01:34,410
+تبعها F of X مسا واحد و كنا commutative لإن كل
+
+14
+00:01:34,410 --> 00:01:39,370
+واحدة عند التعويض تبتعطيني real number يبقى
+
+15
+00:01:39,370 --> 00:01:53,860
+because we know that نبتعرف أن ال Z of Xis a
+
+16
+00:01:53,860 --> 00:01:59,860
+commutative ring
+
+17
+00:01:59,860 --> 00:02:11,400
+with unity اللي هو f of x تساوي 100 تساوي 1 ضايل
+
+18
+00:02:11,400 --> 00:02:17,180
+علينا نثبت ان هذه ال ring مافيهاش zero divisors
+
+19
+00:02:17,180 --> 00:02:24,600
+طبعا يبقى بدنا نفترضإن فيها Zero divisor ونحاول
+
+20
+00:02:24,600 --> 00:02:29,500
+نثبت إن هذا الكلام Zero divisor أو الرقم اللي يجعل
+
+21
+00:02:29,500 --> 00:02:35,680
+نتيجة يسوى صفر إن أحد العناصر يساوي صفر يبقى هنا
+
+22
+00:02:35,680 --> 00:02:47,600
+بعدين بقول assume that إن ال F of X في ال G of X
+
+23
+00:02:47,600 --> 00:02:58,800
+بده يساوي Zeroو ال F و ال G موجودة في Z of X اما
+
+24
+00:02:58,800 --> 00:03:06,640
+ذلك مادام حاصل ضرب Two Pronouns بتسوي Zero يبقى
+
+25
+00:03:06,640 --> 00:03:14,700
+ذلك ال F of X بتسوي Zero او ال G of X بتسوي Zero
+
+26
+00:03:14,700 --> 00:03:24,280
+دائما و أبدا For exampleكتوضيح لذلك بدي أعطيك أبسط
+
+27
+00:03:24,280 --> 00:03:28,540
+الشغلات بدي أعطيك two linear functions يعني two
+
+28
+00:03:28,540 --> 00:03:37,360
+polynomials من الدرجة الأولى يبقى باجي بقول F ال F
+
+29
+00:03:37,360 --> 00:03:47,700
+of X بدي تساوي AX زائد B وال G of X بدي تساوي CX
+
+30
+00:03:47,700 --> 00:03:55,440
+زائد Dو ال A و ال B و ال C و ال D كلها موجودة في Z
+
+31
+00:03:55,440 --> 00:04:06,720
+then ال A X زائد B في ال C X زائد D بده سوى Zero
+
+32
+00:04:06,720 --> 00:04:15,120
+Implies بتروح اضغبها هذه يبقى هذه بتعطيني A C في X
+
+33
+00:04:15,120 --> 00:04:28,390
+ترابيع A C في X ترابيعزائد AD في ال X زائد BC كله
+
+34
+00:04:28,390 --> 00:04:36,130
+في ال X ضال عنا زائد BD كله بده يساوي Zero صار
+
+35
+00:04:36,130 --> 00:04:41,790
+عندى polynomial من الدرجة الثانية تساوي Zero مدام
+
+36
+00:04:41,790 --> 00:04:47,530
+تساوي Zero إذا المعاملات هي اللي خلتها لي تساوي
+
+37
+00:04:47,530 --> 00:04:54,030
+Zeroيبقى بناء عليه ال A C يبقى يساوي 0 المعامل X
+
+38
+00:04:54,030 --> 00:05:01,410
+تربيهه المعامل X اللي هو main A D زائد B C يبقى
+
+39
+00:05:01,410 --> 00:05:09,990
+يساوي 0 الآن B D يبقى يساوي 0 طيب هذول ال A وB وC
+
+40
+00:05:09,990 --> 00:05:16,810
+وD هم انتجات حاصر ضربهم يساوي 0يبدو على الأقل واحد
+
+41
+00:05:16,810 --> 00:05:22,810
+فيهم يساوي Zero هذا معناه ان ال A بده يساوي Zero
+
+42
+00:05:22,810 --> 00:05:31,210
+او ال C بده يساوي Zero وهذا معناه ان ال B تساوي
+
+43
+00:05:31,210 --> 00:05:41,770
+Zero او ال D بدها تساوي Zero طب لو كانت ال A تساوي
+
+44
+00:05:41,770 --> 00:05:47,700
+Zero من هنايبقى ايش بده يكون عندنا بصير المعادلة
+
+45
+00:05:47,700 --> 00:05:56,600
+هذه مايات يبقى F ال A تساوي Zero then تحطها Zero
+
+46
+00:05:56,600 --> 00:06:05,640
+بصير ال B C تساوي Zero هذا معناه ان ال B تساوي
+
+47
+00:06:05,640 --> 00:06:13,840
+Zero او ال C تساوي Zero تمام اذا صارالـ A تساوي
+
+48
+00:06:13,840 --> 00:06:22,400
+زيرو والـ B تساوي زيرو معناته الـ A زائد B الـ A X
+
+49
+00:06:22,400 --> 00:06:30,200
+زائد B بده يساوي زيرو يبقى هنا الـ A تساوي زيرو
+
+50
+00:06:30,200 --> 00:06:37,220
+والـ B تساوي زيرو implies ان الـ A X زائد B تساوي
+
+51
+00:06:37,220 --> 00:06:45,630
+زيرو or الـ Cتساوي Zero وD
+
+52
+00:06:45,630 --> 00:06:54,690
+تساوي Zero implies ان CX زي D تساوي Zero وبناء ان
+
+53
+00:06:54,690 --> 00:07:00,790
+عليه صلة Z of X is an integral domain لإن أخدت
+
+54
+00:07:00,790 --> 00:07:06,410
+حاصل ضرف عنصرين يساوي Zero لقيت M الأول يساوي Zero
+
+55
+00:07:06,410 --> 00:07:18,930
+أو التاني يساوي Zeroيبقى صراحة z of x has
+
+56
+00:07:18,930 --> 00:07:28,510
+no zero divisors مش فيها zero divisors هذا معناته
+
+57
+00:07:28,510 --> 00:07:38,710
+ان z of x is an integral domain
+
+58
+00:07:47,370 --> 00:07:51,330
+ما أخدناه على المعادلة من الدرجة الأولى ممكن
+
+59
+00:07:51,330 --> 00:07:55,890
+تاخدنا الدرجة التانية التالتة الرابعة ممكن واحد من
+
+60
+00:07:55,890 --> 00:07:59,130
+الدرجة الأولى وممكن واحد من الدرجة التانية وممكن
+
+61
+00:07:59,130 --> 00:08:03,150
+معادلة من الأولى وتانية من التالتة زي ما بدك مافي
+
+62
+00:08:03,150 --> 00:08:08,290
+مشكلة في هذه الحالة اروح لمثال اللي بعده اللي هو
+
+63
+00:08:08,290 --> 00:08:17,440
+مثال أربعة example four بيقول لي that's itالذي Z
+
+64
+00:08:17,440 --> 00:08:25,340
+جذر اتنين Z of جذر اتنين اللي العناصر تبعدت على
+
+65
+00:08:25,340 --> 00:08:32,160
+الصيرة A زائد P جذر اتنين بحيث ال A و ال P موجودة
+
+66
+00:08:32,160 --> 00:08:43,820
+في ال set of integers is an integral domain يبقى
+
+67
+00:08:43,820 --> 00:08:45,940
+هذه integral domain
+
+68
+00:08:50,580 --> 00:08:55,620
+طبعا احنا قبل قليل قولنا الـ Integral Domain عبارة
+
+69
+00:08:55,620 --> 00:09:05,120
+عن عبارة عن ايش؟ رنك و community و مافيش فيها Zero
+
+70
+00:09:05,120 --> 00:09:10,740
+Divisor لو حصل انه حصل ضرب أمصر بده يساوي Zero هذا
+
+71
+00:09:10,740 --> 00:09:16,560
+الكلام بده يحصل إذا كان أحدهم يساوي Zero يعني
+
+72
+00:09:16,560 --> 00:09:23,410
+مافيهاش Zero Divisorsعلى الأطلاع طيب الان بيقول
+
+73
+00:09:23,410 --> 00:09:27,930
+يثبت ان ال set هذه عبارة عن integral domain هل
+
+74
+00:09:27,930 --> 00:09:32,530
+أثبتناها سابقا انها هذه communicative ring with
+
+75
+00:09:32,530 --> 00:09:38,770
+unity طبعا لأ اول مرة بنشوفها يبقى الان بدنا نتعمل
+
+76
+00:09:38,770 --> 00:09:43,330
+ال head shake انها عبارة عن communicative ring
+
+77
+00:09:43,330 --> 00:09:50,550
+with unity يبقى هنا المقطة الأولى head shakethat
+
+78
+00:09:50,550 --> 00:10:08,670
+ان Z of gallery 2 is a commutative ring with unity
+
+79
+00:10:08,670 --> 00:10:15,550
+one اللي هو بده ساعة واحد زائد زيرو في gallery 2
+
+80
+00:10:18,330 --> 00:10:21,130
+مكافئة بقى انت بتقولي ان هو sub ring ولا اعطيكوا
+
+81
+00:10:21,130 --> 00:10:26,110
+العافية طبعا فيها ال zero element ان ال zero بكتر
+
+82
+00:10:26,110 --> 00:10:30,350
+اكتر و ال zero زائد zero في جذري اتنين يبقى هنا
+
+83
+00:10:30,350 --> 00:10:35,810
+non empty نطرح عنصرين من بعض مينات في جذري
+
+84
+00:10:35,810 --> 00:10:40,910
+الموجودات في ال ring هنا ناخد عنصرين و نضربهم في
+
+85
+00:10:40,910 --> 00:10:47,150
+بعض والان هنضرب و احنا بنحل وبالتالي بكون شبه جهاز
+
+86
+00:10:47,150 --> 00:10:51,560
+عندكيبقى هذه a commutative ring with unity غير a
+
+87
+00:10:51,560 --> 00:10:55,940
+زي بي جذر اتنين لو ضربتها في c زي d جذر اتنين من
+
+88
+00:10:55,940 --> 00:11:01,200
+الأمين والمشمل بيعطيني نفس النتيجة على كلا الامرين
+
+89
+00:11:01,200 --> 00:11:07,720
+المهم بدي اثبت انه مافيش فيها zero divisor يبقى
+
+90
+00:11:07,720 --> 00:11:11,680
+هنا check that there is a commutative ring with
+
+91
+00:11:11,680 --> 00:11:23,330
+unity يبقى it remains thatيبقى ان ال z of january
+
+92
+00:11:23,330 --> 00:11:37,610
+2 has no zero divisors فوه و لذلك بدى افترض ان
+
+93
+00:11:37,610 --> 00:11:43,490
+عندي عنصرين موجودات فى ال ring هذى وحاصل ضربهما
+
+94
+00:11:43,490 --> 00:11:48,940
+يساوي zero واشوف اين بدى اتوجه الدنيا معاهيبقى for
+
+95
+00:11:48,940 --> 00:11:57,340
+F الـ A زائد P جدري اتنين والـ C زائد جدري اتنين
+
+96
+00:11:57,340 --> 00:12:07,500
+موجودة في الـ Z of جدري اتنين هان اللي هو الـ A
+
+97
+00:12:07,500 --> 00:12:15,100
+زائد B جدري اتنين في الـ C زائد G جدري اتنين بده
+
+98
+00:12:15,100 --> 00:12:22,730
+ساوي Zيبقى افتراض في عندي عنصرين والعنصرين هدول
+
+99
+00:12:22,730 --> 00:12:31,910
+حاصل ضربهما يساوي zero اذا قلت اثبت ان ال a زي ال
+
+100
+00:12:31,910 --> 00:12:38,210
+b جذر اتنين يساوي zero او ال c زي ال d جذر اتنين
+
+101
+00:12:38,210 --> 00:12:44,940
+يساوي zero و تم المطلوب مظبوط يبقى thenبدي أروح
+
+102
+00:12:44,940 --> 00:12:49,540
+أضرب هذول و أشوف إيش بدي يعطيني لإن هذا بنات بدي
+
+103
+00:12:49,540 --> 00:12:58,580
+يعطيني A C D D جذر اثنين في جذر اثنين باثنين زائد
+
+104
+00:12:58,580 --> 00:13:07,140
+اتنين B D هذول كلهم بدي أخدهم مع بعض زادة لإن أضرب
+
+105
+00:13:07,140 --> 00:13:16,410
+هذا بيصير A D في جذر اثنين و هذا B C جذر اثنينيبقى
+
+106
+00:13:16,410 --> 00:13:24,230
+بالدراسية A D زائد B C جذر اتنين يساوزيهم هاي
+
+107
+00:13:24,230 --> 00:13:31,210
+ضاعنا مرة تانية A في C هاي الجذر مع الجذر بطلع
+
+108
+00:13:31,210 --> 00:13:36,930
+اتنين B D هاي اتنين B D هدول مش فيهم جذر اتنين
+
+109
+00:13:36,930 --> 00:13:42,470
+اللي فيهم جذر اتنين بدي اخليهم مع بعض يبقى A D جذر
+
+110
+00:13:42,470 --> 00:13:48,140
+اتنينو بي سي جدر اتنين بدي اخد عمل مشترك جدر اتنين
+
+111
+00:13:48,140 --> 00:13:51,920
+كما بطلع المقدار هذا يساوي زيرو طب هذا هو ال
+
+112
+00:13:51,920 --> 00:13:56,700
+number وقت ايش بطلع زيرو اذا كان الجوس الاول في
+
+113
+00:13:56,700 --> 00:14:02,000
+زيرو والجوس التاني في زيرو بصير كلامنا صحيح يبقى
+
+114
+00:14:02,000 --> 00:14:10,640
+هذا معناه معناه ايش ان ال a c زائد اتنين b d بده
+
+115
+00:14:10,640 --> 00:14:18,090
+يساوي زيرووهذا معناه ان ال A D زائد ال B C يبدو
+
+116
+00:14:18,090 --> 00:14:23,630
+يسوى 0 اغلبت المعادلة الأولى هذه سموها للمعادلة
+
+117
+00:14:23,630 --> 00:14:32,470
+رقم Star طبعا من هذه المعادلة ايش بقدر استنتج؟ بدي
+
+118
+00:14:32,470 --> 00:14:41,150
+اجيب D يبقى من هذه المعادلة D يسوى سالب B C على A
+
+119
+00:14:41,890 --> 00:14:49,090
+وسميه لهذه المعادلة كمان رقم واحد الان بدي أبسك من
+
+120
+00:14:49,090 --> 00:14:53,810
+المعادلة رقم واحد و أعوض في المعادلة الأولى
+
+121
+00:14:53,810 --> 00:14:58,470
+المعادلة الأولى لسه ما اشتغلتش عليها يبقى بدي أعوض
+
+122
+00:14:58,470 --> 00:15:03,910
+أشيل دي و أحط بدل أسالب بي سي على ايه الجيش بصير
+
+123
+00:15:03,910 --> 00:15:12,490
+عندنا هنا بصير a c زيدي اتنين بيفي الديلي ناقص bc
+
+124
+00:15:12,490 --> 00:15:20,030
+على a يساوي 0 بدي أضرب الطرفين في a لو ضربت
+
+125
+00:15:20,030 --> 00:15:29,890
+الطرفين في a بصير a تربيع c ناقص a اتنين b تربيع c
+
+126
+00:15:29,890 --> 00:15:31,490
+يساوي 0
+
+127
+00:15:34,420 --> 00:15:41,940
+بدي يعطينا ان ال a تربيع ناقص اتنين بيه تربيع في c
+
+128
+00:15:41,940 --> 00:15:48,920
+بده يساوي zero هذا ايش بدي يعطينا يا اما ال c بدها
+
+129
+00:15:48,920 --> 00:15:57,280
+تساوي zero يا اما or ال a تربيع ناقص اتنين بيه
+
+130
+00:15:57,280 --> 00:16:03,430
+تربيع يساوي zeroهذا بدي يعطينا ما يأتي يا إما الـ
+
+131
+00:16:03,430 --> 00:16:09,250
+C بدي أتساوي 0 أخرى بدي أنقل هذه على الشجة التالية
+
+132
+00:16:09,250 --> 00:16:16,130
+وأخد الـ January التربيع للطرفين أو الـ A بدي ساوي
+
+133
+00:16:16,130 --> 00:16:24,490
+زائد أو ناقص بيه في January نقل تمام؟
+
+134
+00:16:24,490 --> 00:16:45,220
+يبقى بدادي أخد F الـ C تساوي 0من المعادلة
+
+135
+00:16:45,220 --> 00:16:54,260
+يبقى D تساوي 0 هذا يجب ان اعطيكم ان C زي D جذر
+
+136
+00:16:54,260 --> 00:17:00,920
+اتنين يساوي 0يبقى صار عندنا حصل الضرف هذا يساوي
+
+137
+00:17:00,920 --> 00:17:06,380
+Zero أثبت ان هذا يساوي Zero إذا ال R عبارة عن
+
+138
+00:17:06,380 --> 00:17:10,080
+Integral domain او ال Z أو جدر اتنين عبارة عن
+
+139
+00:17:10,080 --> 00:17:17,640
+Integral domain لو كانت C تساوي Zero طيب افترضي
+
+140
+00:17:17,640 --> 00:17:23,100
+انه كانت ال A تساوي زيد او ناقص B جدر اتنين يبقى
+
+141
+00:17:23,100 --> 00:17:32,840
+هذه حالتينيبقى الحالة الأولى F اللي هو الـ A تساوي
+
+142
+00:17:32,840 --> 00:17:40,720
+B جاذب 2 خلاصة لو كانت C تساوي 0 لأن لو كانت الـ A
+
+143
+00:17:40,720 --> 00:17:51,900
+تساوي B جاذب 2 then from start we have من المعادلة
+
+144
+00:17:51,900 --> 00:17:57,480
+star اللي فوقيبقى بدي أشيل ال a و أحط مكانها بي
+
+145
+00:17:57,480 --> 00:18:05,300
+جذر اتنين يبقى بصير بي جذر اتنين زائد بي جذر اتنين
+
+146
+00:18:05,300 --> 00:18:12,420
+في c زائد d جذر اتنين يساوي zero هذا معناته اتنين
+
+147
+00:18:12,420 --> 00:18:21,380
+جذر اتنين بي في c زائد d جذر اتنين كل هذا الكلام
+
+148
+00:18:21,380 --> 00:18:31,340
+بده يساوي zeroهذا معناه ان اما ال B يسوى 0 او ال C
+
+149
+00:18:31,340 --> 00:18:42,420
+زائد D جدري اتنين يسوى 0 لو كانت ال B تسوى 0 بده
+
+150
+00:18:42,420 --> 00:18:48,660
+اشوف ايش اللي بده يحصل عندك يبقى هنا بروح بقوله if
+
+151
+00:18:48,660 --> 00:19:00,610
+ال B تسوى 0then equation a star is بدي اشيل ال b و
+
+152
+00:19:00,610 --> 00:19:06,390
+اضع مكانها zero ايش مضالب ان اضع مكانها ال a في c
+
+153
+00:19:06,390 --> 00:19:13,770
+زائد d جدر اتنين بدي يساوي zero هذا معناته ان a
+
+154
+00:19:13,770 --> 00:19:22,650
+تساوي zero or c زائد d جدر اتنين يساوي zeroطيب
+
+155
+00:19:22,650 --> 00:19:30,010
+يكون الصار عند V تساوي Zero وA تساوي Zero تمام
+
+156
+00:19:30,010 --> 00:19:38,850
+يبقى هنا صار A تساوي Zero وV تساوي Zero هذا تطلب
+
+157
+00:19:38,850 --> 00:19:47,390
+ان ال A زائد B جانر اتنين يساوي Zero او ال C زائد
+
+158
+00:19:47,390 --> 00:19:53,560
+D جانر اتنين يساوي Zeroهذه بالزيرو وهذه بالزيرو
+
+159
+00:19:53,560 --> 00:19:56,760
+إذا المجموعة بيساوي بالزيرو أو التانية اللي ضالت
+
+160
+00:19:56,760 --> 00:20:05,980
+عندنا بيساوي بالزيرو أمامكم؟ خلصنا هكذا؟ خلصنا ولا
+
+161
+00:20:05,980 --> 00:20:10,900
+لسه؟ لحظتنا
+
+162
+00:20:10,900 --> 00:20:19,140
+إن لو كانت ال A تساوي بجذرتنا او لو كانت بالسالق
+
+163
+00:20:20,420 --> 00:20:25,140
+وتعالى نشوف F
+
+164
+00:20:25,140 --> 00:20:28,540
+ال
+
+165
+00:20:28,540 --> 00:20:39,640
+A تساوي سالب B جدر اتنين then question star S اللي
+
+166
+00:20:39,640 --> 00:20:48,450
+هو ال A زائد B جدر اتنين في C زائد Dجذر اتنين
+
+167
+00:20:48,450 --> 00:20:55,470
+يساوي Zero implies ال A صارت سالب B جذر اتنين يبقى
+
+168
+00:20:55,470 --> 00:21:04,590
+بضل قدش هنا Zero يبقى Zero فمين؟ في C زائد D جذر
+
+169
+00:21:04,590 --> 00:21:12,330
+اتنين يساوي Zero هذا معناه ان ال A زائد B جذر
+
+170
+00:21:12,330 --> 00:21:17,960
+اتنين هو اللي بده يساوي Zero تمام؟معنى كلام ال
+
+171
+00:21:17,960 --> 00:21:23,020
+ring هذه فيها zero divisors على كل الاحتمالات
+
+172
+00:21:23,020 --> 00:21:31,360
+مافيش يبقى بروح و بقول له بص و هكذا ال z of جدر
+
+173
+00:21:31,360 --> 00:21:44,280
+اتنين has no .. has no zero divisors هذا بدي
+
+174
+00:21:44,280 --> 00:21:57,370
+يعطيناإن الـ gallery name is an integral domain
+
+175
+00:21:57,370 --> 00:22:01,450
+يبقى
+
+176
+00:22:01,450 --> 00:22:09,730
+طلعت هذه كلها بإيش اللي هو بال integral domain طيب
+
+177
+00:22:09,730 --> 00:22:16,890
+هذا كان المثال رقم 4 المثال رقمخلاص، في حد ليه
+
+178
+00:22:16,890 --> 00:22:25,850
+تساور هنا بنات؟ ننتقل إلى المثال الذي يليه المثال
+
+179
+00:22:25,850 --> 00:22:36,310
+الذي يليه The ring Z P و ال P is a prime طبعا احنا
+
+180
+00:22:36,310 --> 00:22:43,930
+أثبتنا قبل ذلك ان ZN is a commutative ring صح؟يبقى
+
+181
+00:22:43,930 --> 00:22:49,490
+بتاخد حالة خاصة منها لو كان ال N عدد أولي prime
+
+182
+00:22:49,490 --> 00:22:57,630
+number يبقى ZP وال P is a prime number هذي is an
+
+183
+00:22:57,630 --> 00:23:05,430
+integral domain يجب
+
+184
+00:23:05,430 --> 00:23:11,730
+أن
+
+185
+00:23:11,730 --> 00:23:18,210
+نخبط لهإن ال ZP اللي هي كل الأعداد الصحية integers
+
+186
+00:23:18,210 --> 00:23:24,050
+modulo P is an integral domain طبعا احنا بنعرف
+
+187
+00:23:24,050 --> 00:23:32,090
+سابقا من الأمثلة اللي أخدناها سابقا that ان ال ZP
+
+188
+00:23:32,090 --> 00:23:40,310
+is a commutative ring
+
+189
+00:23:41,890 --> 00:23:54,550
+community bring with unity اللي هو 1 modulo P هذا
+
+190
+00:23:54,550 --> 00:23:58,750
+ال unity تبع ال ring هذا إيش بيضل علينا community
+
+191
+00:23:58,750 --> 00:24:04,590
+bring with unity إيش ضالع نثبت هذه؟ مافيش فيها
+
+192
+00:24:04,590 --> 00:24:11,520
+zero divisor يعني بدنا نحاول نثبتإنه ماعنديش zero
+
+193
+00:24:11,520 --> 00:24:18,920
+divisors على الإطلاق تمام نقول كويس يبقى هنا well
+
+194
+00:24:18,920 --> 00:24:23,760
+to show that
+
+195
+00:24:23,760 --> 00:24:37,720
+بنحاول نثبت ان ال zp has no zero divisors بنثبت
+
+196
+00:24:37,720 --> 00:24:44,480
+بالعكسبدي افترض ان عندي zero divisor بمعنى اخر بدي
+
+197
+00:24:44,480 --> 00:24:51,340
+افترض ان عندي رقمين موجودات في ZP وحاصل ضربهما
+
+198
+00:24:51,340 --> 00:25:02,480
+يساوي Zero فبتروح اقول assume that افترض ان ال M و
+
+199
+00:25:02,480 --> 00:25:11,810
+ال N موجودات في ZP andحاصل ضربهما بده يساوي Zero
+
+200
+00:25:11,810 --> 00:25:16,630
+modulo P ال
+
+201
+00:25:16,630 --> 00:25:23,170
+degree تثبت انه اما ال M بزيرو او ال N بزيرو بكون
+
+202
+00:25:23,170 --> 00:25:29,070
+ايه خلصنا من السؤال التابع عندي طيب نفترض ان في
+
+203
+00:25:29,070 --> 00:25:35,510
+عندي رقمين فينزلتي قبل ما اكمليطر ال M و ال N أكبر
+
+204
+00:25:35,510 --> 00:25:42,450
+من P ولا أصغر من P كل واحد فيهم؟ أقل من P صح ولا
+
+205
+00:25:42,450 --> 00:25:48,730
+لأ؟ يبقى هذ الأرقام أقل من P لأن علاصر ZP ببدأ 0 1
+
+206
+00:25:48,730 --> 00:25:55,630
+2 3 لغاية P minus 1 تمام، إذن هذول دايما وابدا M و
+
+207
+00:25:55,630 --> 00:26:02,500
+N أقل من Pحطي هال معلومة في دماغك لزمالي بعد قليل
+
+208
+00:26:02,500 --> 00:26:09,520
+باجي بقول and ال M بيساوي zero modulo P هذا معناته
+
+209
+00:26:09,520 --> 00:26:18,100
+ايش ان ال M في N بدي يطلع مضاعفات ال P نين P تلاتة
+
+210
+00:26:18,100 --> 00:26:25,700
+P اربعة P عشرين P قبل ما يطلع لذا بروح بقول K في P
+
+211
+00:26:25,700 --> 00:26:34,680
+و ال K هذهعدد صحيح موجب في Z plus يبقى عدد صحيح
+
+212
+00:26:34,680 --> 00:26:41,580
+موجب، كويس طيب، نرجع بالذاكرة إلى جبر حديث واحد ما
+
+213
+00:26:41,580 --> 00:26:46,620
+قبل ال groups في المقدمة أو اللي درسه number three
+
+214
+00:26:46,620 --> 00:26:51,960
+عندي انخي اللي بدو يسوي كيف بيه؟ معنى هذا الكلام
+
+215
+00:26:51,960 --> 00:27:00,560
+انك يتقسم حاصلة ده، صح ولا لا؟يبقى هذا this means
+
+216
+00:27:00,560 --> 00:27:12,980
+that انه P divide M في M طيب، هذا بيعطينا إيش؟ إذا
+
+217
+00:27:12,980 --> 00:27:19,980
+P بتقسم حاصلة ضربي بP بتقسم واحد منهم at least صح؟
+
+218
+00:27:19,980 --> 00:27:28,660
+يبقى هذا يعني يا M P بتقسم ال Mهو الـ P بدأت تبسم
+
+219
+00:27:28,660 --> 00:27:35,900
+للـ N يبقى هذا هذا تمام؟ طيب هو من اللي أكبر؟
+
+220
+00:27:35,900 --> 00:27:41,580
+خصوصا يا ولينا من اللي أكبر ال M ولا ال P؟ ال P
+
+221
+00:27:41,580 --> 00:27:47,800
+يبقى أكبر من أكبر N ولا P؟ ال P يبقى هذا لا يمكن
+
+222
+00:27:47,800 --> 00:27:54,700
+أن يحدث إلا إذا كانت ال M ب Zero أو ال M ب Zeroمش
+
+223
+00:27:54,700 --> 00:27:58,980
+Zero أقل من P؟ تمام، إذا هذا ممكن يقول ليش؟ لإنه
+
+224
+00:27:58,980 --> 00:28:03,720
+بصير Zero عالى P بده يسوى Zero، يبقى بتاعة اسمه
+
+225
+00:28:03,720 --> 00:28:11,180
+ولا لا؟ يبقى هذا، هذا بقول this is a
+
+226
+00:28:11,180 --> 00:28:24,950
+true only when ال M تسوى Zeroor ال N تساوي Zero
+
+227
+00:28:24,950 --> 00:28:36,910
+ايه السبب؟ لأن ال M أقل من P and ال N أقل من P
+
+228
+00:28:36,910 --> 00:28:50,130
+كذلك يبقى هنا ال M تساوي Zero or ال N تساوي Zero
+
+229
+00:28:50,830 --> 00:29:02,930
+معنى هذا الكلام ان ZP has no zero divisors مادام
+
+230
+00:29:02,930 --> 00:29:07,710
+مافيهاش zero divisors مافيهاش مصير integral domain
+
+231
+00:29:07,710 --> 00:29:12,290
+Therefore وليهذا
+
+232
+00:29:12,290 --> 00:29:19,610
+ال ZP is an integral domain
+
+233
+00:29:26,090 --> 00:29:32,490
+integral domain طيب
+
+234
+00:29:32,490 --> 00:29:40,170
+احنا خدنا الآن بدل المثال الخامسة على ال integral
+
+235
+00:29:40,170 --> 00:29:48,710
+domain فبنحاول ناخد بعض الأمثلة على ال rings اللي
+
+236
+00:29:48,710 --> 00:29:57,440
+بتنفعش تكون integral domain يعنيبندور على ال ring
+
+237
+00:29:57,440 --> 00:30:03,120
+ال ring هذه مثلا ماتكونش community تبقى مصير
+
+238
+00:30:03,120 --> 00:30:07,860
+ماهياش integral domain مافيش فيها ال unity يبقى
+
+239
+00:30:07,860 --> 00:30:13,580
+ماهياش integral domain مافيش فيها مافيش فيها ال
+
+240
+00:30:13,580 --> 00:30:18,880
+unity مافيش فيها ال unity مافيش فيها ال unity
+
+241
+00:30:18,880 --> 00:30:18,880
+مافيش فيها ال unity مافيش فيها ال unity مافيش فيها
+
+242
+00:30:18,880 --> 00:30:18,880
+ال unity مافيش فيها ال unity مافيش فيها ال unity
+
+243
+00:30:18,880 --> 00:30:18,880
+مافيش فيها ال unity مافيش فيها ال unity مافيش فيها
+
+244
+00:30:18,880 --> 00:30:19,280
+ال unity مافيش فيها ال unity مافيش فيها ال unity
+
+245
+00:30:19,280 --> 00:30:19,280
+مافيش فيها ال unity مافيش فيها ال unity مافيش فيها
+
+246
+00:30:19,280 --> 00:30:19,280
+ال unity مافيش فيها ال unity مافيش فيها ال unity
+
+247
+00:30:19,280 --> 00:30:19,280
+مافيش فيها ال unity مافيش فيها ال unity مافيش فيها
+
+248
+00:30:19,280 --> 00:30:20,960
+ال unity مافيش فيها ال unity مافيش فيها ال unity
+
+249
+00:30:20,960 --> 00:30:29,270
+مافيش فيها ال unity مافيش فيThe ring هو M2 of Z
+
+250
+00:30:29,270 --> 00:30:37,070
+مين هذي يا بنات؟ مجموعة المصفوفة اللي نظامها اتنين
+
+251
+00:30:37,070 --> 00:30:42,170
+في اتنين والمحدد تبعها يا بده يسوي واحد يا بده
+
+252
+00:30:42,170 --> 00:30:52,450
+يسوي سالب واحد تمام هذه is not an integral
+
+253
+00:30:53,550 --> 00:30:58,270
+دو مين؟
+
+254
+00:30:58,270 --> 00:31:04,970
+because مش commutative هه commutative لأ يبقى step
+
+255
+00:31:04,970 --> 00:31:10,730
+one is two على شكل commutative because M two اه
+
+256
+00:31:10,730 --> 00:31:21,650
+because M two of Z is not commutative
+
+257
+00:31:22,590 --> 00:31:28,750
+يعني سقط أحد شروف الـ Integral domain أن ال ring
+
+258
+00:31:28,750 --> 00:31:33,070
+تكون commutative بدأوا سقطوا ببطلة تصبح الـ
+
+259
+00:31:33,070 --> 00:31:42,570
+Integral domain سابع الأن ال ring هو زده هو ring
+
+260
+00:31:42,570 --> 00:31:49,190
+ولا sub ring؟ sub ring هي ringلأنه قلنا ال sub
+
+261
+00:31:49,190 --> 00:31:55,010
+ring هي subset من ال ring أصلية، بس إيه الشارع؟ ال
+
+262
+00:31:55,010 --> 00:31:58,650
+ring تحت نفس ال two operations، يبقى هي في الحقيقة
+
+263
+00:31:58,650 --> 00:32:04,390
+ring طب هي sub ring من مين؟ من Z itself، يبقى هذه
+
+264
+00:32:04,390 --> 00:32:10,170
+ال sub ring لكنها ليست integral دمية لأنها تحتوي
+
+265
+00:32:10,170 --> 00:32:14,490
+على ال unity اللي هو واحد صحيح، هذا الواحد مش
+
+266
+00:32:14,490 --> 00:32:20,770
+موجود فيهايبقى هذه ال .. the ring is not a
+
+267
+00:32:20,770 --> 00:32:35,690
+integral domain السبب because اتنين زيه has no
+
+268
+00:32:35,690 --> 00:32:44,150
+unity five سمن واحدة zero divisors
+
+269
+00:33:10,510 --> 00:33:17,520
+طبعا هذه الكميوتر تتبنق with unity 1 1طبعا طيب بس
+
+270
+00:33:17,520 --> 00:33:22,880
+بدنا نثبت ان فيها على الأقل و لو zero divisors
+
+271
+00:33:22,880 --> 00:33:28,080
+واحد لكن بعد ما أثبت هقولك فيها مالة نهاية من ال
+
+272
+00:33:28,080 --> 00:33:32,260
+zero divisors طبعا because it is not an integral
+
+273
+00:33:32,260 --> 00:33:40,490
+domain because مثلا تلاتة و Zeroو zero اربع موجودة
+
+274
+00:33:40,490 --> 00:33:48,690
+في ال direct sum موجود صحيح او لا و لا صح؟ and لو
+
+275
+00:33:48,690 --> 00:33:57,010
+ضربناهم في بعض كده ايش بتظهر؟ zero و zero كل عنصر
+
+276
+00:33:57,010 --> 00:34:02,330
+معنى غير ضرب فيه direct sum يبقى طالع zero و zero
+
+277
+00:34:02,330 --> 00:34:08,590
+كويس؟حصل ضرف two elements لا يساوي كل واحد يوم الـ
+
+278
+00:34:08,590 --> 00:34:14,170
+zero وطلع بـ zero يبقى هذا معناه zero divisors هنا
+
+279
+00:34:14,170 --> 00:34:24,630
+بدي أعطيك انه تلاتة و zero and zero أربعة are zero
+
+280
+00:34:24,630 --> 00:34:29,710
+divisors يبقى هنا
+
+281
+00:34:32,550 --> 00:34:45,590
+plus the direct sum is not an integral domain لو
+
+282
+00:34:45,590 --> 00:34:52,430
+واحدة ثانية أخدت رقمين تانية أخدت واحد وزير وزير
+
+283
+00:34:52,430 --> 00:35:03,910
+واتنين in general بدي أخد M وزير وزير وNطبعا و ال
+
+284
+00:35:03,910 --> 00:35:07,450
+M مينما كان يكون و ال N مينما كان يكون يبقى يجداش
+
+285
+00:35:07,450 --> 00:35:13,190
+تصير عدد ال zero divisor تصير infinite zero
+
+286
+00:35:13,190 --> 00:35:16,810
+divisor يبقى عندي عدد لانهائي من ال zero divisor
+
+287
+00:35:16,810 --> 00:35:24,210
+إذا لا يمكن لهذا أن يكون integral domain طبعا طيب
+
+288
+00:35:24,210 --> 00:35:28,570
+بدنا نيجي لأول نظرية لهذا الشبكة
+
+289
+00:35:46,290 --> 00:35:49,190
+النظرية بتقول ما يأتي
+
+290
+00:36:04,180 --> 00:36:10,980
+Integral domain let
+
+291
+00:36:10,980 --> 00:36:21,160
+ال A والB والC موجودات من Integral domain A if ال
+
+292
+00:36:21,160 --> 00:36:29,900
+A لا يساوي Zero and ال A في ال B بدي ساوي ال A في
+
+293
+00:36:29,900 --> 00:36:49,330
+ال C thenالـ B تساوي مين؟ تساوي الـ C مرة
+
+294
+00:36:49,330 --> 00:36:55,910
+تانية بقول أخدنا الـ R Integral Domain تمام؟ و
+
+295
+00:36:55,910 --> 00:36:59,530
+أخدنا تلت عناصر موجودة في الـ Integral Domain الـ
+
+296
+00:36:59,530 --> 00:37:04,300
+A والـ B والـ Cلو كان الـ A لا يساوي Zero وعندي
+
+297
+00:37:04,300 --> 00:37:09,880
+معادلة A في B يبقى يساوي الـ A في C يبقى بدنا نثبت
+
+298
+00:37:09,880 --> 00:37:14,100
+ان الـ B بدها تساوي من الـ C عظمنا خدنا هذه
+
+299
+00:37:14,100 --> 00:37:18,500
+النظرية في ال ring خدناها
+
+300
+00:37:18,500 --> 00:37:24,980
+بس قلنا بي لا تساوي C يبقى في حالة ال ring النظرية
+
+301
+00:37:24,980 --> 00:37:29,230
+كانت غير متحققةلكن في حالة الـ Integral domain
+
+302
+00:37:29,230 --> 00:37:35,530
+النظرية محققة تمام؟ طيب إذا بدنا نروح نثبت صحيحة
+
+303
+00:37:35,530 --> 00:37:40,330
+هذا الكلام يبقى احنا عندنا R Integral domain
+
+304
+00:37:40,330 --> 00:37:50,330
+واخدنا تلت عناصر موجودة فيه بداية أقول F الـ R ال
+
+305
+00:37:50,330 --> 00:37:54,110
+Integral
+
+306
+00:37:54,110 --> 00:37:54,910
+domain
+
+307
+00:37:58,930 --> 00:38:12,270
+الـ A لا تساوي Zero و الـ A في B بيساوي الـ A في C
+
+308
+00:38:12,270 --> 00:38:23,350
+و الـ A و الـ B و الـ C موجودات في R الـ A
+
+309
+00:38:23,350 --> 00:38:29,760
+بتساويش Zero هذا معقولهذه ممكن اعملها معادلة صفرية
+
+310
+00:38:29,760 --> 00:38:39,300
+يبقى and ال a b ناقص ال a c بده يسوي zero هذا بده
+
+311
+00:38:39,300 --> 00:38:45,820
+يعطينا ان ال a بتسويش ال zero وممكن ناخد ال a صيرة
+
+312
+00:38:45,820 --> 00:38:53,800
+ال b ناقص ال c اللي تسوي zero إذا حصل ضرب two
+
+313
+00:38:53,800 --> 00:39:00,330
+elements بده يسوي zeroواحد فيهم لا يساوي Zero إذا
+
+314
+00:39:00,330 --> 00:39:09,390
+نيتاني هو اللي بده يساوي Zero ليش؟ ايوة then ال A
+
+315
+00:39:09,390 --> 00:39:15,930
+لا تساوي Zero implies ان ال B ناقص ال C هي اللي
+
+316
+00:39:15,930 --> 00:39:24,690
+بدها تساوي Zero ليش؟ لأن ال R is an integral
+
+317
+00:39:27,580 --> 00:39:33,500
+domain لإن هذا لايمكن ان يكون zero divisor ليش
+
+318
+00:39:33,500 --> 00:39:38,760
+إمكانية لإن هذا integral domain مافيش فيه zero
+
+319
+00:39:38,760 --> 00:39:43,300
+divisor مدى مافيش فيه zero divisor و ال a لا يساوي
+
+320
+00:39:43,300 --> 00:39:48,140
+zero إذا نجباري عصب اللي مرضى بدي يكون ال b ناقص
+
+321
+00:39:48,140 --> 00:39:54,320
+ال c هو اللي بدي يساوي zero هذا بدي يعطيكإن B
+
+322
+00:39:54,320 --> 00:40:03,760
+تساوي C وهو أول حيث وعدناكوا بيه ال ring و ال
+
+323
+00:40:03,760 --> 00:40:09,040
+integral domain و ال field بظبط تعرضنا لل rings
+
+324
+00:40:09,040 --> 00:40:12,560
+تعرضنا لل integral domain و الأن بدنا نعطي تعريف
+
+325
+00:40:12,560 --> 00:40:17,520
+لل field و بعض الأمثلة البصيفة عليه جبنا
+
+326
+00:40:17,520 --> 00:40:18,400
+definition
+
+327
+00:40:21,860 --> 00:40:31,780
+بيقول a commutative ring a commutative ring with
+
+328
+00:40:31,780 --> 00:40:39,180
+unity with unity is
+
+329
+00:40:39,180 --> 00:40:43,320
+called a
+
+330
+00:40:43,320 --> 00:40:51,200
+field is called a field of every
+
+331
+00:40:52,270 --> 00:41:06,570
+non-zero element non-zero element is
+
+332
+00:41:06,570 --> 00:41:07,510
+a unit
+
+333
+00:41:35,420 --> 00:41:40,960
+فعلا نقف لحظة بسيطة أمام ال integral domain و ال
+
+334
+00:41:40,960 --> 00:41:47,400
+field مشان نقدر نميز بينهم المرة اللي فات قلنا ال
+
+335
+00:41:47,400 --> 00:41:51,500
+.. ال .. ال integral domain هو commutative ring
+
+336
+00:41:51,500 --> 00:41:56,960
+with unity تمام؟ ال field هو commutative ring with
+
+337
+00:41:56,960 --> 00:42:02,880
+unity يبقى أول خاصيتين زي بعض تماما الخلاف وين؟
+
+338
+00:42:02,880 --> 00:42:06,990
+الخاصية التالفةفي حالة الـ Integral domain قلنا
+
+339
+00:42:06,990 --> 00:42:12,370
+الـ R مافيش فيها Zero divisor لو بقدر الله طلع
+
+340
+00:42:12,370 --> 00:42:17,010
+حاصر ضرب عنصرين بده يساوي Zero لازم على الأقل
+
+341
+00:42:17,010 --> 00:42:20,570
+أحدهما يدساوي Zero في ال Integral domain هذا بيقول
+
+342
+00:42:20,570 --> 00:42:26,450
+لي لأ الشرط التالت حطه Zero divisor على شك كل عنصر
+
+343
+00:42:26,450 --> 00:42:31,370
+غير صغري بده يكون Unit يعني إيش Unit؟ يعني هو ملك
+
+344
+00:42:31,370 --> 00:42:38,460
+بليه كاتب Inverseيعني بدى يكون معكوس تحت عملية
+
+345
+00:42:38,460 --> 00:42:45,120
+الضرب والله لو رجعنا بالذاكرة الى جمر حديث واحد
+
+346
+00:42:45,120 --> 00:42:50,840
+بجينا نقول في عندنا abelian group و ال group اللى
+
+347
+00:42:50,840 --> 00:42:56,440
+قبلهم تبقى commutative وفيها ال identity element
+
+348
+00:42:56,440 --> 00:43:02,540
+وكل أنصر له معكوس صح ولا لا؟يبقى كل field هو
+
+349
+00:43:02,540 --> 00:43:07,200
+ability group ولا كل ability group هي field؟ كل
+
+350
+00:43:07,200 --> 00:43:13,280
+ability group هي field، تمام؟ مظبوط هيك يا بنادر؟
+
+351
+00:43:13,280 --> 00:43:17,540
+لأ لإيش؟ لأن ال group عنها بين ال one مية المية،
+
+352
+00:43:17,540 --> 00:43:23,160
+يبقى لا يمكن لل ability group انها تكون field،
+
+353
+00:43:23,160 --> 00:43:27,770
+ليش؟لأن ال field عليها two binary operations بس ال
+
+354
+00:43:27,770 --> 00:43:31,870
+group عليها one binary operation يبقى ال group
+
+355
+00:43:31,870 --> 00:43:36,270
+يقول اه ممكن تعمل الله اخبط عينكم يبقى ال field لا
+
+356
+00:43:36,270 --> 00:43:42,150
+يمكن ان يكون abelian group هذا الكلب مستقل لأن ال
+
+357
+00:43:42,150 --> 00:43:46,070
+abelian group عليها عملية واحدة لكن ال field عليها
+
+358
+00:43:46,070 --> 00:43:50,330
+two binary operations يبقى هذا الفرق في ما بينهم
+
+359
+00:43:52,480 --> 00:43:58,520
+ممكن يكون ال integral domain هو field وممكن ال
+
+360
+00:43:58,520 --> 00:44:04,260
+field يكون integral domain هذا الكلام ما سنجيب
+
+361
+00:44:04,260 --> 00:44:08,400
+عليه في المحاضرة القادمة ان شاء الله هنا فيكوا
+
+362
+00:44:08,400 --> 00:44:13,500
+نظرية every finite integral domain is a field طبعا
+
+363
+00:44:13,500 --> 00:44:19,450
+نظرية في المحاضرة القادمة ان شاء اللهبالضيقة تفهمي
+
+364
+00:44:19,450 --> 00:44:24,530
+إنه إذا كان لي كلمة فيل يبقى كل عنصر إله معكوس على
+
+365
+00:44:24,530 --> 00:44:31,690
+الصفر تمام؟ أه في ال integral دماغ ماعنديش zero
+
+366
+00:44:31,690 --> 00:44:37,230
+divisors لكن عندي units وغير ال units لإنه في حاجة
+
+367
+00:44:37,230 --> 00:44:42,630
+اسمه nil potent element وفي idem potent element
+
+368
+00:44:42,630 --> 00:44:46,950
+فأرناكوا هذا اللي ماكناش نعرفهم في ال group تمام؟
+
+369
+00:44:47,120 --> 00:44:51,280
+يبقى في عناصر لها مسميات أخرى كل اللي بدي أكيد
+
+370
+00:44:51,280 --> 00:44:58,340
+يعرفه انه في الفيل كل عنصر غير صفر يكون له معكس
+
+371
+00:44:58,340 --> 00:45:02,100
+بالنسبة لعملية main بالنسبة لعملية author خلاص
+
+372
+00:45:02,100 --> 00:45:13,000
+نعطي بعض الأمثلة البسيطة example example
+
+373
+00:45:13,000 --> 00:45:20,010
+له set of rational numbersو ال set of real numbers
+
+374
+00:45:20,010 --> 00:45:26,110
+و ال set of complex numbers تمام؟ ال set of
+
+375
+00:45:26,110 --> 00:45:31,850
+complex numbers التلاتة commutative و التلاتة فيهم
+
+376
+00:45:31,850 --> 00:45:37,510
+unity تمام؟ اللي هو الواحد الصحي اللي التلاتة بأيه
+
+377
+00:45:37,510 --> 00:45:43,860
+هو الشرطين اتحققوا؟ كل عصر له ماكوش؟واحد على كل
+
+378
+00:45:43,860 --> 00:45:46,080
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+379
+00:45:46,080 --> 00:45:46,080
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+380
+00:45:46,080 --> 00:45:46,840
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+381
+00:45:46,840 --> 00:45:47,760
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+382
+00:45:47,760 --> 00:45:53,220
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+383
+00:45:53,220 --> 00:45:54,760
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+384
+00:45:54,760 --> 00:45:54,800
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+385
+00:45:54,800 --> 00:45:55,080
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+386
+00:45:55,080 --> 00:45:55,120
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+387
+00:45:55,120 --> 00:45:55,120
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+388
+00:45:55,120 --> 00:45:55,120
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+389
+00:45:55,120 --> 00:45:55,120
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+390
+00:45:55,120 --> 00:45:56,760
+واحد على كل واحد على كل واحد على كل واحد على كل
+
+391
+00:45:56,760 --> 00:46:03,260
+واحد على كل واحد على كل واحد
+
+392
+00:46:03,260 --> 00:46:06,880
+على
+
+393
+00:46:06,880 --> 00:46:06,880
+كل
+
+394
+00:46:35,250 --> 00:46:43,810
+لو أخذنا صوت برنجةمن أحدهم مثلا هل ضروري ال sub
+
+395
+00:46:43,810 --> 00:46:51,230
+ring تبقى فيه؟ لأ زي ايش مثلا ال Z ال Z هدي
+
+396
+00:46:51,230 --> 00:46:56,270
+commutative ring with unity صحيح ولا لأ لكن هل ال
+
+397
+00:46:56,270 --> 00:47:02,330
+Z integral لما؟ لأ ولا حتى field لأن كل عصر مالوش
+
+398
+00:47:02,330 --> 00:47:06,530
+معكس المعكس المقلوب تبعه صار رجل ال number مش
+
+399
+00:47:06,530 --> 00:47:15,600
+موجود في Zيبقى باقى بقول هدول عارفين فقط ولكن الـ
+
+400
+00:47:15,600 --> 00:47:28,840
+Z is a sub ring sub ring of R الـ Z is a sub ring
+
+401
+00:47:28,840 --> 00:47:39,710
+of R فعلا الـ Z is not a fieldبس هي انتقال دماغي
+
+402
+00:47:39,710 --> 00:47:49,430
+بس هي انتقال
+
+403
+00:47:49,430 --> 00:47:51,370
+دماغي بس هي انتقال دماغي بس هي انتقال دماغي بس هي
+
+404
+00:47:51,370 --> 00:47:51,490
+انتقال دماغي بس هي انتقال دماغي بس هي انتقال دماغي
+
+405
+00:47:51,490 --> 00:47:51,490
+بس هي انتقال دماغي بس هي انتقال دماغي بس هي انتقال
+
+406
+00:47:51,490 --> 00:47:51,490
+دماغي بس هي انتقال دماغي بس هي انتقال دماغي بس هي
+
+407
+00:47:51,490 --> 00:47:52,430
+انتقال دماغي بس هي انتقال دماغي بس هي انتقال دماغي
+
+408
+00:47:52,430 --> 00:48:01,890
+بس هي انتقال دماغي بس هي انتقال دماغي بس هي انتقال
+
+409
+00:48:12,260 --> 00:48:18,520
+Inverse مالهاش معكوس على الإطلاق، تقيسي عليها أي
+
+410
+00:48:18,520 --> 00:48:23,580
+عدل.طيب،
+
+411
+00:48:23,580 --> 00:48:29,900
+لو أعطيكي كمان سبب، كم يلجي في الزمن؟ نهر، يبقى
+
+412
+00:48:29,900 --> 00:48:34,180
+واحد، والثاني مافيش غيره، يبقى مش كل أنصار له
+
+413
+00:48:34,180 --> 00:48:46,350
+معكوس، تمام؟also زيادة على ذلك also الذئب has two
+
+414
+00:48:46,350 --> 00:48:58,290
+units only that is الواحد
+
+415
+00:48:58,290 --> 00:49:09,150
+and ثالث واحد مش كل عنصر له معكوز مثال اثنينزد سكس
+
+416
+00:49:09,150 --> 00:49:19,670
+زد سكس is not a field because
+
+417
+00:49:19,670 --> 00:49:25,210
+اتنين
+
+418
+00:49:25,210 --> 00:49:31,730
+unit يا بنات يعني بقدر الاقي رقم في زد ستة اضربه
+
+419
+00:49:31,730 --> 00:49:36,970
+في اتنين يعطيني الواحد الصحيحأو الواحد موديله ستة
+
+420
+00:49:36,970 --> 00:49:41,310
+طبعا لأ لأن اتنية في التلاتة في ستة Zero Divisor و
+
+421
+00:49:41,310 --> 00:49:47,190
+Zero Divisor منفعش يكون له معاكس خاصة في ZN لأن في
+
+422
+00:49:47,190 --> 00:49:53,030
+ZN اي element يا اما unit يا اما Zero Divisor يبقى
+
+423
+00:49:53,030 --> 00:50:08,290
+هنا اتنية موجودة في Z6 and اتنية is azero divisor
+
+424
+00:50:08,290 --> 00:50:20,550
+since اتنين في تلاتة بيسوي zero modulo P يعني هذا
+
+425
+00:50:20,550 --> 00:50:34,160
+ما هو عشان فيه also Z modulo I is not a fieldz
+
+426
+00:50:34,160 --> 00:50:43,900
+modulo of I هو ليس مجلد A ما هو مش مجلد لأن
+
+427
+00:50:43,900 --> 00:50:47,340
+التلاتة
+
+428
+00:50:47,340 --> 00:50:54,700
+موجودة في z of I ان التلاتة فاقدر اكتبها تلاتة زرق
+
+429
+00:50:54,700 --> 00:51:08,690
+زرق في I and التلاتة isnot a unit ملاحظة
+
+430
+00:51:08,690 --> 00:51:20,270
+أخيرة not if ال R is a field لو كان ال R is a
+
+431
+00:51:20,270 --> 00:51:32,310
+field and ال S is a sub ring of Rthen it is not
+
+432
+00:51:32,310 --> 00:51:42,070
+then it is not necessarily it
+
+433
+00:51:42,070 --> 00:51:55,430
+is not necessarily ال S is a theme for example for
+
+434
+00:51:55,430 --> 00:52:05,760
+example كان يخال على ذلكsc set of complex number
+
+435
+00:52:05,760 --> 00:52:26,700
+is a field but ولكن is a field but z of I is a sub
+
+436
+00:52:26,700 --> 00:52:37,610
+ring ofالـ Z of
+
+437
+00:52:37,610 --> 00:52:48,270
+I برنامج قبل قليل is ما .. يعني
+
+438
+00:52:48,270 --> 00:52:51,610
+مالجيش عنصر يلو ما كوز
+
+439
+00:52:58,120 --> 00:53:02,640
+على هيك انتهينا من المحاضرة و بنكمل ان شاء الله
+
+440
+00:53:02,640 --> 00:53:08,400
+المرة الماضية، المرة القادمة ان شاء الله بنكمل نفس
+
+441
+00:53:08,400 --> 00:53:09,020
+الموضوع
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QsYKUGD-G-4_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QsYKUGD-G-4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..49e902a9f864cdffd0288229c1ef9d55971f923f
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/QsYKUGD-G-4_postprocess.srt
@@ -0,0 +1,1424 @@
+1
+00:00:20,990 --> 00:00:26,070
+بسم الله الرحمن الرحيم نكمل اليوم ما ابتدأنا به في
+
+2
+00:00:26,070 --> 00:00:32,950
+المرة الماضية وهو chapter 16 اللي هو ال polynomial
+
+3
+00:00:32,950 --> 00:00:37,470
+rings المرة اللي فاتت عرفنا ال polynomial ring
+
+4
+00:00:37,470 --> 00:00:43,190
+واخدنا جميع two polynomials وكذلك أصل ضرب two
+
+5
+00:00:43,190 --> 00:00:48,010
+polynomials وعطيناكم مثال على ذلك اليوم ان شاء
+
+6
+00:00:48,010 --> 00:00:53,140
+الله بنكمل هذا الموضوعالتعريف الأول هو تذكير بما
+
+7
+00:00:53,140 --> 00:00:59,020
+أخدته في كل في تفاضل وتكافي جفر حديث واحد في
+
+8
+00:00:59,020 --> 00:01:04,740
+المقدمة اللي هي خوارزمية القسمة division algorithm
+
+9
+00:01:04,740 --> 00:01:09,660
+على الأعداد بذكر بهذا التذكير لأنه هنتقل من
+
+10
+00:01:09,660 --> 00:01:16,020
+الأعداد إلى ال polynomial فالتعريف كان بيقول افترض
+
+11
+00:01:16,020 --> 00:01:24,240
+يساوي مضعفات ال BP مضغوط في Q زائد ال R ال R هذا
+
+12
+00:01:24,240 --> 00:01:31,260
+قد يكون صفر و قد يكون أقل من P قال لي where ال R
+
+13
+00:01:31,260 --> 00:01:38,480
+أكبر من أو تساوي zero و less than P السبب ان ال R
+
+14
+00:01:38,480 --> 00:01:45,240
+هذا ممكن يكون صفر و ممكن يكون رقم أقل من P السؤال
+
+15
+00:01:45,240 --> 00:01:52,740
+هوممكن يكون اكبر من B؟ لأ لو كان اكبر من D دخل مع
+
+16
+00:01:52,740 --> 00:02:00,980
+الجزء الاول من هذه المعدة يبقى R اقل من B وقد يكون
+
+17
+00:02:00,980 --> 00:02:09,040
+صفر لو كان صفر معناته ال B بيقسم ال A بدون باقي
+
+18
+00:02:09,040 --> 00:02:15,110
+مضلش باقيلكن لو ضال رقم يبقى بيه اسمه و بيضل ايش و
+
+19
+00:02:15,110 --> 00:02:21,790
+بيضل باقي طيب ال this operation هذه العملية هي
+
+20
+00:02:21,790 --> 00:02:27,710
+اللي بده اسميها division algorithm خوارزمية القسمة
+
+21
+00:02:27,710 --> 00:02:36,020
+على الأعداد هذه طبعا في مقدمة جبر حديث واحدهذه
+
+22
+00:02:36,020 --> 00:02:40,920
+خوازمية وقسمة على الـ fields على ال functions اللي
+
+23
+00:02:40,920 --> 00:02:46,160
+موجودة في ال field فجينا قولنا division algorithm
+
+24
+00:02:46,160 --> 00:02:52,820
+for capital F of X يبقى قولنا خد ال F عبارة عن
+
+25
+00:02:52,820 --> 00:02:59,140
+field وخد ال two elements موجودات في capital F of
+
+26
+00:02:59,140 --> 00:03:08,660
+X يعني F of X وG of XPronomials كثيرات حدود موجودة
+
+27
+00:03:08,660 --> 00:03:14,740
+في ال field اللي هو capital F of X بشرط ان ال G of
+
+28
+00:03:14,740 --> 00:03:20,600
+X ممنوع تساوي Zero زي ما كانت B في التعريف الأول
+
+29
+00:03:20,600 --> 00:03:25,640
+ممنوع تساوي Zero Then there exist a unique
+
+30
+00:03:25,640 --> 00:03:33,680
+pronomials يبقى بنلاقي كثيرات حدود واحداتمافيش
+
+31
+00:03:33,680 --> 00:03:38,160
+غيرهم لل two functions أو ال two polynomials هدول
+
+32
+00:03:38,160 --> 00:03:44,380
+لل Q of X و R of X في نفس ال field اللي هو ال F
+
+33
+00:03:44,380 --> 00:03:51,400
+هذه بس هذه على أعداد صحيحة integers هذه عالمين على
+
+34
+00:03:51,400 --> 00:03:57,680
+polynomials كثيرات حدود يبقى ال polynomial F of X
+
+35
+00:03:58,040 --> 00:04:03,360
+قدرت اكتبها على شكل polynomial في polynomial تانية
+
+36
+00:04:03,360 --> 00:04:08,980
+والباقي قد يكون polynomial وقد يكون constant
+
+37
+00:04:08,980 --> 00:04:16,500
+polynomial جالي قالت ايضا اما R of X تساوي Zero لو
+
+38
+00:04:16,500 --> 00:04:22,120
+كانت R of X تساوي Zero يبقى راحة يبقى صاحي ال F of
+
+39
+00:04:22,120 --> 00:04:31,290
+X يحاصل ضرب لمينلتو Polynomials طبعا؟ طيب يا إما
+
+40
+00:04:31,290 --> 00:04:38,390
+درجة ال R of X أقل من درجة ال G of X يبقى درجة ال
+
+41
+00:04:38,390 --> 00:04:45,950
+R of X أقل من درجة ال G of X بنفع تساويها؟ لو سوى
+
+42
+00:04:45,950 --> 00:04:51,390
+التكانصال R of X ب Zero دخلت في مين؟ في خارج القسم
+
+43
+00:04:51,390 --> 00:04:59,130
+هذهأقل من درجة ال U of X يبقى بظل هذا باقي يبقى
+
+44
+00:04:59,130 --> 00:05:05,030
+هذه المعادلة هذا بسميه خارج القسمة وال R of X
+
+45
+00:05:05,030 --> 00:05:11,150
+بسميه مين بسميه الباقي يبقى ال polynomial ال U of
+
+46
+00:05:11,150 --> 00:05:17,750
+X بسميها quotient يعني خارج القسمة يعني خارج قسمة
+
+47
+00:05:17,750 --> 00:05:25,210
+F على G and ال R of Xبسميه الـ remainder الباقي
+
+48
+00:05:25,210 --> 00:05:32,970
+نتيجة لقسم F of X على مين؟ على G of X إذا لما أقسم
+
+49
+00:05:32,970 --> 00:05:40,870
+F of X على G of X ممكن يظهر نتيجة G of X مضروبة في
+
+50
+00:05:40,870 --> 00:05:47,030
+Q of X فقط وفي هذه الحالة يكون R of X بقدرش؟ بزير
+
+51
+00:05:47,610 --> 00:05:52,270
+طيب لو ما طلعش بزير و طلع زائد شغلة يبقى الشغلة دي
+
+52
+00:05:52,270 --> 00:05:59,170
+بسميها الباقي و درجة الباقي أقل من درجة GeoVec
+
+53
+00:05:59,170 --> 00:06:03,810
+يعني لو كان GeoVec من الدرجة الثانية الباقية بدي
+
+54
+00:06:03,810 --> 00:06:08,470
+يكون يا إما من الدرجة الأولى يا إما من الدرجة
+
+55
+00:06:08,470 --> 00:06:14,630
+الصفرية يعني constant تمام؟لكن إن كان بجسمه على
+
+56
+00:06:14,630 --> 00:06:19,310
+بعض بيكون الاروف اكس زيرو على طول الخط واضح
+
+57
+00:06:19,310 --> 00:06:23,430
+كلامنا؟ طبعا البرهان طويل لإنه بدنا نثبت ال
+
+58
+00:06:23,430 --> 00:06:28,310
+existence وبدنا نثبت من ال uniqueness ويا ما
+
+59
+00:06:28,310 --> 00:06:33,470
+اثبتنا هذا في جبر حديث واحد يبقى انسلط بعد مانعش
+
+60
+00:06:33,470 --> 00:06:38,030
+نضيع فيه وقت لكن كل اللي بدي أكي تعرفيه أن أي two
+
+61
+00:06:38,030 --> 00:06:42,250
+functions في نفس الفيلبقدر اكتب واحدة بدلالة
+
+62
+00:06:42,250 --> 00:06:46,710
+التانية على مين على الصيلة اللى قدامنا هذه يبقى
+
+63
+00:06:46,710 --> 00:06:52,030
+هذه الصيلة هتمر معانا كتير واحنا بنشتغل في ال
+
+64
+00:06:52,030 --> 00:07:00,850
+polynomial rings طيب لان نعطي مثال توضيحى كيف بدي
+
+65
+00:07:00,850 --> 00:07:06,420
+اجيب ال quotient وكيف بدي اجيب ال remainderقال
+
+66
+00:07:06,420 --> 00:07:12,420
+افترض F of X موجودة بالشكل هذا وهي موجودة في Z
+
+67
+00:07:12,420 --> 00:07:21,540
+خمسة of X تمام؟ and G of X موجودة كمان في Z خمسة
+
+68
+00:07:21,540 --> 00:07:25,560
+of X قال هاتلي ال quotient وهاتلي ال remain dark
+
+69
+00:07:25,560 --> 00:07:31,440
+لما نقسم ال F of X على مين؟ على ال G of X قبل
+
+70
+00:07:31,440 --> 00:07:38,850
+المبدأ بدي اسألي السؤال التاليبنفع ناخد polynomial
+
+71
+00:07:38,850 --> 00:07:46,530
+في Z6 و polynomial ثانية في Z6؟
+
+72
+00:07:46,530 --> 00:08:01,670
+بنفع بدون مشاكل؟ بنفع؟ طب أنا بدأ أسأل Z6 في Z6
+
+73
+00:08:01,670 --> 00:08:08,120
+في كيف؟فيها Zero وفيها Zero Divisor Z6 فيه؟ لأ
+
+74
+00:08:08,120 --> 00:08:12,820
+طبعا كيف؟ النظرية فيه من اللي اختلف بـ AFL يعني
+
+75
+00:08:12,820 --> 00:08:19,520
+مانفعش اخد في Z6 كلامنا غلط لإن Z6 is not AFL فيه
+
+76
+00:08:19,520 --> 00:08:24,160
+Non Zero Zero Divisor اتنين في تلاتة بستة يبقى
+
+77
+00:08:24,160 --> 00:08:27,800
+اتنين Zero Divisor والتلاتة Zero Divisor ولا واحد
+
+78
+00:08:27,800 --> 00:08:33,250
+فيهم اللي معكوس مصبوطيبقى Z6 is not a field وإحنا
+
+79
+00:08:33,250 --> 00:08:37,850
+نظريتنا محوطة على مين؟ على ال field يعني بلو
+
+80
+00:08:37,850 --> 00:08:44,790
+استبدل Z5 بZ6 بيكون كلامنا كله خطأ رأسا على عقب
+
+81
+00:08:44,790 --> 00:08:50,890
+ياري بالك، صح، عايز كويس Z5 ماشي الحال، Z7 ماشي
+
+82
+00:08:50,890 --> 00:08:56,910
+الحال، Z11 ماشي الحال، مدام هذا prime ماعناه مشكلة
+
+83
+00:08:56,910 --> 00:09:01,450
+قلص، بيكون هذا ياشفيرAny non-zero element has a
+
+84
+00:09:01,450 --> 00:09:05,450
+multiplicative inverse أي عنصر غير صفري له معكس
+
+85
+00:09:05,450 --> 00:09:10,470
+وبالتالي فهو field إذا إحنا شغولنا على مين؟ على ال
+
+86
+00:09:10,470 --> 00:09:16,890
+field اللي هو حالة خاصة من مين؟ من ال ring تمام؟
+
+87
+00:09:16,890 --> 00:09:23,690
+هي يبقى هي عندي دالة وهي دالة تانية وتنتين موجودة
+
+88
+00:09:23,690 --> 00:09:28,230
+في z خمسة طب ينفع أقول الأولى مثلا موجودة في z
+
+89
+00:09:28,230 --> 00:09:35,710
+خمسةوالتانية موجودة في زيت سبعة ونبدأ نجسب لأن انت
+
+90
+00:09:35,710 --> 00:09:40,590
+صرت بتشتغل في two fields مع بعض و هذا كلام قضى
+
+91
+00:09:40,590 --> 00:09:46,050
+احنا بنشغل دايما و انه أبدا داخل field واحد يبقى
+
+92
+00:09:46,050 --> 00:09:49,790
+كله بده يكون في نفس ال field و ليس في two
+
+93
+00:09:49,790 --> 00:09:56,020
+different fields طيب ماشيالان قليلة ال quotient و
+
+94
+00:09:56,020 --> 00:10:01,100
+هاتلة ال remainder يبقى بدنا نبدأ نقسم و نطلع خارج
+
+95
+00:10:01,100 --> 00:10:08,220
+القسمة و كذلك ال باقى قسمة مطولة زي ما كنا بنقسم
+
+96
+00:10:08,220 --> 00:10:14,180
+في الصف السابع و الصف التامن بس بالشرط شغلنا داخل
+
+97
+00:10:14,180 --> 00:10:18,680
+Z خامسة تمام؟ يبقى بقى اللي بقوله قد أجي ال
+
+98
+00:10:18,680 --> 00:10:24,830
+function اللي عندنا F of X اللي ثلاثة X و أربعزائد
+
+99
+00:10:24,830 --> 00:10:31,950
+اكس تكيب زائد اتنين اكس تربيع زائد واحد بدك زمها
+
+100
+00:10:31,950 --> 00:10:39,790
+عادي جدا على اكس تربيع زائد اربعة اكس زائد اتنين
+
+101
+00:10:39,790 --> 00:10:47,310
+بنبدأ بقسم الأكبر تيرم هي على أكبر تيرم والباقي
+
+102
+00:10:47,310 --> 00:10:53,770
+بالحجوهم طبيعيينيبقى تلاتة X أُس أربعة على X تربيع
+
+103
+00:10:53,770 --> 00:11:01,050
+بيطلع كدهش تلاتة X تربيع في X تربيع يبقى تلاتة X
+
+104
+00:11:01,050 --> 00:11:07,290
+أُس أربعة اللي بعديها تلاتة في أربعة باطماشر X
+
+105
+00:11:07,290 --> 00:11:13,070
+تكييب واحنا بنشغل في Z خمسة يبقى الأتناشر عبارة عن
+
+106
+00:11:13,070 --> 00:11:20,740
+اتنين شيلي خمسين يبقى زائدي اتنين X تكييباللي
+
+107
+00:11:20,740 --> 00:11:29,260
+بعدها زائد ثلاثة في اتنين في ستة X تربيع شيله خمسة
+
+108
+00:11:29,260 --> 00:11:37,340
+يبقى زائد X تربيع فقط هاي زائد بنغير الإشارات
+
+109
+00:11:37,340 --> 00:11:45,680
+وبنجمع يبقى هنا ناقص اتنين X تكيب وزايد X تكيببظل
+
+110
+00:11:45,680 --> 00:11:52,520
+سالب X تكييب واحدة يبقى سالب X تكييب واحدة عندك
+
+111
+00:11:52,520 --> 00:11:58,660
+هنا سالب X تربيع زي اتنين X تربيع بظل قداش زائد X
+
+112
+00:11:58,660 --> 00:12:04,400
+تربيع زائد واحد لكن ماعنديش سالب واحد في زيد خمسة
+
+113
+00:12:04,400 --> 00:12:11,760
+لكن سالب واحد بكافئة أربع يبقى هذه معناته هي أربع
+
+114
+00:12:11,760 --> 00:12:20,900
+X تكييبزائد X تربيع زائد واحد تمام؟ طيب صارت هذا
+
+115
+00:12:20,900 --> 00:12:25,480
+من الدرجة التالتة وهذا من الدرجة التانية بنواصل
+
+116
+00:12:25,480 --> 00:12:34,080
+عملية القسمة يبقى هنا زائد اربع X في X تربيع في
+
+117
+00:12:34,080 --> 00:12:43,130
+اربع X تكييف زائد اربع في اربع16 X تربيع يعني واحد
+
+118
+00:12:43,130 --> 00:12:51,650
+في X تربيع X تربيع واحدة هنا زائد تمانية X شيل من
+
+119
+00:12:51,650 --> 00:12:59,610
+الخمسة بظال ثلاثة X نيجي نغير الإشارات هذه زائد
+
+120
+00:12:59,610 --> 00:13:05,730
+بيصير ناقص ناقص ناقص مع السلامة وهذه غير ملسوف
+
+121
+00:13:05,730 --> 00:13:13,730
+عليهابيبقى ناقص ثلاثة X زائد واحد يبقى ناقص ثلاثة
+
+122
+00:13:13,730 --> 00:13:18,870
+X زائد واحد لكن ماعنديش ناقص ثلاثة في Z خمسة في
+
+123
+00:13:18,870 --> 00:13:25,310
+رقم يو كافر باضيفله قداشر خمسة لما اضفلها خمسة
+
+124
+00:13:25,310 --> 00:13:31,390
+بصير اتنين X زائد واحد هذا من الدرجة الأولى
+
+125
+00:13:31,390 --> 00:13:35,930
+والمقسوم عليهمن الدرجة التانية بقى بس الله يعطيك
+
+126
+00:13:35,930 --> 00:13:41,550
+العافية بيقدر تمشي ولا قطوع بعد ذلك إذا أصبحت ال
+
+127
+00:13:41,550 --> 00:13:47,070
+function اللي عندنا اللي هي ال F of X تساوي مين
+
+128
+00:13:47,070 --> 00:13:53,910
+تساوي تلاتة X أُص أربعة زائد X تخيب زائد اتنين X
+
+129
+00:13:53,910 --> 00:14:00,750
+تربيع زائد واحد تساوي اللي عندنا مين الدالة اللي
+
+130
+00:14:00,750 --> 00:14:07,090
+عندنا اللي هو X تربيعزائد أربع X زائد اتنين في
+
+131
+00:14:07,090 --> 00:14:15,290
+خارج القسمة خارج القسمة اللي هو تلاتة X تربيع زائد
+
+132
+00:14:15,290 --> 00:14:22,330
+أربع X لكن لسه ضايل عند مين يتنين X زائد واحد بده
+
+133
+00:14:22,330 --> 00:14:27,830
+ينقسم على هذا إذا قدرنا نحط ال function اللي عندنا
+
+134
+00:14:27,830 --> 00:14:33,090
+الأساسية على الشكل اللي عندنا هذايبقى هذه مين يا
+
+135
+00:14:33,090 --> 00:14:41,650
+ولد؟ هذه F of X وهذه مين؟ G of X وهذه مين؟ خارج
+
+136
+00:14:41,650 --> 00:14:49,390
+القسم اللي هو Q of X وهذه مين؟ ال remainder اللي
+
+137
+00:14:49,390 --> 00:14:55,050
+هو R of X السؤال كان ليهت الكوشن وهتلي ال
+
+138
+00:14:55,050 --> 00:14:59,870
+remainder لما تكسم اتنين على بعضفبروح بقوله the
+
+139
+00:14:59,870 --> 00:15:09,150
+quotient فارج القسمة is ثلاثة X ترابيع زائد اربعة
+
+140
+00:15:09,150 --> 00:15:15,690
+X and ال remainder الباقي
+
+141
+00:15:15,690 --> 00:15:24,330
+is اتنين X زائد واحد لذلك اشتغلنا شغل صحيحيبقى من
+
+142
+00:15:24,330 --> 00:15:28,650
+الألف أصعدا لما نقسم polynomial على polynomial
+
+143
+00:15:28,650 --> 00:15:34,850
+بطعة المقسوم عليه مضلوب في polynomial أخرى زائد ال
+
+144
+00:15:34,850 --> 00:15:40,190
+remainder درجة ال remainder أقل من درجة المقسوم
+
+145
+00:15:40,190 --> 00:15:46,410
+عليه أو ال remainder ب zero وبالتالي حطينا أي
+
+146
+00:15:46,410 --> 00:15:50,110
+function بدلالة ال function اللي بيعطاني في Q of X
+
+147
+00:15:50,110 --> 00:15:57,670
+زائد البافلة ومينROMPIX طيب فى عنا الآن بعض
+
+148
+00:15:57,670 --> 00:16:03,550
+التسميات هتمر علينا خلال شغلنا فى الpronomial ring
+
+149
+00:16:03,550 --> 00:16:10,070
+بدي اعرف مين هى هذه التسميات يبقى مرت علينا تسمية
+
+150
+00:16:10,070 --> 00:16:15,670
+ال quotient ومرت علينا تسمية ال remainder بدنا نحط
+
+151
+00:16:15,670 --> 00:16:20,650
+كمان تلات أشياء جديدة يبقى definition
+
+152
+00:16:38,240 --> 00:16:48,460
+الـ F of X والـ G of X موجودة في الـ Integral
+
+153
+00:16:48,460 --> 00:16:48,880
+Domain
+
+154
+00:16:53,220 --> 00:17:00,960
+we say that مروح
+
+155
+00:17:00,960 --> 00:17:11,420
+نقول ان ال G of X ال G of X divide ال F of X ان ال
+
+156
+00:17:11,420 --> 00:17:20,140
+G of X بتقسم ال F of X في ال D of X if they exist
+
+157
+00:17:22,860 --> 00:17:34,960
+there exists h of x and d of x such that
+
+158
+00:17:34,960 --> 00:17:45,060
+بحيث أن ال f of x بده يساوي ال g of x مضروبة في
+
+159
+00:17:45,060 --> 00:17:55,580
+من؟ مضروبة في ال h of xيبقى H of X مضروبة في الـ G
+
+160
+00:17:55,580 --> 00:18:06,120
+of X Also هو كذلك نقول نقول نقول نقول نقول نقول
+
+161
+00:18:06,120 --> 00:18:06,220
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+162
+00:18:06,220 --> 00:18:06,260
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+163
+00:18:06,260 --> 00:18:08,000
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+164
+00:18:08,000 --> 00:18:08,900
+نقول نقول نقول نقول نقول نقول نقول نقول نقول نقول
+
+165
+00:18:08,900 --> 00:18:17,140
+نقول نقول نقول نقول
+
+166
+00:18:17,140 --> 00:18:17,600
+نقول
+
+167
+00:18:21,460 --> 00:18:27,960
+تعريف آخر Definition and
+
+168
+00:18:27,960 --> 00:18:40,760
+element a and element a is a zero is a zero أو
+
+169
+00:18:40,760 --> 00:18:53,220
+بنسمي root جذر يا إما zero يا إما root جذرof a
+
+170
+00:18:53,220 --> 00:19:07,080
+polynomial of a polynomial f of x البرنامج f ال f
+
+171
+00:19:07,080 --> 00:19:16,600
+of a تساوي 0 that is if
+
+172
+00:19:16,600 --> 00:19:25,280
+إذا كان ال a inالـ a to the power n a minus ال one
+
+173
+00:19:25,280 --> 00:19:32,920
+a to the power minus ال one زائد a one a زائد a
+
+174
+00:19:32,920 --> 00:19:41,100
+not تساوي زيه ال definition الأخيرة قلت ال FBA
+
+175
+00:19:41,100 --> 00:19:50,620
+field لك ال FBA field and let
+
+176
+00:19:56,940 --> 00:20:06,920
+فال F وال F of X موجود في كابتن F of X We say that
+
+177
+00:20:06,920 --> 00:20:13,580
+نقول
+
+178
+00:20:13,580 --> 00:20:16,640
+We
+
+179
+00:20:16,640 --> 00:20:33,540
+say that ان ال A is a zeroof multiplicity
+
+180
+00:20:33,540 --> 00:20:41,460
+K if
+
+181
+00:20:41,460 --> 00:20:51,040
+ال X ناقص ال A to the power K is a factor
+
+182
+00:20:58,050 --> 00:21:10,750
+is a factor of f of x and x نقص a to the power k
+
+183
+00:21:10,750 --> 00:21:21,390
+plus one is not a
+
+184
+00:21:21,390 --> 00:21:26,050
+factor of
+
+185
+00:21:26,050 --> 00:21:27,230
+f of x
+
+186
+00:21:31,810 --> 00:21:35,890
+R F O X
+
+187
+00:22:07,180 --> 00:22:17,080
+مثلًا احصل على طريق طريق
+
+188
+00:22:17,080 --> 00:22:28,460
+و مرتبطات و مرتبطات
+
+189
+00:22:28,460 --> 00:22:32,860
+كمان عندما نكتب
+
+190
+00:22:39,330 --> 00:22:45,950
+when we write the
+
+191
+00:22:45,950 --> 00:22:53,810
+polynomial when
+
+192
+00:22:53,810 --> 00:23:00,790
+we write the polynomial ال
+
+193
+00:23:00,790 --> 00:23:04,310
+F of X يساوي
+
+194
+00:23:28,660 --> 00:23:38,600
+في الشكل ال F of X يساوي X نقص ال A to the power K
+
+195
+00:23:38,600 --> 00:23:50,920
+LQO of X in the field Z5
+
+196
+00:24:04,400 --> 00:24:09,980
+نذهب الآن لكل تعريف من التعريف الثلاثة نشوف ما هو
+
+197
+00:24:09,980 --> 00:24:14,660
+المقصود بهذا التعريف فبقى بدنا نجي مع التعريف
+
+198
+00:24:14,660 --> 00:24:20,000
+الأول قال خدلي D integral domain خدلي two
+
+199
+00:24:20,000 --> 00:24:26,720
+polynomials موجودات في D of X we see that روح نقول
+
+200
+00:24:26,720 --> 00:24:33,860
+ان الـG of X ابتقسم ال F of X داخل ال domain هذا
+
+201
+00:24:34,250 --> 00:24:38,830
+إذا قدرت ألاقي دالة تانية داخل هذا الـ integral
+
+202
+00:24:38,830 --> 00:24:46,090
+اللي هو domain D هذه الدالة سميتها H of X بحيث أن
+
+203
+00:24:46,090 --> 00:24:52,750
+F of X يساوي G of X مضروبة 8 في الـ H of X يبقى
+
+204
+00:24:52,750 --> 00:24:57,330
+أنا عندي two polynomials واحدة F of X والثانية G
+
+205
+00:24:57,330 --> 00:25:02,730
+of X إذا قدرت ألاقي أن الـ F of Xيساوي ال
+
+206
+00:25:02,730 --> 00:25:07,510
+polynomial G of X مضروبة في polynomial تانية بقول
+
+207
+00:25:07,510 --> 00:25:12,570
+فعلا ال G of X بتقسم مين ال F of X القسمة بدون
+
+208
+00:25:12,570 --> 00:25:17,550
+باقي لاحظي ماقولتش زائد remainder ماعنديش
+
+209
+00:25:17,550 --> 00:25:22,530
+remainder يبقى إن حدث ذلك بقول يبقى ال polynomial
+
+210
+00:25:22,530 --> 00:25:29,630
+G of X بتقسم ال F of X وخارج القسمة هو مين ال H of
+
+211
+00:25:29,630 --> 00:25:29,710
+X
+
+212
+00:25:33,560 --> 00:25:38,100
+الـ R of X تساوي Zero ان شرطنا عند الـ R of X يا
+
+213
+00:25:38,100 --> 00:25:44,680
+Zero يا درجته أقل من درجة الـ G of X المرة هذه الـ
+
+214
+00:25:44,680 --> 00:25:51,000
+R of X بـ Zero إذا الـ G of X بتقسم الـ F of X
+
+215
+00:25:51,000 --> 00:25:58,360
+بدون باقى وكذلك بنقدر نقول ان الـ G of X هي أحد
+
+216
+00:25:58,360 --> 00:26:04,320
+عوامل من الـ F of X لأن لو ضربناالـ U of X في عامل
+
+217
+00:26:04,320 --> 00:26:09,560
+آخر طالع عند من F of X يبقى الـ U of X بسميها أحد
+
+218
+00:26:09,560 --> 00:26:14,020
+عوامل F of X هذا بالنسبة للتعريف الأول و زي ما
+
+219
+00:26:14,020 --> 00:26:19,880
+انتوا شايفين زي الأعداد تماما طيب التعريف التاني
+
+220
+00:26:19,880 --> 00:26:26,860
+ال element ايه بسميه Zero او بسميه ال gender تبعي
+
+221
+00:26:26,860 --> 00:26:31,120
+ال polynomial هو ال Zero تبعي ال polynomialيعني
+
+222
+00:26:31,120 --> 00:26:37,120
+الرقم اللي لو عوضته في ال X تبع ال polynomial بطلع
+
+223
+00:26:37,120 --> 00:26:44,240
+النتج يساوي Zero او بسميه جادر كثيرة الحدود F of X
+
+224
+00:26:44,240 --> 00:26:49,700
+إذا كان ال F of A بديه ساوي من؟ بديه ساوي الصفر
+
+225
+00:26:49,700 --> 00:26:56,120
+بمعنى جيت على كثيرة الحدود شيل كل X وعطيت مكانه
+
+226
+00:26:56,120 --> 00:27:03,590
+من؟و جمعت النتج جدّه Zero يبقى جيت مكان ال X حاطيت
+
+227
+00:27:03,590 --> 00:27:08,170
+A المعامل خلّيته زي ما هو بدل ال X to the power N
+
+228
+00:27:08,170 --> 00:27:12,230
+قلت A to the power N A to the power N minus one A
+
+229
+00:27:12,230 --> 00:27:17,110
+to the power one A naught وجمعت وجدت النتج يسوى
+
+230
+00:27:17,110 --> 00:27:22,910
+مين؟ يسوى Zero إن حدث ذلك يبقى ال A بسمي هو جذر ال
+
+231
+00:27:22,910 --> 00:27:29,290
+polynomial أوالرقم اللذي يجعل ال polynomial تساوي
+
+232
+00:27:29,290 --> 00:27:37,070
+صفرة تم تعريف التالب يقول خد ال F فيه وخد A، A
+
+233
+00:27:37,070 --> 00:27:42,890
+موجودة في ال F وال polynomial F of X موجودة في
+
+234
+00:27:42,890 --> 00:27:49,950
+capital F of X ال A هذا بسميه Zero of multiplicity
+
+235
+00:27:49,950 --> 00:27:56,080
+Kإذا كان ال X ناقص ال A to the power K هو أحد
+
+236
+00:27:56,080 --> 00:28:02,520
+عناصر main ال F of X يعني يا بنات ال F of X كتبتها
+
+237
+00:28:02,520 --> 00:28:08,580
+بدل ال G كتبت X ناقص ال A to the power K في main
+
+238
+00:28:08,580 --> 00:28:15,960
+في ال H of X تمام؟ يبقى ال G of X أصبحت هي X ناقص
+
+239
+00:28:15,960 --> 00:28:22,350
+ال A to the power Kيبقى ال X هو عامل من عوامل F of
+
+240
+00:28:22,350 --> 00:28:29,170
+X لكن لو بختل ال S واحد بصير ما هوش عامل من عوامل
+
+241
+00:28:29,170 --> 00:28:36,990
+مين الدالة F of X يعني وكان ال K أصغر رقم والله
+
+242
+00:28:36,990 --> 00:28:43,770
+أكبر رقم مش أصغر أكبر رقم بيخلي ال X نقص ال A هو
+
+243
+00:28:43,770 --> 00:28:49,470
+أحد عوامل مين ال F of Xهنوضح لكم المفاهيم هذه
+
+244
+00:28:49,470 --> 00:28:58,350
+بمثال عددي المثال بيقول ماذا؟ غليهد للجذر ال
+
+245
+00:28:58,350 --> 00:29:01,610
+multiplicity
+
+246
+00:29:01,610 --> 00:29:07,150
+k إذا جدرنا نكتب ال polynomial هذه على الشكل اللي
+
+247
+00:29:07,150 --> 00:29:12,550
+عندها هذا في ال fields الخامسة لازال شغلنا مع ال
+
+248
+00:29:12,550 --> 00:29:17,040
+field يعني المثال هذا على مين؟على الحالة اللي
+
+249
+00:29:17,040 --> 00:29:21,920
+عمناه الجئاني بتدور في Z خمسة أكام عنصر فيها Z
+
+250
+00:29:21,920 --> 00:29:28,260
+خمسة؟ خمسة عناصر من العنصر اللي من العناصر الخامسة
+
+251
+00:29:28,260 --> 00:29:33,100
+اللي بيخللي ال polynomial تساوي Zero بدي أبدأ
+
+252
+00:29:33,100 --> 00:29:41,060
+أحسبه بدي أقوله ال F of Zero اللي عوض بطلع جدير
+
+253
+00:29:41,710 --> 00:29:47,250
+أربعة يبقى زي مش جذر للchronome يعني لإنه مشان
+
+254
+00:29:47,250 --> 00:29:53,930
+تكون جذر بيطلع النتج يسوى الصفر فبتاجي لل F هو
+
+255
+00:29:53,930 --> 00:29:59,690
+واحد واحد وصف اربعة بواحد في اتنين باتنين وإن ضايل
+
+256
+00:29:59,690 --> 00:30:07,030
+واحد تلاتة و تلاتة ستة شيلي خمسة وضل واحد واحد و
+
+257
+00:30:07,030 --> 00:30:12,100
+اتنين تلاتة واربعةسبعة شيلي خمسة و بضلي اتنين
+
+258
+00:30:12,100 --> 00:30:17,860
+يتقال واحد ما هو مش جادر لل Polynomial تعالى نشوف
+
+259
+00:30:17,860 --> 00:30:26,600
+افقه باتنين نجا اتنين بص اربع ليه و بص اتناش شيلي
+
+260
+00:30:26,600 --> 00:30:32,260
+خمس تاش تانية و خمسة بضلي واحد في اتنين باتنين و
+
+261
+00:30:32,260 --> 00:30:39,780
+هنا تامانية واحد تسعةشيلي خمسة بيبقى القدر اربع
+
+262
+00:30:39,780 --> 00:30:46,660
+اربع وهذه اربع في تلاتة اتناش واربع ستاش شيلي
+
+263
+00:30:46,660 --> 00:30:52,620
+تلاتة خمسات بيبقى الواحد وهذا اتنين في اتنين باربع
+
+264
+00:30:52,620 --> 00:30:55,740
+اتنين
+
+265
+00:30:55,740 --> 00:31:01,080
+لأ لحظة شوية احنا غلطنا مرة تانية الحين هذه ستاش
+
+266
+00:31:01,080 --> 00:31:07,760
+مظبوط ستاش في اتنين في اتنين و تلاتينبيضل شيلي ست
+
+267
+00:31:07,760 --> 00:31:14,140
+خمسات بيضلي اتنين وهنا هنا تمانية تمانية و اتنين
+
+268
+00:31:14,140 --> 00:31:20,860
+عاشرة مع السلامة طيب نيجي هنا اربعة في تلاتة و
+
+269
+00:31:20,860 --> 00:31:27,380
+اتناش بيضلي اتنين اتنين في اتنين اربعة و اتنين
+
+270
+00:31:27,380 --> 00:31:34,380
+بيضلي اربعة و اتنين عاشرة يبقى Zero يبقى F of
+
+271
+00:31:34,380 --> 00:31:40,000
+اتنين يسوى Zeroيبقى الـ2 هو جدر لهذه البرنامج
+
+272
+00:31:40,000 --> 00:31:46,140
+السؤال هو فيها جذور أخرى ولا لأ بنا نكمل شغلنا في
+
+273
+00:31:46,140 --> 00:31:52,620
+زمن خمسة يبقى ضايل علينا ال F of تلاتة يبقى بنفس
+
+274
+00:31:52,620 --> 00:32:00,860
+الطريقة تلاتة في اتنين ستة واربعة صفر خمستين صفر
+
+275
+00:32:00,860 --> 00:32:06,420
+نجينا تلاتة في تلاتةتسعة في تلاتة، تسعة وعشرين،
+
+276
+00:32:06,420 --> 00:32:06,840
+تسعة وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة
+
+277
+00:32:06,840 --> 00:32:09,800
+وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة وعشرين،
+
+278
+00:32:09,800 --> 00:32:10,480
+تسعة وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة
+
+279
+00:32:10,480 --> 00:32:12,480
+وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة وعشرين،
+
+280
+00:32:12,480 --> 00:32:16,040
+تسعة وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة
+
+281
+00:32:16,040 --> 00:32:22,840
+وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة وعشرين،
+
+282
+00:32:22,840 --> 00:32:27,100
+تسعة وعشرين، تسعة وعشرين، تسعة وعشرين، تسعة
+
+283
+00:32:27,100 --> 00:32:31,280
+وعشرين، تسعة
+
+284
+00:32:31,280 --> 00:32:40,260
+وعشريننجل ال F واربع اربع في اتنين تمانية شيلة
+
+285
+00:32:40,260 --> 00:32:44,960
+خمسة بيبقى تلاتة واربع سبعة شيلة خمسة بيبقى ليه
+
+286
+00:32:44,960 --> 00:32:51,340
+اتنين اتنين، هذه ستاش في تلاتة تمانية واربعين
+
+287
+00:32:51,340 --> 00:32:57,560
+واتنين خمسين راحوا هدول مع السلامة نجل هذه اربع
+
+288
+00:32:57,560 --> 00:33:03,030
+وستين اللي هي اربع تكعيبة في اربع وستينشيلي ستين
+
+289
+00:33:03,030 --> 00:33:10,750
+بيضل أربع نيجي هذه ستاشر بواحد وكمان ستاشر بواحد
+
+290
+00:33:10,750 --> 00:33:17,770
+في واحد بواحد في اتنين باتنين اتنين واربع ستة شيلي
+
+291
+00:33:17,770 --> 00:33:25,490
+خمسة يساوي واحد يبقى ماعنديش الا اتنين هو الجدد
+
+292
+00:33:25,490 --> 00:33:42,580
+يبقى هنا سا اتنين ازthe root of the polynomials f
+
+293
+00:33:42,580 --> 00:33:52,760
+of x because ال f of اتنين بده يساوي زيكي خلاصة
+
+294
+00:33:52,760 --> 00:33:59,140
+المطلوب الأول بدنا نيجي للمطلوب الثانيبنطلع الـ X
+
+295
+00:33:59,140 --> 00:34:05,220
+ناقص الـ A كم مرة مكررة يبقى بروح أقسم الفولونوميا
+
+296
+00:34:05,220 --> 00:34:10,780
+العالمية على X ناقص الـ A كدوش الـ A عندي طلعت؟
+
+297
+00:34:10,780 --> 00:34:17,860
+كدوش؟ بإتنين يبقى بدي أقسم الفولونوميا إتنين X و
+
+298
+00:34:17,860 --> 00:34:26,740
+أربع زائد X تكيب زائد تلاتة X ترابيعزائد اتنين X
+
+299
+00:34:26,740 --> 00:34:36,300
+زائد اربعة تقسيم ال X ناقص اتنين طيب نقسم اتنين X
+
+300
+00:34:36,300 --> 00:34:43,860
+قصة اربعة ال X باتنين X تكييف اتنين X تكييف باتنين
+
+301
+00:34:43,860 --> 00:34:52,400
+X قصة اربعة ناقص اربعة X تكييف ناقص اربعة X تكييف
+
+302
+00:34:52,400 --> 00:34:59,820
+تمام؟هذه ازاي؟ بنغير انتشارات وبنبدأ نجمعها اربع
+
+303
+00:34:59,820 --> 00:35:07,400
+واحد خمسة يبقى راحة بي Zero الله سهل عليها تمام؟
+
+304
+00:35:07,400 --> 00:35:12,560
+طيب مين ضلع ان لا يبقى دول خلصوا راح خارج الخصمة
+
+305
+00:35:12,560 --> 00:35:18,420
+تماما اتنين X تقييمة بدي اكسب ثلاثة X تربيع على X
+
+306
+00:35:18,420 --> 00:35:25,680
+يبقى فيها كده؟ ثلاثة Xتلاتة اكس في اكس في تلاتة
+
+307
+00:35:25,680 --> 00:35:34,320
+اكس تربيع تلاتة اكس في ناقص ستة اكس شيلي خمسة وضع
+
+308
+00:35:34,320 --> 00:35:43,300
+ناقص اكس هم بنغير الإشارات بالشكل اللي عندنا هنا
+
+309
+00:35:43,300 --> 00:35:50,640
+بقى القدر شبنة تلاتة اكس زائد الأربع الباقي من
+
+310
+00:35:50,640 --> 00:35:55,730
+الدرجة الأولىوالمقسوم عليه من الدرجة الأولى بنواصل
+
+311
+00:35:55,730 --> 00:36:03,570
+عملية انقسمها تلاتة X على X هي تلاتة تلاتة في X
+
+312
+00:36:03,570 --> 00:36:12,370
+بتلاتة X وتلاتة في ناقص اتنين ناقص ستة شيلي خمسة
+
+313
+00:36:12,370 --> 00:36:20,540
+وظل ناقص واحد نغير الإشارات ونبدأ نجمعواحد واربع
+
+314
+00:36:20,540 --> 00:36:27,160
+خمسة يبقى كل الناتج ب zero يبقى طالع خارج القسمة
+
+315
+00:36:27,160 --> 00:36:35,040
+بدون باقية يبقى صارت ال F of X الأصلية مكتوبة على
+
+316
+00:36:35,040 --> 00:36:42,460
+شكل X ناقص اتنين في مين في اتنين X تكعيد زائد
+
+317
+00:36:42,460 --> 00:36:51,100
+تلاتة X زائد تلاتةهل يا ترى لحد هنا و stop بيجسمش
+
+318
+00:36:51,100 --> 00:36:56,940
+والله بتجسم منقول تعالى نشوف بدي قسمة بدون باقي
+
+319
+00:36:56,940 --> 00:37:00,560
+عندما اوصل لباقي بقول stop الله عطاك الله عافية
+
+320
+00:37:00,560 --> 00:37:07,860
+طيب الان بدي اشوف هذه تجسم على X نقص اتنين ولا لأ
+
+321
+00:37:07,860 --> 00:37:13,020
+اذا عوضت فيها باتنين وطلع انها جساوي Zero يبقى
+
+322
+00:37:13,020 --> 00:37:17,530
+بتجسم وبعدين روحها تجسم الجوس التاني يعنيبتعوض
+
+323
+00:37:17,530 --> 00:37:25,830
+باتنين تمانية اتنين ثم واحد اتنين و تلاتة ستة ثم
+
+324
+00:37:25,830 --> 00:37:32,190
+واحد و واحد و تلاتة ستة تبتجسم و هي التانية بتجسم
+
+325
+00:37:32,190 --> 00:37:37,590
+كمان مرة اذا انا بدى اروح الهامس بنفس الطريقة بدي
+
+326
+00:37:37,590 --> 00:37:45,450
+اجسم اتنين X تكيين زي التلاتة X زي التلاتةعلى اكس
+
+327
+00:37:45,450 --> 00:37:53,970
+ناقص اتنين يبقى فيها اتنين اكس ترابيع باتنين اكس
+
+328
+00:37:53,970 --> 00:38:03,290
+تكيين ناقص اربع اكس ترابيع هذه زاد بصير ناقص وهذه
+
+329
+00:38:03,290 --> 00:38:10,150
+زاد الاربع اكس ترابيع مافيش غيرها وظل تلاتة اكس
+
+330
+00:38:10,150 --> 00:38:16,420
+زائد تلاتةمن الدرجة الثانية من الدرجة الأولى بواصل
+
+331
+00:38:16,420 --> 00:38:21,700
+عملية القسمة اربعة اكس تربيع على اكس بطلع عندك
+
+332
+00:38:21,700 --> 00:38:31,040
+داشر اربعة اكس في اكس اربعة اكس تربيع وهنا اربعة
+
+333
+00:38:31,040 --> 00:38:39,440
+سالب اتنين سالب تمانية اشيل خمسة بظل سالب تلاتة
+
+334
+00:38:39,440 --> 00:38:47,190
+اكسوعندك اه خلصنا يبقى هذه زاد تصير ناقص وهذه زاد
+
+335
+00:38:47,190 --> 00:38:55,690
+مع السلامة تلاتة X و تلاتة X بستة X ستة X شيلي
+
+336
+00:38:55,690 --> 00:39:03,790
+خمسة بيظل واحد مضروف X يبقى ب X زائد تلاتة ال X
+
+337
+00:39:03,790 --> 00:39:11,280
+على X فيها جدير واحد يبقى زائد واحدواحد في اكس
+
+338
+00:39:11,280 --> 00:39:18,040
+باكس وواحد في سالبي اتنين بسالبي اتنين هذه زائد
+
+339
+00:39:18,040 --> 00:39:24,260
+تصبح ناقص وهذه زائد مع السلامة اتنين و تلاتة و
+
+340
+00:39:24,260 --> 00:39:32,240
+خمسة يبقى zero يبقى صارت هذه تساوي ال X ناقص اتنين
+
+341
+00:39:32,240 --> 00:39:40,070
+اجا كمان X ناقص اتنين ضال عند اتنين X تربيعزائد
+
+342
+00:39:40,070 --> 00:39:47,770
+أربعة X زائد واحدة يعني صارت X نقص اتنين لكل
+
+343
+00:39:47,770 --> 00:39:56,730
+ترابيع نين X ترابيع زائد أربعة X زائد واحدة انشوف
+
+344
+00:39:56,730 --> 00:40:02,470
+فيه كمان تكرار و الله خلصنا بنفس المفهوم إذا جيت
+
+345
+00:40:02,470 --> 00:40:08,560
+عوّقت هنا ب X يساوي اتنينوطالع الناتج يساوي Zero
+
+346
+00:40:08,560 --> 00:40:15,980
+كده في عندي كمان X ناقص اتنين اعوض باتنين اربعة في
+
+347
+00:40:15,980 --> 00:40:23,440
+اتنين تمانية شيلة خمسة بظل تلاتة هنا اتنين في
+
+348
+00:40:23,440 --> 00:40:30,240
+اربعة تمانية شيلة خمسة بظل تلاتة و تلاتة ستة بظل
+
+349
+00:40:30,240 --> 00:40:38,000
+واحد واحدمش ممكن يبقى اكتر من هيك ماعنديش تمام
+
+350
+00:40:38,000 --> 00:40:45,540
+يبقى كده مقدار ال multiplicity اتنين تمام يبقى هنا
+
+351
+00:40:45,540 --> 00:40:51,080
+Multiplicity
+
+352
+00:40:51,080 --> 00:40:58,180
+Multiplicity
+
+353
+00:41:00,810 --> 00:41:11,930
+X ناقص اتنين is اتنين.يعني هذا الجسم كرر مرتين، لا
+
+354
+00:41:11,930 --> 00:41:18,390
+ثالثة لأمان. تمام؟ طيب الآن بدنا ندخل على بعض
+
+355
+00:41:18,390 --> 00:41:25,630
+النتائج على النظرية وعنا بدأ للنتيجة تلاتة للمرة
+
+356
+00:41:25,630 --> 00:41:28,230
+القادمة ان شاء الله تعالى.
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..afd4f3b3e78fb57593449a394ad98427f87de9b5
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/RRK0VG1nTYo_postprocess.srt
@@ -0,0 +1,1416 @@
+1
+00:00:21,020 --> 00:00:26,040
+بسم الله الرحمن الرحيم انتهينا من chapter 12 و
+
+2
+00:00:26,040 --> 00:00:31,720
+chapter 13 و الآن بنجي ل chapter 14 اللي العمود
+
+3
+00:00:31,720 --> 00:00:37,760
+الفقري فيه عبارة عن نقطتين ال ideals و هي حالة
+
+4
+00:00:37,760 --> 00:00:42,740
+خاصة من ال subrings و النقطة الثانية هي ال
+
+5
+00:00:42,740 --> 00:00:47,660
+factorings تماما كما أخذنا factor group أو
+
+6
+00:00:47,660 --> 00:00:53,260
+quotient group قبل ذلكاليوم هنبدأ فقط بال ideals
+
+7
+00:00:53,260 --> 00:00:58,320
+وال factor rings بنخليه للمرة القادمة ان شاء الله
+
+8
+00:00:58,320 --> 00:01:04,740
+يبقى بدنا نبدأ بتعريف ال ideal ثم ناخد بعض الأمثلة
+
+9
+00:01:04,740 --> 00:01:08,480
+عليه وكيف نحكم على ال subsidy اللي بناخدها من ال
+
+10
+00:01:08,480 --> 00:01:14,400
+ring هل هي ideal او ليست ideal طب اروح نقول
+
+11
+00:01:14,400 --> 00:01:23,880
+التعريف كتالي يبقى a sub ringA sub ring A
+
+12
+00:01:23,880 --> 00:01:31,640
+of A ring R is called a two-sided ideal كلمة two
+
+13
+00:01:31,640 --> 00:01:36,500
+-sided حطيناها لهدف ممكن ما نقولش two-sided نقول
+
+14
+00:01:36,500 --> 00:01:41,160
+ideal و نسكت و الآن هنقولك ليش سميناها two-sided
+
+15
+00:01:41,160 --> 00:01:46,760
+ideal يبقى sub ring A of A ring R is called a two
+
+16
+00:01:46,760 --> 00:01:48,740
+-sided ideal of R
+
+17
+00:02:00,700 --> 00:02:07,200
+السؤال هو ما هو الفرق بين ال ID و بين ال subring
+
+18
+00:02:07,200 --> 00:02:14,660
+طبعا الفرق واضح من خلال ال definition اتنين من
+
+19
+00:02:14,660 --> 00:02:20,570
+empty هذا كلام صحيح النقطة الثانيةإنه لما ناخد
+
+20
+00:02:20,570 --> 00:02:27,210
+حاصل ضرب element من أين و اين راح element من a و
+
+21
+00:02:27,210 --> 00:02:32,550
+element من a بدي يكون الناتج في a هذا في ال ID لكن
+
+22
+00:02:32,550 --> 00:02:36,750
+لما كنا في ال ring بجينا أخدي اتنين من نفس ال six
+
+23
+00:02:36,750 --> 00:02:42,190
+يعني باخد عنصرين من نفس ال a بدي يكون حاصل ضربهم
+
+24
+00:02:42,190 --> 00:02:48,640
+موجود في a هنا لأ خدي أي عنصر من ال sub ring aو أي
+
+25
+00:02:48,640 --> 00:02:53,760
+عنصر من ال ring نضربهم معاهم بدي يكون موجود داخل
+
+26
+00:02:53,760 --> 00:02:59,060
+ال sub ring ان حدث ذلك يبقى بنسمي هذا ideal سواء
+
+27
+00:02:59,060 --> 00:03:05,100
+كان الضرب من اليمين او من الشمال فلما كان الضرب من
+
+28
+00:03:05,100 --> 00:03:10,740
+الشمال و هنا من اليمين سمنا ايه؟ two sided ideal
+
+29
+00:03:10,740 --> 00:03:17,420
+فإن قلنا two sided ideal او ideal و سكتناالاتنين
+
+30
+00:03:17,420 --> 00:03:22,420
+كله بنفس المعنى، تمام؟ يعني وانت بتقول اللي جيتي
+
+31
+00:03:22,420 --> 00:03:26,500
+كلمة two-sided ideal وما لجيتي كلمة ideal، بدك
+
+32
+00:03:26,500 --> 00:03:31,660
+تفهمي هذه انها two-sided ideal التعريف هذا، بدي
+
+33
+00:03:31,660 --> 00:03:37,440
+أعيد صياغته بطريقة أخرى، بقول this definition can
+
+34
+00:03:37,440 --> 00:03:41,920
+be written as هذا التعريف اتركته على الشكل التالف
+
+35
+00:03:42,140 --> 00:03:48,220
+ال sub ring A of A ring R is called ideal of R إذا
+
+36
+00:03:48,220 --> 00:03:54,560
+كان لو ضربت ال R في عناصر ال ideal كله بتطلع عندي
+
+37
+00:03:54,560 --> 00:04:02,240
+set وهذه set subset من مين؟ من A الأصلية بالمثل لو
+
+38
+00:04:02,240 --> 00:04:09,260
+ضربت في R من جهة اليمين جميع عناصر ال A بيطلع ل
+
+39
+00:04:09,260 --> 00:04:15,380
+set subset من مين؟ من Aإن تحققت لأي R موجودة في R،
+
+40
+00:04:15,380 --> 00:04:19,760
+إن تحققت ال two conditions لإتنين هدول، بقول إن ال
+
+41
+00:04:19,760 --> 00:04:26,460
+A هو عبارة عن ideal أو two-sided ideal، هذه أو
+
+42
+00:04:26,460 --> 00:04:33,040
+كلتل إتنين are the same.بنجر الآن للتعريف الثاني،
+
+43
+00:04:33,040 --> 00:04:39,110
+A is called the proper ideal of Aproper ideal إذا
+
+44
+00:04:39,110 --> 00:04:43,870
+كان الـA هو proper subset من من من الـA إيش يعني
+
+45
+00:04:43,870 --> 00:04:47,670
+معنى proper مثل ما درسناه في ال group؟ إيش يعني
+
+46
+00:04:47,670 --> 00:04:53,370
+proper يا مناد؟ انه subset من ال group الأصلية
+
+47
+00:04:53,370 --> 00:04:59,230
+وكان لا يساوي هذه ال group وهنا نفس القصة ال ideal
+
+48
+00:04:59,230 --> 00:05:06,310
+هو proper subset يعني لا يساوي ال group لا يساوي
+
+49
+00:05:06,310 --> 00:05:12,540
+ال ring الأصليةطب ايش معنى Improper؟ ممكن احتمال
+
+50
+00:05:12,540 --> 00:05:18,340
+يتساوي ممكن احتمال يتساوي ممكن احتمال يتساوي ممكن
+
+51
+00:05:18,340 --> 00:05:19,780
+احتمال يتساوي ممكن احتمال يتساوي ممكن احتمال
+
+52
+00:05:19,780 --> 00:05:21,300
+يتساوي ممكن احتمال يتساوي ممكن احتمال يتساوي ممكن
+
+53
+00:05:21,300 --> 00:05:21,780
+احتمال يتساوي ممكن احتمال يتساوي ممكن احتمال
+
+54
+00:05:21,780 --> 00:05:25,260
+يتساوي ممكن احتمال يتساوي ممكن احتمال يتساوي ممكن
+
+55
+00:05:25,260 --> 00:05:26,000
+احتمال يتساوي ممكن احتمال يتساوي ممكن احتمال
+
+56
+00:05:26,000 --> 00:05:30,040
+يتساوي ممكن احتمال يتساوي ممكن احتمال يتساوي ممكن
+
+57
+00:05:30,040 --> 00:05:31,840
+احتمال يتساوي ممكن ا
+
+58
+00:05:35,790 --> 00:05:40,270
+لكن من حد ما اقولك proper بدك تفهمي ان ال ideal
+
+59
+00:05:40,270 --> 00:05:45,330
+عدد عناصره اقل من عدد عناصر ال ring دائما هو لا
+
+60
+00:05:45,330 --> 00:05:52,530
+يمكن ان يتساوية طيب الآن كيف بدي افحص ان ال 6 اللي
+
+61
+00:05:52,530 --> 00:05:56,570
+خدتها او ال subset اللي خدتها من ال ring الأصلية
+
+62
+00:05:56,570 --> 00:06:03,190
+هي ideal بثلاثة شروط الشرط الأول ان تبقى ال subset
+
+63
+00:06:03,190 --> 00:06:10,160
+هذه مالهاnon-empty non-empty subset A of A ring R
+
+64
+00:06:10,160 --> 00:06:17,000
+بقول عنها ideal إذا كان أخدت عمصرين من الستة اللي
+
+65
+00:06:17,000 --> 00:06:22,140
+طرحتهم من بعض بدي يكون الناتج في A يبقى A minus ال
+
+66
+00:06:22,140 --> 00:06:27,540
+B موجود في A whenever ال A و ال B موجودين في A
+
+67
+00:06:27,540 --> 00:06:33,160
+اللي بعده ال R في A موجود في A وال A في R موجود في
+
+68
+00:06:33,160 --> 00:06:40,670
+Aلكل الـA الموجودة في A والـR الموجودة في R إذا ها
+
+69
+00:06:40,670 --> 00:06:45,250
+ها هذي اللي بيقوللي مشان تفحص هل اللي عندك هذا
+
+70
+00:06:45,250 --> 00:06:51,730
+ideal ولا لأ بدنا نثبت ثلاث نقاط النقطة الأولى أن
+
+71
+00:06:51,730 --> 00:06:55,790
+ال subset اللي أخدتها non-empty النقطة الثانية بدي
+
+72
+00:06:55,790 --> 00:07:00,390
+أخد أي عنصرين من هذه ال subset بدني أثبت أن الفرق
+
+73
+00:07:00,390 --> 00:07:06,370
+بينهما موجودفي نفس ال subset الأمر التالت بدي أخد
+
+74
+00:07:06,370 --> 00:07:10,590
+أي عنصر من هذا ال subset أو أي عنصر من ال ring بدي
+
+75
+00:07:10,590 --> 00:07:14,110
+أضربه فيه من اليمين و الله من الشمال بدي أطلع عنصر
+
+76
+00:07:14,110 --> 00:07:19,470
+موجود وين موجود في نفس ال set A إن حدث ذلك بقول
+
+77
+00:07:19,470 --> 00:07:25,410
+يبقى هذا ideal و من هنا صار هناك فرق ما بين ال
+
+78
+00:07:25,410 --> 00:07:29,950
+ideal و ما بين ال sub ring والفرق بسيط في ال
+
+79
+00:07:29,950 --> 00:07:35,780
+condition الأخر مثل ما كنااللي هو main ها تمام في
+
+80
+00:07:35,780 --> 00:07:40,160
+حالة ال sub ring قولنا بتاخد عنصرين من نفس الستين
+
+81
+00:07:40,160 --> 00:07:44,500
+لأ لأ بدي أخد عنصر من الست و عنصر من ال ring
+
+82
+00:07:44,500 --> 00:07:48,620
+الأصلية أضرب اتنين في بعض من الأمين و من الشمال
+
+83
+00:07:48,620 --> 00:07:53,300
+بدي أطلع عنصر في ال subset اللي أخدت هذه تماما طب
+
+84
+00:07:53,300 --> 00:07:57,960
+بدنا نروح نثبت صحة هذا الكلام يبقى a non empty
+
+85
+00:07:57,960 --> 00:08:03,270
+subset A of A ring R is an idealيبقى أنا خدت ال
+
+86
+00:08:03,270 --> 00:08:07,410
+subset من ال ring الأصلية وكانت هذه ال non-empty
+
+87
+00:08:07,410 --> 00:08:12,350
+إذا انت حقق ال condition اللي مضال علينا main ال
+
+88
+00:08:12,350 --> 00:08:18,290
+two conditions الأخرين السؤال هو هذا مش هو الشرط
+
+89
+00:08:18,290 --> 00:08:25,230
+الأول من شروط ال sub ring صح طيب هذا أليس هذا هو
+
+90
+00:08:25,230 --> 00:08:30,390
+الشرط التاني من ال sub ring وزيادة شويةكيف زيادة
+
+91
+00:08:30,390 --> 00:08:38,170
+شوية؟ لان بجينا جوا عنصرين من ال A عنصرين هنا
+
+92
+00:08:38,170 --> 00:08:42,810
+بيقولوا لأ عنصر من A والتاني من R، والتاني اللي
+
+93
+00:08:42,810 --> 00:08:48,350
+بدي أخطره من R قد يكون من A وقد لا يكون من A، فإن
+
+94
+00:08:48,350 --> 00:08:53,730
+كان من A هو تحصيل حاصل، وإن كان من R فهو زيادة عما
+
+95
+00:08:53,730 --> 00:08:59,240
+كان منين في حالة الصبرينيبقى الأن بروح بقوله the
+
+96
+00:08:59,240 --> 00:09:15,760
+conditions اللي هو I and II make the set is
+
+97
+00:09:15,760 --> 00:09:20,620
+suffering طبعا؟
+
+98
+00:09:20,620 --> 00:09:26,440
+طب ال condition اتالت لحالهبيخلّيه ايش بيخلّيه ID
+
+99
+00:09:26,440 --> 00:09:42,760
+but the second condition الشرط التاني make ال A is
+
+100
+00:09:42,760 --> 00:09:51,280
+an ID يبقى الشرط الثاني لحاله بيخلّي هذا ID إذا من
+
+101
+00:09:51,280 --> 00:09:56,150
+الألف صاعدالما يعطيني الست ويقولي اثبت انها هذه
+
+102
+00:09:56,150 --> 00:10:00,990
+ideal من ال ring الفلانية، بدي اثبتله ثلاثة شروط،
+
+103
+00:10:00,990 --> 00:10:04,830
+ان هذا subset non-empty، اتنين بدي اخد عنصري من
+
+104
+00:10:04,830 --> 00:10:08,470
+نفس ال subset، الفرق بينهما بدي يكون في نفس ال
+
+105
+00:10:08,470 --> 00:10:11,470
+subset اللي أخدناها، تلاتة بدي اخد element من ال
+
+106
+00:10:11,470 --> 00:10:14,900
+subset و element من ال ring الأصلية،أضربه في بعض
+
+107
+00:10:14,900 --> 00:10:18,960
+من جهة اليمين أو جهة الشمال بدي يطلع عنصر موجود في
+
+108
+00:10:18,960 --> 00:10:22,980
+ال subset لأن إن حدث ذلك يبقى هذه ال subset بقول
+
+109
+00:10:22,980 --> 00:10:30,900
+عليها Ideal من ال ring الأصلي نعطي أمثلة يبقى
+
+110
+00:10:30,900 --> 00:10:35,680
+examples أول
+
+111
+00:10:35,680 --> 00:10:40,380
+مثل دائما وابدا في حالة ال subgroup
+
+112
+00:10:43,270 --> 00:10:47,410
+اللي هو main ال identity element او ال group
+
+113
+00:10:47,410 --> 00:10:51,870
+الأصلي هدول اتنين subset من ال group الأصلي صحيح
+
+114
+00:10:51,870 --> 00:10:55,790
+ولا لأ طب و احنا هنا نفس القصة في حالة ال ring
+
+115
+00:10:55,790 --> 00:11:04,970
+يبقى هنا بقوله is zero as a pair and ال are are
+
+116
+00:11:04,970 --> 00:11:24,400
+sub are sub ringsof a and hence a ومن ثم ideals in
+
+117
+00:11:24,400 --> 00:11:28,960
+a ال
+
+118
+00:11:28,960 --> 00:11:38,680
+zero هده الو اشد ال zero is called the atrivial
+
+119
+00:11:38,680 --> 00:11:40,940
+ideal
+
+120
+00:11:42,790 --> 00:11:49,490
+او او او او او او او او او او او او او او او او او
+
+121
+00:11:49,490 --> 00:11:50,530
+او او او او او او او او او او او او او او او او او
+
+122
+00:11:50,530 --> 00:12:00,750
+او او او او او او او او او او او او او او او
+
+123
+00:12:00,750 --> 00:12:00,790
+او او او او او او او او او او او او او او او او او
+
+124
+00:12:00,790 --> 00:12:00,850
+او او او او او او او او او او او او او او او او او
+
+125
+00:12:00,850 --> 00:12:04,790
+او او او او او او او او او او او
+
+126
+00:12:04,790 --> 00:12:04,810
+او
+
+127
+00:12:12,760 --> 00:12:18,380
+بتاخد الـ zero من هنا و أي element R من R نضرب R
+
+128
+00:12:18,380 --> 00:12:25,640
+في Zero او Zero في R ب Zero موجود هنا فلسنا يبقى
+
+129
+00:12:25,640 --> 00:12:31,340
+هيه صار ايديل و ال ring الأصلية مهي نفسها يبقى
+
+130
+00:12:31,340 --> 00:12:36,700
+صارت ايديل من نفسها ال sub ring من نفسها و ينطق
+
+131
+00:12:36,700 --> 00:12:39,500
+تاخد منها element من ال ring الأصلية ال ring
+
+132
+00:12:39,500 --> 00:12:45,470
+الأصلية نفسهاany two elements موجودات في نفس ال
+
+133
+00:12:45,470 --> 00:12:47,910
+ring because it is a clause under multiplication
+
+134
+00:12:47,910 --> 00:12:53,930
+وبالتالي هي sub ring ووضع طبيعي وهذه أبسط أنواع
+
+135
+00:12:53,930 --> 00:12:59,670
+الأمثلة على ال sub rings وعلى ال ideals طيب نتجل
+
+136
+00:12:59,670 --> 00:13:09,770
+الكلام شوية مثال اثنين مثال اثنين بيقول لدرست ان
+
+137
+00:13:11,320 --> 00:13:18,000
+اللي عناصرها هي Zero زيدة ونقص N زيدة ونقص اتنين N
+
+138
+00:13:18,000 --> 00:13:25,180
+زيدة ونقص تلاتة N و هلوم مجرم لما شاء الله is an
+
+139
+00:13:25,180 --> 00:13:34,480
+ideal of Z is an ideal of a set of integers Z
+
+140
+00:13:34,480 --> 00:13:44,660
+because يعرف شو السبب النقطة الأولىMT على جالها
+
+141
+00:13:44,660 --> 00:13:49,180
+يفيها قدامنا الـ Zero تمام؟ لأن الـ Zero موجود في
+
+142
+00:13:49,180 --> 00:13:54,900
+Z تضربيه في أي عنصر من عناصر الـ Z بطلع الـ Z يبقى
+
+143
+00:13:54,900 --> 00:14:05,420
+الـ NZ as non-empty since لإن الـ Zero موجود في
+
+144
+00:14:05,420 --> 00:14:14,670
+الـ NZ النقطة الثانيةبدي اخد عنصرين x و y موجودات
+
+145
+00:14:14,670 --> 00:14:22,330
+في ال n z then ايش ممكن يكون شكل ال x يا بنات n
+
+146
+00:14:22,330 --> 00:14:33,390
+مضروب في عنصر من z يعني بقدر اقول n في z to n and
+
+147
+00:14:33,390 --> 00:14:46,060
+ال y بدي ساوي ال n في z tofor some z1 و z2 اللى
+
+148
+00:14:46,060 --> 00:14:57,120
+موجودة فيه z بدي اخد ال x ناقص ال y يبقى n z1 ناقص
+
+149
+00:14:57,120 --> 00:15:02,680
+ال n z2 بدي استخدم ال distributive law قانون
+
+150
+00:15:02,680 --> 00:15:12,350
+التوزيع يبقى هذا الكلام بيساويموجود في Z1 ناقص Z2
+
+151
+00:15:12,350 --> 00:15:22,670
+موجود في Z1 لا لا موجود في Z1 ليش لإن Z1 ناقص Z2
+
+152
+00:15:22,670 --> 00:15:28,270
+موجودة في Z الفرق بين any two integers is any
+
+153
+00:15:28,270 --> 00:15:38,650
+integer يبقى هذا موجود هنا لإن ال Z1 ناقص Z2موجودة
+
+154
+00:15:38,650 --> 00:15:43,170
+في set of integers يبقى مطابق ال condition التاني
+
+155
+00:15:43,170 --> 00:15:48,390
+بدي أروح لمين لل condition التالت بدي أخد عنصر في
+
+156
+00:15:48,390 --> 00:15:59,490
+z و عنصر في nz يبقى هنا f ال x اللي بتساوي nz1
+
+157
+00:15:59,490 --> 00:16:12,620
+موجودة في nz and ال mموجودة في Z then بتاخد
+
+158
+00:16:12,620 --> 00:16:21,500
+X M بتشوف هل هو موجود في N Z ولا لأ هذا الكلام
+
+159
+00:16:21,500 --> 00:16:32,340
+يثير ال X عندى مجددش N Z 1 يبقى N Z 1 مضروبة في M
+
+160
+00:16:33,020 --> 00:16:37,620
+هدول integers كلهم خاصية ال associativity صحيحة
+
+161
+00:16:37,620 --> 00:16:46,080
+على ال integers يبقى هذا بدي يعطيني N Z 1 M هذه
+
+162
+00:16:46,080 --> 00:16:54,520
+موجودة في N Z ولا لا؟ موجودة في N Z Z 1 M موجودة
+
+163
+00:16:54,520 --> 00:17:00,840
+في Z وبالتالي صارت هذه كلها موجودة في N Z وفي نفس
+
+164
+00:17:00,840 --> 00:17:11,960
+الوقتلو أخدت MX يبقى بده يساوي ال M في NZ1 طيب
+
+165
+00:17:11,960 --> 00:17:16,920
+الآن هذول التلات هار integers خاصية ال
+
+166
+00:17:16,920 --> 00:17:21,680
+associativity صحيحة على ال integers وزيادة على ذلك
+
+167
+00:17:21,680 --> 00:17:26,780
+عملية ضرب commutative على Z ولا لا؟ commutative
+
+168
+00:17:26,780 --> 00:17:34,340
+يبقى بناء عليه هذا بده يساوي ال Nفي ال MZ1 اللى
+
+169
+00:17:34,340 --> 00:17:40,320
+موجودة وين في ال MZ1 يبقى مطابق ال condition اتالت
+
+170
+00:17:40,320 --> 00:17:52,980
+وبناء عليه بناء عليه غصب ال N في Z is an ideal of
+
+171
+00:17:52,980 --> 00:17:59,320
+the ring of integers اللى همين اللى هى ال Z itself
+
+172
+00:18:19,740 --> 00:18:31,360
+ننتقل الى مثال ثالث مثال ثلاثه يقول
+
+173
+00:18:31,360 --> 00:18:43,460
+لات افترض ان الار بيه كميوتاتيف ring with unity
+
+174
+00:18:43,460 --> 00:18:48,960
+ring with unity
+
+175
+00:18:53,120 --> 00:18:59,520
+يتلقى belonging to R افترض ان في عنصر A موجود في
+
+176
+00:18:59,520 --> 00:19:09,800
+set A then the set يبقى set اللي بدأ اكتبها على
+
+177
+00:19:09,800 --> 00:19:15,840
+الشكل اللي عندنا هذا اللي هي تساوي كل ال R في A
+
+178
+00:19:15,840 --> 00:19:27,180
+بحيث ال R موجودة في R is an ideal of Aan ideal of
+
+179
+00:19:27,180 --> 00:19:35,320
+a called .. إيش كنتوا بتسموها في حالة إجروبة هنا؟
+
+180
+00:19:35,320 --> 00:19:42,460
+إيش كنتوا بتسموها؟ Cyclic group؟ ولا كنتوا بتسموها
+
+181
+00:19:42,460 --> 00:19:45,860
+the principle ideal .. the principle ما بعرفيه
+
+182
+00:19:45,860 --> 00:19:50,000
+generated by ايه؟ ال principle صح بيقولوا طيب على
+
+183
+00:19:50,000 --> 00:19:59,600
+أي حالبنسميه the principle ideal
+
+184
+00:19:59,600 --> 00:20:03,900
+generated
+
+185
+00:20:03,900 --> 00:20:07,320
+by
+
+186
+00:20:07,320 --> 00:20:15,400
+A نبقى هذا هو ال principle ideal generated by A
+
+187
+00:20:15,400 --> 00:20:19,340
+ليش هذا كان ideal؟
+
+188
+00:20:25,140 --> 00:20:32,460
+يبقى براحة بقوله Firstly هذا
+
+189
+00:20:32,460 --> 00:20:39,880
+is an ideal بعد
+
+190
+00:20:39,880 --> 00:20:47,480
+ما نثبت انه ideal خيص بدنا نطلق عليه تسمية ال
+
+191
+00:20:47,480 --> 00:20:51,600
+principle ideal generated by A يبقى هو ال ideal
+
+192
+00:20:51,600 --> 00:20:56,750
+المتولد بالأمصر AR commutative ring with unity
+
+193
+00:20:56,750 --> 00:21:01,050
+كميوتاتيف ضرورية زي ما هنشوفه الآن و احنا بنشترك
+
+194
+00:21:01,050 --> 00:21:08,550
+خدي عنصر A موجود في R يبقى ال 6 هذه اللي بنعرفها
+
+195
+00:21:08,550 --> 00:21:16,130
+على انها حاصل ضرب جميع أناصر R كبتة في A بده يطلع
+
+196
+00:21:16,130 --> 00:21:21,550
+عنصر موجود في A موجود في A اللي هو الشكل ان هذا is
+
+197
+00:21:21,550 --> 00:21:26,240
+an ideal of Rالـ ideal هذا هو اللي بيسميه ال
+
+198
+00:21:26,240 --> 00:21:31,240
+principle ideal generated by النقطة الأولى ال
+
+199
+00:21:31,240 --> 00:21:37,380
+principle ideal is non-empty
+
+200
+00:21:37,380 --> 00:21:44,420
+أكيد؟ نقدر نجيب؟ في نفسه بدل ال answer اتنين بس
+
+201
+00:21:44,420 --> 00:21:50,040
+بتاعي مش Zero في R يبقى Zero في A اللي هو بده
+
+202
+00:21:50,040 --> 00:21:55,120
+يساوي Zero موجود في Aصح وها تاني قلت لأ ممكن
+
+203
+00:21:55,120 --> 00:21:59,020
+بيكميوتة ت bring with unity بدل ازي هو دافن الواحد
+
+204
+00:21:59,020 --> 00:22:09,540
+يفجأ is non-empty because ال a بقدر اقول عليها
+
+205
+00:22:09,540 --> 00:22:16,720
+واحد في ايه؟ والواحد موجود في اين؟ موجود في R يعني
+
+206
+00:22:16,720 --> 00:22:24,930
+ال unityيبقى هذا واحد اللي هو موجود في A since
+
+207
+00:22:24,930 --> 00:22:31,290
+الواحد موجود او unity موجود في R يبقى على الأقل
+
+208
+00:22:31,290 --> 00:22:37,730
+إذا من الآن فصاعدا ال element A موجود في ال
+
+209
+00:22:37,730 --> 00:22:43,430
+principle ideal generated by A ال A itself بتكون
+
+210
+00:22:43,430 --> 00:22:48,890
+أحد عناصره تماميبقى هذا حطيه في دماغك مهم جدا، هي
+
+211
+00:22:48,890 --> 00:22:54,370
+النقطة الأولى، النقطة الثانية، بدي أخد عنصريا
+
+212
+00:22:54,370 --> 00:22:59,690
+موجودة في الست اللي عندنا، يبقى لو قل little x و
+
+213
+00:22:59,690 --> 00:23:05,670
+ال y موجودة في الست اللي عندنا، يبقى بدي أعرف قداش
+
+214
+00:23:05,670 --> 00:23:08,450
+أو ما هو شكل ال X
+
+215
+00:23:11,410 --> 00:23:20,370
+يبقى عنصر من R مضروب في A يبقى بقدر اقول R1A وال Y
+
+216
+00:23:20,370 --> 00:23:30,490
+بده ساوي R2A والR1 والR2 عناصر موجودة في ال ring R
+
+217
+00:23:30,490 --> 00:23:42,050
+بدي اخد ال X ناطس ال Yيبقى ال X R1A ناقص R2A طبق
+
+218
+00:23:42,050 --> 00:23:49,370
+ال distributive law بدي أعطيني R1 ناقص R2 في سواد
+
+219
+00:23:49,370 --> 00:23:56,550
+هل هذا موجود في الست اللي عندنا؟ لإن ال R1 موجودة
+
+220
+00:23:56,550 --> 00:24:03,330
+وين؟ في ال R itself يبقى هذا موجود في A because
+
+221
+00:24:05,020 --> 00:24:12,640
+السبب R1 ناقص R2 موجودة في ال ring R يبقى تحقق ال
+
+222
+00:24:12,640 --> 00:24:16,500
+conditioning الثاني بدي أروح لل conditioning
+
+223
+00:24:16,500 --> 00:24:24,200
+التالت بدي أخد عنصر موجود هنا و أي عنصر موجود في R
+
+224
+00:24:24,200 --> 00:24:32,540
+يبقى بدي أقول افترض ان R موجود في R and ال Xاللي
+
+225
+00:24:32,540 --> 00:24:40,960
+هو بده يساوي R 1A موجودة في مين؟ موجودة في الست
+
+226
+00:24:40,960 --> 00:24:46,440
+اللي عندها دي then فده
+
+227
+00:24:46,440 --> 00:24:55,280
+ياخد ال R X بده يشوف عشان تساوي يبقى ال R X عبارة
+
+228
+00:24:55,280 --> 00:25:02,770
+عن R وال X R 1Aخاصية ال associativity الصحيحة على
+
+229
+00:25:02,770 --> 00:25:10,930
+ال things يبقى RR1A يبقى هذا موجود في ال set اللي
+
+230
+00:25:10,930 --> 00:25:17,210
+فوق ولا لا؟ يبقى هذا موجود في ال set اللي عندنا
+
+231
+00:25:17,210 --> 00:25:27,790
+هذه ليش؟ because RR1 موجودة في R لأنه R مغلقة تحت
+
+232
+00:25:27,790 --> 00:25:34,120
+عملية الظبططبعا طيب ضل اتجاه الثاني هنا ضربنا الار
+
+233
+00:25:34,120 --> 00:25:39,860
+من جهتي الشمال بدنا نروح نضرب اين؟ من جهتي اليمين
+
+234
+00:25:39,860 --> 00:25:48,040
+لكن الار commutative يبقى هنا also وكذلك ال XR
+
+235
+00:25:48,040 --> 00:25:58,440
+موجودة في ايه؟ because الار is commutativeيبقى لو
+
+236
+00:25:58,440 --> 00:26:03,340
+شيلنا شرط ال commutative من هنا، من هنا بطلع هذا
+
+237
+00:26:03,340 --> 00:26:07,640
+ring، من هنا بطلع هذا ideal، الإجابة لأ لإن ما
+
+238
+00:26:07,640 --> 00:26:14,360
+نقدرش نحط الجزء الثاني إلا أن thus و هكذا ال
+
+239
+00:26:14,360 --> 00:26:23,660
+principle ideal generated by A is an ideal of A،
+
+240
+00:26:23,660 --> 00:26:26,560
+يبقى هذا ideal في ring A
+
+241
+00:26:31,480 --> 00:26:38,600
+طب هل كل ideal في ال ring اه يكون ال principle؟
+
+242
+00:26:38,600 --> 00:26:45,880
+ليس بالضرورة، ليس بالضرورة كما سنراه من خلال
+
+243
+00:26:45,880 --> 00:26:53,380
+الأمثلة القائمة إن شاء الله.طيب هذا كان المثال رقم
+
+244
+00:26:53,380 --> 00:27:00,180
+3، بدنا نروح للمثال رقم 4، رقم 4
+
+245
+00:27:03,170 --> 00:27:19,690
+the ring z is a sub ring of the cube هو مجموعة
+
+246
+00:27:19,690 --> 00:27:25,230
+الأعداد الصحيحة sub ring من مجموعة الأعداد النسبية
+
+247
+00:27:25,230 --> 00:27:32,000
+السؤال هو هل z هذه idيعني مش كل subring بس هي ال
+
+248
+00:27:32,000 --> 00:27:37,000
+ideal بعضهم بنفع تكون ideal وبعضهم بنفعش تكون
+
+249
+00:27:37,000 --> 00:27:42,180
+ideal طيب هذه ليش؟ يكفينا counterexample واحد
+
+250
+00:27:42,180 --> 00:27:54,320
+تمام؟ يبقى هذه Z subring من Q بقى ولكن Z is not an
+
+251
+00:27:54,320 --> 00:28:04,350
+ideal of Qالسبب because بدنا ناخد element موجود في
+
+252
+00:28:04,350 --> 00:28:14,650
+z خمسة مثلا موجود في z عدد صحيح و طول موجود في ال
+
+253
+00:28:14,650 --> 00:28:23,230
+IQ بط لو كانت ID بدي يكون حاصل ضرب و موجود في z بط
+
+254
+00:28:23,230 --> 00:28:31,700
+خمسة مضروبة في طوليساوي خمسة ع تلاتة ليست عددا
+
+255
+00:28:31,700 --> 00:28:38,440
+صحيحة إذا الـ Z هي عبارة عن sub ring لكنها في
+
+256
+00:28:38,440 --> 00:28:46,580
+الحقيقة ليست ideal في مجموعة الأعداد النسبية نعطي
+
+257
+00:28:46,580 --> 00:28:56,740
+مثال من مواقع آخر الـ R الخامسة بيقول للـ R of X
+
+258
+00:28:58,110 --> 00:29:02,950
+denote the
+
+259
+00:29:02,950 --> 00:29:13,270
+set of all polynomials مجموعة
+
+260
+00:29:13,270 --> 00:29:23,630
+كثيرات الحدود with real coefficients المعاملات
+
+261
+00:29:23,630 --> 00:29:27,450
+كلها أعداد حقيقية
+
+262
+00:29:29,800 --> 00:29:41,240
+و there are coefficients and let ال a be the set
+
+263
+00:29:41,240 --> 00:29:49,880
+of all polynomials كل كثيرات الحدود with constant
+
+264
+00:29:49,880 --> 00:29:56,700
+term zero with constant term
+
+265
+00:29:56,700 --> 00:30:06,070
+zerothen a
+
+266
+00:30:06,070 --> 00:30:20,870
+is an ideal is an ideal of r of x زيادة على ذلك
+
+267
+00:30:20,870 --> 00:30:30,110
+نمر بيه ال a تساويالـ group generated by
+
+268
+00:30:30,110 --> 00:30:35,850
+Geographics هو الـ principle generated by اللي هو
+
+269
+00:30:35,850 --> 00:30:36,950
+Geographics
+
+270
+00:31:03,490 --> 00:31:08,350
+خلّينا نفهم السؤال مرة ثانية قبل ما نبدأ نشتغل قال
+
+271
+00:31:08,350 --> 00:31:14,970
+الاروافكس تمثل مجموعة كثيرات الحدود اللي معاملاتها
+
+272
+00:31:14,970 --> 00:31:21,390
+أعداد حقيقية موجبة، سالبة، كسرية، صفر، بهمنيش، مين
+
+273
+00:31:21,390 --> 00:31:27,490
+المكان يكون خد السد ايه هي كل كثيرات الحدود with
+
+274
+00:31:27,490 --> 00:31:34,060
+constant term zero يعني آخر حد فيها بديكون مينالحد
+
+275
+00:31:34,060 --> 00:31:41,160
+اللي جابله constant في X بس الأولانية constant في
+
+276
+00:31:41,160 --> 00:31:46,280
+X زائد constant زي ما هنشوفه لأ يبقى بدأ نثبت أن
+
+277
+00:31:46,280 --> 00:31:54,320
+هذا عبارة عن ideal يبقى بنات ال R of X من هنا هذه
+
+278
+00:31:54,320 --> 00:32:02,780
+هي كل العناصر F of X بحيث أناالـ f of x بده يساوي
+
+279
+00:32:02,780 --> 00:32:09,120
+a n x to the power n a n minus one x to the power
+
+280
+00:32:09,120 --> 00:32:17,640
+one وضل ماشيين لغاية a one x زائد a naught يبقى a
+
+281
+00:32:17,640 --> 00:32:24,600
+naught هو مقدار ثابت ال a فيها a naught ب zero مش
+
+282
+00:32:24,600 --> 00:32:31,530
+موجوديبقى بدنا نجي لتانية الست اللي أخدناها كل ال
+
+283
+00:32:31,530 --> 00:32:39,430
+polynomial g of x بحيث ان ال g of x يسوى b in x to
+
+284
+00:32:39,430 --> 00:32:44,390
+the power n b in minus ال one x to the power n
+
+285
+00:32:44,390 --> 00:32:52,330
+minus ال one زائد b one x فقط لغير المقدار الثابت
+
+286
+00:32:52,330 --> 00:32:57,570
+بصفر يبقى طار مش موجودبنثبت له ان هذه عبارة عن
+
+287
+00:32:57,570 --> 00:33:05,530
+ايش؟ ideal طيب النقطة الأولى النقطة الأولى هل هذه
+
+288
+00:33:05,530 --> 00:33:13,530
+non-empty على الأقل فيها ال F of Zero كلهم هذول
+
+289
+00:33:13,530 --> 00:33:19,250
+بيقيروا ب Zero يبقى صار ال constant terminal Zero
+
+290
+00:33:19,250 --> 00:33:33,090
+صحيح ولا لا؟ يبقى هنا ال F asممكن because الـG
+
+291
+00:33:33,090 --> 00:33:43,570
+of Zero بدر ساوي Zero وهذا موجود في A هذا النقطة
+
+292
+00:33:43,570 --> 00:33:51,830
+الثانية بدنا ناخد عنصرين موجودين في A ونطرح اتنين
+
+293
+00:33:51,830 --> 00:34:01,190
+من بعضيبقى فاجب اقوله ليه مثلا ال G1 و ال G2
+
+294
+00:34:01,190 --> 00:34:07,710
+موجودات في ايه؟ then بدي اعرف ايه الشكل كل واحد
+
+295
+00:34:07,710 --> 00:34:15,030
+فيهم G1 of X بدي اسميه زي ما احنا مسميه هذه زي ما
+
+296
+00:34:15,030 --> 00:34:27,880
+هي ال B X to the power NBn-1x⁻¹n-1 زائد زائد B1x
+
+297
+00:34:27,880 --> 00:34:41,100
+والـ G2 والـ G2 of X بدل الـ B ممكن أسميه Cnx⁻¹n
+
+298
+00:34:41,100 --> 00:34:48,680
+Cn-1x⁻¹n-1 زائد C1x
+
+299
+00:34:51,110 --> 00:35:00,530
+يبقى بدي أخد g1 ناقص g2 كتأثيره على x هذا الكلام
+
+300
+00:35:00,530 --> 00:35:09,090
+بدي يساوي g1 of x ناقص g2 of x بدي أشوف هل هذا
+
+301
+00:35:09,090 --> 00:35:15,730
+موجود في ايه ولا لأ بمعنى آخر هل آخر term يساوي
+
+302
+00:35:15,730 --> 00:35:21,950
+zero ولا لأ إذا بدنا نطرح كل عنصر من نظيرهيبقى هذا
+
+303
+00:35:21,950 --> 00:35:32,070
+بيصير BN ناقص CN في X to the power N ثالث BN minus
+
+304
+00:35:32,070 --> 00:35:43,790
+ال 1 ناقص CN minus ال 1 CN minus ال 1 كله في X
+
+305
+00:35:43,790 --> 00:35:49,650
+plus N minus ال 1 زايد لغاية ما نوصل لآخر K اللي
+
+306
+00:35:49,650 --> 00:35:56,400
+هو B1نقص c1 كله في x يبقى ال constant term كده اش
+
+307
+00:35:56,400 --> 00:36:02,560
+طالع عندنا ب zero إذا هذه موجودة في ايه ولا لأ إذا
+
+308
+00:36:02,560 --> 00:36:07,040
+هذه موجودة في ايه بدنا نروح الأن لل condition
+
+309
+00:36:07,040 --> 00:36:12,140
+التالت بدنا نضرب اتنين في بعض يبقى بدأي لل
+
+310
+00:36:12,140 --> 00:36:20,080
+condition التالت بدأي أخد عنصر من من ال ring Rوبدي
+
+311
+00:36:20,080 --> 00:36:30,560
+اخد عنصر من A يبقى هنا F ال F موجودة في ال R of X
+
+312
+00:36:30,560 --> 00:36:41,720
+and اللي هو ال G موجودة في A then بدي
+
+313
+00:36:41,720 --> 00:36:50,680
+اخد F G of Xيبقى هذه بدها تساوي ال F of X في ال G
+
+314
+00:36:50,680 --> 00:36:57,500
+of X يساوي يبقى بدنا نيجي نضرب ضرب وين ال F هاي
+
+315
+00:36:57,500 --> 00:37:05,900
+يبقى هذه ال F اللي ناخدتها تمام؟ بدها ضبها في عنصر
+
+316
+00:37:05,900 --> 00:37:12,160
+من هنا اللي هو G term اللي عندنايبقى لو ضربتش بصير
+
+317
+00:37:12,160 --> 00:37:26,440
+a n b n x أوسي 2n يبقى بصير a n b n x أوسي 2n زي
+
+318
+00:37:26,440 --> 00:37:33,440
+.. لما أدرب اللي بعد هذه a n minus ال one في ال b
+
+319
+00:37:33,440 --> 00:37:43,790
+n يبقى aن نقص
+
+320
+00:37:43,790 --> 00:37:51,010
+واحد ونفضل ماشيين لغاية ما نوصل لمين لغاية ما نوصل
+
+321
+00:37:51,010 --> 00:37:58,670
+هذهها بدها تصير مين اخر حاجة في القهر هذه اخر حاجة
+
+322
+00:37:58,670 --> 00:38:11,580
+عند مين a naught يبقى زائداللي هو a نود b in او
+
+323
+00:38:11,580 --> 00:38:18,480
+هنا x to the power n بعد هيك نبقى الماشي لسه
+
+324
+00:38:18,480 --> 00:38:24,880
+مخلصناش لغاية ما نوصل لحاصل ضرب اخر term من هنا في
+
+325
+00:38:24,880 --> 00:38:30,360
+اخر term يبقى من اللي يكون عندنا a نود b one x
+
+326
+00:38:30,360 --> 00:38:41,500
+يبقى زائدA نار B one X في عندي ثابت؟ لأ يبقى هذه
+
+327
+00:38:41,500 --> 00:38:48,220
+بصير كلها موجودة وين؟ موجودة في ال A يبقى تحققت
+
+328
+00:38:48,220 --> 00:38:54,660
+الشروط التلاتة بلا ان علي أصبحت ال A is A صارت A
+
+329
+00:38:54,660 --> 00:39:02,890
+هذا لما ضربنا ضربنا من وين؟ ضربنا لسهاللي هو من ال
+
+330
+00:39:02,890 --> 00:39:12,590
+F في G Similarly يبقى Similarly بنفس الطريقة ال G
+
+331
+00:39:12,590 --> 00:39:20,150
+في ال F as a function of X يساوي ال G of X في ال F
+
+332
+00:39:20,150 --> 00:39:26,950
+of X هذه كمان موجودة في ال A يبقى بناء عليه ضاص
+
+333
+00:39:26,950 --> 00:39:39,760
+وهكذا ال P is anideal of R of X نجي لنمرى B
+
+334
+00:39:39,760 --> 00:39:47,420
+بيقوللي ايش في B؟ بيقوللي ال ideal اللي عندك هذا
+
+335
+00:39:47,420 --> 00:39:57,850
+يمكن ان يولد بعنصر واحد هالي ونمرى B هي IBهو
+
+336
+00:39:57,850 --> 00:40:04,010
+العنصر الذي يولد بهذا العنصر طيب الآن لما نجي يا
+
+337
+00:40:04,010 --> 00:40:13,890
+بنات نقول بدي أجي أاخد ال Z F من وين من R و أجي
+
+338
+00:40:13,890 --> 00:40:24,910
+أاخد F of X في ال G of X بحيث ال F موجودة في R of
+
+339
+00:40:24,910 --> 00:40:33,130
+X andالـ G موجودة في إيه؟
+
+340
+00:40:33,130 --> 00:40:39,630
+هذا الكلام بالشكل اللي عندنا هذا مش هو الخاصية
+
+341
+00:40:39,630 --> 00:40:46,030
+اللي فوق هذه؟ وين طلعت؟ موجودة في إيه؟ طيب حسب
+
+342
+00:40:46,030 --> 00:40:51,550
+تعريف ال principle ideal generated by GeoVix مش هي
+
+343
+00:40:51,550 --> 00:40:58,400
+هذه؟ صح ولا لأ؟ يبقى هذه هنااللي هي ال principle
+
+344
+00:40:58,400 --> 00:41:06,940
+id generated by gx هذا الكلام جيبناه من وين from
+
+345
+00:41:06,940 --> 00:41:17,480
+part اللي هو triple I of A
+
+346
+00:41:17,480 --> 00:41:23,860
+يبقى هذا من المطلوب الأول النقطة التالتة فيه يبقى
+
+347
+00:41:23,860 --> 00:41:30,880
+صار هذاهو الذي يولد بهذا العمصر يبقى صارة الـG of
+
+348
+00:41:30,880 --> 00:41:36,300
+X هذه هو ال principle ideal generated by A يبقى كل
+
+349
+00:41:36,300 --> 00:41:42,460
+ال polynomials اللي آخرتين فيهم مقدارا ثابتا
+
+350
+00:41:42,460 --> 00:41:48,260
+بكونون صبرا وبالتالي ideal بسميه ال principle
+
+351
+00:41:48,260 --> 00:41:54,820
+ideal generated by واحدة منهماللي هي مثلا الـ G of
+
+352
+00:41:54,820 --> 00:42:00,380
+X اللي الحد فيها يساوي مين؟ يساوي K نص طن هنا،
+
+353
+00:42:00,380 --> 00:42:09,080
+تمام؟ طيب، إلى هنا يكفينا اليوم و لسه لا يزال
+
+354
+00:42:09,080 --> 00:42:14,680
+قدامنا مزيد من الأمثلة للمرة الحاضرة
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..007720a7f60e704870f597e14419dbb54e1f7b95
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/UBzK3MMvOtQ_raw.srt
@@ -0,0 +1,1528 @@
+1
+00:00:20,990 --> 00:00:25,430
+بسم الله الرحمن الرحيم نكمل اليوم ما ابتدأناه في
+
+2
+00:00:25,430 --> 00:00:29,970
+المرة الماضية وهو موضوع ال ring homomorphism اللي
+
+3
+00:00:29,970 --> 00:00:36,790
+هو chapter 15 من الكتاب فينا نظرية اليوم، النظرية
+
+4
+00:00:36,790 --> 00:00:41,070
+بتقول افترض ان Phi من R الى S عبارة عن ring
+
+5
+00:00:41,070 --> 00:00:47,010
+homomorphism نحاول نثبت ان ال kernel لهذا ال
+
+6
+00:00:47,010 --> 00:00:50,430
+homomorphism هو عبارة عن ideal
+
+7
+00:00:53,080 --> 00:00:58,600
+البرهان كالتالي بان نروح نثبت ال three conditions
+
+8
+00:00:58,600 --> 00:01:06,020
+تبعات ال I دى فبدالي ال condition الأول وهو ان
+
+9
+00:01:06,020 --> 00:01:14,220
+الكرن اللى الفاى is non-empty ما هو السبب لذلك
+
+10
+00:01:14,220 --> 00:01:24,440
+because الفاىof zero بده يساوي zero هذا يعني ان ال
+
+11
+00:01:24,440 --> 00:01:32,520
+zero موجود في كيرنل الفارق و لذلك الكيرنل
+
+12
+00:01:32,520 --> 00:01:38,940
+هذا is non-empty النقطة الثانية بدي اخد عنصرين
+
+13
+00:01:38,940 --> 00:01:43,960
+موجودات في الكيرنل يبقى بدي اقول له افترض ان اقار
+
+14
+00:01:43,960 --> 00:01:51,030
+واحد و اقار اتنينموجودات الكيرنل للـ Phi اذا ايش
+
+15
+00:01:51,030 --> 00:01:57,510
+بدنا نثبت؟ بدنا نثبت ان الفرق بينهما موجود في
+
+16
+00:01:57,510 --> 00:02:05,290
+الكيرنل طيب R1 موجود في الكيرنل ماذا يعني هذا؟ هذا
+
+17
+00:02:05,290 --> 00:02:12,410
+يعني ان Phi of R1 بدي سوى ال zero element اللي هو
+
+18
+00:02:12,410 --> 00:02:23,010
+تبع من؟ تبع ال Sو and ال 5 of R2 بدي سوى 0 كذلك
+
+19
+00:02:23,010 --> 00:02:30,770
+تبع ال S طيب الان لو روحنا و طرحناهم من بعض طرحنا
+
+20
+00:02:30,770 --> 00:02:37,770
+ال اتنين من بعض في اي واحد فبدي بقوله ال 5 of R1
+
+21
+00:02:37,770 --> 00:02:44,080
+ناقص 5 of R2بديوا يساوي Zero ناقص Zero بديوا يساوي
+
+22
+00:02:44,080 --> 00:02:50,040
+كده؟ Zero هذا بديوا يعطينا قاللي في راسي المسألة
+
+23
+00:02:50,040 --> 00:02:55,280
+Phi عبارة عن homomorphism قال خاصية الأولى من خواص
+
+24
+00:02:55,280 --> 00:03:02,940
+ال homomorphism ان Phi of R1 ناقص R2 كله بديوا
+
+25
+00:03:02,940 --> 00:03:07,740
+يساوي مين؟ بديوا يساوي Zero هذا معناه ايه؟ ان ال
+
+26
+00:03:07,740 --> 00:03:15,170
+R1-R2 موجود في الكيرن اللى فاعد ان صورته تسوى الـ
+
+27
+00:03:15,170 --> 00:03:23,170
+zero element تبع الاسم يبقى هذا معناه ان R1-R2 كله
+
+28
+00:03:23,170 --> 00:03:29,590
+موجود في الكيرن اللى الفاعد إذا أثبتنا النقطة
+
+29
+00:03:29,590 --> 00:03:30,370
+الثانية
+
+30
+00:03:33,700 --> 00:03:40,320
+النقطة الثالثة والاخيرة اللى بدنا نثبت فيها ان ال
+
+31
+00:03:40,320 --> 00:03:46,940
+kernel هو عبارة عن ID يبقى بدنا ناخد element من ال
+
+32
+00:03:46,940 --> 00:03:52,180
+set اللى عندنا و element من ال ring الأصلية ونثبت
+
+33
+00:03:52,180 --> 00:03:57,850
+ان حاصر ضربه ما موجود في ال kernel اوفاي لحاصل
+
+34
+00:03:57,850 --> 00:04:03,410
+ضرفيها مابتساوة كده Zero ان حدث ذلك يبقى بقوله في
+
+35
+00:04:03,410 --> 00:04:08,670
+هذه الحالة ان ال set اللي عندها هذه او ال kernel
+
+36
+00:04:08,670 --> 00:04:17,830
+صار عبارة عن id يبقى بجي بقوله if ال R موجودة في R
+
+37
+00:04:17,830 --> 00:04:29,110
+and ناخد element في ال kernel and مثلاالـ X موجود
+
+38
+00:04:29,110 --> 00:04:40,050
+في كيرن الـ Phi الـ Phi of R وين بدها تكون موجودة؟
+
+39
+00:04:40,050 --> 00:04:51,050
+في S يبقى then ال Phi of R موجودة في S and ال Phi
+
+40
+00:04:51,050 --> 00:05:00,010
+of X بدها تسوي قداش Zeroبنروح أخد Phi of R في X
+
+41
+00:05:00,010 --> 00:05:06,090
+نظرا لإن ال Phi عبارة عن homomorphism إذا الهدف
+
+42
+00:05:06,090 --> 00:05:12,670
+بده يساوي Phi of R في Phi of X Phi of X عندي
+
+43
+00:05:12,670 --> 00:05:19,010
+بقداشر هشيلها و أحط مكانها Zero يبقى بده يساوي Phi
+
+44
+00:05:19,010 --> 00:05:25,240
+of R is Zero اللي هو بده يساوي قداشر؟ Zeroإذا صار
+
+45
+00:05:25,240 --> 00:05:30,380
+تأثير Phi على ال element Rx بده يساوي Zero معناه
+
+46
+00:05:30,380 --> 00:05:36,900
+هذا الكلام ان ال Rx موجودة وين؟ في ال Kern اللي
+
+47
+00:05:36,900 --> 00:05:44,520
+فيه بنفس الطريقة Similarly بنفس الطريقة اللي هو ال
+
+48
+00:05:44,520 --> 00:05:50,000
+XR موجودة في ال Kern اللي مين؟ في ال Phi يبقى
+
+49
+00:05:50,000 --> 00:05:56,570
+أثبتنا شروط ال Ideal وخلصنايبقى بقول الله صحيح
+
+50
+00:05:56,570 --> 00:06:08,570
+وهكذا الـ Kernel للـ Phi is an ideal of R وهو
+
+51
+00:06:08,570 --> 00:06:16,430
+المفروض بنجي الآن للنظرية التي تليها وهذه نظرية
+
+52
+00:06:16,430 --> 00:06:21,330
+مهمة ومشهورة في كل كتب الجبر اللي بيسموها ال first
+
+53
+00:06:21,330 --> 00:06:26,490
+isomorphismأو الـ Fundamental Theorem of Ring
+
+54
+00:06:26,490 --> 00:06:34,070
+Homomorphism يبقى الـ Theorem بنسميها
+
+55
+00:06:34,070 --> 00:06:40,150
+الـ First Isomorphism
+
+56
+00:06:40,150 --> 00:06:49,750
+Theorem أو بنسميها الـ Fundamental Theorem
+
+57
+00:06:49,750 --> 00:06:51,910
+of
+
+58
+00:06:52,880 --> 00:06:57,040
+bearing homomorphism
+
+59
+00:06:57,040 --> 00:07:00,640
+الان
+
+60
+00:07:00,640 --> 00:07:07,760
+بدنا نجلع نص النظرية ومن ثم نقوم ببرهانها نص
+
+61
+00:07:07,760 --> 00:07:17,100
+النظرية بيقول my little five من a الى s bearing
+
+62
+00:07:17,100 --> 00:07:18,640
+homomorphism
+
+63
+00:07:23,120 --> 00:07:31,820
+Homomorphism then the mapping then the mapping
+
+64
+00:07:31,820 --> 00:07:41,400
+الدلة او ال function F psi من ال R موديول الكيرن
+
+65
+00:07:41,400 --> 00:07:55,350
+للفاي إلى فاي of capital R defined bydefined by
+
+66
+00:07:55,350 --> 00:08:05,790
+والمعرفة بيه شكل التالي Psi of R زي الكون للـ Phi
+
+67
+00:08:05,790 --> 00:08:14,150
+بتساوي Phi of R لكل الـ R اللي موجودة في capital R
+
+68
+00:08:14,150 --> 00:08:20,650
+is an isomorphism is an isomorphism
+
+69
+00:08:21,410 --> 00:08:31,230
+that is بطريقة مختصرة that is اللي هو ال R modulo
+
+70
+00:08:31,230 --> 00:08:48,710
+الكيرني لل FI isomorphic لمين لل FI of R نرجع
+
+71
+00:08:48,710 --> 00:08:54,670
+لنص النظرية مرة ثانيةحاول نفهم شو الشغل اللى بدنا
+
+72
+00:08:54,670 --> 00:09:00,890
+نشتغله حتى نشتغل شغل صحيح قال لي فاي من R إلى S
+
+73
+00:09:00,890 --> 00:09:07,390
+همومورفيزيوم ماشي بعدين قال لي أعرف دالة إبساعد من
+
+74
+00:09:07,390 --> 00:09:13,470
+ال factor ring ال R modular kernel لفاي لفاي of R
+
+75
+00:09:13,470 --> 00:09:21,310
+يعني لمين اللي بناد؟ لل range تبع من؟ تبع الفاي
+
+76
+00:09:21,620 --> 00:09:26,480
+الرينج تبع الفاي هذا موجود وين؟ في ارس تمام يعني
+
+77
+00:09:26,480 --> 00:09:32,300
+مش الارس كله وإنما لمن؟ للرينج تبع الفاي الفاي of
+
+78
+00:09:32,300 --> 00:09:39,900
+R العرفه كالتاني ابصيه R زائد الكيرن للفاي بده سوى
+
+79
+00:09:39,900 --> 00:09:46,620
+فاي of R اللي موجودة في فاي of R كبتة يبقى R زائد
+
+80
+00:09:46,620 --> 00:09:51,940
+الكيرن لفوهاElement موجود في ال factor ring R
+
+81
+00:09:51,940 --> 00:09:58,020
+modulo curly فما Phi of R هو Element موجود في Phi
+
+82
+00:09:58,020 --> 00:10:03,400
+of R لكل الـR اللي موجودة فيها مش بدنا نثبت بدنا
+
+83
+00:10:03,400 --> 00:10:09,740
+نثبت ان Phi عبارة عن isomorphism يبقى بدنا نثبت
+
+84
+00:10:09,740 --> 00:10:17,960
+homomorphism one to one و one to و خلاص لأ ما خلصش
+
+85
+00:10:18,260 --> 00:10:23,240
+هذه الـ left cosets يجب أن تثبت أيضًا إن هذه الـ
+
+86
+00:10:23,240 --> 00:10:28,740
+function is well-defined معظفة تعريفًا صحيحة يبقى
+
+87
+00:10:28,740 --> 00:10:32,780
+هذه الخطوة الأولى اللى بنبدأ فيها وبعدين بنروح
+
+88
+00:10:32,780 --> 00:10:37,920
+لمين؟ لـ isomorphism يبقى الخطوة الأولى اللى بدى
+
+89
+00:10:37,920 --> 00:10:42,840
+أثبتله إن Psi is well-defined
+
+90
+00:10:45,910 --> 00:10:51,590
+كيف عرفنا كيف علمنا كتثبت هذا well defined؟ بنقول
+
+91
+00:10:51,590 --> 00:10:57,090
+عكس اثبات انه لبساي one to one يعني انا باخد
+
+92
+00:10:57,090 --> 00:11:05,230
+عنصرين متساويين و باثبت ان صورتيهما متساويتان،
+
+93
+00:11:05,230 --> 00:11:11,410
+مظبوط هيك؟ يبقى بلاء العلم دي اقوله let افترض ان
+
+94
+00:11:11,410 --> 00:11:24,780
+اه الواحد زي ال kernel للفعلبدي أثبت
+
+95
+00:11:24,780 --> 00:11:29,960
+أن صورة العنصر الأول هي نفس صورة العنصر الثاني
+
+96
+00:11:29,960 --> 00:11:38,260
+يبقى then هذه بدي أحاول أكتبها بطريقة أخرى لو جينا
+
+97
+00:11:38,260 --> 00:11:44,120
+قلنا R واحد ناقص R اتنين زائد ال kernel للـ Phi
+
+98
+00:11:44,360 --> 00:11:50,000
+يبقى على الشجة اليمين اللي هو main الكيرنل الفائض
+
+99
+00:11:50,000 --> 00:11:57,420
+ما تفسيرك لهذه الجملة أرواح ناقص R2 موجودة في
+
+100
+00:11:57,420 --> 00:12:04,160
+الكيرنل يبقى هذا بده يعطينا أن أرواح ناقص R2
+
+101
+00:12:04,160 --> 00:12:12,180
+موجودة في الكيرنل الفائض موجودة في الكيرنل الفائض
+
+102
+00:12:13,150 --> 00:12:18,970
+مدام موجودة في الكيرنال يبقى صورتها Zero يبقى هذا
+
+103
+00:12:18,970 --> 00:12:27,230
+معناه ان Phi of R1 minus R2 بيساوي مين؟ ال Zero
+
+104
+00:12:27,230 --> 00:12:33,310
+تبع Phi of R تمام؟ طيب كويس، ايش قال في رأس
+
+105
+00:12:33,310 --> 00:12:38,770
+المسألة؟ Phi معنو؟ مدام Phi هومومورفزين، اذا بقدر
+
+106
+00:12:38,770 --> 00:12:45,450
+اجلز اهدي او افكهايبقى هذا معناه ان فاي of R1
+
+107
+00:12:45,450 --> 00:12:53,090
+minus فاي of R2 بده يسوي Zero او هذا معناه ان فاي
+
+108
+00:12:53,090 --> 00:13:02,430
+of R1 بده يسوي فاي of R2 لكن لو رجعنا للتعريف فاي
+
+109
+00:13:02,430 --> 00:13:11,150
+of R1 هو XI لل R1 زي الكيرنيت صح؟ من التعريفيبقى
+
+110
+00:13:11,150 --> 00:13:17,810
+هذا بده يعطينا مين؟ ان إبسايد of R1 زائد الكرن
+
+111
+00:13:17,810 --> 00:13:25,990
+للفاية بده يساوي L إبسايد of R2 زائد الكرن للفاية
+
+112
+00:13:25,990 --> 00:13:32,170
+هذا ما جيبناهوش عشوائيا ولكن from the definition
+
+113
+00:13:32,170 --> 00:13:38,340
+من التعريف جيبناه أيوة يبقى شو اللي حصل؟أخدت
+
+114
+00:13:38,340 --> 00:13:46,000
+عنصرين متساويين أثبت أن صورتيهم متساويتان زي ما
+
+115
+00:13:46,000 --> 00:13:51,620
+انتوا شايفين طيب يبقى أثبتنا ال will define بدنا
+
+116
+00:13:51,620 --> 00:13:58,040
+نيجي الإبصاي is homomorphism يبقى الإبصاي is a
+
+117
+00:13:58,040 --> 00:14:04,620
+homomorphism white يبقى بدأ أخد تأثير إبصاي على
+
+118
+00:14:04,620 --> 00:14:12,550
+مجموع عنصرين ثمعلى حصل ضربهما يبقى بتاخد إبساي of
+
+119
+00:14:12,550 --> 00:14:20,510
+العنصر الأول من ال factoring هو R1 زائد الكيرنل
+
+120
+00:14:20,510 --> 00:14:29,610
+للفاي زائد العنصر الثاني اللي هو R2 زائد الكيرنل
+
+121
+00:14:29,610 --> 00:14:38,220
+للفاي بتاخد تأثير الإبساي عليهمهك بقدرش اخل اللي
+
+122
+00:14:38,220 --> 00:14:47,240
+بقى يتأثر عليهم إلا بعد أن أجعلهم عنصرا واحدا يبقى
+
+123
+00:14:47,240 --> 00:14:56,140
+هذا و هذا معناته R1 زائد R2 زائد الكيرن للفار
+
+124
+00:14:56,140 --> 00:14:59,500
+تمام؟
+
+125
+00:14:59,500 --> 00:15:04,200
+يبقى صار هذا اللي كان مجموع عنصرين صار عنصرا واحدة
+
+126
+00:15:05,120 --> 00:15:10,060
+التعريف بيقول إذا Psi of R زي الكرنل بيكون Psi of
+
+127
+00:15:10,060 --> 00:15:12,580
+R زي الكرنل Psi of R زي الكرنل Psi of R زي الكرنل
+
+128
+00:15:12,580 --> 00:15:15,180
+Psi of R زي الكرنل Psi of R زي الكرنل Psi of R زي
+
+129
+00:15:15,180 --> 00:15:19,520
+الكرنل Psi of R زي الكرنل Psi of R زي الكرنل Psi
+
+130
+00:15:19,520 --> 00:15:19,900
+of R زي الكرنل Psi of R زي الكرنل Psi of R زي
+
+131
+00:15:19,900 --> 00:15:19,900
+الكرنل Psi of R زي الكرنل Psi of R زي الكرنل Psi
+
+132
+00:15:19,900 --> 00:15:19,900
+of R زي الكرنل Psi of R زي الكرنل Psi of R زي
+
+133
+00:15:19,900 --> 00:15:19,900
+الكرنل Psi of R زي الكرنل Psi of R زي الكرنل Psi
+
+134
+00:15:19,900 --> 00:15:24,600
+of R زي الكرنل Psi of R زي الكرنل P
+
+135
+00:15:33,570 --> 00:15:43,070
+بدي اساوي منه اللي هو Phi of R1 زائد Phi of R2 ليش
+
+136
+00:15:43,070 --> 00:15:48,990
+كتبت الخطوة هذه لأن Phi عبارة عن homomorphism بدي
+
+137
+00:15:48,990 --> 00:15:56,090
+أرجع للتعريف ثماني Phi of R1 هي Minimum of Phi of
+
+138
+00:15:56,090 --> 00:16:04,230
+R1 زائد الكيرنات يبقى هذه تساوي Phi of R1زائد
+
+139
+00:16:04,230 --> 00:16:13,090
+الكيرن للـ Phi زائد إبسايد of R2 زائد الكيرن للـ
+
+140
+00:16:13,090 --> 00:16:18,250
+Phi يبقى تحققت الخطوة الأولى من الخطوات
+
+141
+00:16:18,250 --> 00:16:25,370
+الهمومورفزية بدأ أروح للخطوة الثانية and Phi بدل
+
+142
+00:16:25,370 --> 00:16:32,750
+المجموع بدي أخد حاصل الضرب يبقى R1زايد الكيرنل
+
+143
+00:16:32,750 --> 00:16:43,210
+للفاي بدي اضربه في R2 زايد الكيرنل للفاي هذا طبعا
+
+144
+00:16:43,210 --> 00:16:52,770
+إبساي إبساي ونجد فاي إبساي او تمام يبقى هذا الكلام
+
+145
+00:16:52,770 --> 00:17:02,870
+بدي يسوي إبساي او نضرب هدول يبقى R1 R2زائد الكيرن
+
+146
+00:17:02,870 --> 00:17:10,270
+للـ Phi الان R1 R2 عنصر موجود وين؟ في R يبقى على
+
+147
+00:17:10,270 --> 00:17:18,210
+طول الخاط هذا بقدر أقول هو مين Phi of R1 R2 يبقى
+
+148
+00:17:18,210 --> 00:17:26,890
+هذا بده يسوي Phi of R1 R2 فهي تمام Phi قاللي في
+
+149
+00:17:26,890 --> 00:17:32,490
+راسي المسألة homomorphismإذا هذا بده يساوي Phi of
+
+150
+00:17:32,490 --> 00:17:41,890
+R1 في Phi of R2 هذا بده يساوي مين؟ بده يساوي Epsi
+
+151
+00:17:41,890 --> 00:17:51,430
+of R1 زائد الكيرنل للـ Phi مضغوبا في Epsi of R2
+
+152
+00:17:51,430 --> 00:17:59,270
+زائد الكيرنل للـ Phi يبقى تحقق الشرطانالخاصان بالـ
+
+153
+00:17:59,270 --> 00:18:05,470
+Homomorphism إذا أصبح إبساي is a homomorphism باين
+
+154
+00:18:05,470 --> 00:18:12,470
+علينا إيش؟ شغلتين نثبت إن الإبساي هذه is one to
+
+155
+00:18:12,470 --> 00:18:19,310
+one and undo إن تملنا ذلك بقول يبقى هذه عبارة عن
+
+156
+00:18:19,310 --> 00:18:26,030
+إيش؟ عبارة عن إيش؟ Isomorphism تمامإذا بدنا نيجي
+
+157
+00:18:26,030 --> 00:18:34,490
+نثبت ان Psi is one to one يبقى بداخل صورتين
+
+158
+00:18:34,490 --> 00:18:42,430
+متساويتين و أثبت أن أصلهما متساوين فبعدين بقول ا
+
+159
+00:18:42,430 --> 00:18:50,170
+assume افترض ان في عندنا صورتين متساويتين يعني Psi
+
+160
+00:18:50,170 --> 00:18:58,980
+of R1 زائد الكيرنل للـPhiبتساوي F Psi of R2 زائد
+
+161
+00:18:58,980 --> 00:19:07,480
+الكيرن للـ Phi ثم هذه
+
+162
+00:19:07,480 --> 00:19:15,800
+مين صورتها؟ Phi of R1 والتانية صورتها مين؟ Phi of
+
+163
+00:19:15,800 --> 00:19:28,710
+R1 بتساوي Phi of R2هذا معناه إن الـ Phi of R1
+
+164
+00:19:28,710 --> 00:19:35,590
+minus الـ Phi of R2 بديوا يسووا Zero. نرجع، في رأس
+
+165
+00:19:35,590 --> 00:19:41,410
+المسألة Phi هم مورفزيه، إذا هذا بده يعطينا ميم، إن
+
+166
+00:19:41,410 --> 00:19:46,550
+الـ Phi of R1 ناقص R2 بديوا يسووا 200.
+
+167
+00:19:50,830 --> 00:19:57,950
+موجودة في ال kernel يبقى هذا معناه ان ال R1 minus
+
+168
+00:19:57,950 --> 00:20:07,010
+R2 موجودة في ال kernel الفاية او معناه ان ال R1
+
+169
+00:20:07,010 --> 00:20:11,770
+ناقص R2 زائد ال kernel
+
+170
+00:20:18,030 --> 00:20:27,510
+أو بمعنى أخر ار واحد زائد الكيرنل للفاي بده يساوي
+
+171
+00:20:27,510 --> 00:20:37,650
+R اتنين زائد الكيرنل للفاي، مصبوط هم؟ 7.1؟ خلاص؟
+
+172
+00:20:37,650 --> 00:20:45,320
+يبقى أنا أخد صورتين متساويتينأثبت أن أصليهما
+
+173
+00:20:45,320 --> 00:20:52,640
+متساوين R1 زايد كيرنل للـ Phi يساوي R2 زايد كيرنل
+
+174
+00:20:52,640 --> 00:21:03,020
+للـ Phi بقيت النقطة الأخيرة if Psi is onto R تبقى
+
+175
+00:21:03,020 --> 00:21:09,180
+بدى أروح أخد element في الـ Phi of Rإذا قدرت أن
+
+176
+00:21:09,180 --> 00:21:15,020
+أجيله أصل في ال factor A، يكون خلاصنا، يبقى بناءً
+
+177
+00:21:15,020 --> 00:21:22,640
+عليه. بدأ اقول له افترض ان ال X موجودة في ال Phi
+
+178
+00:21:22,640 --> 00:21:32,360
+of R. يبقى موجودة في ال Phi of R. لأن بدي أعرف أيش
+
+179
+00:21:32,360 --> 00:21:40,190
+شكلها ال X هذه.يبقى ال X بدأ يساوي في of R one
+
+180
+00:21:40,190 --> 00:21:48,070
+مثلا تمام four والله خليا في of R دوري في of R
+
+181
+00:21:48,070 --> 00:21:57,190
+four some R اللي موجودة في R يبقى عنصر شكله بدأ
+
+182
+00:21:57,190 --> 00:22:04,520
+يكون على شكل في of Rيبقى الـ X سواء فيه of R بتدري
+
+183
+00:22:04,520 --> 00:22:10,540
+على التعريف مين هي الـ Fi of R؟ إب ساي of R زي ال
+
+184
+00:22:10,540 --> 00:22:17,840
+kernel يبقى هذه بدها تساوي إب ساي لل R زي ال
+
+185
+00:22:17,840 --> 00:22:26,000
+kernel لل Fi يبقى أي element في ال Fi of R لاجتله
+
+186
+00:22:26,000 --> 00:22:32,620
+أصل في ال R موديل الكرنلمظبوط ولا لا يبقى Phi is
+
+187
+00:22:32,620 --> 00:22:39,760
+unto خلص كل ما يلزم يبقى Phi إبساى إيش صارت؟ أزو
+
+188
+00:22:39,760 --> 00:22:49,140
+مورفزي يبقى بص وهكذا الإبساى من ال ring اللي عندنا
+
+189
+00:22:49,140 --> 00:22:56,970
+هذه اللي قلناها ال R موديول الكيرن لل Phi إلىاللي
+
+190
+00:22:56,970 --> 00:23:08,150
+هو five of arcs and isomorphism وهو المفلوض هذه
+
+191
+00:23:08,150 --> 00:23:13,490
+النظرية بتلعب دور كبير في شغلنا في الجبر خلال
+
+192
+00:23:13,490 --> 00:23:21,550
+تدريسنا لمادة الجبر الحديد وهذه لا يكاد يحلو منها
+
+193
+00:23:21,550 --> 00:23:29,820
+أي كتاب جبر بتحدث عناللي هو ال rings نجي للنظرية
+
+194
+00:23:29,820 --> 00:23:43,120
+اللتي تاليها بتقول ما يأتي every ideals
+
+195
+00:23:43,120 --> 00:23:54,860
+of the ring are is the kernel is the kernel
+
+196
+00:23:56,750 --> 00:24:01,450
+of a ring
+
+197
+00:24:01,450 --> 00:24:06,550
+homomorphism
+
+198
+00:24:06,550 --> 00:24:20,410
+of a ring are itself in particular an ideal
+
+199
+00:24:20,410 --> 00:24:21,130
+I
+
+200
+00:24:28,070 --> 00:24:33,790
+الآن قاعدين A
+
+201
+00:24:33,790 --> 00:24:45,430
+is the kernel of the
+
+202
+00:24:45,430 --> 00:24:46,210
+mapping.
+
+203
+00:24:49,990 --> 00:25:02,110
+the mapping Phi من R إلى Rmodulo a given by given
+
+204
+00:25:02,110 --> 00:25:15,990
+by phi of r تساوي ال R زائد ال a اللحية
+
+205
+00:25:15,990 --> 00:25:17,650
+هذه حد بده منها شيء
+
+206
+00:25:49,460 --> 00:25:55,180
+نرجع لنص النظرية مرة ثانية يقول أي ايديل في ال
+
+207
+00:25:55,180 --> 00:26:03,020
+ring R هو يمثل كيرنل ل ring homomorphism على R مين
+
+208
+00:26:03,020 --> 00:26:08,620
+ما يكون هذا ال homomorphism له كيرنل الكيرنل هو
+
+209
+00:26:08,620 --> 00:26:13,900
+احد ال ideals اللي موجودة في ال ring R بدي اوضح
+
+210
+00:26:13,900 --> 00:26:19,700
+هذا الكلام فرح اقولك ال ideal ايههو الـ Kernel
+
+211
+00:26:19,700 --> 00:26:25,800
+لمن؟ لل homomorphism هذا تمام؟ لل homomorphism هذا
+
+212
+00:26:25,800 --> 00:26:31,480
+او للدالة هذه given by five of R يساوي R زي ليه؟
+
+213
+00:26:31,480 --> 00:26:38,320
+ماجليش homomorphism قللي مافيه ماعليش مقلوبة او
+
+214
+00:26:38,320 --> 00:26:42,660
+الخطوة الأولى بتثبتى انه homomorphism من البداية
+
+215
+00:26:42,660 --> 00:26:53,060
+ثم بعد ذلك نثبتان الكيرنل هذا هو ايش المعرف بهذه
+
+216
+00:26:53,060 --> 00:26:59,880
+الطريقة هو عبارة عن الكيرنل تبع هذه الـ Phi مرة
+
+217
+00:26:59,880 --> 00:27:07,360
+تانية ال ideal A اللي أخده من ال ring R هو يمثل
+
+218
+00:27:07,360 --> 00:27:12,520
+الكيرنل لهذه ال function يبقى أنا بدي أعمل قطوة
+
+219
+00:27:12,520 --> 00:27:16,470
+تانيةالخطوة الأولى بدي أثبت انه Phi homomorphism
+
+220
+00:27:16,470 --> 00:27:22,630
+المعطى اثنين بدي أثبت ان الكيرن لهذه ال Phi هو ال
+
+221
+00:27:22,630 --> 00:27:28,890
+ideal A إذا تم ذلك من خلاص برهنة نظرية والحمد لله
+
+222
+00:27:28,890 --> 00:27:33,150
+يبقى هنا ال proof بدي أمشي بالشكل التام
+
+223
+00:27:38,100 --> 00:27:47,300
+بنثبت إن الـ Phi is a homomorphic لذلك بنروح ناخد
+
+224
+00:27:47,300 --> 00:27:55,200
+عنصرين في R فبده أجي أقول له افترض عندي R واحد وR
+
+225
+00:27:55,200 --> 00:28:04,960
+اتنين موجودة في أرضان بدي أخد Phi of R واحد زائد R
+
+226
+00:28:04,960 --> 00:28:11,040
+اتنينهذا الكلام يسوي حسب ال definition اللي عندك
+
+227
+00:28:11,040 --> 00:28:20,780
+يسوي R1 زائد R2 زائد ال ideal A يبقى R1 زائد R2
+
+228
+00:28:20,780 --> 00:28:26,540
+زائد ال ideal A اللي بقدر اكتبه على الشكل التالي
+
+229
+00:28:26,540 --> 00:28:36,270
+R1 زائد ال ideal A زائد ال R2 زائد ال ideal Aهذه
+
+230
+00:28:36,270 --> 00:28:44,410
+من ايه يا عزيزي؟ FI of R1 يبقى هذه FI of R1 plus
+
+231
+00:28:44,410 --> 00:28:59,050
+FI of R2 and تاخد FI of R1 مضروبة في R2 يبقى R1 R2
+
+232
+00:28:59,050 --> 00:29:06,560
+زائد ال A اللي بقدر اكتبه على صيغة حاصل ضربالـ two
+
+233
+00:29:06,560 --> 00:29:14,520
+elements R1 plus A في R2 plus A يعني اللي هو mean
+
+234
+00:29:14,520 --> 00:29:28,640
+Phi of R1 في Phi of R2 so Phi is a homomorphism
+
+235
+00:29:28,640 --> 00:29:34,630
+الجدال اللي أعطاه هالي هذا ال mapping أثبت لهإنه
+
+236
+00:29:34,630 --> 00:29:40,670
+هي homomorphism وهي المعرفة بهذا الشكل.بدي أثبت إن
+
+237
+00:29:40,670 --> 00:29:49,930
+كيرن لـ Phi هو مين هو الـ ideal إيه؟ يبقى باجي
+
+238
+00:29:49,930 --> 00:29:55,870
+بقوله finally I want to prove that
+
+239
+00:30:00,540 --> 00:30:07,800
+إن الكيرن للـ Phi هو الـ ID لإيه طبعا اتعلمنا في
+
+240
+00:30:07,800 --> 00:30:12,800
+ال principle of mathematics two sets are equal إذا
+
+241
+00:30:12,800 --> 00:30:16,800
+كانت الأولى subset من الثانية والثانية subset من
+
+242
+00:30:16,800 --> 00:30:23,040
+الأولى لذلك بدأ نستخدم نفس الفكرة هذه إذا لو جيت
+
+243
+00:30:23,040 --> 00:30:30,550
+قلت لك خدي لي X موجود في كيرن للـ Phiإذا قدرت أثبت
+
+244
+00:30:30,550 --> 00:30:35,850
+إن الـ X موجودة في الـ A بيكون تم المطلوب يبقى
+
+245
+00:30:35,850 --> 00:30:43,750
+then كداش ال 5 of X و أنا؟ سفر يسوى كداش؟ يسوى
+
+246
+00:30:43,750 --> 00:30:50,850
+Zero طيب، احنا عندنا ال function من وين؟ من هذه ل
+
+247
+00:30:50,850 --> 00:30:58,960
+.. من R إلى R modulo A، من ال Zero هنا؟الـ L Zero
+
+248
+00:30:58,960 --> 00:31:06,160
+زائد الـ L والـ A الصلفة يبقى هذا Zero زائد الـ L
+
+249
+00:31:06,160 --> 00:31:15,320
+والـ A الصلفة لكن حسب التعريف but from the
+
+250
+00:31:15,320 --> 00:31:26,300
+definition of Phi we have ان Phi of Xبدو يساوي ال
+
+251
+00:31:26,300 --> 00:31:33,460
+X زائد ال A تعريف مظبوط؟ طيب من الاتنين هدول مع
+
+252
+00:31:33,460 --> 00:31:40,160
+بعض ف I of X يساوي ايه؟ ف I of X يساوي X زائد ال A
+
+253
+00:31:40,160 --> 00:31:47,600
+يبقى بصير عندنا ال X زائد ال A يساوي كده؟ ال A ايش
+
+254
+00:31:47,600 --> 00:31:54,030
+معنى هذا الكلام؟ ال X وين موجودة؟ ال Aطيب أخد X
+
+255
+00:31:54,030 --> 00:32:00,830
+موجودة في الكيرن اللي جيه تمين يبقى
+
+256
+00:32:00,830 --> 00:32:07,410
+ساق الكيرن اللي ال five subset من ال A ويعتبر هذه
+
+257
+00:32:07,410 --> 00:32:12,670
+العلاقة رقم واحد بدي أمشي الاتجاه الثاني يبقى on
+
+258
+00:32:12,670 --> 00:32:20,910
+the other hand بدي أخد X موجودة في ال ID ال A
+
+259
+00:32:24,000 --> 00:32:30,660
+ال X موجودة في ال ID ال A مدي أثبت إنها موجودة في
+
+260
+00:32:30,660 --> 00:32:36,920
+ال kernel يبقى ذلك مدام ال X موجودة في ال A يبقى
+
+261
+00:32:36,920 --> 00:32:45,960
+ال X زائد ال A بيساوي مين؟ بيساوي ال A، أه؟ طيب ال
+
+262
+00:32:45,960 --> 00:32:53,000
+X زائد ال A من هنا حسب التعريفالـ X زائد الـ A هي
+
+263
+00:32:53,000 --> 00:33:01,100
+مين؟ الـ Phi of X يبقى هذا بده يعطينا ان هذه Phi
+
+264
+00:33:01,100 --> 00:33:10,520
+of X بده ساوي الـ A مين هو الـ A؟ Zero element في
+
+265
+00:33:10,520 --> 00:33:16,500
+ال factoring يبقى معنى الـ X وين موجودة هذه؟ وين؟
+
+266
+00:33:16,500 --> 00:33:24,020
+في ال kernel تبع الـ Phi صح؟يبقى هذا معناه ان ال X
+
+267
+00:33:24,020 --> 00:33:30,060
+موجودة في ال kernel للفاي يبقى أخدت ال X موجودة في
+
+268
+00:33:30,060 --> 00:33:35,260
+ال ID ال A طلعت ال X موجودة وين؟ في ال kernel
+
+269
+00:33:35,260 --> 00:33:42,000
+فبروح بقول له Sir ال ID ال A صابست من ال kernel
+
+270
+00:33:42,000 --> 00:33:48,120
+للفاي وهذه العلاقة رقم اتنين طلعولي من واحد واتنين
+
+271
+00:33:48,420 --> 00:33:57,240
+طب اروح و اقول from واحد and اتنين we have ان
+
+272
+00:33:57,240 --> 00:34:04,940
+الكيرنل للـ Phi بده يساوي ال ideal A كما هو مطلوب
+
+273
+00:34:04,940 --> 00:34:13,160
+في النظرية يبقى ال ideal A هو الكيرنل لمين لهذا ال
+
+274
+00:34:13,160 --> 00:34:16,540
+homomorphism نعطي مثال
+
+275
+00:34:19,810 --> 00:34:30,430
+نربط هذا المثال بال chapter الماضي ال example
+
+276
+00:34:30,430 --> 00:34:38,410
+بيقول ما يعني show that five
+
+277
+00:34:38,410 --> 00:34:45,330
+المعرفة من z of x onto
+
+278
+00:34:47,770 --> 00:34:55,610
+on to z given by والمعطى
+
+279
+00:34:55,610 --> 00:35:09,010
+بي five لل F of X بده يساوي ال F of zero is a ring
+
+280
+00:35:09,010 --> 00:35:12,190
+homomorphism
+
+281
+00:35:12,190 --> 00:35:14,710
+with
+
+282
+00:35:17,120 --> 00:35:21,900
+الكرنة للـ 5 بدى يساوي لـ principle ideal
+
+283
+00:35:21,900 --> 00:35:23,780
+generated by X
+
+284
+00:35:50,400 --> 00:35:54,840
+خلّيني أعطيكم دلّة
+
+285
+00:35:54,840 --> 00:36:01,060
+في من مجموعة الـ functions اللي العرامل تبعتهم
+
+286
+00:36:01,060 --> 00:36:09,260
+أعداد صحيحة on to z يعني بغطي الـ z كلها given by
+
+287
+00:36:09,260 --> 00:36:14,340
+في of f of x بده ساوي f of zero قال لي بدك تثبت أن
+
+288
+00:36:14,340 --> 00:36:18,900
+هذا ring همو مرتزم الخطوة الأولى الخطوة الثانية
+
+289
+00:36:19,190 --> 00:36:23,150
+تثبت أن الـ Kernel هو الـ principal ideal
+
+290
+00:36:23,150 --> 00:36:28,650
+generated by X طبعا لأول واحدة بنقول إيش جاب لجاب
+
+291
+00:36:28,650 --> 00:36:32,730
+هذا في شجة وانا إيش جابهم لبعض لكن بنقوله بسيطة
+
+292
+00:36:32,730 --> 00:36:36,750
+تعالى يشوفها الحين خلينا في الأول نثبت بس حكاية ال
+
+293
+00:36:36,750 --> 00:36:40,690
+ring homomorphic الـ Phi homomorphism يبقى بداجي
+
+294
+00:36:40,690 --> 00:36:48,370
+أقولهم Phi is a homomorphism أيه اللي بنكتبهإذا
+
+295
+00:36:48,370 --> 00:36:55,750
+بتاخد two element sales يرجى بتقوله let ال F of X
+
+296
+00:36:55,750 --> 00:37:06,550
+وال G of X موجودة في ال ring اللي عندها then بتاخد
+
+297
+00:37:06,550 --> 00:37:15,030
+تأثير ال Phi على مين على ال F of X زائد ال G of X
+
+298
+00:37:15,850 --> 00:37:21,930
+هدول مجموع دلتين مجموعهم من ال calculus بكتبوا F
+
+299
+00:37:21,930 --> 00:37:29,830
+زائد G كله as a one function of X بيطبق اللي
+
+300
+00:37:29,830 --> 00:37:36,570
+التعريف اللي احنا حطنا هذا بدر ساوي تأثير هذه ال
+
+301
+00:37:36,570 --> 00:37:43,410
+function على ال zero يبقى هذا بدر ساوي ال F زائد G
+
+302
+00:37:43,410 --> 00:37:50,630
+تأثيره على ال zeroأو ان شئتم فقولوا ال F of Zero
+
+303
+00:37:50,630 --> 00:37:57,850
+زائد ال G of Zero لو رجعت للتعريف Of ال F of Zero
+
+304
+00:37:57,850 --> 00:38:06,710
+هو Phi لل F of X يبقى هذا يساوي Phi لل F of X زائد
+
+305
+00:38:06,710 --> 00:38:14,810
+Phi لمين لل G of Xإذا أثبتنا الشرط الأول من شروط
+
+306
+00:38:14,810 --> 00:38:20,630
+ال homomorphism بروح بقوله الآن بجيب الشرط الثاني
+
+307
+00:38:20,630 --> 00:38:28,650
+five لل F of X مضروبة في G of X لو رجعنا إلى ال
+
+308
+00:38:28,650 --> 00:38:35,970
+calculus نقول هذه كل F مضروبة في G as a function
+
+309
+00:38:35,970 --> 00:38:43,370
+of X يبقى صارت function واحدةنتجة من حاصل الضرب لل
+
+310
+00:38:43,370 --> 00:38:49,110
+FG حسب ال definition اللي احنا حاطينه هذا الكلام
+
+311
+00:38:49,110 --> 00:38:57,250
+بدي يسوى FG as a function of zero طيب هذا من ال
+
+312
+00:38:57,250 --> 00:39:04,630
+calculus بقوله F of zero ال G of zero F of zero
+
+313
+00:39:04,630 --> 00:39:13,970
+فاي لل F of X يبقى هذا فايلل F of X مضروبة في Phi
+
+314
+00:39:13,970 --> 00:39:22,090
+لل G of X يبقى ندالك صارت ال
+
+315
+00:39:22,090 --> 00:39:28,810
+Phi is a homomorphism انتهينا من المقبض الأول
+
+316
+00:39:28,810 --> 00:39:34,710
+المقبض الثاني قال لي with كيرن اللي ال Phi بتسوي ل
+
+317
+00:39:34,710 --> 00:39:39,650
+principle ideal generated biasلو رجعنا الى المثال
+
+318
+00:39:39,650 --> 00:39:47,010
+الأخر من شفتر 14 السابق تمام؟ المثال الأخير عرفني
+
+319
+00:39:47,010 --> 00:39:55,170
+ال principle ideal generated by X وقول لها ان ال
+
+320
+00:39:55,170 --> 00:40:01,090
+principle ideal generated by X كل ال X مضوبة في G
+
+321
+00:40:01,090 --> 00:40:10,890
+of X بحيث ان ال G of Xموجودة في Z of X مفروض يا
+
+322
+00:40:10,890 --> 00:40:19,810
+بنات؟ صح؟ و أثبتنا ان هذا الكلام بالضبط هو كل ال F
+
+323
+00:40:19,810 --> 00:40:29,750
+of X اللي موجودة في Z of X such that ال F of Zero
+
+324
+00:40:29,750 --> 00:40:34,620
+بده يساوي Zero أثبتنا ان اتنين هذول نفس الشيءلأن
+
+325
+00:40:34,620 --> 00:40:40,400
+آراء كبيرة هذا كلام في آخر مثال في chapter 14
+
+326
+00:40:40,400 --> 00:40:46,500
+مظبوط هيك؟ بناء على هذه المعلومات بدنا نروح
+
+327
+00:40:46,500 --> 00:40:54,740
+نستخدمها نستخدمها في اثبات ان الكيرن الها ده كله
+
+328
+00:40:54,740 --> 00:40:58,780
+سوى مين؟ ال principle idea generated by it اذا
+
+329
+00:40:58,780 --> 00:41:07,900
+بزوحها كله افترضإن ال F of X موجودة في كيرنل الفا
+
+330
+00:41:07,900 --> 00:41:13,640
+تجي واحد يقول طب احنا بناخد دايما X موجودة في
+
+331
+00:41:13,640 --> 00:41:19,080
+الكيرنل لأ ال ring اللي عندنا Z of X كل اللي فيها
+
+332
+00:41:19,080 --> 00:41:26,440
+functions إذا بروح باخد function يبقى then مادام
+
+333
+00:41:26,440 --> 00:41:32,030
+هذه موجودة في الكيرنل يبقى تأثير الفاعلى ال F of X
+
+334
+00:41:32,030 --> 00:41:40,930
+كده؟ Zero يبقى هذا الكلام متساوي Zero طيب الفايلة
+
+335
+00:41:40,930 --> 00:41:49,110
+ال F of X حسب التعريف اللي عندنا كده؟ Zero يبقى
+
+336
+00:41:49,110 --> 00:41:54,350
+هذا بدي يعطينا هذه هشيل او اكتب فدالة F of Zero
+
+337
+00:41:54,350 --> 00:42:00,350
+متساوي مين؟ Zero اللي هو مين؟اللي عندنا هذا يبقى
+
+338
+00:42:00,350 --> 00:42:05,270
+ال F of X موجودة في ال principle ideal generated
+
+339
+00:42:05,270 --> 00:42:11,610
+by X من التعريف اللي عندنا يبقى هذا بده يعطينا ان
+
+340
+00:42:11,610 --> 00:42:16,870
+ال F of X موجودة في ال principle ideal generated
+
+341
+00:42:16,870 --> 00:42:24,550
+by X يبقى ال kern اللي ال Phi هو صادر من ال
+
+342
+00:42:24,550 --> 00:42:30,330
+principle ideal generated by Xيمشي لاتجاه الثاني
+
+343
+00:42:30,330 --> 00:42:41,770
+يبقى on the other hand بدي اخد ال F of X موجودة في
+
+344
+00:42:41,770 --> 00:42:48,890
+ال principle ideal generated by X then ايه شكل ال
+
+345
+00:42:48,890 --> 00:42:55,650
+F of X يا بناه حسب التعريف هو من X في ال G of X
+
+346
+00:42:56,270 --> 00:43:03,670
+يبقى هذا الكلام بده يساوي X في G of X طب لو حبيت
+
+347
+00:43:03,670 --> 00:43:12,850
+أحسب ال F of Zero يبقى بدها تساوي Zero في G of
+
+348
+00:43:12,850 --> 00:43:19,370
+Zero يبقى طالع عند ال F of Zero كده بده يساوي Zero
+
+349
+00:43:19,370 --> 00:43:25,560
+يبقى طالع عندنا ال F of Zero بده يساوي Zeroمعناته
+
+350
+00:43:25,560 --> 00:43:31,580
+.. معناته إيش؟ مين هي ال F of Zero حسب ال
+
+351
+00:43:31,580 --> 00:43:37,940
+definition؟ هي ال Phi لل F of X يبجى هذا معناته إن
+
+352
+00:43:37,940 --> 00:43:45,220
+ال Phi لل F of X بدي يسوي Zero. هذه إيش معناها؟ ال
+
+353
+00:43:45,220 --> 00:43:51,270
+F of X موجودة في ال kernelيبقى هذا معناه ان F of X
+
+354
+00:43:51,270 --> 00:43:59,150
+موجودة في الكيرني للفارق تمام؟ يبقى أخد F of X
+
+355
+00:43:59,150 --> 00:44:03,610
+موجودة في ال principle ID ال generated by X وجدتها
+
+356
+00:44:03,610 --> 00:44:08,070
+موجودة في الكيرني يبقى فاجي بقول للثالث ال
+
+357
+00:44:08,070 --> 00:44:13,070
+principle ID ال generated by X صابست من الكيرني
+
+358
+00:44:13,070 --> 00:44:19,570
+للفارق الأولى هذه العلاقة رقم واحدةهذه العلاقة رقم
+
+359
+00:44:19,570 --> 00:44:27,910
+اتنين بقول له from واحد and اتنين we have ان ال
+
+360
+00:44:27,910 --> 00:44:32,810
+principle او ال kernel الفاية هو ال principle
+
+361
+00:44:32,810 --> 00:44:40,730
+ideal generated by X طبعا شو نشتغل فيه من نفاية و
+
+362
+00:44:40,730 --> 00:44:47,960
+الله كله كلام طب احنا ايش أثبتنافي آخر مثال في
+
+363
+00:44:47,960 --> 00:44:52,520
+chapter 14 ايوة ايوة ايوة ايوة ايوة ايوة ايوة ايوة
+
+364
+00:44:52,520 --> 00:44:55,000
+ايوة ايوة ايوة ايوة ايوة ايوة ايوة ايوة ايوة ايوة
+
+365
+00:44:55,000 --> 00:44:55,740
+ايوة
+
+366
+00:45:16,000 --> 00:45:21,920
+يبقى ضياب لطريقة أسهل للحل من الطريقة اللي حلناها
+
+367
+00:45:21,920 --> 00:45:28,800
+في شفتر أربع عشر آخر مثل كيف الآن لحد هنا انتهى
+
+368
+00:45:28,800 --> 00:45:34,880
+شغلنا فانتبهنا النظرية لكن بدنا نستفيد من هذه
+
+369
+00:45:34,880 --> 00:45:41,940
+النظرية فبجب نقول هنا from from
+
+370
+00:45:41,940 --> 00:45:50,560
+ايزو مارفزن فيرنfrom first isomorphism theorem we
+
+371
+00:45:50,560 --> 00:46:01,880
+have ان ال Z of X اللي هي ال ring modular كيرن
+
+372
+00:46:01,880 --> 00:46:15,020
+للفاي هذه isomorphic لمن؟ للفاي of R للفاي ofz of
+
+373
+00:46:15,020 --> 00:46:18,880
+x مظبوط
+
+374
+00:46:18,880 --> 00:46:26,980
+؟ طيب هنا أثبتنا هذي بالشكل اللي عندنا هذي إبارة
+
+375
+00:46:26,980 --> 00:46:32,680
+عن اللي هو هذي الصورة اللي عندنا لما كانت أنتوا
+
+376
+00:46:32,680 --> 00:46:39,400
+غطتها كلها يعني هذي بقول عليها مين بقول عليها z
+
+377
+00:46:39,400 --> 00:46:46,850
+itself تمام ؟يبقى من ال first isomorphism theorem
+
+378
+00:46:46,850 --> 00:46:53,510
+ال Z of X modular kernel isomorphic لمين لل Phi of
+
+379
+00:46:53,510 --> 00:46:59,950
+R؟ مين R ان دي؟ Z of X Z of X اللي هى مين هنا؟ Z
+
+380
+00:46:59,950 --> 00:47:07,110
+تمام يعني Z أجت مكان Phi of R بالطبع تمام طيب ال
+
+381
+00:47:07,110 --> 00:47:13,210
+kernel هذا أثبت و أنا مين؟بتشيله وحط مدالة الـ
+
+382
+00:47:13,210 --> 00:47:18,250
+principal ideal generated by X يبقى هذا بده يعطينا
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7774ce625059cc587bd0ab62021a3cb50416e19f
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/X0Dl8YgrPTQ.srt
@@ -0,0 +1,1566 @@
+1
+00:00:20,910 --> 00:00:25,930
+بسم الله الرحمن الرحيم. نكمل ما كنا نعمل به المرة
+
+2
+00:00:25,930 --> 00:00:29,950
+الماضية في نفس الشفقة. وللمرة التي فاتت في نهاية
+
+3
+00:00:29,950 --> 00:00:34,630
+المحاضرة، أعطيناكم مثالاً، ولما ننتهي منه، يبقى بدنا
+
+4
+00:00:34,630 --> 00:00:39,390
+نعمل عليه مرة سريعة، ثم ننهي هذا المثال، ثم ننتقل
+
+5
+00:00:39,390 --> 00:00:44,510
+إلى المثال الذي يليه. We will construct a field of
+
+6
+00:00:44,510 --> 00:00:51,810
+order تمام. باقي 8، أيش ممكن أحطها؟ عدد مرفوع لأس
+
+7
+00:00:51,810 --> 00:00:57,790
+عدد أو prime مرفوع لأس، يبقى 8 عبارة عن مين؟
+
+8
+00:00:57,790 --> 00:01:06,890
+2 أس 3، ممتاز جداً، يبقى هذه 2 أس 3. 2 هو الـ prime و
+
+9
+00:01:06,890 --> 00:01:14,240
+3 هو الأس. وكأنه بيقول لي هذه polynomial من الدرجة
+
+10
+00:01:14,240 --> 00:01:20,640
+الثالثة، وتكون irreducible على Z. واضح؟ كأنه
+
+11
+00:01:20,640 --> 00:01:25,240
+بيقول لي هات هذه، ووسيلة الرقم الذي عندي، أحطه prime
+
+12
+00:01:25,240 --> 00:01:30,880
+مرفوع لأس. الـ prime بيكون هو مين؟ هو الـ field Z
+
+13
+00:01:30,880 --> 00:01:36,320
+لهذا الرقم، بيكون هو الـ field. والقصد اللي فوق بيكون
+
+14
+00:01:36,320 --> 00:01:40,320
+هو درجتي الـ following. هو نفسه كأنه مغششني، بيقول
+
+15
+00:01:40,320 --> 00:01:46,380
+اتفضل خد اللي هو السؤال هذا، أقوله تفضل طيب، يبقى
+
+16
+00:01:46,380 --> 00:01:53,780
+احنا جينا للحل المرة التي فاتت، وقلنا let الـ F(x)
+
+17
+00:01:53,780 --> 00:02:02,100
+تساوي قد ايش؟ x تكعيب زائد x. أخذنا x زي واحد، زي x زي
+
+18
+00:02:02,100 --> 00:02:10,220
+واحد، مش هيك؟ طيب. تلقاه بدي آجي على Z<sub>p</sub>، قلنا on Z<sub>p</sub>
+
+19
+00:02:10,220 --> 00:02:15,940
+مين p عندنا؟ قلنا هنا بقراه اثنين، على Z<sub>2</sub>. We
+
+20
+00:02:15,940 --> 00:02:21,760
+have بدنا نحسب قيمة الدالة عند صفر، العنصر الأول
+
+21
+00:02:21,760 --> 00:02:28,060
+من Z<sub>2</sub>، يبقى بيعطيني قد ايش؟ واحد. بدنا نحسب قيمة الدالة
+
+22
+00:02:28,060 --> 00:02:34,290
+عند F(1). واحد زائد واحد، ثلاثة في زيّته
+
+23
+00:02:34,290 --> 00:02:40,150
+جديد. معناته أن الدالة هذه ما لهاش zeros على Z<sub>2</sub>.
+
+24
+00:02:40,150 --> 00:02:49,990
+يبقى هنا Sir، الـ F(x) has no zeros on Z<sub>2</sub>
+
+25
+00:02:49,990 --> 00:02:55,190
+دي اثنين، فهيبقى معاه no zeros على Z<sub>2</sub>.
+
+26
+00:02:55,190 --> 00:02:59,550
+اتفجر، ما فيش ولا حاجة، ولا واحدة بيساويها؟ طيب الـ
+
+27
+00:02:59,550 --> 00:03:09,010
+degree بتاعت الـ F قد ايش؟ ثلاثة. والـ degree على الـ F
+
+28
+00:03:09,010 --> 00:03:13,790
+بده يساوي ثلاثة طبعاً. أخذنا الـ degree على الـ F
+
+29
+00:03:13,790 --> 00:03:17,990
+اثنين أو ثلاثة، أو النظرية معنا مشكلة، صحيح ولا لا؟
+
+30
+00:03:18,060 --> 00:03:23,560
+ما دام هالأمور هيك، يبقى الدالة irreducible على Z<sub>2</sub>
+
+31
+00:03:23,560 --> 00:03:27,300
+وبالتالي irreducible على الـ Q. مش هيك؟ آخذ نص
+
+32
+00:03:27,300 --> 00:03:36,680
+النظرية، يبقى هنا بروح بقول لهم فالـ F(x) بده تساوي
+
+33
+00:03:36,680 --> 00:03:45,940
+x تكعيب زائد x زائد 1 is irreducible over
+
+34
+00:03:46,830 --> 00:03:56,530
+اللي هو Z<sub>2</sub>. هذا بدي يعطينا by a previous theorem
+
+35
+00:03:56,530 --> 00:04:06,070
+بدي يكون الـ F(x) اللي هو x تكعيب زائد x زائد 1 is
+
+36
+00:04:06,070 --> 00:04:12,990
+irreducible over الـ Q.
+
+37
+00:04:21,430 --> 00:04:27,470
+Irreducible على الـ Q، عالي كويس. لما ده الـ F(x)
+
+38
+00:04:27,470 --> 00:04:33,850
+صارت Irreducible على الـ Q، هذا بيولد لي Ideal، و
+
+39
+00:04:33,850 --> 00:04:39,890
+Ideal  maximum، نتيجة رقم واحد، أخذناها على
+
+40
+00:04:39,890 --> 00:04:47,250
+اللي هو النظرية الأخيرة، المحاضرة الماضية. يبقى هنا
+
+41
+00:04:47,250 --> 00:04:53,970
+اللي هو الـ x تكعيب زائد x زائد 1، هذا الـ ideal is
+
+42
+00:04:53,970 --> 00:05:02,750
+maximal. مدام maximal، هذا بده يعطينا أن Z<sub>2</sub>[x]
+
+43
+00:05:02,750 --> 00:05:08,710
+modulo الـ principle ideal generated by x تكعيب زائد
+
+44
+00:05:08,710 --> 00:05:17,380
+x زائد 1 is a field. هذا الـ field زعمنا أنه يحتوي
+
+45
+00:05:17,380 --> 00:05:25,180
+على ثمانية عناصر، وقلنا شكله على الشكل التالي: Z<sub>2</sub>[x]
+
+46
+00:05:25,180 --> 00:05:31,960
+modulo principle ideal generated by x تكعيب زائد
+
+47
+00:05:31,960 --> 00:05:38,180
+واحد. بالدقة ها الـ ideal من الدرجة الثالثة.
+
+48
+00:05:38,180 --> 00:05:43,100
+يبقى اللي قبله من الدرجة الثانية أو الأولى
+
+49
+00:05:43,100 --> 00:05:48,060
+أو الصفرية، يعني أقل من الدرجة الثالثة، يبقى هذا
+
+50
+00:05:48,060 --> 00:05:54,600
+بيكون على الشكل ax<sup>2</sup> + bx + c + الـ
+
+51
+00:05:54,600 --> 00:06:00,240
+principle ideal generated by x تكعيب زائد واحد.
+
+52
+00:06:00,240 --> 00:06:06,890
+وبحيث أن الـ a والـ b والـ c كلها موجودة وين؟ موجودة
+
+53
+00:06:06,890 --> 00:06:14,030
+في Z<sub>2</sub>، يعني يا إما صفر يا إما... يا إما واحد. إحنا
+
+54
+00:06:14,030 --> 00:06:20,350
+زعمنا أنه هدف ثمانية عناصر. بدنا نعرف ما هي هذه
+
+55
+00:06:20,350 --> 00:06:25,530
+الثمانية عناصر، وقلنا لكم يلا حضروها للمرة القادمة.
+
+56
+00:06:25,530 --> 00:06:32,460
+وها قد حضرت المرة القادمة، وصارت المرة الحالية. يبقى
+
+57
+00:06:32,460 --> 00:06:39,000
+هذه العناصر عبارة عن مين؟ (متكرر كثيراً "انا")
+
+58
+00:06:39,000 --> 00:06:39,640
+(متكرر كثيراً "انا")
+
+59
+00:06:39,640 --> 00:06:39,900
+(متكرر كثيراً "انا")
+
+60
+00:06:39,900 --> 00:06:40,300
+(متكرر كثيراً "انا")
+
+61
+00:06:40,300 --> 00:06:40,820
+(متكرر كثيراً "انا")
+
+62
+00:06:40,820 --> 00:06:41,580
+(متكرر كثيراً "انا")
+
+63
+00:06:41,580 --> 00:06:45,700
+(متكرر كثيراً "انا")
+
+64
+00:06:45,700 --> 00:06:49,460
+(متكرر كثيراً "انا")
+
+65
+00:06:49,460 --> 00:06:51,260
+(متكرر كثيراً "انا")
+
+66
+00:06:51,260 --> 00:06:59,520
+(متكرر كثيراً "انا")
+
+67
+00:06:59,520 --> 00:07:05,610
+أنا. طيب ماذا؟ و x<sup>2</sup> + 1، و x<sup>2</sup> + x،
+
+68
+00:07:05,610 --> 00:07:11,050
+و x<sup>2</sup> + x + 1. واحد، اثنين، ثلاثة،
+
+69
+00:07:11,050 --> 00:07:16,010
+أربعة، خمسة، ستة، سبعة، ثمانية. هدول على كل واحد
+
+70
+00:07:16,010 --> 00:07:20,750
+فيهم بدي أضيف الـ principle ideal generated by x
+
+71
+00:07:20,750 --> 00:07:27,590
+تكعيب زائد x زائد واحد. هاي جميع العناصر، هدول كلهم
+
+72
+00:07:27,590 --> 00:07:32,500
+ثمانية عناصر. يعني يا بنات عندنا صفر، زي ده، ده left
+
+73
+00:07:32,500 --> 00:07:37,860
+coset. عندنا الواحد، زي الـ principle ideal left coset
+
+74
+00:07:37,860 --> 00:07:42,260
+الثانية، x، زي الـ principle ideal left coset الثالثة، وهكذا.
+
+75
+00:07:42,260 --> 00:07:48,780
+بالنسبة لمن؟ للباقي، هاي العناصر، يبقى هدول ثمانية
+
+76
+00:07:48,780 --> 00:07:57,420
+عناصر. يبقى لما أكتب هيك، كأنه أنا بغششك، قد ايش؟ اللي هو
+
+77
+00:07:57,420 --> 00:08:01,880
+الـ Z<sub>p</sub> بدي يكون مين؟ هو الـ prime اللي بدك تأخذيه،
+
+78
+00:08:01,880 --> 00:08:06,700
+وقد ايش درجة الـ polynomial اللي لازم تأخذيه مشان
+
+79
+00:08:06,700 --> 00:08:13,380
+يطلع كلامك صحيح. وسنثبت لك هذا كمان بمثال بعده.
+
+80
+00:08:13,380 --> 00:08:17,280
+المثال الذي بعده... آه، قبل المثال الذي بعده، لو
+
+81
+00:08:17,280 --> 00:08:24,370
+بدنا نضرب عنصرين في بعض من هذا الـ field، النتيجة بدي
+
+82
+00:08:24,370 --> 00:08:29,430
+يطلع داخل ولا برا؟ طب تعال نضرب ونشوف، يطلع داخل
+
+83
+00:08:29,430 --> 00:08:34,670
+ولا برا؟ مش احنا بنزعُم أنه في الـ  و closed under
+
+84
+00:08:34,670 --> 00:08:37,550
+multiplication، و closed under الجمع وغيرها
+
+85
+00:08:37,550 --> 00:08:41,630
+الجمع، مش هيأثر على الدرجة، يبقى ما فيش فيه مشكلة،
+
+86
+00:08:41,630 --> 00:08:47,070
+المشكلة في الضرب. يبقى لو جينا نضرب، على ضرب داخل
+
+87
+00:08:47,070 --> 00:08:52,410
+هذا field، مثلاً لو رحت آخذ، على سبيل المثال، x<sup>2</sup> زائد
+
+88
+00:08:52,410 --> 00:08:58,090
+واحد، مع هذا، مع الـ principle ideal، يبقى لو بدي
+
+89
+00:08:58,090 --> 00:09:02,830
+أضرب، أضرب العناصر داخل هذا الـ field، بدي آخذ x
+
+90
+00:09:02,830 --> 00:09:09,970
+تربيع زائد واحد زائد principle ideal، بدي أضربه في
+
+91
+00:09:09,970 --> 00:09:15,870
+مين؟ في العنصر الثاني، x<sup>2</sup> زائد x زائد واحد زائد
+
+92
+00:09:15,870 --> 00:09:24,010
+principle ideal. x تكعيب زائد x زائد واحد، أشوف النتيجة
+
+93
+00:09:24,010 --> 00:09:29,410
+قد ايش بده يساوي. يبقى x تربيع في x تربيع قد ايش؟
+
+94
+00:09:29,410 --> 00:09:37,110
+x أس أربعة. وهنا زائد x تكعيب، وهنا زائد x تربيع
+
+95
+00:09:37,110 --> 00:09:46,390
+وزائد كمان x تربيع، وزائد x، زائد واحد، زائد الـ
+
+96
+00:09:46,390 --> 00:09:53,350
+principle ideal generated by الـ x تكعيب زائد x زائد
+
+97
+00:09:53,350 --> 00:09:59,550
+واحد. طلعوا هدول مع بعض كده، شو بيعطونيه؟ اثنين x تربيع
+
+98
+00:09:59,550 --> 00:10:04,630
+داخل زائد اثنين. مع السلامة، الله يسهل عليهم، وغير
+
+99
+00:10:04,630 --> 00:10:09,950
+مقصود عليهم. يبقى بقى عندي يا بنات، بقى عندي x<sup>4</sup> و
+
+100
+00:10:09,950 --> 00:10:17,780
+يطلع x تكعيب زائد x زائد واحد موجود هنا، يبقى
+
+101
+00:10:17,780 --> 00:10:24,640
+بدي يطلع نفس العنصر هذا، يبقى x أس أربعة زائد الـ x
+
+102
+00:10:24,640 --> 00:10:30,960
+تكعيب زائد الـ x زائد واحد. يبقى طلعت polynomial من
+
+103
+00:10:30,960 --> 00:10:37,160
+الدرجة الرابعة كـ left coset مع الـ x تكعيب زائد x
+
+104
+00:10:37,160 --> 00:10:42,000
+زائد واحد. واحنا بنزعم هنا أن هذا بدي يكون من
+
+105
+00:10:42,000 --> 00:10:48,290
+الدرجة الثانية. نشوف هل هذا الكلام صحيح، والله مش
+
+106
+00:10:48,290 --> 00:10:52,890
+صحيح، يعني بنخفض الدرجة، بحيث تصير من الدرجة
+
+107
+00:10:52,890 --> 00:10:58,410
+الثانية، يعني أنا لو رحت وخليته تصير شغلة نقص
+
+108
+00:10:58,410 --> 00:11:03,350
+شوية، بننقص درجات، بتكملي بحيث فعلاً يكون على
+
+109
+00:11:03,350 --> 00:11:07,930
+الصيغة التي عندنا هذه. طب كيف بتخفضه؟ هناك
+
+110
+00:11:07,930 --> 00:11:14,490
+طريقتان، الطريقة الأولى long division، إيش يعني؟
+
+111
+00:11:14,850 --> 00:11:20,010
+القسمة المطولة. نقسم قسمة مطولة عادي، ونشوف وين ما توصل
+
+112
+00:11:20,010 --> 00:11:25,870
+معنا الدنيا. إذا لو جيت في الهامش، بدي أقسم x أس
+
+113
+00:11:25,870 --> 00:11:33,470
+أربعة، على الـ x تكعيب زائد x زائد واحد. x أس أربعة
+
+114
+00:11:33,470 --> 00:11:39,930
+على x تكعيب هي أجيب الـ x، والباقي ألحقه فيها. يبقى
+
+115
+00:11:39,930 --> 00:11:48,390
+هاي x أس أربعة زائد x تربيع زائد x. بنغير الإشارات
+
+116
+00:11:48,390 --> 00:11:55,310
+وبنجمع. مع السلامة، بظل عندي ناقص x تربيع ناقص x، لكن
+
+117
+00:11:55,310 --> 00:12:00,230
+إحنا بنشتغل وين؟ في Z<sub>2</sub>. في Z<sub>2</sub>، بدي
+
+118
+00:12:00,230 --> 00:12:08,210
+أضيف هنا اثنين، بظل x تربيع، وهذه زيها x، يبقى صارت
+
+119
+00:12:08,210 --> 00:12:15,500
+الـ x أس أربعة زائد الـ principle ideal generated by
+
+120
+00:12:15,500 --> 00:12:21,560
+هذا الـ element، بتساوي خارج القسمة، اللي هو يعني x
+
+121
+00:12:21,560 --> 00:12:28,560
+في x تكعيب زائد x زائد واحد، زائد خارج القسمة اللي
+
+122
+00:12:28,560 --> 00:12:33,220
+هو x تربيع زائد x، زائد الـ principle ideal
+
+123
+00:12:33,220 --> 00:12:39,860
+generated by x تكعيب زائد x زائد واحد، تمام.
+
+124
+00:12:42,380 --> 00:12:47,260
+طيب، كويس. هذا الـ element موجود في الـ principle ولا
+
+125
+00:12:47,260 --> 00:12:54,660
+لا. يبقى على طول الخط هذا، بتساوي الـ x تربيع زائد x
+
+126
+00:12:54,660 --> 00:13:01,200
+زائد الـ principle ideal generated by x تكعيب زائد
+
+127
+00:13:01,200 --> 00:13:07,760
+x زائد 1. صارت من أي درجات؟ ثانية. بهذا يتفق مع
+
+128
+00:13:07,760 --> 00:13:13,670
+الكلام الذي أحنا زعمناه قبل قليل، تمام؟ طبعاً زعمناه
+
+129
+00:13:13,670 --> 00:13:19,950
+مش شك، زعمناه يعني من ضمانة، ضامنين مية بالمية إن
+
+130
+00:13:19,950 --> 00:13:24,370
+هذا الكلام. طبعاً هذا الكلام اللي أنا بقوله مش من
+
+131
+00:13:24,370 --> 00:13:31,090
+عندي، من القرآن الكريم، ولما في قصة سيدنا يوسف، لما
+
+132
+00:13:31,090 --> 00:13:36,890
+المكيال الذي جاء، اللي بيجيب المكيال هذا، إله حمله
+
+133
+00:13:36,890 --> 00:13:41,610
+بغير، وأنا به زعيم. يعني اللي يجيب هو، أنا بعطيه حمل
+
+134
+00:13:41,610 --> 00:13:47,390
+بغير زيادة. يبقى نظاماً من الضمانة وليس للشك، يبقى
+
+135
+00:13:47,390 --> 00:13:53,070
+إحنا هنا اللي زعمناه قبل قليل، هيأكد لنا مين؟ عملياً
+
+136
+00:13:53,070 --> 00:13:58,550
+بهذا الكلام. هذه هي الطريقة الأولى. وكأن x أس
+
+137
+00:13:58,550 --> 00:14:05,430
+أربعة في هذا الـ field تكافئ x تربيع زائد x، لأنه
+
+138
+00:14:05,430 --> 00:14:10,820
+شيلناها وحطينا بدلها x تربيع زائد x. ونستطيع أن نؤكد
+
+139
+00:14:10,820 --> 00:14:17,180
+هذا الكلام بطريقة أخرى. ما هي الطريقة الأخرى؟ هنشوف.
+
+140
+00:14:17,180 --> 00:14:22,100
+إحنا عندنا x تكعيب زائد x زائد 1 زائد الـ principle
+
+141
+00:14:22,100 --> 00:14:27,480
+ideal generated by x تكعيب زائد x زائد 1، هو الـ
+
+142
+00:14:27,480 --> 00:14:33,120
+principle ideal generated by x تكعيب زائد 1، صح؟
+
+143
+00:14:33,120 --> 00:14:40,760
+يعني هذا بزيرو، تمام؟ يعني هذا بيصير x تكعيب زائد الـ x
+
+144
+00:14:40,760 --> 00:14:46,720
+زائد واحد بيصير زيرو، يعني الـ x تكعيب تساوي ناقص x
+
+145
+00:14:46,720 --> 00:14:54,420
+ناقص واحد. إحنا بنشتغل وين؟ في Z<sub>2</sub>. في Z<sub>2</sub> هذا
+
+146
+00:14:54,420 --> 00:15:00,880
+معناه أن x زائد واحد in Z<sub>2</sub>، بتنضرب بالـ x، يبقى يصير
+
+147
+00:15:00,880 --> 00:15:06,100
+أن كمان الـ x تكعيب في الشغل اللي بنشتغله هذا، ممكن
+
+148
+00:15:06,100 --> 00:15:11,120
+أبدلها بمين؟ x زائد واحد. يعني لو مرّ في السؤال كان
+
+149
+00:15:11,120 --> 00:15:15,360
+في عندي x تكعيب، يمكن استبداله بـ x زائد واحد، يبقى
+
+150
+00:15:15,360 --> 00:15:19,920
+نزلنا الدرجة الثالثة إلى الدرجة الأولى، زي ما نزلنا
+
+151
+00:15:19,920 --> 00:15:24,890
+الدرجة الرابعة إلى الدرجة الثانية. طب هذه المعادلة
+
+152
+00:15:24,890 --> 00:15:31,470
+لو ضربت الطرفين في x، بصير x أس 4 يساوي x في x زائد
+
+153
+00:15:31,470 --> 00:15:38,630
+1، يعني x تربيع زائد x، هي اللي فوق مظبوط؟ يبقى
+
+154
+00:15:38,630 --> 00:15:44,490
+صارت هي عندك. مدى الطريقة، طريقتين مشان ننزل الدرجة
+
+155
+00:15:44,490 --> 00:15:48,290
+من الدرجة الرابعة إلى الدرجة الثانية أو الأولى أو
+
+156
+00:15:48,290 --> 00:15:52,540
+الصفرية، حسب طبيعة هذا المثال. لو جينا سؤال في
+
+157
+00:15:52,540 --> 00:15:57,060
+الامتحان، أو قلنا لك هاتي للـ multiplicative تبع الـ
+
+158
+00:15:57,060 --> 00:16:03,360
+two elements، ووصلتي إلى شغل زي هذا، وقول والله حليت
+
+159
+00:16:03,360 --> 00:16:08,380
+صح، وجامش لأ. أنت حليته نص الحل، ضايل عليك النص
+
+160
+00:16:08,380 --> 00:16:13,560
+الثاني، أنه تنزلي الدرجة إلى درجة مين؟ الثانية، و
+
+161
+00:16:13,560 --> 00:16:21,000
+هكذا. طيب الآن، في عندنا كمان مثال آخر، بس بتغير عدد
+
+162
+00:16:21,000 --> 00:16:27,340
+العناصر. كده، عدد العناصر هنا ثمانية، بدي أغير هذه
+
+163
+00:16:27,340 --> 00:16:34,200
+الطريقة. المثال الذي بعده، هو بيقول
+
+164
+00:16:34,200 --> 00:16:40,120
+بنفس الطريقة. Example: Construct
+
+165
+00:16:40,120 --> 00:16:43,260
+a
+
+166
+00:16:43,260 --> 00:16:47,160
+field. Construct
+
+167
+00:16:47,160 --> 00:17:00,510
+a field of order، of order تسعة، مش ث
+
+223
+00:23:18,510 --> 00:23:24,790
+ف يبقى الـ a عنصر غير صفري وموجود في الـ f المطلوب
+
+224
+00:23:24,790 --> 00:23:33,450
+نمرة c بيقول إذا كان الـ f of x زائد a is
+
+225
+00:23:33,450 --> 00:23:35,950
+irreducible
+
+226
+00:23:39,340 --> 00:23:52,140
+الـ Q ثم الـ F is أو الـ F of X is irreducible
+
+227
+00:23:52,140 --> 00:24:00,400
+over الـ Q itself
+
+228
+00:24:00,400 --> 00:24:07,620
+المعلومة
+
+229
+00:24:07,620 --> 00:24:13,120
+اللي عندنا أن الـ F of X زائد A والـ A موجود في F
+
+230
+00:24:13,120 --> 00:24:18,080
+مهما كان يكون بشرط ألا يكون العنصر الصفري، لو كان
+
+231
+00:24:18,080 --> 00:24:23,140
+unity أو unit، كل معناه مش مشكلة، يبقى هنا
+
+232
+00:24:23,140 --> 00:24:32,880
+بإمكاني أقول that الـ F of X زائد A be irreducible
+
+233
+00:24:32,880 --> 00:24:42,900
+over Q، إيش بدون إثبات يا بنات؟ إن الـ F of X
+
+234
+00:24:42,900 --> 00:24:49,380
+بدون A irreducible، والعلامات على الـ EQ طبعا هذا الـ
+
+235
+00:24:49,380 --> 00:24:54,420
+chapter، غلبنا بالتناقض يبقى حدش يحسن من حد، هنبرهن
+
+236
+00:24:54,420 --> 00:25:03,700
+بالتناقض كذلك، يبقى باقي بيقول: افترضوا that
+
+237
+00:25:03,700 --> 00:25:17,910
+أن الـ F of X is reducible over الـ Q، فالـ
+
+238
+00:25:17,910 --> 00:25:26,690
+F of X بقدر أكتبها كحاصل ضرب two polynomials اللي
+
+239
+00:25:26,690 --> 00:25:36,530
+هما مين؟ الـ G of X في الـ H of X بحيث الـ G of X والـ
+
+240
+00:25:36,530 --> 00:25:44,250
+H of X موجودة فين؟ في الـ Q of X، والاثنتين are of
+
+241
+00:25:44,250 --> 00:25:54,970
+lower degree، موجودة وof lower degree يعني درجة
+
+242
+00:25:54,970 --> 00:26:02,470
+الـ G ودرجة الـ H أقل من درجة، أقل من درجة اللي
+
+243
+00:26:02,470 --> 00:26:12,000
+هو الـ F، طيب الآن بدنا نشيل كل X ونحط مكانه X زائد A
+
+244
+00:26:12,000 --> 00:26:19,500
+ونشوف إيش اللي بده يحصل، طيب الـ F of X زائد A هتساوي
+
+245
+00:26:19,500 --> 00:26:30,180
+G of X زائد A في H of X زائد A، طب استنوا شوية خلي
+
+246
+00:26:30,180 --> 00:26:37,040
+المعلومة هنا، بدنا نشوف هل هذا معناه أن الـ F of X
+
+247
+00:26:37,040 --> 00:26:41,700
+زائد الـ A is reducible، تعالوا نشوف إذا
+
+248
+00:26:41,700 --> 00:26:46,400
+الدرجات  جد بعض؟ آه والله بصير مش جد بعض، يبقى ليس
+
+249
+00:26:46,400 --> 00:26:51,360
+صحيحة، خليني أسألكوا السؤال الثالث، لو قلت لكم أنا عندي
+
+250
+00:26:51,360 --> 00:26:58,560
+X تربيع وعندي X زائد واحد، لكل تربيع قداش درجة
+
+251
+00:26:58,560 --> 00:27:05,470
+الأولى والثانية زي بعض، لو قلت لكم عندي الأولى X تربيع
+
+252
+00:27:05,470 --> 00:27:15,290
+زائد واحد وعندي X زائد خمسة عشر، لكل تربيع نفس الشيء،
+
+253
+00:27:15,290 --> 00:27:20,430
+يبقى إضافة الـ constant لا يغير من درجة الـ
+
+254
+00:27:20,430 --> 00:27:25,410
+polynomial، بيغير من شكلها صحيح لكن لا يغير من درجة الـ
+
+255
+00:27:25,410 --> 00:27:32,350
+polynomial، يبقى بناء عليه لو بدنا degree لمين؟
+
+256
+00:27:33,280 --> 00:27:43,000
+للـ G of X زائد الـ A، هل هي الـ degree للـ G of X؟
+
+257
+00:27:43,000 --> 00:27:48,320
+مضبوط تماما، لا بتغيرهاش، طب والـ degree للـ G of X
+
+258
+00:27:48,320 --> 00:27:56,330
+أقل من الـ degree للـ F of X صحيح ولا لأ؟ والـ degree
+
+259
+00:27:56,330 --> 00:28:01,270
+للـ F of X مش هي نفس الـ degree تبع الـ F of X زائد
+
+260
+00:28:01,270 --> 00:28:09,010
+الـ A، يبقى هي نفس الـ degree تبع الـ F of X زائد
+
+261
+00:28:09,010 --> 00:28:17,830
+الـ A، قريت، عجبتكم؟ بس إن الـ degree للـ H of X زائد
+
+262
+00:28:17,830 --> 00:28:26,430
+الـ A مش هي عبارة عن الـ degree للـ H of X، صح؟ والـ
+
+263
+00:28:26,430 --> 00:28:33,210
+degree للـ H of X أقل من الـ degree للـ F of X اللي
+
+264
+00:28:33,210 --> 00:28:41,650
+هي بدها تساوي الـ degree للـ F of X زائد الـ A، إذا
+
+265
+00:28:41,650 --> 00:28:48,850
+صارت درجة F of X زائد الـ A بده يقابلها درجة G
+
+266
+00:28:48,850 --> 00:28:56,230
+و درجة الـ H اللي هما أقل، درجة G of X زائد A اللي هما
+
+267
+00:28:56,230 --> 00:29:02,950
+أقل من درجة F of X زائد A، يبقى صاروا اثنين هذول of
+
+268
+00:29:02,950 --> 00:29:09,630
+lower degree، صحيح ولا لأ؟ يبقى صارت هذه بتوصف بشكل
+
+269
+00:29:09,630 --> 00:29:18,090
+هذا، الـ F of X زائد A بتساوي الـ G of X زائد A في الـ
+
+270
+00:29:18,090 --> 00:29:21,130
+H of X زائد A
+
+271
+00:29:25,380 --> 00:29:35,720
+زائد الـ A، والـ H of X زائد الـ A are of lower degree
+
+272
+00:29:35,720 --> 00:29:42,500
+مدام lower degree يبقى هذا principle ولا لأ؟ just
+
+273
+00:29:42,500 --> 00:29:52,080
+irreducible ولا لأ؟ صحيح، يبقى this means that هذا
+
+274
+00:29:52,080 --> 00:30:01,270
+يعني أن الـ F of X زائد الـ A is reducible، is
+
+275
+00:30:01,270 --> 00:30:10,110
+reducible على مين؟ على الـ Q، على .. على .. شغلنا
+
+276
+00:30:10,110 --> 00:30:16,430
+كان في الـ F وفي الـ Q، reducible على الـ Q وعلى الـ
+
+277
+00:30:16,430 --> 00:30:17,850
+F، على
+
+278
+00:30:21,380 --> 00:30:26,660
+على F وليس على Q يا عزيزي، يبقى الـ reducible على
+
+279
+00:30:26,660 --> 00:30:36,500
+F، وهذه صحيحة على F، جل من لا يسكت، يبقى كل
+
+280
+00:30:36,500 --> 00:30:43,640
+شغلنا هذا على F، وهذه كلها على F، لو قلنا على Q صح
+
+281
+00:30:43,640 --> 00:30:49,040
+بسم الله، أخذنا حالة خاصة، لأن الـ Q is إيه فيه؟ لكن
+
+282
+00:30:49,040 --> 00:30:56,520
+إحنا كل شغلنا على مين؟ على F of X، كل Q حطي
+
+283
+00:30:56,520 --> 00:31:02,480
+مكانها F of X تمام؟ يبقى هذا معناه أنه reducible
+
+284
+00:31:02,480 --> 00:31:10,820
+over اللي هو مين؟ over F، تناقض؟ آه إحنا إحنا إحنا
+
+285
+00:31:10,820 --> 00:31:16,200
+افترضنا أنه reducible، يبقى صار عندنا
+
+286
+00:31:16,200 --> 00:31:17,440
+contradiction
+
+287
+00:31:19,890 --> 00:31:26,230
+يبقى فرضنا اللي فرضناه غلط، وعكسه هو الصح، يبقى هنا
+
+288
+00:31:26,230 --> 00:31:39,110
+السؤال الـ F of X is irreducible over F وهو المفهوم
+
+289
+00:31:39,110 --> 00:31:47,300
+طيب، الآن هذا ننتقل للسؤال نمرة D من السؤال، بده
+
+290
+00:31:47,300 --> 00:31:57,380
+تطبيق عملي على الحالة C، فراح قال: ليش نمرة D، نمرة
+
+291
+00:31:57,380 --> 00:32:08,640
+D من السؤال بيقول use for C، استخدم for C to prove
+
+292
+00:32:08,640 --> 00:32:19,220
+to prove that، مش هتروح تثبت أنه التمامية x تكعيب
+
+293
+00:32:19,220 --> 00:32:28,420
+ناقص 6x زائد الواحد is irreducible على الكيوب is
+
+294
+00:32:28,420 --> 00:32:39,600
+irreducible over الكيوب، solution
+
+295
+00:32:44,430 --> 00:32:49,590
+يبقى الـ feed اللي عندنا هذا يا بنات صار من؟ صار الـ
+
+296
+00:32:49,590 --> 00:32:55,490
+Q، كويس؟ وقال استخدم النتيجة اللي استخدمتها
+
+297
+00:32:55,490 --> 00:33:01,310
+هنا لإثبات أنه هذه الـ function f of x is
+
+298
+00:33:01,310 --> 00:33:06,070
+irreducible على الـ Q، بقول: كويس، يبقى إحنا عندنا
+
+299
+00:33:06,070 --> 00:33:11,750
+f of x، اللي هي 8x تكعيب، نعطي الـ 6x زائد 1
+
+300
+00:33:13,340 --> 00:33:21,500
+طبعا ببدأ بأخذ a موجودة في الـ Q، بس بشرط الـ a
+
+301
+00:33:21,500 --> 00:33:27,040
+عنصر غير صفري، وأبسط الشغلات خذ واحد صحيح، الواحد
+
+302
+00:33:27,040 --> 00:33:35,140
+موجود في الـ Q عادي جدا، يبقى أنا لو أخدت الـ F of X
+
+303
+00:33:35,140 --> 00:33:43,240
+plus one، يبقى هذا 8 في X plus one لكل تكعيب
+
+304
+00:33:43,240 --> 00:33:50,420
+ناقص 6 في X plus one زائد 1، بدي أفك هذا الكلام،
+
+305
+00:33:50,420 --> 00:33:55,840
+يبقى هذا 8 X تكعيب زائد 3 X تربيع
+
+306
+00:33:55,840 --> 00:34:05,200
+زائد 3 X زائد 1 ناقص 6 X ناقص 6 في
+
+307
+00:34:05,200 --> 00:34:13,220
+X زائد 1 زائد 1، هذه لو فكتها بده يصير F of
+
+308
+00:34:13,220 --> 00:34:21,220
+X زائد واحد، يصير 8 X تكعيب زائد 24 X
+
+309
+00:34:21,220 --> 00:34:29,100
+تربيع زائد 24 X زائد 8 ناقص 6 X
+
+310
+00:34:29,100 --> 00:34:36,940
+ناقص 6 زائد 1، بمعنى آخر صار الـ F of X زائد
+
+311
+00:34:36,940 --> 00:34:44,700
+واحد يساوي 8 X تكعيب، يا باشا، مش مشكلة الـ 24
+
+312
+00:34:44,700 --> 00:34:51,100
+X تربيع، يا باشا مش مشكلة، طلعوا لي هنا ناقص 6 X و زائد
+
+313
+00:34:51,100 --> 00:34:57,900
+24 X، بيضل قد ايه؟ زائد 18 X، وعندك
+
+314
+00:34:57,900 --> 00:35:04,710
+8 ناقص 1 = 9 ناقص 6 بيضل قد ايه؟ بيضل 3
+
+315
+00:35:06,230 --> 00:35:15,970
+الآن بتلاحظوا هذه النظرية موجودة في Z6، معاملات
+
+316
+00:35:15,970 --> 00:35:25,530
+كلهم موجودات في Z،  انتبهتوا صح ولا لأ؟ يبقى هذه
+
+317
+00:35:25,530 --> 00:35:34,900
+الـ polynomial كلها موجودة في Z6، تمام؟ للعناصر
+
+318
+00:35:34,900 --> 00:35:41,100
+هذول، الـ 3 prime بتقسمهم ولا لأ؟ ولا بتقسم
+
+319
+00:35:41,100 --> 00:35:46,480
+الـ 8، والـ 3 تربيع = 9 لا تقسم الـ 3.
+
+320
+00:35:46,500 --> 00:35:53,620
+إيه؟ هذه نظرية كذلك؟ ولا لأ؟ يرجعنا الآن الـ 3
+
+321
+00:35:53,620 --> 00:35:58,980
+لا تقسم الـ 8، لكن الـ 3 بتقسم الـ 24
+
+322
+00:35:58,980 --> 00:36:05,760
+والـ 3 بتقسم الـ 18، والـ 3 بتقسمي
+
+323
+00:36:05,760 --> 00:36:13,540
+الـ 3،  أندي الـ 3 ترجع تسعة لتقسم الـ 3
+
+324
+00:36:13,540 --> 00:36:20,380
+يبقى الدالة هذه إيش؟ R دي وسبب على الـ Q، يبقى هنا
+
+325
+00:36:20,380 --> 00:36:32,800
+by previous theorem، من نظرية السابقة الـ F of X زائد
+
+326
+00:36:32,800 --> 00:36:45,420
+واحد is irreducible over the cube، طب طلعوا هنا لو
+
+327
+00:36:45,420 --> 00:36:50,920
+كانت هذه irreducible على الـ F يبقى الـ F of X من دون
+
+328
+00:36:50,920 --> 00:36:57,960
+الـ a irreducible، يبقى five exercises
+
+329
+00:36:57,960 --> 00:37:08,280
+خمسة part c، الـ F of X اللي هي 8 X تكعيب ناقص
+
+330
+00:37:08,280 --> 00:37:19,940
+6 X زائد 1 is irreducible over Q، هو المطلوب
+
+331
+00:37:19,940 --> 00:37:27,240
+. طيب ولك في مسائل لسه جاية بتنحل على part B و part
+
+332
+00:37:27,240 --> 00:37:32,140
+A، يعني ضروري تروح تثبت الـ A والـ B زي ما
+
+333
+00:37:32,140 --> 00:37:37,680
+برهنّا الـ C حرفيا، كما يعني بدك تاخد polynomial
+
+334
+00:37:37,680 --> 00:37:42,280
+بدي إياك أنت تبقيها irreducible، أنت فرضها irreducible
+
+335
+00:37:42,280 --> 00:37:48,560
+وتروح تحلليها ونحو ذلك، كان هذا هو المثال أو
+
+336
+00:37:48,560 --> 00:37:54,960
+السؤال رقم خمسة دي، بدنا نروح لسؤال رقم ستة وهو
+
+337
+00:37:54,960 --> 00:38:02,260
+تعميم للحالة اللي خدناها قبل شوية، construct field
+
+338
+00:38:02,260 --> 00:38:08,740
+الـ order له ثمانية أو الـ order له تسعة، هذا السؤال
+
+339
+00:38:08,740 --> 00:38:16,220
+اللي هو سؤال ستة، سؤال ستة بيقول: افترض أن عندنا الـ
+
+340
+00:38:16,220 --> 00:38:26,020
+F of X موجودة في ZP وهو هذه irreducible، هذه الـ F
+
+341
+00:38:26,020 --> 00:38:28,320
+الـ F of X is
+
+342
+00:38:32,740 --> 00:38:43,000
+irreducible، irreducible over اللي هو الـ P والـ
+
+343
+00:38:43,000 --> 00:38:49,780
+الـ P is prime و الـ degree للـ F بده يساوي الـ N والـ
+
+344
+00:38:49,780 --> 00:38:58,890
+degree للـ F بده يساوي الـ N again، اثبت أن هذا is a
+
+345
+00:38:58,890 --> 00:39:05,950
+field، show that، نزل
+
+346
+00:39:05,950 --> 00:39:13,850
+ZP of X modulo the principle ideal generated by F of X
+
+347
+00:39:13,850 --> 00:39:21,870
+معناه is a field with
+
+348
+00:39:25,340 --> 00:39:26,740
+P⁻⁹
+
+349
+00:40:10,810 --> 00:40:18,090
+خذ polynomial F of X من الدرجة N موجودة في ZP
+
+350
+00:40:18,090 --> 00:40:24,410
+ZP of X modulo الـ principle ideal generated by هذه
+
+351
+00:40:24,410 --> 00:40:30,010
+الـ polynomial، وعدد العناصر يساوي P to the
+
+352
+00:40:30,010 --> 00:40:37,210
+power N، زي المثالين اللي اتعملوا قبل قليل، P أس درجة
+
+353
+00:40:37,210 --> 00:40:41,590
+الـ polynomial، الـ polynomial من الدرجة N يبقى
+
+354
+00:40:41,590 --> 00:40:48,910
+أس N، الـ P هو الـ prime تبع ZP، يبقى بدنا
+
+355
+00:40:48,910 --> 00:40:54,470
+نيجي نبرهن صحة هذا الكلام، المعلومات اللي عندنا F of
+
+356
+00:40:54,470 --> 00:41:03,410
+X is irreducible على مين؟ على P، يبقى هنا let F of
+
+357
+00:41:03,410 --> 00:41:15,050
+X be an irreducible polynomial on
+
+358
+00:41:18,430 --> 00:41:27,110
+ZP، ما هو معنى هذا الكلام؟ نختصر
+
+359
+00:41:27,110 --> 00:41:31,470
+الدليل على طول الخط، يبقى الـ principle ideal
+
+360
+00:41:31,470 --> 00:41:36,310
+الـ generated by F of X هو maximal، طبق قليل نظرية
+
+361
+00:41:36,310 --> 00:41:43,890
+يبقى هنا by a previous theorem
+
+362
+00:41:46,270 --> 00:41:58,470
+by previous theorem، ZP of X الـ F of X is
+
+363
+00:41:58,470 --> 00:42:06,690
+maximal ideal in
+
+364
+00:42:06,690 --> 00:42:11,510
+ZP of X
+
+365
+00:42:15,830 --> 00:42:23,930
+هو maximal ideal، بالكورلري رقم واحد، هذا عبارة
+
+366
+00:42:23,930 --> 00:42:28,130
+عن field، يبقى
+
+367
+00:42:28,130 --> 00:42:33,650
+باين، إحنا
+
+368
+00:42:33,650 --> 00:42:44,130
+مش بدنا نثبت أن هذا field، صحيح؟ يبقى باين
+
+369
+00:42:47,040 --> 00:42:53,820
+by previous corollary، نتيجة
+
+370
+00:42:53,820 --> 00:43:06,580
+السابقة، we have أن ZP of X modulo principle ideal
+
+371
+00:43:06,580 --> 00:43:12,340
+i.e. generated by F of X is a
+
+372
+00:43:17,770 --> 00:43:25,050
+شو شكله؟ شكله
+
+373
+00:43:25,050 --> 00:43:33,310
+هو ZP of X modulo الـ principle ideal generated
+
+374
+00:43:33,310 --> 00:43:45,910
+by الـ F of X، بده يساوي مين؟ G of X زائد the
+
+375
+00:43:45,910 --> 00:43:52,050
+principle ideal generated by F of X such that أن
+
+376
+00:43:52,050 --> 00:43:59,470
+الـ G of X موجودة في ZP of X، الشكل اللي عامله
+
+377
+00:43:59,470 --> 00:44:06,970
+twice، ف أنا بدي الـ G of X دي، يمكن الدرجة تبعها أقل
+
+378
+00:44:06,970 --> 00:44:12,830
+من الـ F of X، ويمكن تكون أكبر من الـ F of X، إذا أقل
+
+379
+00:44:12,830 --> 00:44:16,530
+من درجة الـ F of X، خلاص انتهينا من الموضوع لأنه في
+
+380
+00:44:16,530 --> 00:44:21,530
+المثالين اللي قبل قليل، الـ principle ideal بقينا
+
+381
+00:44:21,530 --> 00:44:28,150
+بيقولوا الـ remainder درجته أقل من درجة اللي هو الدالة
+
+382
+00:44:28,150 --> 00:44:32,250
+اللي ولدت الـ principle ideal، صحيح ولا لأ؟ إذا
+
+383
+00:44:32,250 --> 00:44:38,510
+هذه النتيجة تكون أقل وقد تكون أكبر، يبقى بعمل الـ
+
+384
+00:44:38,510 --> 00:44:43,530
+division algorithm أو long division، يبقى بالـ
+
+385
+00:44:43,530 --> 00:44:50,030
+division algorithm هذه بقدر أقول هي F of X في Q
+
+386
+00:44:50,030 --> 00:44:56,410
+of X زائد R of X زائد الـ principle ideal
+
+387
+00:44:56,410 --> 00:45:04,690
+generated by F of X وبشرط أن الـ R of X بده يساوي 0
+
+388
+00:45:04,690 --> 00:45:14,660
+أو الـ degree للـ R of X أقل من الـ degree للـ F of X
+
+389
+00:45:14,660 --> 00:45:22,000
+مظبوط هيك؟ يبقى أنا شيلت الـ G وحطيتها in general
+
+390
+00:45:22,000 --> 00:45:27,880
+السؤال هو: هذا الـ element موجود في هذا ideal؟
+
+391
+00:45:27,880 --> 00:45:34,760
+يبقى صحيح إني أكتب الـ R of X زائد الـ principle
+
+392
+00:45:34,760 --> 00:45:41,930
+ideal generated by F of X بحيث الـ R of X يساوي Zero
+
+393
+00:45:41,930 --> 00:45:
+
+445
+00:52:06,120 --> 00:52:19,640
+تكيب زائد X تربيع زائد اتنين هذا is a field طب
+
+446
+00:52:19,640 --> 00:52:31,580
+مين العناصر تبقى؟ where؟ حيث الـ Z3 of X موديولو الـ
+
+447
+00:52:31,580 --> 00:52:38,060
+principle ideal generated by X تكيب زائد X تربيع
+
+448
+00:52:38,060 --> 00:52:46,040
+زائد اتنين بده يساوي أكثرية أكثرية
+
+449
+00:52:46,040 --> 00:52:54,840
+أكثرية أكثرية أكثرية أكثرية أكثرية أكثرية
+
+450
+00:52:54,840 --> 00:52:58,560
+أكثرية أكثرية أكثرية أكثرية أكثرية أكثرية
+
+451
+00:52:58,560 --> 00:53:00,300
+أكثرية أكثرية أكثرية أكثرية أكثرية
+
+452
+00:53:02,060 --> 00:53:10,420
+وبحيث أن الـA والـB والـC موجودة كلها هذه في Z3
+
+453
+00:53:10,420 --> 00:53:19,240
+كم عنصر في هذا؟ سبعة وعشرون عنصر تمام؟ بدك إيه؟
+
+454
+00:53:19,240 --> 00:53:22,140
+أنا براها إيه في البيت؟ أنا براها إيه في البيت؟
+
+455
+00:53:22,140 --> 00:53:22,820
+أنا براها إيه في البيت؟ أنا براها إيه في البيت؟
+
+456
+00:53:22,820 --> 00:53:24,340
+أنا براها إيه في البيت؟ أنا براها إيه في البيت؟
+
+457
+00:53:24,340 --> 00:53:24,440
+أنا براها إيه في البيت؟ أنا براها إيه في البيت؟
+
+458
+00:53:24,440 --> 00:53:24,740
+أنا براها إيه في البيت؟ أنا براها إيه في البيت؟
+
+459
+00:53:24,740 --> 00:53:28,940
+أنا براها إيه
+
+460
+00:53:28,940 --> 00:53:35,960
+في البيت؟ أنا بخلص؟ وضاربهم وجامعهم وطرحهم زي
+
+461
+00:53:35,960 --> 00:53:40,680
+اللي قبل؟ فهي عندنا الآن سؤال عشرة، السؤال طبعاً
+
+462
+00:53:40,680 --> 00:53:47,540
+عشرة حاطط فيه خمسة مطالب، مش هحل إلاّ مطلوبين، مطلوب
+
+463
+00:53:47,540 --> 00:53:52,960
+اليوم ومطلوب المرة الجاية لكن نمرة A ونمرة C زي
+
+464
+00:53:52,960 --> 00:54:01,410
+بعض، يبقى نمرة A بتأخذ اللي هو العدد ثلاثة لا يقسم
+
+465
+00:54:01,410 --> 00:54:05,290
+معامل الـ X أس خمسة لكن بيقسم معامل الـ X أس أربعة و
+
+466
+00:54:05,290 --> 00:54:09,850
+بيقسم معامل الـ X أس أربعة و بيقسم الستة والتلاتة
+
+467
+00:54:09,850 --> 00:54:15,550
+يبقى طبقاً للنظرية هذه Irreducible نمرة C
+
+468
+00:54:15,550 --> 00:54:19,230
+نفس الطريقة إيه؟ X أس أربعة زي التلاتة X التربيعي
+
+469
+00:54:19,230 --> 00:54:23,330
+زي التلاتة، التلاتة بتقسم آخر معامل، بتقسمش الأول
+
+470
+00:54:23,330 --> 00:54:28,670
+مربعة أعلى، يقسم العدد الآخر يبقى Irreducible يبقى
+
+471
+00:54:28,670 --> 00:54:33,750
+الأولى والثالثة زي بعض وحلهم سطر واحد من النص
+
+472
+00:54:33,750 --> 00:54:41,190
+النظرية مباشرة لكن لو جيتي لنمرة P، نمرة P بيقول لي
+
+473
+00:54:41,190 --> 00:54:50,330
+اللي هي X أس أربعة زائد X زائد واحد زائد X زائد
+
+474
+00:54:50,330 --> 00:54:56,150
+واحد، بدي
+
+475
+00:54:56,150 --> 00:55:04,160
+أشتغل على مين؟ على field يبقى بجيب أقول له مثلاً أن
+
+476
+00:55:04,160 --> 00:55:09,600
+زي توضيح هذه
+
+477
+00:55:09,600 --> 00:55:15,920
+الـ F of X هذه في السؤال، تشوفوا هل هذا reducible
+
+478
+00:55:15,920 --> 00:55:21,380
+والله إيه؟ reducible على الـ Q، سؤالي الخمس نقاط كله
+
+479
+00:55:21,380 --> 00:55:26,260
+تشوفوا هل reducible والله irreducible على الـ
+
+480
+00:55:26,260 --> 00:55:32,460
+جيت للـ F bar يا بنات of X، ليه الـ X وصار بعوض الـ X
+
+481
+00:55:32,460 --> 00:55:37,360
+ده اللي هتتغير؟ هي نفسها يبقى سعر الـ degree للـ F هي
+
+482
+00:55:37,360 --> 00:55:43,020
+الـ degree لمين؟ للـ F bar يبقى هذا بدي يعطينا أن الـ
+
+483
+00:55:43,020 --> 00:55:49,000
+degree للـ F هي نفس الـ degree للـ F bar، ذكرت رحنا
+
+484
+00:55:49,000 --> 00:55:54,440
+نظرية؟ خلاصنا؟ طيب ضلّ علينا شغلة بسيطة، ناسي إحنا
+
+485
+00:55:54,440 --> 00:56:01,690
+بنشتغل بمين؟ يبقى الـ F of zero يساوي واحد، والـ F of
+
+486
+00:56:01,690 --> 00:56:10,990
+واحد يساوي واحد، يبقى صارت has no zeros، يبقى هذا
+
+487
+00:56:10,990 --> 00:56:22,190
+بدي يعطينا الـ F bar of X has no zeros on Z two، والـ
+
+488
+00:56:22,190 --> 00:56:28,000
+degree للـ F بتساوي الـ degree للـ F bar يبقى صورة الـ
+
+489
+00:56:28,000 --> 00:56:39,620
+F bar irreducible على Z2 يبقى الصورة F bar of X is
+
+490
+00:56:39,620 --> 00:56:50,980
+irreducible over Z2، هذا بده يعطي كمان أن F الأصلية
+
+491
+00:56:50,980 --> 00:56:58,430
+is irreducible على Z2، هدفه هي يعطيكي أن الـ F of X X
+
+492
+00:56:58,430 --> 00:57:09,790
+أس أربعة زائد X زائد واحد is irreducible over Z2
+
+493
+00:57:09,790 --> 00:57:13,450
+خديني
+
+494
+00:57:13,450 --> 00:57:21,130
+هالمثال بآشي طبعاً نمرة إيه؟ اللي هو آخر السؤال
+
+495
+00:57:21,130 --> 00:57:27,090
+يعطيناكوا مثال حرفي زيه يبقى بتحلوه بنفس الطريقة،
+
+496
+00:57:27,090 --> 00:57:40,150
+جاري أقول لكم في السؤال 12 وسؤال 14 وسؤال 18 وسؤال
+
+497
+00:57:40,150 --> 00:57:44,870
+23 وسؤال
+
+498
+00:57:44,870 --> 00:57:45,670
+25
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/eG2yGcxr3_A_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/eG2yGcxr3_A_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c75bab3366fbf0edd61444af288c66fa4b4d71d0
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/eG2yGcxr3_A_raw.srt
@@ -0,0 +1,1996 @@
+1
+00:00:20,810 --> 00:00:25,430
+بسم الله الرحمن الرحيم نكمل اليوم ما ابتدأنا به
+
+2
+00:00:25,430 --> 00:00:30,510
+وهو حل أسئلة من مسائل التمرين على .. التمرين على
+
+3
+00:00:30,510 --> 00:00:38,310
+Chapter 14 وصلنا المرة الماضية إلى سؤال 38 سؤال 38
+
+4
+00:00:38,310 --> 00:00:43,690
+بيقول شو ذات بييل لي أن ال principle ideal
+
+5
+00:00:43,690 --> 00:00:50,420
+generated by 2 زي 2I is not a primeفي ال ring Z of
+
+6
+00:00:50,420 --> 00:00:56,640
+I اتنين بدي اعرف مين عناصر ال ring Z of I موديولو
+
+7
+00:00:56,640 --> 00:00:59,760
+ال principle of ideal generation بقى اتنين زائد
+
+8
+00:00:59,760 --> 00:01:04,340
+اتنين يعني اكم انصر عندي اكم انصر هو ما يمثل ال
+
+9
+00:01:04,340 --> 00:01:08,560
+order المين لهذه ال ring المطلوب التالف بدي اقدرش
+
+10
+00:01:08,560 --> 00:01:12,920
+ال characteristic لهذه ال ring طبعا عرفنا قبل ذلك
+
+11
+00:01:12,920 --> 00:01:18,220
+ال characteristic هو اصغر رقمبضربه في جميع أنواع
+
+12
+00:01:18,220 --> 00:01:22,760
+الرنج بيعطيني الـ zero element تمام تمام إذا
+
+13
+00:01:22,760 --> 00:01:27,880
+نخليني مع المطلوب الأول اللي هو Nemra A يبقى Nemra
+
+14
+00:01:27,880 --> 00:01:32,760
+A قال لي بيجيلي ان ال principle ideal generated by
+
+15
+00:01:32,760 --> 00:01:37,920
+اتنين زتنين I is not a prime ideal في ال Z of I
+
+16
+00:01:37,920 --> 00:01:44,800
+ماشي الآنيا بنات لو جينا أقول لـ2 زائد 2I موجودة
+
+17
+00:01:44,800 --> 00:01:51,620
+في الـprinciple ID generated by 2I صح ولا لأ؟ طيب،
+
+18
+00:01:51,620 --> 00:02:01,200
+الآن لو جيت قلت 2 زائد 2I أليس 2 في 1 زائد I؟ وهذا
+
+19
+00:02:01,200 --> 00:02:07,560
+كذلك موجود في الـprinciple ID generated by 2 زائد
+
+20
+00:02:07,560 --> 00:02:13,770
+2Iلكن السؤال هو هل الإتنين موجود في الـother ideal
+
+21
+00:02:13,770 --> 00:02:22,790
+ولا حتى الواحد زائد I يبقى هنا but ولكن الإتنين مش
+
+22
+00:02:22,790 --> 00:02:27,630
+موجود في ال principle ideal generated by اتنين
+
+23
+00:02:27,630 --> 00:02:34,530
+زائد اتنين I and الواحد زائد I بصي مقبله لل
+
+24
+00:02:34,530 --> 00:02:39,230
+principle ideal generated by اتنين Iإيش معنى هذا
+
+25
+00:02:39,230 --> 00:02:46,230
+الكلام؟ الحاصل ضرب عنصرين من ال ring موجودات فيه،
+
+26
+00:02:46,230 --> 00:02:52,170
+حاصل ضرب عنصرين موجودة في ال ideal لكن للعنصر
+
+27
+00:02:52,170 --> 00:02:57,150
+الأول موجود في ال ideal وللعنصر التاني موجود هنا،
+
+28
+00:02:57,150 --> 00:03:04,360
+هذا مش موجود وكذلك هذا مش موجود، هذا بده يعطيناإن
+
+29
+00:03:04,360 --> 00:03:11,380
+الـ principal id generated by 2 زائد 2i is not
+
+30
+00:03:11,380 --> 00:03:19,140
+right يبقى هذا هو المطموب الأول هذا حل مباشر مش
+
+31
+00:03:19,140 --> 00:03:25,000
+صحيح ممكن عن طريق و هو أن تتبت لما هوش integral
+
+32
+00:03:25,000 --> 00:03:29,120
+domain لو ماكنش integral domain مبطل يصير هذا
+
+33
+00:03:29,120 --> 00:03:34,080
+أفرعينا من الماشي لهذابس بتاعي هذا أسهل و أسرع
+
+34
+00:03:34,080 --> 00:03:38,440
+بيعطيني الإجابة على السريع مباشرة طب النقطة
+
+35
+00:03:38,440 --> 00:03:44,260
+الثانية قاللي بدي عناصر مين؟ بدي عناصر ال
+
+36
+00:03:44,260 --> 00:03:50,100
+factoring اللي عندنا، كم واحد؟ وإيش شكلهم كمان؟
+
+37
+00:03:50,100 --> 00:03:55,440
+كداش وإيش شكلهم؟ طب خلينا ناخد بعض المعلومات في
+
+38
+00:03:55,440 --> 00:04:00,380
+الأول قبل ما نبدأ لإن خلاصنا المطلوب الأولالسؤال
+
+39
+00:04:00,380 --> 00:04:06,160
+اللي بدي أسأله هل الأربع موجودة في الـprinciple ID
+
+40
+00:04:06,160 --> 00:04:10,340
+الـgenerated by اتنين زائد اتنين I؟ لأ لأ مش
+
+41
+00:04:10,340 --> 00:04:14,420
+موجودة طب و ذاتها لقيت موجودة او اتنين زائد زيرو
+
+42
+00:04:14,420 --> 00:04:19,660
+زائد زيرو في I طلع يلي هلو الان لو جيت قلت اتنين
+
+43
+00:04:19,660 --> 00:04:25,540
+زائد اتنين I ضربتها في واحد ناقص I مش هذا موجود في
+
+44
+00:04:25,540 --> 00:04:30,420
+ال ring اللي فوقوهذا موجود في الـ ideal اللي عندنا
+
+45
+00:04:30,420 --> 00:04:34,620
+إذا حسب تعريف الـ ideal حاصل ضربهم بيكون في الـ
+
+46
+00:04:34,620 --> 00:04:38,860
+ideal itself إذا حاصل ضرب هذول موجود في ال
+
+47
+00:04:38,860 --> 00:04:43,280
+principle ideal generated by اتنين زائد اتنين I
+
+48
+00:04:43,280 --> 00:04:51,360
+طيب هذا لو جيت ضربته قدش بديكون؟ اتنين وهنا I في I
+
+49
+00:04:51,360 --> 00:04:56,200
+سالب واحد مع سالب بيصير موجة بواحد في اتنين باتنين
+
+50
+00:04:56,590 --> 00:05:03,890
+يبقى اتنين زائد اتنين وهذا بيصير اتنين I وسالب
+
+51
+00:05:03,890 --> 00:05:09,870
+اتنين I ب Zero مع السلامة يبقى هذا بيعطيني اربعة
+
+52
+00:05:09,870 --> 00:05:14,410
+موجودة في Main موجودة في ال principle ideal
+
+53
+00:05:14,410 --> 00:05:19,670
+generated by اتنين زائد اتنين I خليلي هذه المعلومة
+
+54
+00:05:19,670 --> 00:05:26,730
+عندك بتنزمنيأطلع منها كمان شغلة تانية أطلع منها
+
+55
+00:05:26,730 --> 00:05:32,410
+كمان شغلة زي إيش مثلا الأربعة هذه مش موجودة في هذا
+
+56
+00:05:32,410 --> 00:05:39,110
+إذا بقدر أقول هذه أول معلومة جدرت أجدها المعلومة
+
+57
+00:05:39,110 --> 00:05:46,190
+التانية بقدر أقول الأربعة زي ال principle ideal
+
+58
+00:05:46,190 --> 00:05:51,660
+generated by اتنين زي اتنين Iهذه تساوي
+
+59
+00:05:51,660 --> 00:05:55,840
+الـprinciple ID الـgenerated by إتنين وإتنين
+
+60
+00:05:55,840 --> 00:05:56,680
+وإتنين وإتنين وإتنين وإتنين وإتنين وإتنين وإتنين
+
+61
+00:05:56,680 --> 00:05:56,920
+وإتنين وإتنين وإتنين وإتنين وإتنين وإتنين وإتنين
+
+62
+00:05:56,920 --> 00:05:57,500
+وإتنين وإتنين وإتنين وإتنين وإتنين وإتنين وإتنين
+
+63
+00:05:57,500 --> 00:06:06,340
+وإتنين وإتنين وإتنين وإتنين وإتنين وإتنين
+
+64
+00:06:06,340 --> 00:06:07,300
+وإتنين وإتنين وإتنين وإتنين وإتنين وإتنين وإتنين
+
+65
+00:06:07,300 --> 00:06:17,360
+وإتنين وإتنين وإتنين وإتنين وإتنين وإت
+
+66
+00:06:17,910 --> 00:06:22,590
+أو شعر، صح ولا لا؟ و سوناكوا قبل هيك مثال من
+
+67
+00:06:22,590 --> 00:06:26,570
+هالموديل مش جزيرة يعني، مش أول مرة يعني طب خلّي
+
+68
+00:06:26,570 --> 00:06:31,110
+هذه المعلومات تانية عندك و تعالى نشوف هيك ما هو
+
+69
+00:06:31,110 --> 00:06:39,030
+شكل العنصر اللى موجود في Z of I يبقى باجب اقول any
+
+70
+00:06:39,030 --> 00:06:43,550
+element A
+
+71
+00:06:43,550 --> 00:06:55,570
+زائد BI اللي موجود في الـ Z of I is written as
+
+72
+00:06:55,570 --> 00:07:03,050
+بقدر
+
+73
+00:07:03,050 --> 00:07:10,590
+أكتفه على الشكل الترمي الـ A زائد الـ BI يساوي
+
+74
+00:07:10,590 --> 00:07:19,910
+شوفولي هالكلام هذا صحيح ولا لأA نقطة بي زائد بي في
+
+75
+00:07:19,910 --> 00:07:28,170
+ايه في واحد زائد ايه في
+
+76
+00:07:28,170 --> 00:07:36,290
+نفس الكلام اللي صحيح هنا بي في واحد بيه وصارت A
+
+77
+00:07:36,290 --> 00:07:42,780
+زائد بيهطيب اه هيناقص بي وزاية بي مع السلامة ضال
+
+78
+00:07:42,780 --> 00:07:51,380
+عندي وزاية بي في IUA يبقى أي عنصر بقدر اكتبه على
+
+79
+00:07:51,380 --> 00:07:56,760
+الشكل اللي عندها خلي المعلومة ده دي عندك لازمالي
+
+80
+00:07:56,760 --> 00:08:01,180
+طيب السؤال هو ال A و ال B انتجت ولا لا يا بنات؟
+
+81
+00:08:01,810 --> 00:08:07,910
+يبقى الفرق بينهما واحد أو حتى .. ليش واحد؟ يمكن
+
+82
+00:08:07,910 --> 00:08:12,170
+يطلع خمس أو تلاتين، مش بعرفيه، ستة أو تلاتين ناقص
+
+83
+00:08:12,170 --> 00:08:15,350
+واحد، خمس أو تلاتين، اربعة أو تلاتين زاد واحد، مش
+
+84
+00:08:15,350 --> 00:08:20,030
+مشكلة، يبقى قد ما يكون الفرق ما بينهما، بهمن هدول
+
+85
+00:08:20,030 --> 00:08:24,790
+انتجر، يبقى الفرق في ما بينهما انتجر طيب، الآن لو
+
+86
+00:08:24,790 --> 00:08:32,920
+جينا، قولنا not that، لاحظي ليه؟الـA نقص الـB
+
+87
+00:08:32,920 --> 00:08:43,860
+يساوي 4K زائد الـR 4K زائد الـR، 4K زائد الـR، 4K
+
+88
+00:08:43,860 --> 00:08:44,380
+زائد الـR، 4K زائد الـR، 4K زائد الـR، 4K زائد
+
+89
+00:08:44,380 --> 00:08:44,560
+الـR، 4K زائد الـR، 4K زائد الـR، 4K زائد الـR، 4K
+
+90
+00:08:44,560 --> 00:08:44,580
+زائد الـR، 4K زائد الـR، 4K زائد الـR، 4K زائد
+
+91
+00:08:44,580 --> 00:08:45,180
+الـR، 4K زائد الـR، 4K زائد الـR، 4K زائد الـR، 4K
+
+92
+00:08:45,180 --> 00:08:47,160
+زائد الـR، 4K زائد الـR، 4K زائد الـR، 4K زائد
+
+93
+00:08:47,160 --> 00:08:57,360
+الـR، 4K زائد الـR، 4K زائد الـR، 4K زائدوالـ R
+
+94
+00:08:57,360 --> 00:09:03,020
+هذه مش حيالنا الـ R موجودة في Z أربعة يعني إيش
+
+95
+00:09:03,020 --> 00:09:10,000
+بتاخد قيام؟ Zero واحد، اتنين، تلاتة، بس خلاصنا؟ طب
+
+96
+00:09:10,000 --> 00:09:21,100
+استنى شوية and لو حطيت الـ B تساوي اتنين L زائد
+
+97
+00:09:21,100 --> 00:09:30,200
+الـ S و الـ S موجودة هذه في Z2S موجودة في Z2 يعني
+
+98
+00:09:30,200 --> 00:09:35,580
+تاخدوا قيمة قداشر يعني إيش قصدك تقول بالظبط لو الـ
+
+99
+00:09:35,580 --> 00:09:41,780
+S سوى الـ 0 بيكون الـ B عدد زواجي و لو كانت بواحد
+
+100
+00:09:41,780 --> 00:09:46,820
+بيصير عدد فردي يبقى هذا مش شطرة هذي بأي element
+
+101
+00:09:46,820 --> 00:09:52,200
+الـ B قد يكون عدد فردي و قد يكون عدد زواجي بتاخد
+
+102
+00:09:52,200 --> 00:09:56,500
+اتنين مرة واحدةإتنين سواء كان عدد فردي و الله
+
+103
+00:09:56,500 --> 00:10:00,760
+عزيزي زوجي و أشوف أين بدأ توصدنا الشغل هذا ممتاز
+
+104
+00:10:00,760 --> 00:10:05,760
+جدا، الآن احنا قلنا كل عنصر بنحطه على الشكل هذا،
+
+105
+00:10:05,760 --> 00:10:11,960
+مظبوط؟ إذا هذا العنصر بدي أشوف ممكن أختصه لحد وين،
+
+106
+00:10:11,960 --> 00:10:20,880
+فباجي بقول now ال a زائد ال b في ال I بدي ساوي،
+
+107
+00:10:20,880 --> 00:10:28,990
+قلنا بنحط a ناقص bيبقى الـ A ناقص الـ B زائد الـ B
+
+108
+00:10:28,990 --> 00:10:36,270
+في الـ 1 زائد الـ I الـ A ناقص B لـ 4K زائد الـ A
+
+109
+00:10:36,270 --> 00:10:46,430
+والـ B 2L زائد الـ S 8 في الـ 1 زائد الـ I طيب و
+
+110
+00:10:46,430 --> 00:10:57,940
+بعدين بقدر أقول هذه 4Kو هذه بقدر اقول زائد L L لما
+
+111
+00:10:57,940 --> 00:11:04,600
+اضربها هنا بتدخلي اتنين جوه اتنين زائد اتنين I و
+
+112
+00:11:04,600 --> 00:11:15,420
+زائد S في واحد زائد I مصبوط هيك؟ و ضالة من عندك؟ و
+
+113
+00:11:15,420 --> 00:11:23,880
+هتزعلش و هاي زائد ال IY زائد الـR زائد الـS في 1
+
+114
+00:11:23,880 --> 00:11:31,300
+زائد الـR تمام؟ طيب، بدي أدخل العنصر هذا مع
+
+115
+00:11:31,300 --> 00:11:34,660
+الـfactoring أو بدي أدخليه من عناصر الـfactoring
+
+116
+00:11:34,660 --> 00:11:42,520
+فبروح بقول للـA زائد الـBI زائد الـprinciple ideal
+
+117
+00:11:42,520 --> 00:11:52,770
+generated by 2 زائد 2I تمام؟يبقى متساوى 4K زائد ال
+
+118
+00:11:52,770 --> 00:12:01,570
+L 2I زائد R زائد ال S 1 زائد I زائد ال principle
+
+119
+00:12:01,570 --> 00:12:10,710
+ID generated by 2 زائد 2I السؤال هو هذا هنا موجود
+
+120
+00:12:10,710 --> 00:12:18,990
+في ال ideal؟ ممتاز هذاموجود الـ ideal يبقى مجموعة
+
+121
+00:12:18,990 --> 00:12:24,490
+هما هذا بيعطينا الـ ideal itself مظبوط يبقى هذا
+
+122
+00:12:24,490 --> 00:12:31,910
+الكلام يبدو يساوي الـ a زائد ال S في واحد زائد ال
+
+123
+00:12:31,910 --> 00:12:42,090
+I زائد اتنين زائد اتنين I يبقى اي element في ال
+
+124
+00:12:42,090 --> 00:12:47,180
+factoring اللي عندكبتكون على الشكل اللي عندنا هذا
+
+125
+00:12:47,180 --> 00:12:53,380
+و ال S يا Zero يا واحد و ال R Zero واحد اتنين
+
+126
+00:12:53,380 --> 00:13:00,220
+تلاتة كويس؟ الان بتاخد لو كانت ال S ب Zero بطير
+
+127
+00:13:00,220 --> 00:13:05,560
+هذا و بظل ال R Zero واحد اتنين و تلاتة عند ال Zero
+
+128
+00:13:05,560 --> 00:13:15,920
+بظل هذا صح ولا لا؟ إذا بصير ال Z of Iموديلو لـ
+
+129
+00:13:15,920 --> 00:13:21,120
+principal ideal generated by اتنين I بتدور أشوف من
+
+130
+00:13:21,120 --> 00:13:26,860
+عناصرها لو كانت ال S بزيرو وال R بزيرو، إيش بطلع
+
+131
+00:13:26,860 --> 00:13:35,260
+عندنا؟ لإتنين زائد اتنين I لو كانت ال S بزيرو وال
+
+132
+00:13:35,260 --> 00:13:42,780
+R بواحد، يبقى إيش مصيرك؟ بواحد زائد اتنين زائد
+
+133
+00:13:42,780 --> 00:13:51,360
+اتنين Iلو كانت الـ S بـ 0 و الـ R بـ 2 يبقى 2 زائد
+
+134
+00:13:51,360 --> 00:14:00,300
+2 زائد 2 I لو كانت الـ S بـ 0 و الـ R بـ 3 يبقى 3
+
+135
+00:14:00,300 --> 00:14:09,740
+زائد 2 زائد 2 I وصلنا لـ 4 تعطيني 0 و 5 تعطيني 1 و
+
+136
+00:14:09,740 --> 00:14:18,140
+6 يبقى تتكرريبقى هاي جبت أربع عناصر لما كانت الـS
+
+137
+00:14:18,140 --> 00:14:26,880
+بـ0 والـR 0 1 2 3 طب الـS ممكن تكون بـ1 لأن عناصر
+
+138
+00:14:26,880 --> 00:14:34,720
+Z و الـ0 هو 1 يبقى بدالي أاخد لو كانت الـS بـ1
+
+139
+00:14:34,720 --> 00:14:43,560
+والـR بـ0 إيش بتطلع عندك؟ 1 زائد Iزائد ال
+
+140
+00:14:43,560 --> 00:14:50,700
+principle ideal generated بالإتنين زائد اتنين I ال
+
+141
+00:14:50,700 --> 00:14:59,200
+S بواحد و R بواحد يبقى بصير مين؟ بصير واحد زائد
+
+142
+00:14:59,200 --> 00:15:05,660
+واحد زائد I زائد ال principle ideal generated by
+
+143
+00:15:05,660 --> 00:15:14,830
+اتنين زائد اتنين I تماملو كانت الـ S بـ0 و R بـ2
+
+144
+00:15:14,830 --> 00:15:23,770
+بـ2 بدي أصير مين؟ اتنين زائد اللي هو واحد زائد I
+
+145
+00:15:23,770 --> 00:15:29,910
+زائد ال principle ideal generated by اتنين زائد
+
+146
+00:15:29,910 --> 00:15:37,310
+اتنين I لو كانت R تلاتة بصير تلاتة زائد واحد زائد
+
+147
+00:15:37,310 --> 00:15:42,820
+Iزي ال principle ideal generated بالشكل اللي
+
+148
+00:15:42,820 --> 00:15:50,780
+عندها، فيه غير هيك؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟
+
+149
+00:15:50,780 --> 00:15:50,780
+ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟
+
+150
+00:15:50,780 --> 00:15:50,780
+ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟
+
+151
+00:15:50,780 --> 00:15:50,800
+ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟
+
+152
+00:15:50,800 --> 00:15:50,800
+ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟
+
+153
+00:15:50,800 --> 00:15:50,820
+ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟
+
+154
+00:15:50,820 --> 00:15:56,660
+ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟ ليه؟
+
+155
+00:15:56,660 --> 00:16:01,040
+ليه؟
+
+156
+00:16:01,040 --> 00:16:02,060
+ليه
+
+157
+00:16:05,230 --> 00:16:11,390
+هذا الكلام بده يساوي قداش تمانية عناصر خلصنا بيه
+
+158
+00:16:11,390 --> 00:16:16,030
+نمرسيه سؤال بس بدي أرجع انا لبيه تالي بس صبر عليا
+
+159
+00:16:16,030 --> 00:16:20,070
+شوية بس بدي قبل اللي هضيع المعلومة هاي العناصر
+
+160
+00:16:20,070 --> 00:16:27,190
+قدامك دوري من الرقم اللي لو ضربتيه في جميع العناصر
+
+161
+00:16:27,190 --> 00:16:36,570
+كلهم بيعطيك ال zero element يلا الواحد بنفعالاربعة
+
+162
+00:16:36,570 --> 00:16:43,950
+تمام الاربعة اضربيه في أي عنصر بيطلع من؟ بيطلع من
+
+163
+00:16:43,950 --> 00:16:47,930
+الـ zero element يعني ال principle الـ ideal
+
+164
+00:16:47,930 --> 00:16:52,610
+general supply اتنين طلع يشافه الاربعة موجودة هنا
+
+165
+00:16:52,610 --> 00:16:58,670
+لو ضربته فيه بيطلع نفسه اربعة في ضاحن اربعة اهم
+
+166
+00:16:58,670 --> 00:17:02,910
+موجود يبطلع نفسه اربعة في اتنين تلاتة في اربعة كل
+
+167
+00:17:02,910 --> 00:17:07,890
+موجوديجي هنا أربعة بصير اتنين في اتنين زائد اتنين
+
+168
+00:17:07,890 --> 00:17:12,310
+I موجود يبقى الـ zero زائد ال principle هنا
+
+169
+00:17:12,310 --> 00:17:17,270
+الأربعة في واحد باربعة موجود طارت أربعة في هذه
+
+170
+00:17:17,270 --> 00:17:23,510
+موجود طارت و هكذا يبقى أخر حاجة نمرسي بقى دي بقوله
+
+171
+00:17:23,510 --> 00:17:30,730
+ال characteristic ل Z of I modular principle ideal
+
+172
+00:17:30,730 --> 00:17:36,580
+generated by اتنينزائد اتنين I بده يساوي كده اش
+
+173
+00:17:36,580 --> 00:17:41,300
+أربعة لإن الأربعة هذه لو ضربت في أي عنصر من
+
+174
+00:17:41,300 --> 00:17:48,980
+العناصر الثمانية يساوي مين؟ يساوي Zero ايه الخاطر؟
+
+175
+00:17:48,980 --> 00:17:55,480
+أوريكوا كيف الحسابات العملية داخل هذه ال ring احنا
+
+176
+00:17:55,480 --> 00:18:02,280
+حسبنا حسابات نظريةورحنا طلعنا شكل العناصر لكن لو
+
+177
+00:18:02,280 --> 00:18:09,200
+بدي أحسب حسابات عددية مثلا بيّلي هذا توضيح ليس إلا
+
+178
+00:18:09,200 --> 00:18:15,940
+خمسة زيد ستة I زيد ال principle ID generated by
+
+179
+00:18:15,940 --> 00:18:20,900
+اتنين زيد اتنين I بيّلي إن هذا العنصر هو واحد من
+
+180
+00:18:20,900 --> 00:18:22,100
+التمانية دول
+
+181
+00:18:26,630 --> 00:18:32,470
+لنثبت إن هذا واحد من هدول نقوله بسيطة هذه ها ها
+
+182
+00:18:32,470 --> 00:18:41,870
+يقول واحد زائد اتنين I زائد اربعة زائد اربعة I
+
+183
+00:18:41,870 --> 00:18:46,570
+زائد ال principle ideal generated by اتنين زائد
+
+184
+00:18:46,570 --> 00:18:54,220
+اتنين I، صح؟ طيب، هذه الأن يساوي واحدزايد اتنين I
+
+185
+00:18:54,220 --> 00:18:59,340
+زايد اتنين في اتنين زايد اتنين I ال principle ID
+
+186
+00:18:59,340 --> 00:19:03,940
+is generated by اتنين زايد اتنين I هذه موجودة في
+
+187
+00:19:03,940 --> 00:19:09,160
+ال ID يساوي
+
+188
+00:19:09,160 --> 00:19:14,180
+واحد زايد اتنين I اتنين زايد اتنين I
+
+189
+00:19:23,040 --> 00:19:28,360
+شكل هو لا واحد منهم، مظبوط؟ طيب تعالى نشوف هو منهم
+
+190
+00:19:28,360 --> 00:19:33,660
+ولا مش منهم شو رأيك لو أضفت واحد واطرحت واحد ستكون
+
+191
+00:19:33,660 --> 00:19:38,260
+ثلاثة، أه صح تمام، يبقاش بصيري عندنا سالب واحد
+
+192
+00:19:38,260 --> 00:19:46,780
+زائد واحد واحد اتنين زائد اتنين I زائد اتنين زائد
+
+193
+00:19:46,780 --> 00:19:52,460
+اتنين I اللي هو ال ID هذا موجود فيه ولا لا؟يبقى
+
+194
+00:19:52,460 --> 00:19:57,420
+إيش صار يا بناتي؟ صار ناقص واحد لإثنين زائد اتنين
+
+195
+00:19:57,420 --> 00:20:04,560
+قبل شوية مسحناها وقلنا لكوا سلم واحد هو تلاتة يبقى
+
+196
+00:20:04,560 --> 00:20:09,900
+هذا الكلام تلاتة زائد اتنين زائد اتنين والله طلع
+
+197
+00:20:09,900 --> 00:20:16,560
+صحيح واحد منهم أيه العنصر الأخير؟ مظبوط؟ مافيش
+
+198
+00:20:16,560 --> 00:20:17,620
+رأيك لو جلبت
+
+199
+00:20:21,830 --> 00:20:29,530
+بطء ولكن ستة زائد خمسة I يطلع واحد من هذول مثلا؟
+
+200
+00:20:29,530 --> 00:20:40,310
+هانشوف هذه بقدر اقول اتنين زائد I بضل اربعة زائد
+
+201
+00:20:40,310 --> 00:20:49,810
+اربعة I إذا الستة زائد خمسة I زائد ال principle ID
+
+202
+00:20:49,810 --> 00:20:57,430
+بده يساويإتنين زائد I زائد اتنين في اتنين زائد
+
+203
+00:20:57,430 --> 00:21:05,410
+اتنين I زائد ال principle ID هذا موجود فيه مع
+
+204
+00:21:05,410 --> 00:21:11,810
+السلامة طالع عندنا مين؟ طالع عندنا اتنين زائد I
+
+205
+00:21:11,810 --> 00:21:21,100
+زائد اتنين زائد اتنين I كprinciple ID2 زائد I ولا
+
+206
+00:21:21,100 --> 00:21:28,740
+واحد من هدول شكله لكن حقيقة هذا الكلاب بقدر اقول
+
+207
+00:21:28,740 --> 00:21:35,840
+واحد زائد واحد زائد I زائد ال principle ideal
+
+208
+00:21:35,840 --> 00:21:43,040
+generated by اتنين صار منهم ولا لا منهم يبقى اي
+
+209
+00:21:43,040 --> 00:21:50,280
+رقمين اعداد صحيحة يجي في برق اتحطيهمبتقدر تحوليها
+
+210
+00:21:50,280 --> 00:21:55,760
+على أي شكل من الأشكال الثمانية أظن أجبناها سؤالك
+
+211
+00:21:55,760 --> 00:22:00,120
+اللي كنت بدت تسأليه و لا لكلت بدت أجبنا ما هو
+
+212
+00:22:00,120 --> 00:22:03,840
+السؤال احنا حكينا أن الأعياء فلان موجودة في العربة
+
+213
+00:22:03,840 --> 00:22:08,700
+صح؟ طيب ليش كتابت آية قصفية على شكل أربعة كتابة؟
+
+214
+00:22:08,700 --> 00:22:13,500
+صح ولا غلط؟ طب ليش؟ بس قولي الـEquals صح ولا غلط
+
+215
+00:22:13,500 --> 00:22:19,300
+الأول؟ طيب صح صح ممتاز جدايبقى انا حاطيت شغلة
+
+216
+00:22:19,300 --> 00:22:27,000
+نظرية وكأني بدي اقولك بعدك انه كل عنصر من عناصر ال
+
+217
+00:22:27,000 --> 00:22:31,480
+ring بديكون عليها ال I احنا بديكون علي الشكل اللي
+
+218
+00:22:31,480 --> 00:22:38,500
+انت قولتيله A ناقص B زائد B في واحد زائد I لا مش
+
+219
+00:22:38,500 --> 00:22:44,710
+هكذا كده مش هكذا A ناقص B سبق 4K زائد Iهذه أو هذه؟
+
+220
+00:22:44,710 --> 00:22:50,530
+آه الفرضية هذه يعني؟ آه يعني هذه ليش و هذه ليش؟ آه
+
+221
+00:22:50,530 --> 00:22:54,250
+والله هذه مفهومة ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟
+
+222
+00:22:54,250 --> 00:22:55,470
+ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟
+
+223
+00:22:55,470 --> 00:22:55,470
+ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟
+
+224
+00:22:55,470 --> 00:22:55,470
+ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟
+
+225
+00:22:55,470 --> 00:22:55,630
+ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟
+
+226
+00:22:55,630 --> 00:22:57,350
+ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟ ليش؟
+
+227
+00:22:57,350 --> 00:23:02,870
+ليش؟ ليش؟ ليش؟ ليش؟
+
+228
+00:23:02,870 --> 00:23:06,830
+ليش؟
+
+229
+00:23:06,830 --> 00:23:12,410
+ليش؟
+
+230
+00:23:12,510 --> 00:23:20,470
+إن الـ B عدد زوجي أو عدد فردي فيها مشكلة؟ مش عناصر
+
+231
+00:23:20,470 --> 00:23:24,770
+زد يا إما عدد زوجي يا إما عدد فردي يعني كأنه أنا
+
+232
+00:23:24,770 --> 00:23:29,010
+جمعت الحالتين بمرة واحدة مديش أقول لو كان العدد
+
+233
+00:23:29,010 --> 00:23:33,350
+عدد زوجي إذا كذا واروح أثبت وإذا كان ال N عدد فردي
+
+234
+00:23:33,350 --> 00:23:36,770
+واروح أثبت لأ أخدت الحالتين مرة واحدة سواء كان
+
+235
+00:23:36,770 --> 00:23:40,470
+زوجي و لا فردي وصلت لميل وصلت للنتيجة
+
+236
+00:23:48,750 --> 00:23:54,190
+زد اتنين من عناصرها Zero و واحد، إذا لو كانت ال S
+
+237
+00:23:54,190 --> 00:23:58,990
+بي Zero، بتطلع العدد الزوجي، ولو كانت ال S بواحد،
+
+238
+00:23:58,990 --> 00:24:03,890
+بتطلع العدد الفردي، صح ولا لا؟ يعني أنا جيب كل
+
+239
+00:24:03,890 --> 00:24:08,330
+الأعداد الفردية والأعداد الزوجية مرة واحدة، شو
+
+240
+00:24:08,330 --> 00:24:13,050
+المشكلة فيها هذه؟ في هاي شهادة؟
+
+241
+00:24:14,570 --> 00:24:17,270
+يختار عناصر ضد عبارة عن إيش؟ مش أعداد فردية
+
+242
+00:24:17,270 --> 00:24:22,590
+بزوجية؟ وإن تنزل يبقى أنا بدي أجمعهم في إشارة
+
+243
+00:24:22,590 --> 00:24:26,590
+بشكل؟ دكتور هي لك تحكي ليش يعني إحنا عملنا زي هيك؟
+
+244
+00:24:26,590 --> 00:24:29,990
+يعني كيف بدنا أن إحنا نبتدع الحل هذا؟ إحنا كهذه
+
+245
+00:24:29,990 --> 00:24:38,330
+وسيلة لإختصار شكل العناصر في Z of I من أي شكل إلى
+
+246
+00:24:38,330 --> 00:24:46,140
+الشكل المبسط اللي عندناصح؟ يعني بعد اختصارات طلع
+
+247
+00:24:46,140 --> 00:24:51,960
+رقم زيد رقم في I زيد واحد زيد ال ID صحيح ولا لأ؟
+
+248
+00:24:51,960 --> 00:24:56,200
+يبقى هذا هو كل سؤال دلوقت فيه الوضع بسيط بيختلف عن
+
+249
+00:24:56,200 --> 00:25:00,280
+التاني مش كل واحد يعني احنا ال A زيد B استطعنا
+
+250
+00:25:00,280 --> 00:25:04,840
+كتابتها الشكل هذا غلط ولا صح؟ لا صح مليون مية صح
+
+251
+00:25:04,840 --> 00:25:09,000
+مليون مية ورياضيات كيف تتلاعبي بالأشكال اللي عندي
+
+252
+00:25:09,000 --> 00:25:13,210
+فهي تصلي النتيجة اللي انت بدك إياهافلما أحط بيه
+
+253
+00:25:13,210 --> 00:25:16,530
+عدد زوجي أو عدد فردي بالشكل هذا، شو المشكلة في
+
+254
+00:25:16,530 --> 00:25:24,430
+ذلك؟ إذا S بـ0، يبقى بـ2 العدد زوجي، وإذا S بـ1،
+
+255
+00:25:24,430 --> 00:25:31,930
+عناصر زد اتنين، إذا S بـ1، بصير عدد فردي، ممتازة،
+
+256
+00:25:31,930 --> 00:25:36,650
+أربعة كذا إذا أربعة كذا، افترضي أن الفرق بين A وB
+
+257
+00:25:36,650 --> 00:25:42,970
+يسوي Zero، كلهم بيسووا بعض، يبقى R مجدد Aأفترض أن
+
+258
+00:25:42,970 --> 00:25:49,170
+يكون R يساوي واحد الفرق بينهم يبقى واحد يبقى K في
+
+259
+00:25:49,170 --> 00:25:53,730
+Zero أربعة في Zero في Zero ويبقى واحد اتنين تلاتة
+
+260
+00:25:53,730 --> 00:25:57,830
+يبقى .. لو كان أكبر من الأربعة تظهر عند مين
+
+261
+00:25:57,830 --> 00:26:04,050
+الاربعة K يعني لو كان عندي أربعة تمانية اتناشت
+
+262
+00:26:04,050 --> 00:26:10,890
+ستاشت عشرين مش هيظهر عندي R بزيرو وبصير مضاعفات
+
+263
+00:26:15,770 --> 00:26:20,530
+الفرق ما بين اتنين جولت ايه ادعيت انه اربعة كيز اد
+
+264
+00:26:20,530 --> 00:26:27,130
+ألاف صح؟ الـK قد تكون صفر، تفهم قداش؟ وR انا
+
+265
+00:26:27,130 --> 00:26:30,910
+ماخدها وين؟ يعني يا صفر، يا واحد، يا اتنين، يا
+
+266
+00:26:30,910 --> 00:26:37,330
+تلاتة، وهي ظهرت في الجواب النهائي، صح؟ طيب، افترضي
+
+267
+00:26:37,330 --> 00:26:42,800
+هذا كانت أربع، يبقى صفروفترضي كان تمانية يبقى مظلش
+
+268
+00:26:42,800 --> 00:26:48,760
+الا ات ماشي مظلش الا ال ات طيب افترضي سبعة يبقى
+
+269
+00:26:48,760 --> 00:26:53,760
+أربعة في واحد زائد تلاتة صح ولا لا؟ يبقى موجودة
+
+270
+00:26:53,760 --> 00:26:58,680
+هنا ولا لا؟ أي رقم تاخديه بدي يطلع عندك هنا يعني
+
+271
+00:26:58,680 --> 00:27:02,060
+الفرق بين ايه و بيه إن كان سبعة إن كان تمانية إن
+
+272
+00:27:02,060 --> 00:27:05,560
+كان عشر عشرين جد ما يكون بقدر أحطه على الصيغة اللي
+
+273
+00:27:05,560 --> 00:27:11,640
+عندها دي مظبوط ولا لا؟ يبقى فيها مشكلة؟و هداك عدل
+
+274
+00:27:11,640 --> 00:27:19,220
+زودي و فردي فيها مشكلة في هدى هدى؟
+
+275
+00:27:19,220 --> 00:27:25,200
+شوفت هدى هدى ممكن اضرب هدى هنا و اضرب هدى هيا هنا
+
+276
+00:27:25,200 --> 00:27:32,600
+و هيها هدى هنا و طلته شو المشكلة؟ طلعت هدى هنا في
+
+277
+00:27:32,600 --> 00:27:36,680
+ال principal ID و طلعت هدى في ال principal ID
+
+278
+00:27:36,680 --> 00:27:44,660
+مضلوش عندى الا هدىاللي هو الشكل العام لعناصر من ال
+
+279
+00:27:44,660 --> 00:27:55,100
+factoring اللي عندي نفس
+
+280
+00:27:55,100 --> 00:28:00,940
+السؤال طيب بيختلف كليا الشغل الشغل هو اللي تثبت
+
+281
+00:28:00,940 --> 00:28:08,960
+أنه ما هوش prime أثبتناالآن بدك تروح تجيبك صيغة
+
+282
+00:28:08,960 --> 00:28:13,660
+تتناسب مع الصيغة اللي عندكها لأنه لو غيرت السؤال
+
+283
+00:28:13,660 --> 00:28:19,720
+أو ال ID اللي بتتغير الصيغة وعندك سؤال 56 بنفس
+
+284
+00:28:19,720 --> 00:28:26,600
+الطريقة طالبه الأصل كوني جاي حلال يوم نفس الفكرة
+
+285
+00:28:26,600 --> 00:28:34,510
+بدك تدوري على صيغة مثل الصيغة اللي عندك هناقريبة
+
+286
+00:28:34,510 --> 00:28:41,070
+منها بس مش هي اه تمام و اتكملي شغلك زيها خلصنا اه
+
+287
+00:28:41,070 --> 00:28:44,090
+طب انا بعتبر انه لما أسحبت اثنين عام المشترك هنا
+
+288
+00:28:44,090 --> 00:28:49,090
+بطريقة .. بطريقة العددية هي طريقة يعني خطوة زيادة
+
+289
+00:28:49,090 --> 00:28:51,870
+طب انا ليش مابقول ان اسحب أربع عام المشترك و
+
+290
+00:28:51,870 --> 00:28:54,310
+الأربع بتسوي ال zero و راح .. و انت وين الأربع
+
+291
+00:28:54,310 --> 00:28:59,050
+اللي عندك؟ اللي فات هذي؟ لأ في الخطوة الأولى هذي؟
+
+292
+00:28:59,050 --> 00:29:02,070
+اه عندي أربع زائد أربع ايه بسحب الأربع عام المشترك
+
+293
+00:29:02,070 --> 00:29:05,120
+و الأربع بتسوي ال zero و خلاص و راحمش أسحب اتنين
+
+294
+00:29:05,120 --> 00:29:10,600
+هادي والله هادي فيها مشكلة تقولوا هادي سويته وارضه
+
+295
+00:29:10,600 --> 00:29:14,320
+صح لإن الأربعة موجودة فيه ماحدش يلو كلام عندك بس
+
+296
+00:29:14,320 --> 00:29:19,780
+أنا بدياها هنا بدي أبيلك إنه أنا طيرتها لشان عمصر
+
+297
+00:29:19,780 --> 00:29:24,540
+موجود هنا طيريها ماشي في ال ring الأساسية ماعنديش
+
+298
+00:29:24,540 --> 00:29:27,160
+مشكلة اتبريد ال zero تبقى ال ring الأساسية مش
+
+299
+00:29:27,160 --> 00:29:31,650
+والمشكلة يعني في دالةانا باهمنى اكتبي بس كتابة
+
+300
+00:29:31,650 --> 00:29:36,530
+صحيحة مش لما اناجى احسب ان انا جاية غلط لأ بدي
+
+301
+00:29:36,530 --> 00:29:40,850
+اكتب كتابة صحيحة مبنية على قاعدة علمية صحيحة خلصنا
+
+302
+00:29:40,850 --> 00:29:46,810
+طيب هى انتهينا من سؤال 38 واخد اكتر من اللاجئ
+
+303
+00:30:06,940 --> 00:30:14,780
+طيب هذا كان سؤال 38 بعده سؤال 41 سؤال 41 شافه مش
+
+304
+00:30:14,780 --> 00:30:19,900
+حكتب ولا كلمة باختصار بيقول لو جينا على ال ring و
+
+305
+00:30:19,900 --> 00:30:25,490
+أخدنا كل ال ideal مش ring integral domainواخدنا كل
+
+306
+00:30:25,490 --> 00:30:29,750
+ال ideals اللي في ال integral domain هدول وطلع كل
+
+307
+00:30:29,750 --> 00:30:34,630
+واحد فيهم principle ideal بقول ال integral domain
+
+308
+00:30:34,630 --> 00:30:40,930
+اسمه principle ideal domain واضح صح؟ إذا كانت ال
+
+309
+00:30:40,930 --> 00:30:45,210
+integral domain كل ideal is a principle بدي أطلق
+
+310
+00:30:45,210 --> 00:30:49,650
+عليه تسمية principle ideal domain يعني كل ideal
+
+311
+00:30:49,650 --> 00:30:54,670
+فيه عبارة عن ال principle طيب السؤال هوالـ z عندك
+
+312
+00:30:54,670 --> 00:30:58,210
+قال لي أثبت إن هذا principle ideal دمية السؤال هو
+
+313
+00:30:58,210 --> 00:31:03,430
+هل الـ z integral domain أثبتناها
+
+314
+00:31:03,430 --> 00:31:08,410
+قبل هيك انتجرال دومين هي واحدة، أيه الثانية؟ بدي
+
+315
+00:31:08,410 --> 00:31:12,310
+أثبت إن كل فريق دي is a principle ما هو شكل ال
+
+316
+00:31:12,310 --> 00:31:19,480
+ideal فيها في ال z أيش شكل ال ideal؟تثبتناها قبلك
+
+317
+00:31:19,480 --> 00:31:28,000
+ان اي ideal في ال Z على شكل NZ مظبوط يبقى NZ هو
+
+318
+00:31:28,000 --> 00:31:32,180
+ideal موجود طب ال NZ مش هو ال principle ideal
+
+319
+00:31:32,180 --> 00:31:39,000
+generated by N صح ولا لأ يبقى كل ideal فيها هذا
+
+320
+00:31:39,000 --> 00:31:42,820
+principle إذا هي principle ideal دومين وهو المطلوب
+
+321
+00:31:42,820 --> 00:31:52,060
+تمامطيب، الآن جينا لسؤال 42 جاطاني بلغة المصفوفات
+
+322
+00:31:52,060 --> 00:31:59,400
+42 قاللي
+
+323
+00:31:59,400 --> 00:32:05,520
+كويس، قاللي اه مستوى كل المصفوفات اللي على صيغة a
+
+324
+00:32:05,520 --> 00:32:14,450
+,b,0,d، بحيث ال a و ال b، ال aو ال B و ال D أعداد
+
+325
+00:32:14,450 --> 00:32:23,390
+صحيحة وطال ال S هي كل ال R و S و T ال R و S و Zero
+
+326
+00:32:23,390 --> 00:32:30,930
+و T بحيث ال R و ال S و ال T برضه أعداد صحيحة
+
+327
+00:32:30,930 --> 00:32:37,670
+بالشكل اللي عندنا هذا تمام؟ بس قلل ال S هذا مانو
+
+328
+00:32:37,670 --> 00:32:45,580
+عدد زوجييبقى بدل ما اكتبوا S بدي اكتبوا مثلا اتنين
+
+329
+00:32:45,580 --> 00:32:54,300
+K تمام؟ قال لي لو كانت هذه عبارة عن ideal ال S
+
+330
+00:32:54,300 --> 00:33:00,500
+كانت ideal شو العلاقة ما بين ال R و T؟ ايش بتقدر
+
+331
+00:33:00,500 --> 00:33:04,840
+تقول عن العلاقة ما بين R و T؟ بقولكوا اسم، عشان
+
+332
+00:33:04,840 --> 00:33:09,720
+تكون هذه idealبدي يكون الضرب من اليمين و من الشمال
+
+333
+00:33:09,720 --> 00:33:17,440
+موجود وين؟ موجود في S يعني لو ضربنا A, B, 0, D في
+
+334
+00:33:17,440 --> 00:33:24,940
+من؟ في A و 2K و 0 و T بدي هيكون في S يبقى هذا
+
+335
+00:33:24,940 --> 00:33:30,200
+الكلام بدي يساوي الصف الأول في العمودي الأولي A, A
+
+336
+00:33:30,200 --> 00:33:37,980
+الصف الأول في العمودي التاني يبقى 2A, Aزائد B T
+
+337
+00:33:37,980 --> 00:33:43,900
+وهذا Zero وصف التاني في العمود التاني بـ D T لو
+
+338
+00:33:43,900 --> 00:33:52,960
+ضربنا من الشمال يبقى R 2 K 0 T في ال A B 0 D هذا
+
+339
+00:33:52,960 --> 00:33:58,480
+الكلام يساوي صف الأول في العمود الأول بـ R A صف
+
+340
+00:33:58,480 --> 00:34:08,680
+الأول في العمود الثاني يبقى R Bزائد اتنين كد وهذا
+
+341
+00:34:08,680 --> 00:34:17,120
+زيرو وهذا في العمود التاني كد هذا الان مشان يكون
+
+342
+00:34:17,120 --> 00:34:23,700
+ideal هذا يجب أن يكون في اسم مشان يكون في اسم يجب
+
+343
+00:34:23,700 --> 00:34:29,260
+العدد هذا يكون عدد زوج طيب هذا زوجي إذا ملزمني هذا
+
+344
+00:34:29,260 --> 00:34:37,060
+يكون زوجموجود في S إذا كان ال B في ال T بتسوي
+
+345
+00:34:37,060 --> 00:34:45,900
+اتنين M وهذا موجود في S إذا كان ال R في B بتسوي
+
+346
+00:34:45,900 --> 00:34:53,500
+اتنين N مثلا يبقى في هذه الحالة إن حدث ذلك بقول
+
+347
+00:34:53,500 --> 00:35:01,900
+هذا اللي هو IDطيب إيش ماقدر أستفيد من هذا الشغل؟
+
+348
+00:35:01,900 --> 00:35:07,820
+لو طرحتم مع بعض والله جمعتم مع بعض سيانة مثلا لو
+
+349
+00:35:07,820 --> 00:35:15,280
+طرحتم ال B عامل مشترك وظل T ناقص ال R يساوي 2 في
+
+350
+00:35:15,280 --> 00:35:21,640
+ال M ناقص ال M قال إيش بتقدر تقول عن T و R؟ بقول
+
+351
+00:35:21,640 --> 00:35:29,740
+إن مضاعفاتهم يكونوا عددا زوجيابدي ساوي عدد زودي
+
+352
+00:35:29,740 --> 00:35:40,440
+هذا بدي يعطينا ان ال multiple of R minus T is even
+
+353
+00:35:40,440 --> 00:35:48,980
+إذا حدث ذلك بيصير هدوي دين غير ذلك يبعت الله طيب
+
+354
+00:35:48,980 --> 00:35:54,060
+نيجي لسؤال خمسة و عشرين خمسة و عشرين ال R commuted
+
+355
+00:35:54,060 --> 00:36:00,020
+و ال A subsetمن ال R بيّللي ان ال annihilator is
+
+356
+00:36:00,020 --> 00:36:08,820
+an ID ال annihilator سؤال خمسة واربعين ال H silent
+
+357
+00:36:08,820 --> 00:36:18,200
+يا بنات فبقول ال annihilator of
+
+358
+00:36:18,200 --> 00:36:30,620
+A لحديله الرمز annihilator لل AR اللي موجودة في R
+
+359
+00:36:30,620 --> 00:36:41,040
+بحيث R of A أو R في A بده يساوي Zero لكل ال A اللي
+
+360
+00:36:41,040 --> 00:36:48,280
+موجودة في A لكل ال A اللي موجودة في A يعني كل
+
+361
+00:36:48,280 --> 00:36:53,360
+العناصر اللي موجودة في Rاللي لو ضربته في جميع
+
+362
+00:36:53,360 --> 00:36:59,180
+عناصر ال ring بدي يعطيلي ال zero هذا بده نثبت انه
+
+363
+00:36:59,180 --> 00:37:04,340
+ideal الخطوات التلاتة المعروفات ننقم تي ناخد
+
+364
+00:37:04,340 --> 00:37:07,860
+عنصرين الفرق بينهما نجيب عنصر في اخر عنصر من انه
+
+365
+00:37:07,860 --> 00:37:13,720
+نضربهم يطلع من يطلع ال zero يبقى هذا بده نثبت انه
+
+366
+00:37:13,720 --> 00:37:22,120
+ideal شغل روتيني مباشر فيش فيه حدسؤال 46 are
+
+367
+00:37:22,120 --> 00:37:31,980
+commutative لنعرف حاجة اسمها ال radical 46 لنعرف
+
+368
+00:37:31,980 --> 00:37:41,380
+حاجة اسمها ال radical ال radical of ال ideal A
+
+369
+00:37:41,380 --> 00:37:52,130
+اللي هو كل ال N of Aيعني كل العناصر R اللي موجودة
+
+370
+00:37:52,130 --> 00:38:02,130
+في R such that R في N موجودة in for some N اللي
+
+371
+00:38:02,130 --> 00:38:12,570
+موجودة في Z plus قال لي اثبتلي ان هذا is an ideal
+
+372
+00:38:14,020 --> 00:38:16,640
+هذا أصعب من السؤال اللي جاب السؤال اللي جابله
+
+373
+00:38:16,640 --> 00:38:22,560
+مباشرة مافيش للف ولا دوران الخطوات بتيجي مباشرة
+
+374
+00:38:22,560 --> 00:38:29,400
+مرة تانية يا بنات ال null radical لل ideal A هدله
+
+375
+00:38:29,400 --> 00:38:34,520
+رمز N of A يبقى N of A رمز لل null radical أنا
+
+376
+00:38:34,520 --> 00:38:39,120
+بديش الرمز بدي المعنى الرياضي المعنى الرياضي كل
+
+377
+00:38:39,120 --> 00:38:44,540
+العناصر اللي موجودة في ال ring Rاللي ورافعتها لأُس
+
+378
+00:38:44,540 --> 00:38:50,860
+مثلا ترميع تكييب تلاتة عشرة أي أُس تقدر عليه
+
+379
+00:38:50,860 --> 00:38:55,640
+تلاقيه موجود في إيه يبقى في هذه الحالة بقول هذا
+
+380
+00:38:55,640 --> 00:39:00,660
+عنصر موجود في الـNil Radical تمام؟ في الـNil
+
+381
+00:39:00,660 --> 00:39:05,680
+Radical إيه؟ بنا نثبت إن هذا عبارة عن ID أول شيء،
+
+382
+00:39:05,680 --> 00:39:13,220
+النقطة الأولى، هل هذا MT وما من MT؟ما نمكن نجيب
+
+383
+00:39:13,220 --> 00:39:20,000
+عنصر واحد فقط موجود فيه ال zero موجود في ال R ولا
+
+384
+00:39:20,000 --> 00:39:26,700
+لا ال zero لو رفعتيه لأسقين قداش بطلع ال zero يبقى
+
+385
+00:39:26,700 --> 00:39:33,740
+هدف يبدو يعطيلك ان ال zero موجود في ال radical of
+
+386
+00:39:33,740 --> 00:39:41,170
+A لأن ال zero موجود في ال ID Aيبقى Zero وهذا موجود
+
+387
+00:39:41,170 --> 00:39:48,470
+في ال IDLA لحد هنا هذا مباشر الامدرول خدى ل X وY
+
+388
+00:39:48,470 --> 00:39:56,550
+موجودة في النل Radical of A then ال X بده يساوي او
+
+389
+00:39:56,550 --> 00:40:05,290
+ال X موجودة ال X بده يساوي A مثلا then
+
+390
+00:40:05,950 --> 00:40:11,490
+X موجودة في الـ Radical يبقى X to the power of N
+
+391
+00:40:11,490 --> 00:40:16,850
+موجودة في A و Y to the power of N موجودة في الـ A
+
+392
+00:40:16,850 --> 00:40:22,810
+طبعاً اللي بتعرفها يعني الرقم N مش ثابت يختلف من
+
+393
+00:40:22,810 --> 00:40:28,610
+عنصر إلى آخر عنصر الأول يمكن تربيع يطلع Zero عنصر
+
+394
+00:40:28,610 --> 00:40:33,190
+التاني يمكن أس خمسة يطلع Zero يبقى الأس هذا ليس
+
+395
+00:40:33,190 --> 00:40:41,660
+أسا ثابتاًبدي أخد الـ X ناقص الـ Y إذا جدرت أرفع
+
+396
+00:40:41,660 --> 00:40:50,200
+أو أقس و أجد هذا موجود في الـ ID المعنى هو X ناقص
+
+397
+00:40:50,200 --> 00:40:57,480
+Y موجودة في الـ radical إذا لو جيتك يا بنات N زائد
+
+398
+00:40:57,480 --> 00:41:05,390
+M مثلا يبقى هذا مركوك ذات الحددالـ Binomial صحيح
+
+399
+00:41:05,390 --> 00:41:13,790
+ولا لا؟ يرجع هذا X أُس N زائد M ناقص N زائد M قعف
+
+400
+00:41:13,790 --> 00:41:22,270
+واحد X أُس N زائد M ناقص واحد Y أُس واحد بعد النقص
+
+401
+00:41:22,270 --> 00:41:30,020
+بيجينا زائد اللي هو N زائد M قعف اتنينالـ X أُس N
+
+402
+00:41:30,020 --> 00:41:36,700
+زائد الـ M ناقص اتنين Y تربيع أه هذه ناقص هذه زائد
+
+403
+00:41:36,700 --> 00:41:44,200
+اللي بعدها ناقص هنوصل لناقص واحد أس M الـ N زائد
+
+404
+00:41:44,200 --> 00:41:53,780
+الـ M التوافيق الـ M مضروبة في X أس N في الـ Y أس
+
+405
+00:41:53,780 --> 00:42:00,280
+M تمامونظل ماشيين على الشائعات اللي هاتي لما نوصل
+
+406
+00:42:00,280 --> 00:42:07,240
+لل Y أس N زائد ال M بدا أشوف هذا وين موجود وين هذه
+
+407
+00:42:07,240 --> 00:42:15,400
+موجودة يا بنات؟ موجودة في إيه؟ مش X أس N في إيه؟
+
+408
+00:42:15,400 --> 00:42:21,460
+يبقى X أس N في U و X أس M في R حاصل ضربهم في إيه؟
+
+409
+00:42:21,460 --> 00:42:28,040
+لأن ال A ديإذاً هذه كأني بقدر أقول X أُس N في X
+
+410
+00:42:28,040 --> 00:42:34,660
+أُس M وهذا ناقص هذا كله رقم مالوش دعوة وهذا بقدر
+
+411
+00:42:34,660 --> 00:42:40,960
+أقول X أُس M في X أُس M ناقص واحد في ال Y وهذا
+
+412
+00:42:40,960 --> 00:42:46,360
+زائد إلى أخرى إلى غاية ما توصل إلى الآخر زائد Y
+
+413
+00:42:46,360 --> 00:42:52,620
+أُس N في Y أُس M خلّعيلي هنا هذا موجود في A ولا
+
+414
+00:42:52,620 --> 00:43:00,250
+لا؟طبعا هاي ال X و Z موجود في ايه؟ ضربنا في
+
+415
+00:43:00,250 --> 00:43:06,070
+element من ال ring بصير كله موجود في ايه؟ اذا هذا
+
+416
+00:43:06,070 --> 00:43:11,670
+كله موجود في ايه؟ و هذا بنفس الطريقة كله موجود في
+
+417
+00:43:11,670 --> 00:43:18,270
+ايه؟ و الظلم ماشي كمان هذا في ايه؟ و لا هذا virus
+
+418
+00:43:18,270 --> 00:43:23,810
+المظبط و هذا كله موجود في ايه؟إذا هذا المجموع كله
+
+419
+00:43:23,810 --> 00:43:31,570
+موجود في الـ A X ناقص Y مرفوعة لوس موجود في الـ A
+
+420
+00:43:31,570 --> 00:43:41,650
+معناه هذا الكلام إن X ناقص Y موجود في الـ A نقطة
+
+421
+00:43:41,650 --> 00:43:53,140
+الأخيرة لو أخذنا الـ R موجودة في R andالـ X موجودة
+
+422
+00:43:53,140 --> 00:43:59,980
+في النل Radical للـ A بدي أثبت أن حاصل ضربهما
+
+423
+00:43:59,980 --> 00:44:06,560
+موجود في النل Radical لـ A يبقى then الـ R موجودة
+
+424
+00:44:06,560 --> 00:44:13,440
+في R أن الـ X موجودة في النل Radical معناته إن الـ
+
+425
+00:44:13,440 --> 00:44:23,490
+X موجودة في A طبعاطب الآن لو أخدت R X أُص N هشوف
+
+426
+00:44:23,490 --> 00:44:28,890
+كده إيش تساوي الـ R كان لـ commutative من البداية
+
+427
+00:44:28,890 --> 00:44:34,970
+يبقى مدام commutative R N X to the power N هذا
+
+428
+00:44:34,970 --> 00:44:42,190
+موجود في A والـ A عادل يبقى ضررته في element من ال
+
+429
+00:44:42,190 --> 00:44:51,170
+ring R بدي يكون موجود وين؟ موجود في Aand الـ R and
+
+430
+00:44:51,170 --> 00:44:58,490
+الـ X R to the power N هذا X to the power N R أُس
+
+431
+00:44:58,490 --> 00:45:04,870
+N هذا موجود في أيه؟ ضربت في element من R، موجود في
+
+432
+00:45:04,870 --> 00:45:13,400
+أيه؟ موجود في أيه؟ معنى هذا الكلام إن الـ R Xوالـ
+
+433
+00:45:13,400 --> 00:45:21,140
+XR موجودة في الـ Radical of A يبقى ساعة إن الـ
+
+434
+00:45:21,140 --> 00:45:30,920
+Radical of A is an ideal السؤال هو تبدأ تحسب
+
+435
+00:45:30,920 --> 00:45:40,780
+الحسابات المختلفة لهذه ال ideals لشأن نجيب على هذا
+
+436
+00:45:40,780 --> 00:45:48,370
+السؤالبنذهب لسؤال 48 اللي يعتبر تطبيق مباشر عليه
+
+437
+00:45:48,370 --> 00:45:58,310
+يبدأ سؤال 48 سؤال 48 بيقولني
+
+438
+00:45:58,310 --> 00:46:11,190
+ال R هي Z 36 N Z 36 ده اللي ارتع انداالـ A نل
+
+439
+00:46:11,190 --> 00:46:17,410
+راديكل لل principle ideal generated by 0 والنل
+
+440
+00:46:17,410 --> 00:46:22,510
+راديكل للprinciple ideal generated by 4 والنل
+
+441
+00:46:22,510 --> 00:46:27,510
+راديكل للprinciple ideal generated by 6 يبقى انا
+
+442
+00:46:27,510 --> 00:46:34,550
+اذا سويتلك اتنين سياتك بتروح تسوي مين اتنين اول شي
+
+443
+00:46:34,550 --> 00:46:42,370
+ازد ستة وتلاتين فيها كام عنصر36 عنصر تمام بدا نيجي
+
+444
+00:46:42,370 --> 00:46:49,110
+لل principle id generated by zero منهم؟ في غيرهم؟
+
+445
+00:46:49,110 --> 00:46:56,470
+لأ ممتاز جدا يبقى بدا نيجي لأن ال radical of zero
+
+446
+00:46:56,470 --> 00:47:04,010
+من العناصر طبقا للتعريف من العناصر اللي موجودة في
+
+447
+00:47:04,010 --> 00:47:09,260
+Rواللي لو رفعته واستربيه تكييب خمسة، عشرة، مبارح،
+
+448
+00:47:09,260 --> 00:47:16,940
+كده يطلع فيه A، من الـ A هي صح؟ طيب، نجد العناصر
+
+449
+00:47:16,940 --> 00:47:21,140
+الـ Zero موجود في الـ 36، ارفعه إلى أي قصر، كدهش
+
+450
+00:47:21,140 --> 00:47:26,320
+بيكون؟ Zero يعني صار فإن اللي رادي كان يبقى صار
+
+451
+00:47:26,320 --> 00:47:34,530
+Zero طيب، الواحدوأمره مصير Zero رفعتين قص واحدة لأ
+
+452
+00:47:34,530 --> 00:47:45,750
+حُط علشان تقبل اتنين تلاتة الخمسة طب الستة ستة
+
+453
+00:47:45,750 --> 00:47:51,870
+تربيع ستة وتلاتين تعالى Zero صح ولا لأ يبقى الستة
+
+454
+00:47:51,870 --> 00:47:57,530
+موجودة في الدنيا اللي رادي كان طب السامة تمانية
+
+455
+00:47:57,530 --> 00:47:58,530
+ستة
+
+456
+00:48:01,370 --> 00:48:07,530
+معنى لو كملت حسابات تصير تمنتاشر واربع وعشرين
+
+457
+00:48:07,530 --> 00:48:13,330
+وتلاتين يعني ال principle ideal generated by ستة،
+
+458
+00:48:13,330 --> 00:48:18,790
+تمام؟ طب هذا سهل، ليش؟ لأنه في الشغل ال zero، بدي
+
+459
+00:48:18,790 --> 00:48:22,730
+أي element أرفع للأس يطلع zero، طلع العناصر اللي
+
+460
+00:48:22,730 --> 00:48:27,470
+عندناطب بدالي هذه النمرة ايه؟ بدالي النمرة بيبدن
+
+461
+00:48:27,470 --> 00:48:31,270
+ال radical ال principle ideal generated by اربعة
+
+462
+00:48:31,270 --> 00:48:38,910
+مين هو ال principle ideal generated by اربعة؟ روح،
+
+463
+00:48:38,910 --> 00:48:45,230
+زيرو، اربعة، تمانية، اتنان، ستة، عشرين، اربعة و
+
+464
+00:48:45,230 --> 00:48:50,540
+عشرين، تمانية و عشرين، اتنين و تلاتين، مظبوط؟يبقى
+
+465
+00:48:50,540 --> 00:48:56,380
+أنا بدي أبدأ في عناصر الـ 36 كل واحد فيهم مين اللي
+
+466
+00:48:56,380 --> 00:49:02,100
+بدي أرفع أو أقص يطبع واحد من هدول، تمام؟ يبقى انا
+
+467
+00:49:02,100 --> 00:49:06,660
+اللي radical اللي أرفع، الـ0 منهم؟ لأن الـ0 أرفع
+
+468
+00:49:06,660 --> 00:49:13,700
+ولا يقص، الـ0 هي وموجود، طيب الواحد منهم؟ ارفع ولا
+
+469
+00:49:13,700 --> 00:49:17,990
+يقص بضل واحد ولا واحد منهميبقى واحد صفحة شجة أنت
+
+470
+00:49:17,990 --> 00:49:26,170
+مش عندك، طب اتنين، اتنين تاربيع ماربع، اتنين
+
+471
+00:49:26,170 --> 00:49:30,070
+تاربيع في هيو موجود، طب التلاتة، اتنين تاربيع في
+
+472
+00:49:30,070 --> 00:49:30,390
+هيو موجود، طب التلاتة، اتنين تاربيع في هيو موجود،
+
+473
+00:49:30,390 --> 00:49:30,730
+طب التلاتة، اتنين تاربيع في هيو موجود، طب التلاتة،
+
+474
+00:49:30,730 --> 00:49:31,310
+اتنين تاربيع في هيو موجود، طب التلاتة، اتنين
+
+475
+00:49:31,310 --> 00:49:32,370
+تاربيع في هيو موجود، طب التلاتة، اتنين تاربيع في
+
+476
+00:49:32,370 --> 00:49:38,130
+هيو موجود، طب التلاتة، اتنين تاربيع في هيو موجود،
+
+477
+00:49:38,130 --> 00:49:44,980
+طب التلاتة، اتنين تاربيع فيأه بيطلع Zero، ستة
+
+478
+00:49:44,980 --> 00:49:50,120
+دقيقة بيطلعوا Zero موجودة، بيبجوا الست أو السبع،
+
+479
+00:49:50,120 --> 00:49:57,380
+التمانية، يللا، تمانية، عشر، أطلاش، لغاية أربعة و
+
+480
+00:49:57,380 --> 00:50:02,480
+تلاتين، كل الأعداد الزوجية يهيب ال principle ID ال
+
+481
+00:50:02,480 --> 00:50:09,690
+generator fire nameالحسابات حسبت من خلال نص
+
+482
+00:50:09,690 --> 00:50:16,330
+التعريف اللي عليها طيب يا بنات اضايق لان السؤال
+
+483
+00:50:16,330 --> 00:50:22,050
+اكتر او اكتر؟ تلات احنا هذا ستة و تمانية و اربعين
+
+484
+00:50:22,050 --> 00:50:28,930
+خلاص طيب الخمسين الخمسين هذا اللي كثير طيب الخمسين
+
+485
+00:50:31,220 --> 00:50:38,080
+هذا بيكتب كأنه نل لنل radical of A يساوي ال N of A
+
+486
+00:50:38,080 --> 00:50:43,100
+بدي أخد عنصر هنا و أثبت إنه موجود هنا و من ثم أخد
+
+487
+00:50:43,100 --> 00:50:49,200
+عنصر هنا و أثبت إنه موجود هنا الأول أسهل كثير من
+
+488
+00:50:49,200 --> 00:50:55,000
+التاني التاني صعوب أن يتفاج مش أكتر كيف؟ بدي أمسك
+
+489
+00:50:55,000 --> 00:51:01,710
+في التاني و دي لل X موجود في ال N of Aالـ N of A
+
+490
+00:51:01,710 --> 00:51:06,990
+تحتاني ID قبل قليل، إذا لو قلت X تربيع، موجودة هنا
+
+491
+00:51:06,990 --> 00:51:15,630
+ولا لا؟ طب X تربيع؟ طب X أُس N؟ أنا بدي أقول إن X
+
+492
+00:51:15,630 --> 00:51:25,890
+أُس N موجودة في الـ N of A since لإن الـ N of A is
+
+493
+00:51:25,890 --> 00:51:39,780
+an ID، تمام؟فماش معنى هذا الكلام ان ال X موجودة و
+
+494
+00:51:39,780 --> 00:51:50,300
+موجودة في ال N لل N of A صح ولا لأ؟ طيب طيب كل ال
+
+495
+00:51:50,300 --> 00:51:58,220
+R بحث انا عندي R of N موجودة في A يبقى ال A يبقى
+
+496
+00:51:58,220 --> 00:52:05,210
+ال Rبدا تكون موجودة في ال N لل N of A يبقى بنوع
+
+497
+00:52:05,210 --> 00:52:10,830
+انا علي اخدت element هنا اللي موجود هنا يبقى بقدر
+
+498
+00:52:10,830 --> 00:52:19,310
+اروح اقوله يبقى ال N of A صافس من ال N لل N of A
+
+499
+00:52:19,310 --> 00:52:22,550
+التاني سهل مش فيه مشكلة خالص ولا حاجة
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..db62ce204712efded3d1795e069d164837e9f89c
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/fMZdwGT6Zgo_postprocess.srt
@@ -0,0 +1,1876 @@
+1
+00:00:20,860 --> 00:00:26,000
+بسم الله الرحمن الرحيم المرة اللي فاتت إبتدانا في
+
+2
+00:00:26,000 --> 00:00:33,680
+حل exercises على chapter 16 ووصلنا إلى السؤال رقم
+
+3
+00:00:33,680 --> 00:00:40,980
+.. السؤال رقم 12 أنا ما أذكر يعني، مظلوم؟ وقلنا
+
+4
+00:00:40,980 --> 00:00:46,720
+هذا بدنا يأكل good exercises اتمرنوا إيديكوا فيه
+
+5
+00:00:46,720 --> 00:00:53,670
+وزي وزي سؤال 11 اللي قبللا أدري حلته ولا لا ممتازة
+
+6
+00:00:53,670 --> 00:00:58,050
+يبقى بدي أقول الفكرة الشفاوية اللي ماعرفتش أتحل ثم
+
+7
+00:00:58,050 --> 00:01:03,130
+ننتقل إلى السؤال اللي بعد طبعا احنا بدنا نقسم في
+
+8
+00:01:03,130 --> 00:01:09,290
+سؤال اتناشر خمسة اكسوس اربع على تلاتة اكس تربيه
+
+9
+00:01:09,290 --> 00:01:18,250
+احنا بنشتغل وين في Z سبعة of X مظبوط يبقى في Z
+
+10
+00:01:18,250 --> 00:01:24,760
+سبعة of Xفي Z7 لما أجي أجسم خمسة على تلاتة، يبقى
+
+11
+00:01:24,760 --> 00:01:29,560
+فيش حاجة اسم الخمسة على تلاتة، هذا كسر مش موجود في
+
+12
+00:01:29,560 --> 00:01:36,840
+Z، فماذا نعمل؟ بنروح، بنضيف لخمسة مضاعفات السبعة
+
+13
+00:01:36,840 --> 00:01:42,280
+لغاية ما تجسم على تلاتة، يبقى أنا عندي خمسة،
+
+14
+00:01:42,280 --> 00:01:46,280
+أضيفيلها سبعة سبعة تانية، Zero في Z7، يعني كأني
+
+15
+00:01:46,280 --> 00:01:51,710
+ماعملتش حاجة، فبصير سبعة وخمسةأتناشى و بتقسم ع مين
+
+16
+00:01:51,710 --> 00:01:57,490
+على تلاتة لو مانقسمتش باضيف كمان سابعة بضل اضيف
+
+17
+00:01:57,490 --> 00:02:02,770
+سبعت لما تقسم بيكون هى النتيجة المطلوبة فانت سبعة
+
+18
+00:02:02,770 --> 00:02:08,110
+و خمسة اتناش بس اتناش ع تلاتة باربع اكس تربيع
+
+19
+00:02:08,110 --> 00:02:13,250
+وهكذا بكمل مثل القسم العادى وانا اعطيتكوا قبل ذلك
+
+20
+00:02:13,430 --> 00:02:17,930
+مثال قسمة بس ماكانش كان المعامل هنا واحد والمعامل
+
+21
+00:02:17,930 --> 00:02:22,290
+هنا واحد وبالتالي لم تظهر المشكلة لكن لما كانوا
+
+22
+00:02:22,290 --> 00:02:28,270
+أرقام مختلفة هنا ظهرت المشكلة وحلها المضيف مضاعفات
+
+23
+00:02:28,270 --> 00:02:33,950
+السبعة بحيث تتم القسمة طبعا؟ إذا سؤال اتناش very
+
+24
+00:02:33,950 --> 00:02:41,260
+easy بروح الأقل سؤال سبعتاشروهذا سؤال سبعتاش أخدنا
+
+25
+00:02:41,260 --> 00:02:46,240
+لإنه لازملي في شبطر سبعتاش و لازملي أي شبطر طبعا
+
+26
+00:02:46,240 --> 00:02:52,620
+تحت إذن هذا يجب أن نحله لإنه لازملي قدام يبقى بالي
+
+27
+00:02:52,620 --> 00:02:59,140
+لمين لسؤال سبعتاش سؤال سبعتاش بيقول دي integral
+
+28
+00:02:59,140 --> 00:03:06,260
+domain يبقى دي is is integral domain
+
+29
+00:03:08,690 --> 00:03:15,110
+و عندنا ال F of X و ال G of X موجودة في D و ال F
+
+30
+00:03:15,110 --> 00:03:25,610
+of X و ال G of X عناصر موجودة في ال D of X بيقول
+
+31
+00:03:25,610 --> 00:03:29,290
+لي بعدك اثبت ان ال degree لحاصل الضرب تساوي ال
+
+32
+00:03:29,290 --> 00:03:38,250
+degree ل الجمع يفى المطلوب الأول النقطة الأولى شإن
+
+33
+00:03:38,250 --> 00:03:46,210
+ال degree لمن؟ لل F of X بال G of X تساوي ال
+
+34
+00:03:46,210 --> 00:03:53,330
+degree لل F مضافا إليها ال degree لل G هذا المطلوب
+
+35
+00:03:53,330 --> 00:03:58,650
+الأول المطلوب الثاني بيقول هذي commutative ring
+
+36
+00:03:58,650 --> 00:04:03,470
+بحيث هذي تكون مش صحية كيف يعني مش صحية يعني يكون
+
+37
+00:04:03,470 --> 00:04:10,910
+ال degree لحاصل الضرب أقلمن ال degree لمن؟ للجامعة
+
+38
+00:04:10,910 --> 00:04:14,510
+بس مش في ال integral domain ال integral domain ده
+
+39
+00:04:14,510 --> 00:04:18,970
+كلام صحيح دايما أبدا قلت لأ في commutative ring
+
+40
+00:04:18,970 --> 00:04:25,390
+ليس بالضرورة أن تكون integral domain طيب خلّي
+
+41
+00:04:25,390 --> 00:04:29,770
+المطلوب التاني بعد ما نخلص المطلوب الأول يبدأ أنا
+
+42
+00:04:29,770 --> 00:04:35,700
+بدي أخد ال two polynomials موجودة في D of Xيبقى ال
+
+43
+00:04:35,700 --> 00:04:42,680
+solution على الوجه التالي نقطة واحدة بداية اقول
+
+44
+00:04:42,680 --> 00:04:50,280
+افترضوا ان ال f of x هي a n x to the power n a
+
+45
+00:04:50,280 --> 00:04:57,920
+minus ال one لل x أُس n minus ال one زائد زائد إلى
+
+46
+00:04:57,920 --> 00:05:07,060
+a one x زائد ال a naughtوفي المقابل ال a n does
+
+47
+00:05:07,060 --> 00:05:12,840
+not equal to zero مشان أضمن أن أعلى degree عندي
+
+48
+00:05:12,840 --> 00:05:20,640
+جداش اللي هو m وفي نفس الوقت ال g of x بدي يسوي b
+
+49
+00:05:20,640 --> 00:05:26,840
+m x to the power m b minus ال one x to the power m
+
+50
+00:05:26,840 --> 00:05:33,460
+minus ال one زائد b one x زائد ال b nonو ال BM
+
+51
+00:05:33,460 --> 00:05:40,880
+كذلك لا تساوي 0 والتنتين هدول كلهم موجودات في مين؟
+
+52
+00:05:40,880 --> 00:05:47,800
+في ال integral domain D of X الآن بدي أخد حاصل
+
+53
+00:05:47,800 --> 00:05:55,940
+ضربهما يبقى بدي أخد ال F of X في ال G of X يبقى
+
+54
+00:05:55,940 --> 00:06:04,450
+لما أبدأ أضربهم هقول AN BM في X أُس Nزائد ال M
+
+55
+00:06:04,450 --> 00:06:12,430
+تمام زائد ونظل ماشيين لغاية ما نوصل لمين لل A node
+
+56
+00:06:12,430 --> 00:06:21,310
+B1 زائد A1 B node في ال X زائد ال A node B node
+
+57
+00:06:21,310 --> 00:06:29,070
+يبقى هاد هاش هاد حاصل الضرر الآن أنا بتهمني ال
+
+58
+00:06:29,070 --> 00:06:37,180
+degreeهذه الان بي ام ممكن تكون بزيرو لأ لأ لأ لأ
+
+59
+00:06:37,180 --> 00:06:40,420
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+60
+00:06:40,420 --> 00:06:40,920
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+61
+00:06:40,920 --> 00:06:41,040
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+62
+00:06:41,040 --> 00:06:41,920
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+63
+00:06:41,920 --> 00:06:42,100
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+64
+00:06:42,100 --> 00:06:47,980
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+65
+00:06:47,980 --> 00:06:52,260
+لأ لأ لأ لأ لأ
+
+66
+00:06:52,260 --> 00:06:58,140
+لأ
+
+67
+00:06:58,140 --> 00:07:04,850
+لألا هدف Zero ولا هدف Zero يعني بنفع لما الهدف
+
+68
+00:07:04,850 --> 00:07:09,630
+ماهياش ب Zero وهدف ماهياش ب Zero حاصل درجة مايكونش
+
+69
+00:07:09,630 --> 00:07:15,990
+Zero فهي احتمال ان يكون Zero بس لما كان Integral
+
+70
+00:07:15,990 --> 00:07:22,310
+domain يبقى لا يمكن ان يساوي Zero يبقى هدف لا
+
+71
+00:07:22,310 --> 00:07:27,550
+يساوي Zero لسببين السبب الأول ولا واحدة فيهم ب
+
+72
+00:07:27,550 --> 00:07:38,460
+Zero والسبب الثانيالـ D is an integral domain
+
+73
+00:07:38,460 --> 00:07:43,240
+تمام؟
+
+74
+00:07:43,240 --> 00:07:47,580
+لأن في ال integral domain مافيش عندي zero divisors
+
+75
+00:07:47,580 --> 00:07:52,680
+تمام؟ لكن لو ماكنش integral domain ممكن هذه
+
+76
+00:07:52,680 --> 00:07:58,580
+لاتساوي zero وهذه لاتساوي zero وحاصل ضربه مايساوي
+
+77
+00:07:58,580 --> 00:08:02,610
+zeroيعني في احتمال يكون واحد فيهم Zero divisor
+
+78
+00:08:02,610 --> 00:08:08,690
+وبالتالي هذا الكلام ليس صحيحا إذا هذا لا يكون
+
+79
+00:08:08,690 --> 00:08:13,810
+يساوي Zero لسببين ولا واحد فيهم Zero اتنين دي
+
+80
+00:08:13,810 --> 00:08:21,630
+انتجرال دمية مدام هيك جداش ال degree لهذه M زائد M
+
+81
+00:08:21,630 --> 00:08:30,980
+يبقى هنا ساعة ال degree لل F of Xفي الـ G of X هي
+
+82
+00:08:30,980 --> 00:08:37,340
+عند استبعاد تهدي ب Zero يبقى هذا بده ساوي ال N
+
+83
+00:08:37,340 --> 00:08:47,240
+زائد ال F and ال degree لمن؟ لل F زائد ال degree
+
+84
+00:08:47,240 --> 00:08:53,420
+لل G كده ايش بده ساوي؟ الأولى هي ال degree تبعها N
+
+85
+00:08:53,420 --> 00:09:00,370
+لانه اشترقنا ان ال A N لا تساوي Zeroوالتانية M لأن
+
+86
+00:09:00,370 --> 00:09:05,850
+اشتراطنا ال BM لا تساوي Zero يبقى ال degree تبعها
+
+87
+00:09:05,850 --> 00:09:11,450
+M وال degree تبعها N من الاتنين هدول يبقى ال
+
+88
+00:09:11,450 --> 00:09:19,810
+degree لل F of X في ال G of X يساوي ال degree لل F
+
+89
+00:09:19,810 --> 00:09:27,770
+of X زائد ال degree لل G of Xهذا المطلوب الأول
+
+90
+00:09:27,770 --> 00:09:35,430
+مطلوب التاني قال لي هذي commutative ring بحب تجيب
+
+91
+00:09:35,430 --> 00:09:38,890
+ال polynomial في الأول و ال polynomial في التانية
+
+92
+00:09:38,890 --> 00:09:44,290
+و ال degree اللي حصل الدرب يكون أقل من ال degree
+
+93
+00:09:44,290 --> 00:09:49,230
+للأولى لل degree للتانية المطلوب الأول انجيب
+
+94
+00:09:49,230 --> 00:09:56,850
+commutative ring حد فيك أجابتها؟ Z6 ممتاززد ستة
+
+95
+00:09:56,850 --> 00:10:02,390
+ماهياش integral domain لكنها commutative ring لأن
+
+96
+00:10:02,390 --> 00:10:05,910
+اتنين في تلاتة تساوي zero وبالتالي اتنين و تلاتة
+
+97
+00:10:05,910 --> 00:10:11,130
+zero divisor يبقى هذه not integral domain ولكنها
+
+98
+00:10:11,130 --> 00:10:20,250
+ring يبقى هنا بعدين بقول زد ستة هذه is a
+
+99
+00:10:20,250 --> 00:10:22,210
+commutative
+
+100
+00:10:25,490 --> 00:10:33,250
+Ring but not an
+
+101
+00:10:33,250 --> 00:10:42,310
+integral domain لأنها ليست انتجرال دومان طيب ادور
+
+102
+00:10:42,310 --> 00:10:47,870
+على two polynomial فيه واجيب degree الأولى و
+
+103
+00:10:47,870 --> 00:10:52,270
+degree الثانية و نضرب و يطلع ال degree اللي حصل
+
+104
+00:10:52,270 --> 00:10:58,320
+الضربأقل من مجموع الـ two degrees يبقى فكري ممكن
+
+105
+00:10:58,320 --> 00:11:04,140
+two polynomials و لا ممكن عشرات مش يعني واحدة
+
+106
+00:11:04,140 --> 00:11:08,940
+والله اشي كتير جد ما بدك غير الأرقام زي ما بدك
+
+107
+00:11:08,940 --> 00:11:19,040
+باحد الأرقام تكون في Z6 فمثلا لو أخدنا take مثلا
+
+108
+00:11:19,040 --> 00:11:29,460
+ال F of Xيساوي 2X أُص 4 على سبيل المثال and الـG
+
+109
+00:11:29,460 --> 00:11:33,420
+of X تساوي شوفوا يا بني كيف بدنا نجيب الـG of X
+
+110
+00:11:33,420 --> 00:11:44,340
+هذه 2X أُص 4 بدي أخد هنا الرقم في X في X تربية في
+
+111
+00:11:44,340 --> 00:11:49,260
+X تكييب اللي بدك هي في حيث الحاصل ضربهم يطلع Zero
+
+112
+00:11:49,980 --> 00:11:55,840
+وبالتالي ال degree بتنزل طبيعي يبقى لما قلت اتنين
+
+113
+00:11:55,840 --> 00:12:00,680
+اكس تربية هذه اليوم بدأ اخدها تلاتة لان تلاتة في
+
+114
+00:12:00,680 --> 00:12:05,760
+اتنين هي zero يبقى ال degree نزلت تلاتة ايش؟ تلاتة
+
+115
+00:12:05,760 --> 00:12:12,160
+مثلا اكس تربية زيد خمس على سبيل المثال هي عندك
+
+116
+00:12:12,160 --> 00:12:17,080
+اتنين والتلاتة والخمسة موجودة في Z6
+
+117
+00:12:20,980 --> 00:12:25,540
+سبعة تعني واحد تمانية تعني اتنين يبقى لها هذه
+
+118
+00:12:25,540 --> 00:12:29,880
+العقام عندى احط الرقم اللى بدكى ياه من zero لغاية
+
+119
+00:12:29,880 --> 00:12:38,940
+خمسة كله موجود وين في Z6 طيب then بدي
+
+120
+00:12:38,940 --> 00:12:48,060
+اخد ال degree لمن لل F زائد ال degree لل G كدهش ال
+
+121
+00:12:48,060 --> 00:12:58,140
+degree لل أولىوالتانية 3 يبقى 4 زائد 2 ويساوي كده؟
+
+122
+00:12:58,140 --> 00:13:04,620
+ويساوي 6 طب بداجي أضربهم في بعض بداجي أخد ال F of
+
+123
+00:13:04,620 --> 00:13:14,560
+X في ال G of X يبقى 2 X أُص 4 في 3 X تربيع زائد 5
+
+124
+00:13:14,560 --> 00:13:24,310
+ويساوي 3 في 2ستة تعني Zero Zero في X أُس ستة يبقى
+
+125
+00:13:24,310 --> 00:13:31,630
+Zero في X أُس ستة هنا زرع اتنين في خمسة في عشرة
+
+126
+00:13:31,630 --> 00:13:41,910
+عشرة في زيت ستة تعني اربع يبقى اربع X أُس اربع مرة
+
+127
+00:13:41,910 --> 00:13:48,520
+تانية اتنين في دلاتر بالزيت في ستة X أُس ستةالستة
+
+128
+00:13:48,520 --> 00:13:56,580
+الأولى بـ 0 يبقى X أُس 6 التانية 2×5 بـ 10 X أُس 4
+
+129
+00:13:56,580 --> 00:14:04,720
+العشرة هذه تانية 4 في Z6 يبقى 4 في Z6 النتج يزاوي
+
+130
+00:14:04,720 --> 00:14:14,460
+4 X أُس 4 هذا بدي يعطينا أن ال degree لل F of X في
+
+131
+00:14:14,460 --> 00:14:23,830
+ال G of X بيساوي كدهاش؟أربعة والاربعة أقل من الستة
+
+132
+00:14:23,830 --> 00:14:29,270
+نفجر هى جيبناله two pronomials ال degree للأولى
+
+133
+00:14:29,270 --> 00:14:33,970
+وال degree للتانية ستة وحصل ضربه ما طلع ال degree
+
+134
+00:14:33,970 --> 00:14:38,690
+يساوي أربعة وبالتالي الأربعة أقل من الستة يبقى ال
+
+135
+00:14:38,690 --> 00:14:43,750
+degree اللى حصل ضرب أقل من ال degree للجامعة لما
+
+136
+00:14:43,750 --> 00:14:50,850
+شيلنا من المثلة كلمة integraldomain طبعا يبقى يكون
+
+137
+00:14:50,850 --> 00:14:54,790
+شغلنا دقيقه احنا نشغل في ring في integral domain
+
+138
+00:14:54,790 --> 00:14:59,210
+في field إلى اخرى يبقى هذا المطلوب الثاني من
+
+139
+00:14:59,210 --> 00:15:06,270
+السؤال رقم سبعتاشر رقم تمانتاشر بيقول اثبتلي ان ال
+
+140
+00:15:06,270 --> 00:15:11,150
+principle ideal generated by X هو maximum ideal في
+
+141
+00:15:11,150 --> 00:15:15,370
+ال Q of X سؤال تمانتاشر
+
+142
+00:15:17,020 --> 00:15:23,100
+that أن ال principle ideal generated by X is
+
+143
+00:15:23,100 --> 00:15:30,440
+maximal in الهوليكي
+
+144
+00:15:30,440 --> 00:15:35,960
+و X solution
+
+145
+00:15:35,960 --> 00:15:42,860
+طيب
+
+146
+00:15:42,860 --> 00:15:46,860
+نروي على موضوعنا احنا بينا نثبتإن ال principle
+
+147
+00:15:46,860 --> 00:15:53,540
+ideal generated by X هو maximum ideal في ال Q of X
+
+148
+00:15:53,540 --> 00:15:58,880
+نقول كويس لو رجعنا يا بنات لل isomorphism theorem
+
+149
+00:15:58,880 --> 00:16:05,320
+إذا جدرنا نثبت إن ال Q of X موديالو ال principle
+
+150
+00:16:05,320 --> 00:16:13,140
+ideal generated by X هذا عبارة عن field يبقى بسيط
+
+151
+00:16:13,420 --> 00:16:16,660
+ال principle of ideal generated by X is maximal
+
+152
+00:16:16,660 --> 00:16:22,380
+وبيكون خلصا من هالشغل هذا، مظبوط؟ يبقى الفكرة اني
+
+153
+00:16:22,380 --> 00:16:26,480
+أثبت ان ال Q of X modular principle of ideal
+
+154
+00:16:26,480 --> 00:16:31,140
+generated by X is E فيه وعتانى ما عجبتاش الفكرة
+
+155
+00:16:31,140 --> 00:16:36,260
+التبعتي، قالت لأ أنا بدأ أدور على ideal تاني ويكون
+
+156
+00:16:36,260 --> 00:16:39,880
+subset منه وهذا بيسوي الشهده، انا بدأ أثبت انه
+
+157
+00:16:39,880 --> 00:16:44,650
+بيسوي ال ringهي طرق تنفيه غيرهم إذا عارفين غيرهم
+
+158
+00:16:44,650 --> 00:16:48,370
+دلوني عليهم فاش يا الطريق هذي و يا الطريق هذي لكي
+
+159
+00:16:48,370 --> 00:16:54,810
+أثبت ال maximum ل هذا ال ID نقوله بسيطة طيب بدا
+
+160
+00:16:54,810 --> 00:17:00,190
+نشتغل جهود جامد شوية فدققوا معانا بروح أعرف
+
+161
+00:17:00,190 --> 00:17:09,350
+function من ال Q of X إلى ال Q طب ليش ال Q يعني ما
+
+162
+00:17:09,350 --> 00:17:15,670
+هي السؤالالحين بنجاوبه بقبله هقوله define a
+
+163
+00:17:15,670 --> 00:17:22,730
+function والله mapping اللي بدك ايه فاي من ال q of
+
+164
+00:17:22,730 --> 00:17:31,070
+x إلى ال q set of rational number باي اللي هو
+
+165
+00:17:31,070 --> 00:17:41,500
+الفاي of f of x بدي ساوي ال a node where حيثهال F
+
+166
+00:17:41,500 --> 00:17:48,480
+of X هي A N X to the power N A minus ال one X to
+
+167
+00:17:48,480 --> 00:17:53,880
+the power N minus ال one زائد A one X زائد ال A
+
+168
+00:17:53,880 --> 00:17:59,720
+node يبقى عرفنا مين هي ال A node عرفناها مين هي
+
+169
+00:17:59,720 --> 00:18:06,800
+الجزء الثابت من ال polynomial يبقى Phi of X node
+
+170
+00:18:06,800 --> 00:18:13,810
+هي ال A nodeهو جزء ثابت من هذه الـ polynomial إذا
+
+171
+00:18:13,810 --> 00:18:21,030
+قدرت أثبت إنه هذا homomorphism وجبتله
+
+172
+00:18:21,030 --> 00:18:27,230
+ال kernel يبقى بيصير في Q of X موديول الكيرنيل
+
+173
+00:18:27,230 --> 00:18:35,860
+ايزو مورفك لمين؟ للكيو طب لكيو فيلديبقى بصير الرنج
+
+174
+00:18:35,860 --> 00:18:39,220
+عندنا فيه اللي يبقى ال absolute value يبقى ال
+
+175
+00:18:39,220 --> 00:18:44,100
+principle ideal generated by X is maximal. ويكون
+
+176
+00:18:44,100 --> 00:18:48,200
+خلصنا هذه الشغلات. طب تستعجلش شوية شوية لو سمحت.
+
+177
+00:18:48,740 --> 00:18:52,540
+تعالى نمشي شوية شوية. بدأ نثبت ان هذه في الأول هي
+
+178
+00:18:52,540 --> 00:18:58,300
+homomorphism. فهذه بقوله الـ Phi is a
+
+179
+00:18:58,300 --> 00:19:06,640
+homomorphism. تمام؟يبقى بدها خدمة ال F of X بدها
+
+180
+00:19:06,640 --> 00:19:14,560
+تساوي ال A N X N A N minus ال one X N minus ال one
+
+181
+00:19:14,560 --> 00:19:20,140
+زائد زائد اللي هو A one X زائد ال A naught
+
+182
+00:19:20,140 --> 00:19:27,780
+والتانية ال G of X يساوي B M X to the power M B M
+
+183
+00:19:27,780 --> 00:19:34,950
+minus ال one X M minus ال oneزائد بي ون X زائد بي
+
+184
+00:19:34,950 --> 00:19:41,310
+نوع وهذا مناسب، بدي أقول ال A N لا يساوي Zero و ال
+
+185
+00:19:41,310 --> 00:19:48,950
+B M لا يساوي Zero، والاتنين هدول موجودات في ال Q
+
+186
+00:19:48,950 --> 00:20:02,800
+of X. Then بدي أخد Phi of ال F of Xزائد ال G of X
+
+187
+00:20:02,800 --> 00:20:08,780
+هذا الكلام بده يساوي في فاي اوك بده اجمع ال two
+
+188
+00:20:08,780 --> 00:20:14,520
+polynomials اول ما بدأنا هذا ال chapter عرفناكوا
+
+189
+00:20:14,520 --> 00:20:23,120
+كيف نجمع ال polynomials قولنا لك هذا AN زائد او AS
+
+190
+00:20:23,120 --> 00:20:33,820
+زائد BS في X قص Sمين الـ S هذا يا بناه؟ الرقم ليه
+
+191
+00:20:33,820 --> 00:20:39,700
+كبير في M أو N؟ لأن الـ N بيسويش الـ M يمكن الأولى
+
+192
+00:20:39,700 --> 00:20:43,100
+تكون من الدرجة العاشرة والتانية من الدرجة الرابعة
+
+193
+00:20:43,100 --> 00:20:48,000
+مثلا أو الخامسة، يبقى دولة دي كعدد عناصرها فيها
+
+194
+00:20:48,000 --> 00:20:52,640
+عشرة، هذه فيها خمسة، خمستر مجموعة بعض بعض، يبقى
+
+195
+00:20:52,640 --> 00:20:58,380
+واحدة فيهم بتكون بالـ Zero والتانية بتكون بأنصر
+
+196
+00:20:58,380 --> 00:21:07,350
+محدديبقى ال S هو الرقم الكبير في M و N زاد ال A S
+
+197
+00:21:07,350 --> 00:21:13,810
+minus ال one زاد ال B S minus ال one X أُس S minus
+
+198
+00:21:13,810 --> 00:21:22,330
+ال one نيجي زاد زاد A one زاد B one في X زاد ال A
+
+199
+00:21:22,330 --> 00:21:28,810
+naught زاد ال B naught كلهالـ Phi ستؤثر على هذا
+
+200
+00:21:28,810 --> 00:21:36,630
+العنصر تبقى للتعريف اللى احنا عرفناه للـ Phi يبقى
+
+201
+00:21:36,630 --> 00:21:41,650
+هذا بيدى يسوى مين المقدار التابع اللى همين A نوت
+
+202
+00:21:41,650 --> 00:21:48,110
+زائد B نوت يسوى A نوت زائد B نوت طب ال A نوت اللى
+
+203
+00:21:48,110 --> 00:21:56,480
+همين Phi لل F of X وال B نوت اللى هو Phi زائدالـ
+
+204
+00:21:56,480 --> 00:22:07,400
+Phi للـ G of X. انا بدي اقعد اخد Phi للـ F of X في
+
+205
+00:22:07,400 --> 00:22:15,420
+الـ G of X. تمام؟ هذا الكلام بيسوي Phi R. بإنه نجي
+
+206
+00:22:15,420 --> 00:22:20,140
+للضرب. الضرب بتلزمنيش الكلك على كلها. تبعد كل
+
+207
+00:22:20,140 --> 00:22:24,460
+عنصر، ياكفيني أول عنصر و آخر عنصر.يبقى لو جينا
+
+208
+00:22:24,460 --> 00:22:35,060
+ضربناهم في بعض تصير a n b m x أس n زائد ال m زائد
+
+209
+00:22:35,060 --> 00:22:40,540
+زائد لما نوصل لآخر عنصر اللي هو من أو ما قبل
+
+210
+00:22:40,540 --> 00:22:47,000
+الأخير اللي هو a naught b one زائد a one b naught
+
+211
+00:22:47,000 --> 00:22:54,370
+x زائد a naught b naughtيبقى هاي باشتصار حاصل
+
+212
+00:22:54,370 --> 00:22:58,570
+الضرب هذا كله انا مش لازملي النتيجة هي الكون
+
+213
+00:22:58,570 --> 00:23:03,230
+الصحيبي بيهمنا مين ال a naught b naught يبقى هذا
+
+214
+00:23:03,230 --> 00:23:09,970
+الكلام a naught b naught ال a naught اللي في of x
+
+215
+00:23:09,970 --> 00:23:21,090
+و ال b naught اللي هو في of g of x يبقى هنا سا في
+
+216
+00:23:21,940 --> 00:23:30,020
+is a homomorphism طريقة كويسة لو كانت فاي on two
+
+217
+00:23:30,020 --> 00:23:36,680
+بقدر استخدم ال first isomorphism فيرمه باشرة
+
+218
+00:23:36,680 --> 00:23:43,780
+يكفيني ان تكون الفاي is on two وليس بالضرورة ان
+
+219
+00:23:43,780 --> 00:23:46,100
+تكون one to one
+
+220
+00:23:55,760 --> 00:24:04,660
+طيب، بنحاول نثبت إنه Phi is only يبقى
+
+221
+00:24:04,660 --> 00:24:10,160
+بدأ أخد عنصر وين في الـQ و أبين إنه إيه أصل في
+
+222
+00:24:10,160 --> 00:24:17,080
+الـQ of X يبقى لو جيت، قلت، ليه الـEQ موجودة في
+
+223
+00:24:17,080 --> 00:24:21,920
+الـQ؟ يبقى الـQ variable و لا constant
+
+224
+00:24:24,390 --> 00:24:29,210
+يبقى then لكيو
+
+225
+00:24:29,210 --> 00:24:40,790
+as لكيو as كونستان يعني إذا ممكن أاخده هو الكنستان
+
+226
+00:24:40,790 --> 00:24:51,210
+تبع أي polynomial صح ولا لأ يبقى then ال
+
+227
+00:24:51,210 --> 00:24:59,450
+f of xبادها تساوي اللي هو مثلا او ليش و ليش يقول
+
+228
+00:24:59,450 --> 00:25:11,450
+خلاص كونستان هذا يساوي كونستان then ليكيو is a
+
+229
+00:25:11,450 --> 00:25:21,110
+constant of a polynomial of polynomial f of x for
+
+230
+00:25:21,110 --> 00:25:22,570
+some
+
+231
+00:25:24,490 --> 00:25:36,710
+f of x اللي موجودة في ال EQ of x that is ال
+
+232
+00:25:36,710 --> 00:25:45,750
+EQ هذا بدي يسوى فاي لل F of X تبقى من هنا صارت on
+
+233
+00:25:45,750 --> 00:25:52,930
+الان بقوله by then first
+
+234
+00:25:55,660 --> 00:26:05,700
+isomorphism theorem we have ان ال Q of X موديول
+
+235
+00:26:05,700 --> 00:26:17,060
+الكيرن للفاي isomorphic لمن؟ للفاي of Q of X مشيك
+
+236
+00:26:17,060 --> 00:26:21,800
+نص الفيروس isomorphism theorem طيب الفاي أثبتناها
+
+237
+00:26:21,800 --> 00:26:28,940
+أنها ontoيبقى هذه كلها مين هين؟ Phi of cubics
+
+238
+00:26:28,940 --> 00:26:35,500
+عبارة عن مين؟ عبارة عن الـQ. يبقى هذه اللي هي الـQ
+
+239
+00:26:35,500 --> 00:26:42,660
+itself. ضالت علينا واحدة بس. إذا جدرنا نثبت إن
+
+240
+00:26:42,660 --> 00:26:46,900
+الكرن للـPhi هو ال principle ideal generated by X،
+
+241
+00:26:46,900 --> 00:26:54,230
+بيقول خلصنا. خلصنا خلاص. يبقى الآن one to showone
+
+242
+00:26:54,230 --> 00:27:00,850
+two sure ان ال principle ideal generated by X هو
+
+243
+00:27:00,850 --> 00:27:09,210
+الكيرن للفعل سمولي العلاقة هذه رقم واحدة اذا
+
+244
+00:27:09,210 --> 00:27:16,530
+بدأ اقول خدي ال F of X موجودة في الكيرن للفعل
+
+245
+00:27:16,530 --> 00:27:20,230
+تمام؟ then
+
+246
+00:27:22,730 --> 00:27:30,630
+الـ Phi لل F of X بده يساوي Zero لإنها موجودة وين؟
+
+247
+00:27:30,630 --> 00:27:36,310
+في ال curve طب ال Phi لل F of X يبقى ده شبناها A
+
+248
+00:27:36,310 --> 00:27:42,410
+naught يبقى هذا بده يعطيك إن ال A naught بده يساوي
+
+249
+00:27:42,410 --> 00:27:48,350
+Zero تمام؟ يبقى هذا إذا كانت A naught تساوي Zero
+
+250
+00:27:48,720 --> 00:27:54,080
+يبقى شكل ال F of X اللي موجودة في ال kernel بدي
+
+251
+00:27:54,080 --> 00:28:01,160
+يكون على الشكل التالي ال F of X بدي يسوي A N X N A
+
+252
+00:28:01,160 --> 00:28:07,460
+N minus ال one X N minus ال one زائد اللي هو main
+
+253
+00:28:07,460 --> 00:28:14,320
+زائد A one X فقط لغير مش عندي A naught لإنه A
+
+254
+00:28:14,320 --> 00:28:20,040
+naught بزيهطيب شو رأيك؟ بدك تكتب هذه بطريقة ثانية
+
+255
+00:28:20,040 --> 00:28:28,880
+شو الطريقة الثانية؟ a n x أس n minus ال 1 زائد a n
+
+256
+00:28:28,880 --> 00:28:37,720
+minus ال 1 x n minus 2 زائد زائد a 1 كله في x
+
+257
+00:28:37,720 --> 00:28:45,250
+بنفع؟ Distributive law قانون التوزيعطيب هذا ال
+
+258
+00:28:45,250 --> 00:28:49,950
+element وين موجود؟ ال principle ideal generated by
+
+259
+00:28:49,950 --> 00:28:54,510
+X لأنه تحسب تعريف ال principle ideal هو ال X مضروب
+
+260
+00:28:54,510 --> 00:28:58,510
+في polynomial هي ال polynomial الموجودة هي ال X
+
+261
+00:28:58,510 --> 00:29:04,290
+إذا هذا موجود في ال principle ideal generated by X
+
+262
+00:29:04,290 --> 00:29:11,410
+يبقى أصبح ان الكيرن لل Phi هو ال subset من ال
+
+263
+00:29:11,410 --> 00:29:15,340
+principle ideal generated by Xإذا نمشي للعملية
+
+264
+00:29:15,340 --> 00:29:21,600
+العكسية يبقى بالداجة اقول انه افترض ان ال F of X
+
+265
+00:29:21,600 --> 00:29:26,940
+موجودة في ال principle ideal generated by X then
+
+266
+00:29:26,940 --> 00:29:36,400
+ايش شكل ال F of X؟ بده يكون ال X نفسها مضروبة في
+
+267
+00:29:36,400 --> 00:29:45,680
+polynomial والتكن G of X صحيح؟يعني هذه بدها تكون X
+
+268
+00:29:45,680 --> 00:29:54,860
+في مين؟ في الـ B M X M B M minus ال one X M minus
+
+269
+00:29:54,860 --> 00:30:05,560
+ال one زائد ال B one X زائد ال B نقطة طيب تدفك هذه
+
+270
+00:30:05,560 --> 00:30:16,380
+بصير B M X أس M plus one زائدpm-1xm
+
+271
+00:30:16,380 --> 00:30:26,040
+بزائد بزائد b1x ترابيع بزائد b نوت في ال x يبقى
+
+272
+00:30:26,040 --> 00:30:31,040
+الخنصار ال term صرف كم؟ ب zero يبقى هذه موجودة في
+
+273
+00:30:31,040 --> 00:30:37,180
+ال kernel يبقى هذه موجودة في ال kernel لل file
+
+274
+00:30:37,180 --> 00:30:43,850
+يبقى الصرف of x اللي أخدتها هناهي هذه امشي امشي
+
+275
+00:30:43,850 --> 00:30:48,750
+وجدتها موجودة وين؟ في الـ Kernel يبقى بقدر اقوله
+
+276
+00:30:48,750 --> 00:30:53,590
+ال principle ideal generated by X subset من ال
+
+277
+00:30:53,590 --> 00:31:00,490
+Kernel للـ Phi يبقى ذات و هكذا ال Kernel للـ Phi
+
+278
+00:31:00,490 --> 00:31:06,510
+بالضبط هو ال principle ideal generated by X ناخد
+
+279
+00:31:06,510 --> 00:31:12,030
+هذه المعلومة و نعود في Mainفي الولاقة رقم واحد
+
+280
+00:31:12,030 --> 00:31:18,810
+يبقى باجي بقوله هنا Substitute
+
+281
+00:31:18,810 --> 00:31:25,930
+N1 نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+282
+00:31:25,930 --> 00:31:29,010
+نحن
+
+283
+00:31:29,010 --> 00:31:29,490
+نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن نحن
+
+284
+00:31:29,490 --> 00:31:38,210
+نحن نحن نحن نحن نحن
+
+285
+00:31:38,210 --> 00:31:48,380
+نهذا isomorphic لمين يا بنات؟ لكيو لكيو فيه؟ يبقى
+
+286
+00:31:48,380 --> 00:31:52,360
+part لكيو
+
+287
+00:31:52,360 --> 00:32:03,340
+is a field مدام field هذا بدي يعطيكي ان لكيو of x
+
+288
+00:32:03,340 --> 00:32:11,350
+modular principle is a fieldطب مدى فيه يبقى ال
+
+289
+00:32:11,350 --> 00:32:18,310
+ideal هذا ماله؟ maximum يبقى هذا بدي يعطيكي ال
+
+290
+00:32:18,310 --> 00:32:27,570
+maximum ideal في اللي هو الرنجل اللي عندك هذا فيكم
+
+291
+00:32:27,570 --> 00:32:35,330
+اي تساؤل؟ حلت المشكلة؟ بلاص؟ يبقى انا كان بدي
+
+292
+00:32:35,330 --> 00:32:39,330
+الفكرة الاساسية يقول الفكرة كلمة في الشريفيا إما
+
+293
+00:32:39,330 --> 00:32:43,510
+استخدام ال first isomorphism theorem يا إما نستخدم
+
+294
+00:32:43,510 --> 00:32:48,030
+التعريف تبع ال maximal ideal بأي طريقة بهذه أو
+
+295
+00:32:48,030 --> 00:32:53,490
+بهذه نوصل ماعندنا مشكلة هذا كان سؤال تمنتاشر من
+
+296
+00:32:53,490 --> 00:32:57,850
+التدريبين قبل ما أنا لان سؤال أربعة وعشرين
+
+297
+00:32:57,850 --> 00:33:01,850
+qualitative theory of z of x is not a principle
+
+298
+00:33:01,850 --> 00:33:14,700
+ideal domain سؤال أربعة وعشرين شهرthat z of x is
+
+299
+00:33:14,700 --> 00:33:28,840
+not a principal ideal domain وإيش
+
+300
+00:33:28,840 --> 00:33:34,040
+معنى principal ideal domain لكل ideal يكون
+
+301
+00:33:34,040 --> 00:33:39,480
+principal صحيح ولا لأ؟يعني احنا لو جيبنا ID الواحد
+
+302
+00:33:39,480 --> 00:33:44,480
+واثبتنا انه هذا not a principle خلاص بتبطّر أصير
+
+303
+00:33:44,480 --> 00:33:48,700
+principle ID الدومية مش هي الفكرة؟ يعني جيبنا
+
+304
+00:33:48,700 --> 00:33:53,880
+counter example ضد انها تكون principle ID الدومية
+
+305
+00:33:53,880 --> 00:33:59,880
+بيكون حلنا الإشكالية أعتقد ولا واحدة حلت السؤال؟
+
+306
+00:33:59,880 --> 00:34:02,840
+طيب ده الفكرة بس هالكش .. بس هالكش .. بس هالكش ..
+
+307
+00:34:02,840 --> 00:34:05,380
+بس هالكش .. بس هالكش .. بس هالكش .. بس هالكش .. بس
+
+308
+00:34:05,380 --> 00:34:05,900
+هالكش .. بس هالكش .. بس هالكش .. بس هالكش .. بس
+
+309
+00:34:05,900 --> 00:34:09,640
+هالكش .. بس هالكش ..الان بدنا نبدأ بشيء انتوا
+
+310
+00:34:09,640 --> 00:34:14,820
+اخدتهوا قبل ذلك ايديل اخدتهوا عارفينه واشتغلنا
+
+311
+00:34:14,820 --> 00:34:20,720
+عليه قبل ذلك في امتلة سابعة الان لو جاتى بنات لمن؟
+
+312
+00:34:20,720 --> 00:34:29,200
+لال ايديل اللى هو ال X و 2 اللى كل العناصر X في ال
+
+313
+00:34:29,200 --> 00:34:36,220
+F of X زي ال 2 في ال U of Xبحيث ان ال F of X و G
+
+314
+00:34:36,220 --> 00:34:46,620
+of X موجود في Z of X موجود في Z of X شوفناها قبل
+
+315
+00:34:46,620 --> 00:34:50,280
+ايديك و قبل ايديك ولا لا؟ شوفناها و كتبناها و
+
+316
+00:34:50,280 --> 00:34:55,800
+إشتغلناها و حلناها بعدد مسائل طيب إذا كنت أثبت ان
+
+317
+00:34:55,800 --> 00:35:01,280
+هذا مشي principle خلاص بصي Z of X is not a
+
+318
+00:35:01,280 --> 00:35:13,230
+principle صحيح؟طيب if we show that ان ال .. ال ..
+
+319
+00:35:13,230 --> 00:35:21,990
+ال ideal x و 2 is not principal then
+
+320
+00:35:21,990 --> 00:35:30,050
+z of x is not
+
+321
+00:35:33,300 --> 00:35:39,800
+a principle is not a principle ideal domain خلاص
+
+322
+00:35:39,800 --> 00:35:47,740
+بقى
+
+323
+00:35:47,740 --> 00:35:53,480
+مرة تانية أنا خدت ideal موجود في zip of x وبدى
+
+324
+00:35:53,480 --> 00:35:58,900
+أحاول أثبت هذا انه is not a principle يعني ايشيعني
+
+325
+00:35:58,900 --> 00:36:04,380
+بدي اثبت ان هذا ال ID لا يمكن ان يولد بعنصر واحد
+
+326
+00:36:04,380 --> 00:36:10,140
+لا يمكن ان يولد ببولنوميا لان العنصر هنا بولنوميا
+
+327
+00:36:10,140 --> 00:36:14,580
+لمعاملات واعداد صحيحة اللي هي جاية من وين؟ جاية من
+
+328
+00:36:14,580 --> 00:36:21,840
+هنا يبقى that is
+
+329
+00:36:21,840 --> 00:36:24,900
+f
+
+330
+00:36:24,900 --> 00:36:45,800
+vshow that ان الـ X و 2 is not generated but by
+
+331
+00:36:45,800 --> 00:36:54,620
+a single polynomial then
+
+332
+00:36:54,620 --> 00:36:56,780
+we
+
+333
+00:36:58,660 --> 00:37:09,280
+the result يعني
+
+334
+00:37:09,280 --> 00:37:14,880
+إذا قدرنا نثبت إن الـ ideas اللي عندنا لأ يمكن أن
+
+335
+00:37:14,880 --> 00:37:20,160
+يولد ب polynomial واحدة بيكون حصلنا مين حصلنا على
+
+336
+00:37:20,160 --> 00:37:25,620
+النتيجة بتأثبت بال contradiction assume not مش
+
+337
+00:37:25,620 --> 00:37:27,540
+صحيح يبقى
+
+338
+00:37:32,480 --> 00:37:40,720
+not ليش يعني اسيوم not؟ يعني that is ان ال
+
+339
+00:37:40,720 --> 00:37:46,340
+principle id generated by x و 2 بدي يولد بكثير
+
+340
+00:37:46,340 --> 00:37:56,240
+حدود و أنت كون P of x where حيث ال P of x هي
+
+341
+00:37:56,240 --> 00:38:01,000
+polynomial موجودة وين Pz of x
+
+342
+00:38:06,920 --> 00:38:11,860
+إذا أنا بأحاول أثبت بالتناقض بإن أنا بدي أثبت إن
+
+343
+00:38:11,860 --> 00:38:17,200
+هداك لا يمكن أن يولد بعنصر واحد و تفترض أنه ولد
+
+344
+00:38:17,200 --> 00:38:22,220
+بعنصر واحد اللي هو P of X بدي أشوف هذا بدي يقودني
+
+345
+00:38:22,220 --> 00:38:26,620
+إلى شغل صح و الله إلى شغل خطر إذا الله قادي إلى
+
+346
+00:38:26,620 --> 00:38:32,120
+شغل خطر يبقى فرض اللي فرضته غلط و عكسه هو إيه هو
+
+347
+00:38:32,120 --> 00:38:37,410
+الصح يعني لا يمكن لهذا اللي أيديه ال X و 2هنيولد
+
+348
+00:38:37,410 --> 00:38:44,370
+بعمطرين واحد يبقى ذاتس فرقته انه يولد بال P of X
+
+349
+00:38:44,370 --> 00:38:51,870
+السؤال هو هال اتنين يا بنات موجود في ال ID ال X و
+
+350
+00:38:51,870 --> 00:38:58,830
+اتنين ؟ موجود صحيح ايه ؟ خط X بالزيرو و G of X
+
+351
+00:38:58,830 --> 00:39:02,290
+بالواحد او G of Zero بالواحد فلسنا يبقى الاتنين
+
+352
+00:39:02,290 --> 00:39:10,670
+موجود طيب مدان موجودthen الاتنين موجود في P of X
+
+353
+00:39:10,670 --> 00:39:20,030
+او موجود في P of X ال incident ideal generated by
+
+354
+00:39:20,030 --> 00:39:28,750
+P of X مظبوط يعني يعني شو شكلوا الاتنين هذا بدي
+
+355
+00:39:28,750 --> 00:39:35,460
+يعطينا ان الاتنين بدي يساوي P of X تمامفي
+
+356
+00:39:35,460 --> 00:39:41,740
+polynomial تانية P of X مش شيف تعريف ال principle
+
+357
+00:39:41,740 --> 00:39:48,320
+ال principle ال P of X في polynomial تانية بده
+
+358
+00:39:48,320 --> 00:39:53,480
+يعطينا ال element اللي هو اتنين الآن ما هو تفسير و
+
+359
+00:39:53,480 --> 00:39:59,140
+كنا لهذه المعادلة الأخيرة شو علاقة ال P of X
+
+360
+00:39:59,140 --> 00:40:06,850
+بالاتنين؟و تقسم تقسم تمام كلامي كويس يبقى هدف اللي
+
+361
+00:40:06,850 --> 00:40:17,490
+بده يعطينا ان ال PRX divide لإتنين طب ما هي قاسم
+
+362
+00:40:17,490 --> 00:40:23,150
+إتنين واحد و سالب واحد و اتنين و سالب اتنين واحد و
+
+363
+00:40:23,150 --> 00:40:28,030
+سالب واحد مستبعد لإن هذا بيجيبلي عنصر واحد فقط
+
+364
+00:40:28,030 --> 00:40:35,410
+واحد مش غيرمظبوط طيب الان يبقى مفضلش عندي يا إما
+
+365
+00:40:35,410 --> 00:40:43,350
+اتنين يا إما مين سالب اتنين يبقى هذا معناته ان ال
+
+366
+00:40:43,350 --> 00:40:50,390
+P of X يا إما بده يسوي سالب اتنين يا إما ال P of X
+
+367
+00:40:50,390 --> 00:40:57,030
+بده يسوي كده؟ بده يسوي اتنين يجي علي كل الأمرين ال
+
+368
+00:40:57,030 --> 00:41:04,820
+P of X بده يسوي constantمظبوط؟ يبقى هذا معناته ان
+
+369
+00:41:04,820 --> 00:41:12,920
+ال P of X بده يساوي K وال K يا اما زائد او ناقص
+
+370
+00:41:12,920 --> 00:41:21,300
+اتنين طبعا؟ طيب كويس نجي لصحة هذا الكلام اللي احنا
+
+371
+00:41:21,300 --> 00:41:28,580
+ابنه يبقى ايش صار عندنا؟ صار عندنا ال P of X بده
+
+372
+00:41:28,580 --> 00:41:35,580
+يساوي Kيبقى هنا ال principle او ال ideal ال X
+
+373
+00:41:35,580 --> 00:41:40,980
+والإتنين هو ال principle ال ideal generated by X
+
+374
+00:41:40,980 --> 00:41:47,280
+وهو ال principle ال ideal generated by K وال K هذي
+
+375
+00:41:47,280 --> 00:41:54,680
+زائد او لاقص اتنين كمان سؤال ايش من هنا؟ نين
+
+376
+00:41:54,680 --> 00:42:04,490
+موجودة هنا السؤال هو ال X موجودةهنا ولا لا؟ لما؟
+
+377
+00:42:04,490 --> 00:42:15,590
+ال X بدها تساوي آه، إيش بدها تساوي؟ كده؟
+
+378
+00:42:15,590 --> 00:42:22,070
+مش داريه، مش شايف كله قدامي هنا ولا لا؟ بقالي بدي
+
+379
+00:42:22,070 --> 00:42:29,090
+أجرب هالك أكتر، ال X موجودةمعناته ال X موجودة في
+
+380
+00:42:29,090 --> 00:42:34,410
+ال principle ideal generated by K مظبوط يعني
+
+381
+00:42:34,410 --> 00:42:44,610
+معناته ان ال X بده ساوي H of X في K وكتيش
+
+382
+00:42:44,610 --> 00:42:50,610
+بيكون الكلام هذا صحيح لو كان ال H of X هي
+
+383
+00:42:50,610 --> 00:42:58,090
+polynomial من الدرجة الأولىفي غير هيكد؟ لأ لإن X
+
+384
+00:42:58,090 --> 00:43:02,790
+polynomial من الدرجة الأولى يبقى هذا كيفش هذا
+
+385
+00:43:02,790 --> 00:43:08,110
+الكلام صحيح فقط إذا كانت H of X polynomial من
+
+386
+00:43:08,110 --> 00:43:17,890
+الدرجة الأولى يبقى this is a proof when
+
+387
+00:43:17,890 --> 00:43:21,590
+ال
+
+388
+00:43:21,590 --> 00:43:29,590
+H of Xيساوي ax او ax زائد b ناخدها الأبسط اكس
+
+389
+00:43:29,590 --> 00:43:38,350
+ومدناشر ال b طيب هذا بدي يعطينا ان ال x بدي ساوي
+
+390
+00:43:38,350 --> 00:43:51,190
+ax في k او ال x بدي ساوي ak في xطب هدول ال A و ال
+
+391
+00:43:51,190 --> 00:43:57,770
+K أرقام و ال X موجودة وين؟ في Z نشتغل في Z احنا و
+
+392
+00:43:57,770 --> 00:44:05,330
+Z X تمام؟ يبقى هذا معناته ان ال A K بقداش يا بنات؟
+
+393
+00:44:05,330 --> 00:44:11,270
+بقداش؟ واحد، بواحد، تمام، لكن لو كان فيش فيها
+
+394
+00:44:11,270 --> 00:44:16,190
+الواحد ال Z بصير كلامنا مش صحيح، لكن الواحد موجود
+
+395
+00:44:16,190 --> 00:44:24,550
+في ال Zإذا الـ A K يبقى أحد السؤال هو واجتيش من
+
+396
+00:44:24,550 --> 00:44:30,010
+خلال هذه المعادلة لأن K معروفة أنها مجدد شبنات
+
+397
+00:44:30,010 --> 00:44:38,410
+اتنين و سالب اتنين إذا هذا الكلام ليس صحيحا إلا
+
+398
+00:44:38,410 --> 00:44:46,510
+إذا كانت A مرة بسالب نص و مرة نص مظبوط يبقى هنا
+
+399
+00:44:48,470 --> 00:44:56,510
+فالـ K تساوي سالب اتنين ثم ال A تساوي سالب نصر،
+
+400
+00:44:56,510 --> 00:45:05,070
+مظبوط؟ طيب لو كانت ال K تساوي اتنين ثم ال A تساوي
+
+401
+00:45:05,070 --> 00:45:11,270
+نصر، حاصل ضربهما بالواحد اللي هناك، حاصل ضربهما
+
+402
+00:45:11,270 --> 00:45:19,030
+بالواحد اللي هناك السؤال هذا موجود في Zلأ لأ هذا
+
+403
+00:45:19,030 --> 00:45:26,270
+موجود في Z لأ طب احنا لما نجينا خدنا ال H of X ال
+
+404
+00:45:26,270 --> 00:45:32,970
+A هذه وين موجودة يا بناها Z ولا لأ Z لإن احنا مش
+
+405
+00:45:32,970 --> 00:45:41,570
+خالع Z و ZX يبقى هذه موجودة في Z أصلا تمام طب هنا
+
+406
+00:45:41,570 --> 00:45:48,820
+A موجودة في Zقطلة A تصير موجودة في Z يبقى إيش هذا
+
+407
+00:45:48,820 --> 00:45:55,860
+بيعطينا هذا contradiction to
+
+408
+00:45:55,860 --> 00:46:02,860
+ال A موجودة في Z مدام تناقض يبقى شو جاب التناقض
+
+409
+00:46:02,860 --> 00:46:11,880
+جاب الخرض الغلط بظبط يبقى هنا أساس اللي هو ال X
+
+410
+00:46:12,730 --> 00:46:18,170
+والإتنين cannot be
+
+411
+00:46:18,170 --> 00:46:21,350
+generated
+
+412
+00:46:21,350 --> 00:46:33,670
+by a single polynomial معناته
+
+413
+00:46:33,670 --> 00:46:40,500
+لا يمكن أن يكون هذا ال principle، that isالـ X و
+
+414
+00:46:40,500 --> 00:46:48,280
+الأتنين is not a principal ID
+
+415
+00:46:48,280 --> 00:46:54,520
+مدى ما هوش principal ID، هاي جيبناله ك example
+
+416
+00:46:54,520 --> 00:47:03,760
+يبقى Z of X is not a principal ID
+
+417
+00:47:08,840 --> 00:47:15,360
+يبقى نجيبناله counter example بيكفي للإجابة على
+
+418
+00:47:15,360 --> 00:47:20,560
+السؤال هذا كان سؤال اربعة وعشرين الآن بنجي لسؤال
+
+419
+00:47:20,560 --> 00:47:25,480
+تلاتين سؤال
+
+420
+00:47:25,480 --> 00:47:32,800
+تلاتين بقول ال F فيه وزيادة
+
+421
+00:47:32,800 --> 00:47:42,060
+على ذلك ال F of Xبدي أساوي a n x to the power n
+
+422
+00:47:42,060 --> 00:47:48,380
+minus ال one x to the power n minus ال one a one x
+
+423
+00:47:48,380 --> 00:47:57,200
+زائد ال a naught موجود وموجود في كتاب تبقى full
+
+424
+00:47:57,200 --> 00:48:06,080
+text بيقول لما ياتي المطلوب prove that prove that
+
+425
+00:48:07,140 --> 00:48:17,160
+من ال X ناقص الواحد is a factor of F of X if and
+
+426
+00:48:17,160 --> 00:48:25,960
+only if F and only if ال A N زائد ال A N minus ال
+
+427
+00:48:25,960 --> 00:48:31,920
+one زائد ال A one زائد ال A naught يساوي زيو
+
+428
+00:48:43,910 --> 00:48:49,570
+سؤال مرة تانية نعطينا ال field بطلنا integral
+
+429
+00:48:49,570 --> 00:48:55,850
+domain يبقى كل أنصر له معكوس أخدنا polynomial ring
+
+430
+00:48:55,850 --> 00:49:01,430
+في هذا ال field تمام على الشكل اللي عندنا هذا
+
+431
+00:49:01,430 --> 00:49:08,090
+فجالي اثبت ان ال X ماقص واحد هو factor لل F of X F
+
+432
+00:49:08,090 --> 00:49:13,990
+and all F إذا كان مجموع المعاملات يساوي Zكلمة f
+
+433
+00:49:13,990 --> 00:49:19,610
+and o left تعني ان القرآن بيصير اتجاهين يبقى ناخد
+
+434
+00:49:19,610 --> 00:49:28,150
+الاتجاه الأول assume that افترض ان ال x ناقص
+
+435
+00:49:28,150 --> 00:49:41,830
+الواحد is a factor of ال f of x افترض انه 30 طيب
+
+436
+00:49:42,720 --> 00:49:47,520
+أخدنا كرولري السابقة بتقول إن هذا لو كان factor
+
+437
+00:49:47,520 --> 00:49:53,660
+يبقى X يساوي واحد هو مين؟ Zero للدالة يعني لو
+
+438
+00:49:53,660 --> 00:49:58,980
+عوضنا بال X بواحد النتج بدي يعطينا جدير يساوي Zero
+
+439
+00:49:58,980 --> 00:50:09,920
+يبقى assume that then ال X يساوي واحد is a zero of
+
+440
+00:50:09,920 --> 00:50:22,530
+F of Xthat is أي أن ال F of واحد بده يساوي Z طيب
+
+441
+00:50:22,530 --> 00:50:29,970
+هذا معناه وين ال F؟ هاي يبقى Zero بده يساوي ال F
+
+442
+00:50:29,970 --> 00:50:37,690
+of واحد بده يساوي ال A N الواحد to the power N A N
+
+443
+00:50:37,690 --> 00:50:43,530
+minus ال one مرة في واحد أس N minus ال oneزائد
+
+444
+00:50:43,530 --> 00:50:51,030
+زائد a one في واحد زائد ال a nine طب هذا ايش
+
+445
+00:50:51,030 --> 00:50:57,230
+معناته؟ معناته انه zero يساوي واحد ترفيع ولا واحد
+
+446
+00:50:57,230 --> 00:51:02,370
+تكيب ولا واحد قص مية ولا واحد قص الف كله يقلب واحد
+
+447
+00:51:02,370 --> 00:51:10,330
+يبقى هذا معناه a n زائد a n minus ال one زائد a
+
+448
+00:51:10,330 --> 00:51:16,200
+oneزائد ال a نوت اظنوا هو المفترض خلاص من اتجاه
+
+449
+00:51:16,200 --> 00:51:23,060
+الاول من جهة اتجاه التانية on the other hand
+
+450
+00:51:23,060 --> 00:51:26,640
+assume
+
+451
+00:51:26,640 --> 00:51:38,740
+ترضوا that ان ال a n زائد ال a n minus ال one زائد
+
+452
+00:51:38,740 --> 00:51:48,880
+ال a oneزائد ال a0 يساوي زيه ايش بدى اثبت X ناقص
+
+453
+00:51:48,880 --> 00:51:57,620
+واحد عبارة عن factor لمن ل ال polynomial f of X او
+
+454
+00:51:57,620 --> 00:52:03,940
+لو جدرت اثبت ان الواحد هو عبارة عن zero لهذه ال
+
+455
+00:52:03,940 --> 00:52:09,500
+polynomial بكره اللي اثنين عندكمبدي يكون ال X ناقص
+
+456
+00:52:09,500 --> 00:52:16,060
+واحد هو عبارة عن factor طيب
+
+457
+00:52:16,060 --> 00:52:21,540
+بدي أحاول المعادلة هذه أكتبها بصيغة أخرى و أشوف
+
+458
+00:52:21,540 --> 00:52:30,820
+يبجد ان ال A N في الواحد أس N يبجد ايه ايه ايه A N
+
+459
+00:52:30,820 --> 00:52:40,000
+ايه A N ماساويش شي تمام زادan-1 في الواحد أس n-1
+
+460
+00:52:40,000 --> 00:52:48,460
+زاد زاد a1 في الواحد زاد a0 ليست ب zero طب ايش
+
+461
+00:52:48,460 --> 00:52:56,600
+تفسيرك لهذه ان الواحد عبارة عن zero يبقى هنا this
+
+462
+00:52:56,600 --> 00:53:04,200
+means that ان الواحد is
+
+463
+00:53:06,600 --> 00:53:15,520
+A0 of the polynomial F
+
+464
+00:53:15,520 --> 00:53:22,120
+of X اللي عندنا هذا الـ F of X الأساسي يعني أين
+
+465
+00:53:22,120 --> 00:53:28,280
+راح تقيم يبقى هذا معناته أن واحد حل لمين بهذه
+
+466
+00:53:28,280 --> 00:53:32,460
+المثل مدام حل يبقى Pi
+
+467
+00:53:36,690 --> 00:53:42,330
+إتنين اللي خدناها المرة اللي فاتت ال X ناقص الواحد
+
+468
+00:53:42,330 --> 00:53:56,610
+is a factor is a factor of the polynomial F
+
+469
+00:53:56,610 --> 00:53:57,470
+of X
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/iH5Kjc7tIXA_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/iH5Kjc7tIXA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1951a03433b17590af6f204c061b559d23eb38d8
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/iH5Kjc7tIXA_postprocess.srt
@@ -0,0 +1,1508 @@
+1
+00:00:20,740 --> 00:00:24,140
+بسم الله الرحمن الرحيم، ابتدأنا المرة اللي فاتت في
+
+2
+00:00:24,140 --> 00:00:27,900
+شهر خمس عشر، اللي هو Ring Homomorphism، اعطينا
+
+3
+00:00:27,900 --> 00:00:31,260
+تعريف للـ Ring Homomorphism، وأخذنا على ذلك، اللي
+
+4
+00:00:31,260 --> 00:00:36,480
+هو خمسة أمثلة، مضبوط؟ نعم صح طيب، بدي أسألك سؤالي
+
+5
+00:00:36,480 --> 00:00:37,140
+تاني،
+
+6
+00:00:49,940 --> 00:00:58,800
+لمن؟ للإتنين Z هل الـ Z isomorphic للإتنين Z؟
+
+7
+00:00:58,800 --> 00:01:02,960
+لحلقة؟ آه آه، رنقة لإن هذا الـ U نفسي هو الواحد،
+
+8
+00:01:02,960 --> 00:01:07,420
+هذا الشيء يعني مية لمية، بقول two rings مشان يكون
+
+9
+00:01:07,420 --> 00:01:11,060
+بينهم isomorphism بيكون جميع الخواصة الرياضية لل
+
+10
+00:01:11,060 --> 00:01:16,040
+rings أولى، لو التانية لهم نفسي الخواصة الرياضية،
+
+11
+00:01:16,040 --> 00:01:23,500
+two rings لهم نفس ال propertiesمن ناحية الرياضية Z
+
+12
+00:01:23,500 --> 00:01:27,260
+فيها ال unity بس اتنين Z مافيه unity بجهته اللي
+
+13
+00:01:27,260 --> 00:01:36,900
+يمكن ان يكون isomorphic ل بعضهما يبقى ال answer Z
+
+14
+00:01:36,900 --> 00:01:46,880
+is not isomorphic لل اتنين Z السبب because Z
+
+15
+00:01:50,700 --> 00:02:05,940
+unity unity but بط اللي هو اتنين زد هزة لا unity
+
+16
+00:02:05,940 --> 00:02:11,540
+طيب
+
+17
+00:02:11,540 --> 00:02:13,780
+نواصل example 6
+
+18
+00:02:19,610 --> 00:02:26,570
+مثال 6 بيقول determine حدد
+
+19
+00:02:26,570 --> 00:02:33,430
+all ring homomorphisms
+
+20
+00:02:33,430 --> 00:02:42,930
+from Z12 to Z30
+
+21
+00:03:02,200 --> 00:03:08,120
+السؤال مرة تانية يقول حدد لي كام homomorphism من
+
+22
+00:03:08,120 --> 00:03:14,800
+Z12 إلى Z30 يمكن يطلع أكتر ويمكن يطلع اتنين بيسوا
+
+23
+00:03:14,800 --> 00:03:18,900
+بعض، يمكن تلاتة بيسوا بعض، هذول التلاتة اللي بيسوا
+
+24
+00:03:18,900 --> 00:03:22,560
+بعض أو اتنين بيسوا بعض يعتبر مين؟ homomorphism
+
+25
+00:03:22,560 --> 00:03:27,800
+واحد فقط، إذا بدنا نحدد مين هم ال discrete
+
+26
+00:03:27,800 --> 00:03:31,730
+homomorphism أو ال destined homomorphismمين ال
+
+27
+00:03:31,730 --> 00:03:35,670
+homomorphism اللي ولا واحد زي التاني تعالى نشوف
+
+28
+00:03:35,670 --> 00:03:46,790
+كتب نحلل مثلا بدي بقوله any homomorphism Phi من Z
+
+29
+00:03:46,790 --> 00:03:59,310
+12 إلى Z 30 is defined by بروح نعرفه بالشكل التاني
+
+30
+00:03:59,910 --> 00:04:13,410
+فاي اف اكس بده يساوي ال X موديولو تلاتين طيب
+
+31
+00:04:13,410 --> 00:04:21,590
+الان لو جيت لفاي اف اكس فاي اف اكس ال X وين موجودة
+
+32
+00:04:21,590 --> 00:04:25,350
+هذه يا بنات؟ زد اتناش يعني ممكن يكون Zero واحد
+
+33
+00:04:25,350 --> 00:04:31,620
+اتنين تلاتة لغاية احداشر تمامإذا بقدر أقول هي في
+
+34
+00:04:31,620 --> 00:04:39,260
+of واحد زائد واحد زائد زائد واحد كداش؟ X times
+
+35
+00:04:39,260 --> 00:04:44,660
+يعني X من المرات يعني لو كانت في of تلاتة بديكون
+
+36
+00:04:44,660 --> 00:04:48,180
+واحد زائد واحد زائد واحد كانت في of سبعة بدي أحط
+
+37
+00:04:48,180 --> 00:04:51,960
+واحد زائد واحد سبعة مرات في of عشر ايه بيجي واحد
+
+38
+00:04:51,960 --> 00:04:57,740
+زائد واحد عشر مرات و هكذا طيب الآن فيجايلي
+
+39
+00:04:57,740 --> 00:05:04,460
+homomorphism تمام؟ إذا هذا بيبقى يساوي في of one
+
+40
+00:05:04,460 --> 00:05:13,620
+زائد في of one زائد في of one كم مرة هتقول؟ X يبقى
+
+41
+00:05:13,620 --> 00:05:22,140
+هذا الكلام بيبقى يساوي X في في of one تمام؟ وهذا
+
+42
+00:05:22,140 --> 00:05:29,910
+الكلام لكل ال X اللي موجودة في Z12إذا صار Phi of X
+
+43
+00:05:29,910 --> 00:05:36,210
+اللي عندنا يساوي X في Phi of 1 تمام؟ يبقى إيش اللي
+
+44
+00:05:36,210 --> 00:05:45,810
+صار عندنا؟ صار عندنا Phi of X يساوي X في Phi of 1
+
+45
+00:05:45,810 --> 00:05:53,450
+بهذا الشكل، طيب لو جيت ال Phi of 1، هذا element
+
+46
+00:05:53,450 --> 00:05:59,880
+وين؟بزي التلاتين بدي اسميه ا مثلا على سبيل المثال
+
+47
+00:05:59,880 --> 00:06:07,260
+يبقى هنا بحتاج اقوله put phi of one يساوي a و
+
+48
+00:06:07,260 --> 00:06:12,360
+بعدين نبحث ايه الشكل ال a ممكن يكون اذا هذا بدي
+
+49
+00:06:12,360 --> 00:06:23,900
+يكون x في a تمام اللي ممكن اسمه لسه هو phi a of x
+
+50
+00:06:25,690 --> 00:06:32,530
+يبقى في X والله في A of X هو نفس الشيء ويسوى حصل
+
+51
+00:06:32,530 --> 00:06:38,310
+ضرب ال X في من؟ في ال A سيبقى ليها المعلومة هذه
+
+52
+00:06:38,310 --> 00:06:48,210
+وحنرجعلها ان شاء الله بعد قليل نيجي لل A ال A بده
+
+53
+00:06:48,210 --> 00:06:54,620
+يسوى في of one احنا فرضينايبقى بيصير ال order لل
+
+54
+00:06:54,620 --> 00:07:02,320
+إيه بيسوي ال order لل five of one بظبط؟ إيش ال
+
+55
+00:07:02,320 --> 00:07:09,600
+order؟ أصغر عدد صحيح موجد بحطه أسلل إيه بتبعطيني
+
+56
+00:07:09,600 --> 00:07:17,100
+ال identity أو ال unity عندنا طيب الآن ال order
+
+57
+00:07:17,100 --> 00:07:22,720
+ليه؟ بيقول يسوي ال order لل five of oneلو راجعنا
+
+58
+00:07:22,720 --> 00:07:27,080
+لل groups لو
+
+59
+00:07:27,080 --> 00:07:31,780
+كان ال five isomorphism يبقى ال order لل five of a
+
+60
+00:07:31,780 --> 00:07:37,000
+هو ال order لل a لكن لما يكون ال five homomorphism
+
+61
+00:07:37,000 --> 00:07:42,980
+فال order لل five of a بيقسم ال order لل a يبقى ال
+
+62
+00:07:42,980 --> 00:07:51,310
+order لل five of one بيقسم ال order لل oneيبقى هذا
+
+63
+00:07:51,310 --> 00:07:58,710
+بده يقسم ال order لل what تعالوا نتفهم إيش هذا
+
+64
+00:07:58,710 --> 00:08:06,110
+الكلام هذا بده يعطينا ال order لل a بده يساوي ال
+
+65
+00:08:06,110 --> 00:08:12,130
+order لل five of one يبقى ال order لل a بده يساوي
+
+66
+00:08:12,130 --> 00:08:13,670
+هو ال a و ايه الموجود
+
+67
+00:08:20,260 --> 00:08:26,980
+يبقى ال order اللى بدى يقسم التلاتين صح ولا لأ؟
+
+68
+00:08:26,980 --> 00:08:34,160
+يبقى هذا ال order اللى بدى يقسم التلاتين implies
+
+69
+00:08:34,160 --> 00:08:40,180
+ان ال order للإيه ممكن يكون واحد و ممكن يكون اتنين
+
+70
+00:08:40,180 --> 00:08:46,100
+و تلاتة اربعة تقسم التلاتينممكن يكون خمسة، ممكن
+
+71
+00:08:46,100 --> 00:08:53,400
+يكون ستة، ممكن عشرة، ممكن خمس، عشرة، ممكن تلاتين،
+
+72
+00:08:53,400 --> 00:08:58,780
+كل احتمالات هذه وردة، تمام؟ الحين بنقول ال order
+
+73
+00:08:58,780 --> 00:09:04,340
+لل five يقسم ال order لل one ال one هذا وين موجود؟
+
+74
+00:09:04,340 --> 00:09:12,160
+ال z12، ال five of one يبقى ال one هذا تبع ال z12
+
+75
+00:09:12,860 --> 00:09:21,860
+يبقى ال order لل إيه اللي هو هذا بده يقسم اللي هو
+
+76
+00:09:21,860 --> 00:09:29,680
+ال 12 بده يقسم ال order لل واحد بده يقسم ال order
+
+77
+00:09:29,680 --> 00:09:34,080
+لل واحد اللي هو بده يساوي 12 هذا معناته ان ال
+
+78
+00:09:34,080 --> 00:09:40,460
+order لل إيه ممكن يكون واحد او اتنين او تلاتة او
+
+79
+00:09:40,460 --> 00:09:48,480
+اربعتقسمه اتناش أو ستة او اتناش، في غير هدد؟ لأ،
+
+80
+00:09:48,480 --> 00:09:51,460
+يبقى هاي الاحتمالات الوردة، بدي اشوف مين
+
+81
+00:09:51,460 --> 00:09:56,400
+الاحتمالات الصحيحة فيهم، وبالتالي بروح بقول يبقى
+
+82
+00:09:56,400 --> 00:10:03,680
+من الاتنين هدول مع بعض، بدل استنتج ما يأتي، ان ال
+
+83
+00:10:03,680 --> 00:10:07,960
+order للإيه، يا إما احد، يا اتنين،
+
+84
+00:10:11,680 --> 00:10:15,660
+لأ لأنه خمسة موجودة فوق ومش موجودة ساحة أربعة
+
+85
+00:10:15,660 --> 00:10:20,880
+موجودة تحت ومش موجودة فوق يبقى ستة في غير هكذا؟ لأ
+
+86
+00:10:20,880 --> 00:10:29,660
+طيب إذا بدي أدور على ال A إيش ممكن تكون ال A هي ال
+
+87
+00:10:29,660 --> 00:10:32,860
+order يا واحد يا اتنين يا تلاتة يا ستة، بدي أروح
+
+88
+00:10:32,860 --> 00:10:39,340
+أدور على العناصر اللي في Z تلاتين لأن ال A في Z
+
+89
+00:10:39,340 --> 00:10:44,260
+تلاتينمين العناصر اللي في زي التلاتين ال order لها
+
+90
+00:10:44,260 --> 00:10:48,340
+يسوى واحد او اتنين او تلاتة او ستة؟ طب ال order
+
+91
+00:10:48,340 --> 00:10:53,500
+يسوى واحد لمين؟ لـ Zero، Zero أسوا واحد يسوى Zero،
+
+92
+00:10:53,500 --> 00:11:01,720
+يبقى ال A ممكن يكون Zero، طيب ال order يسوى اتنين،
+
+93
+00:11:01,720 --> 00:11:07,260
+خمسة عشر، خمسة عشر صحيح، اتنين ات سلاتين، اتنان
+
+94
+00:11:07,260 --> 00:11:14,800
+تلاتة، عشر، عشر، عشرين؟بينفع بينفع يبقى عشرة او
+
+95
+00:11:14,800 --> 00:11:19,980
+عشرين العشرة و العشرين اللي ال order تبعهم تلاتة
+
+96
+00:11:19,980 --> 00:11:24,220
+تلاتة في عشرين بستين تعني zero تلاتة في عشرة
+
+97
+00:11:24,220 --> 00:11:28,280
+بتلاتين تعني zero في غير اتنين هدول بالنسبة
+
+98
+00:11:28,280 --> 00:11:35,080
+لتلاتة؟ لأ طيب اللي ال order إلها يسوى ستة زي مين؟
+
+99
+00:11:35,080 --> 00:11:41,990
+خمسة و خمسة و خمسة و عشرين خمسة و عشرينخمسة وعشرين
+
+100
+00:11:41,990 --> 00:11:47,830
+كمال انه ستة في خمسة وعشرين بصير مية وخمسين او ما
+
+101
+00:11:47,830 --> 00:11:53,330
+يعني و المية وخمسين تعني زيرو بالنسبة للتلاتين
+
+102
+00:11:53,330 --> 00:12:00,270
+يبقى خمسة وعشرين مظبوط تمام يبقى هذا كل العناصر
+
+103
+00:12:00,270 --> 00:12:06,930
+اللي ممكن ناخدها من ال Z تلاتين والتي تحقق five of
+
+104
+00:12:06,930 --> 00:12:11,630
+one يساوي ايهيبقى هذا بصير الـ 0 والخمسة وعشرة
+
+105
+00:12:11,630 --> 00:12:16,010
+والعشر والعشرين والخمسة والخمسة وعشرين يعني أفهم
+
+106
+00:12:16,010 --> 00:12:22,890
+من هذا الكلام أنه أنا قول Phi A of X يعني بده يطلع
+
+107
+00:12:22,890 --> 00:12:30,830
+عندي ستة homomorphisms قد يكون وقد لا يكون طب بدي
+
+108
+00:12:30,830 --> 00:12:37,190
+أحصلهم بالضبط جداش هم ستة والله أقل من ستة بقول أه
+
+109
+00:12:37,190 --> 00:12:42,480
+استنى شويةتعالى نشوفهم هم ستة بالضبط مائة بالمائة
+
+110
+00:12:42,480 --> 00:12:47,680
+والله أقل من ذلك الحين لو جينا سألناكوا يا باراتي
+
+111
+00:12:47,680 --> 00:12:52,360
+قولنالكوا إيه؟ قولنالكوا إن الواحد في الواحد يسوى
+
+112
+00:12:52,360 --> 00:12:58,060
+كده؟ واحد طيب إذا five of one في واحد يبقى five of
+
+113
+00:12:58,060 --> 00:13:06,260
+one في واحد يبقى five of one مصبوط؟ طيب هذا الكلام
+
+114
+00:13:06,260 --> 00:13:14,470
+five of oneفى five of one يساوي five of one طب
+
+115
+00:13:14,470 --> 00:13:21,170
+five of one مقداش ايه فرضينا يبقى هذا بده يعطينا
+
+116
+00:13:21,170 --> 00:13:29,330
+ان ال a فى ال a بده يساوي ال a وكأن ال a
+
+117
+00:13:29,330 --> 00:13:35,490
+idempotent element لأن ال a ترميه يساوي ال a بداتى
+
+118
+00:13:35,490 --> 00:13:40,610
+اشوف الأرقام اللى أنا جايبهاهل تحقق هذه المعادلة
+
+119
+00:13:40,610 --> 00:13:46,770
+ولا لا؟ يبقى كل واحد بيحقق هذه المعادلة بيكون ايش؟
+
+120
+00:13:46,770 --> 00:13:51,650
+homomorphism تعالى نشوف كلامنا هذا صحيح؟ والله فيه
+
+121
+00:13:51,650 --> 00:13:56,690
+يا عليك كلام نمسك النقطة الأولى هى عندك Zero في
+
+122
+00:13:56,690 --> 00:14:01,530
+Zero قداش بيعطينا؟ Zero اه مافيش فيها مشكلة A في A
+
+123
+00:14:01,530 --> 00:14:07,950
+بدي اعطيني ايه؟ طب نمسك اللى بعثها خمساش في خمساش
+
+124
+00:14:08,540 --> 00:14:15,340
+متين وخمسة وعشرين، سبعة في تلاتين، متين وعشرة، من
+
+125
+00:14:15,340 --> 00:14:19,780
+متين و .. متين و .. و .. و .. وخمسة وعشرين، بيطلوا
+
+126
+00:14:19,780 --> 00:14:25,140
+الخمستاشر. يبقى، وهذه كمان تحقق المعادلة اللي
+
+127
+00:14:25,140 --> 00:14:30,320
+عندنا إيه في إيه يساوي إيه. بعد الخمستاشر عندنا
+
+128
+00:14:30,320 --> 00:14:37,120
+عشرة في عشرة. كده؟ شيري تلت تلاتينات في السن بيطل
+
+129
+00:14:37,120 --> 00:14:43,620
+عشرة.يبقى وهذه بتحققها، ندي بعد العشرة عشرين، فيها
+
+130
+00:14:43,620 --> 00:14:48,320
+عشرين؟ اربعمية، طبعا تلاتمية وتسعين بتقسمها
+
+131
+00:14:48,320 --> 00:14:54,080
+تلاتين، فيها تلتاشر، مظبوط؟ يبقى بيضال قداشر، عشر،
+
+132
+00:14:54,080 --> 00:15:01,640
+اه هذه مش مظبوطة، صح؟ هذه ماتقطنش ان ا في ا يساوي
+
+133
+00:15:01,640 --> 00:15:07,960
+الـA، الآن بعد العشرين، بتاخد خمسة في خمسة، فجدال
+
+134
+00:15:08,140 --> 00:15:16,860
+خمسة وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة
+
+135
+00:15:16,860 --> 00:15:20,400
+وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة وعشرين،
+
+136
+00:15:20,400 --> 00:15:20,660
+خمسة وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة
+
+137
+00:15:20,660 --> 00:15:24,480
+خمسة وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة
+
+138
+00:15:24,480 --> 00:15:27,360
+وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة وعشرين،
+
+139
+00:15:27,360 --> 00:15:36,640
+خمسة وعشرين، خمسة وعشرين، خمسة وعشرين، خمسة وعشرين
+
+140
+00:15:39,380 --> 00:15:44,840
+أيوة، ماحققوش ال homomorphism، ماحققوش المعادلة
+
+141
+00:15:44,840 --> 00:15:49,380
+اللي عندي هذه، تمام؟ ماحققوش المعادلة، يبقى هدول
+
+142
+00:15:49,380 --> 00:15:54,480
+بدنا نستثنيهم، لإنهم ماحققوش المعادلة دي، بيبقوا
+
+143
+00:15:54,480 --> 00:16:00,320
+قداش عندهم، أربع homomorphism فقط، لا غير، طب و
+
+144
+00:16:00,320 --> 00:16:05,020
+اتنين المستثنين هدول، اتنين المستثنين هيسووا واحد
+
+145
+00:16:05,020 --> 00:16:09,050
+منهم، كل واحد هيسوي واحد،كيف الحين بوريكوا
+
+146
+00:16:09,050 --> 00:16:13,290
+وبالتالي إذا ما يكون اتنين homomorphism بيقدوا نفس
+
+147
+00:16:13,290 --> 00:16:17,270
+النتيجة بعتبر واحد مش اتنين يبقى بستبعد واحد و
+
+148
+00:16:17,270 --> 00:16:28,630
+بيخلي التاني و هكذا طيب يبقى هنا so we have four
+
+149
+00:16:28,630 --> 00:16:35,670
+homomorphisms تمام؟ مين الأول؟ الأول five
+
+150
+00:16:37,410 --> 00:16:45,610
+فاي اللي هو zero of X بده يساوي ال X في Zero اللي
+
+151
+00:16:45,610 --> 00:16:52,390
+هو بده يساوي Zero التاني فاي خمستاشر of X هو يساوي
+
+152
+00:16:52,390 --> 00:17:01,650
+خمستاشر X التالت اللي هو فاي of استبعدنا الخمستاشر
+
+153
+00:17:01,650 --> 00:17:02,490
+في عشر
+
+154
+00:17:16,820 --> 00:17:22,620
+طيب اما انت لو ان انا بدى احسس فاي خمستاش كده
+
+155
+00:17:22,620 --> 00:17:29,380
+تساوي انا بدى يعطينا بدى اعرف كده فاي خمستاش اش ال
+
+156
+00:17:29,380 --> 00:17:35,130
+range تبعهايبقى خمستاشر في زيرو بدي أشيل X و أحط
+
+157
+00:17:35,130 --> 00:17:40,170
+زيرو واحد و اتنين و تلاتة لغاية اتناش تمام فاي اف
+
+158
+00:17:40,170 --> 00:17:46,210
+زيرو فزيرو و لما تبقى X بواحد خمستاشر واحد خمستاشر
+
+159
+00:17:46,210 --> 00:17:52,650
+و لما تبقى X باثنين خمستاشر تلاتين تعني زيرو هي
+
+160
+00:17:52,650 --> 00:17:57,710
+طيب بعد اتنين تلاتة في خمستاشر خمسة واربعين أشيله
+
+161
+00:17:57,710 --> 00:18:02,120
+تلاتين و أبقى خمستاشر هيأربعة، خمسة، ستة، اتناش،
+
+162
+00:18:02,120 --> 00:18:06,780
+ماتلاقيش غير العنصرين هدول، مافيش غيرهم. إذا فاي
+
+163
+00:18:06,780 --> 00:18:12,020
+خمستاشر قبل X هم موفزن الـ range له two elements
+
+164
+00:18:12,020 --> 00:18:16,620
+فقط. طيب تعالى نشوف فاي يا دي اللي عندنا. اللي
+
+165
+00:18:16,620 --> 00:18:21,980
+قدشته ساعة. عشرة في Zero في Zero. عشرة في واحد
+
+166
+00:18:21,980 --> 00:18:30,150
+عشرة. عشرة في اتنين عشرين. عشرة في دلاتة Zero.عشرة
+
+167
+00:18:30,150 --> 00:18:36,150
+في اربع اربعين شيله تلاتين بيظل عشرة عشرة في غمزة
+
+168
+00:18:36,150 --> 00:18:41,130
+خمسين شيله تلاتين بيصير عشرين عشرة في ستة و صفر
+
+169
+00:18:41,130 --> 00:18:47,030
+هاي و هكذا يبقى هذا مافيش فيه غير اللي هو مين اللي
+
+170
+00:18:47,030 --> 00:18:55,330
+هو zero و عشرة و عشرين السؤال هو هل هذا هو five
+
+171
+00:18:55,330 --> 00:19:03,120
+عشرين of x؟عشرين في زيرو في زيرو، عشرين في واحد في
+
+172
+00:19:03,120 --> 00:19:11,120
+عشرين، عشرين في اتنين في تلاتين عشرة، عشرين في
+
+173
+00:19:11,120 --> 00:19:17,100
+تلاتة في ستين، تعني زيرو، عشرين في أربعة في
+
+174
+00:19:17,100 --> 00:19:22,900
+تمانين، تعني عشرين، عشرين في خمسة في مية، تعني عشر
+
+175
+00:19:22,900 --> 00:19:27,590
+يبقى هى .. يبقى هذا الاستبعدنية أمنةطبع الفاي
+
+176
+00:19:27,590 --> 00:19:33,270
+عشرين بل هو الفاي عشرة ولذلك استبعدى بجهدول اتنين
+
+177
+00:19:33,270 --> 00:19:40,910
+لكن فى الحقيقة واحد فقط داغية طيب الان نجى لفاي
+
+178
+00:19:40,910 --> 00:19:45,750
+اللى هو خمسة وعشرين اكس عند ال zero في zero وعند
+
+179
+00:19:45,750 --> 00:19:52,870
+الواحد خمسة وعشرين وعندي اثنين بخمسين شيلى تلاتين
+
+180
+00:19:52,870 --> 00:19:59,010
+بيعطينى عشرين وفاي تلاتةخمسة وسبعين، شيلي ستين
+
+181
+00:19:59,010 --> 00:20:04,790
+اللي هو مضاعفات التلاتين، بتطلع خمستاشر عشرة خمسة،
+
+182
+00:20:04,790 --> 00:20:10,050
+يبقاش ما يطلع بيطلع أي عناصر، تمام؟ طيب، أليس هذا
+
+183
+00:20:10,050 --> 00:20:16,850
+هو five أو خمسة؟ خمسة في zero ب zero، خمسة في واحد
+
+184
+00:20:16,850 --> 00:20:22,130
+بخمسة، خمسة في اتنين بعشرة، خمستاشر عشرين، خمسة
+
+185
+00:20:22,130 --> 00:20:28,140
+عشر عشرين، وهكذا، تمام؟إذا طلع المستبعدات حسبناهم
+
+186
+00:20:28,140 --> 00:20:34,820
+حسبناهم طلع مكررات هذه النتيجة هي هذه النتيجة يبقى
+
+187
+00:20:34,820 --> 00:20:39,680
+باخد اتنين هذول و بسيط مين بسيط اتنين هذول يبقى
+
+188
+00:20:39,680 --> 00:20:45,160
+طالع عندنا اربعة homomorphisms و اتنين مكررات
+
+189
+00:20:45,160 --> 00:20:52,180
+بناخدهمش يبقى بصير عند الأربعة هذول هم الاربعة
+
+190
+00:20:52,180 --> 00:20:58,540
+homomorphisms اللي عندنافقط لا غير، تمام؟ وجبتلك
+
+191
+00:20:58,540 --> 00:21:04,160
+ال ring لكل منهم، خلاص؟ طبعا هذا شغل زيادة بس
+
+192
+00:21:04,160 --> 00:21:09,120
+لمجرد التوضيح، علشان نعرف ان الاستبعالناهم هدول
+
+193
+00:21:09,120 --> 00:21:13,860
+موجودات، خلاص؟ يبقى استبعالنا التكرار. طب احنا من
+
+194
+00:21:13,860 --> 00:21:18,140
+أول لما كان عند القادر بساوة ثلاثة طلع الاية عشر
+
+195
+00:21:18,140 --> 00:21:21,000
+او عشرين. طيب شيء مفيد. هيطلع من التلتنة سويا من
+
+196
+00:21:21,000 --> 00:21:24,650
+الأول. دي بواحدة منهم، لأ بس تاني شويةيمكن هذه
+
+197
+00:21:24,650 --> 00:21:28,210
+تجيبلي شيء وهذه تجيبلي شيء آخر، أنا مش عارف، بس
+
+198
+00:21:28,210 --> 00:21:32,370
+أنا أكتل الآن للكلام اللي انت بتقوله بتلعب صراحة
+
+199
+00:21:32,370 --> 00:21:38,370
+عندي التأكيد، مافيش أدنى شككة طيب، الآن في ملاحظة
+
+200
+00:21:38,370 --> 00:21:45,630
+بدنا نقولكوا عنها الملاحظة ان انا اي انتجة بكثب
+
+201
+00:21:45,630 --> 00:21:52,030
+على شكل كثيرة حدود الشكلة تعالوا نشوف الشكلة،
+
+202
+00:21:52,030 --> 00:21:56,310
+تمام؟يبقى طبعا هذا الكلام لازم ليه بعد قليل
+
+203
+00:21:56,310 --> 00:22:03,950
+وبالتالي لازم نشير اليه ايه
+
+204
+00:22:03,950 --> 00:22:08,410
+مارك؟
+
+205
+00:22:08,410 --> 00:22:12,690
+look
+
+206
+00:22:12,690 --> 00:22:16,770
+look
+
+207
+00:22:16,770 --> 00:22:19,830
+او دي normal
+
+208
+00:22:24,060 --> 00:22:29,240
+عندما هتيلك رقم بال آلاف للعشرة آلاف اللى بدك هيه
+
+209
+00:22:29,240 --> 00:22:34,220
+يلّا قولي أي رقم يعني اشتريه مليون اشتريه بالألف و
+
+210
+00:22:34,220 --> 00:22:37,520
+خمسية و أربعين خمس ألاف و كم؟ ألف و خمسية و أربعين
+
+211
+00:22:37,520 --> 00:22:42,340
+خمس ألاف و خمسية و أربعين خمس ألاف و خمسية و
+
+212
+00:22:42,340 --> 00:22:44,220
+أربعين خمس ألاف و خمسية و أربعين خمس ألاف و خمسية
+
+213
+00:22:44,220 --> 00:22:47,360
+و أربعين خمس ألاف و خمسية و أربعين خمس ألاف و
+
+214
+00:22:47,360 --> 00:22:52,660
+خمسية و أربعين خمس ألاف و خمسية و أربعين خمس ألاف
+
+215
+00:22:52,660 --> 00:22:57,280
+و خمسية و أربعين خمس ألاف و خعلى ايه؟ هي خمس تلات
+
+216
+00:22:57,280 --> 00:23:03,120
+وستمية واتنين واربعين أشياء ساعة. بقدر أقول خمس
+
+217
+00:23:03,120 --> 00:23:12,580
+تلات زائر ستمية زائر واربعين زائر اتنين. شغل
+
+218
+00:23:12,580 --> 00:23:18,260
+ابتدائي صح؟ شغل ابتدائي، لكن احنا هادفين، مش يعني
+
+219
+00:23:18,260 --> 00:23:29,670
+نكتب أي كلام. طيب، هذا يرسمخمسة في عشرة تكيب خمسة
+
+220
+00:23:29,670 --> 00:23:35,650
+في عشرة تكيب خمسة في عشرة تكيب خمسة في عشرة تكيب
+
+221
+00:23:35,650 --> 00:23:35,670
+تكيب خمسة في عشرة تكيب خمسة في عشرة تكيب خمسة في
+
+222
+00:23:35,670 --> 00:23:41,850
+عشرة تكيب خمسة في عشرة تكيب خمسة في عشرة تكيب خمسة
+
+223
+00:23:41,850 --> 00:23:45,750
+في عشرة تكيب خمسة في عشرة تكيب خمسة في عشرة تكيب
+
+224
+00:23:45,750 --> 00:23:48,350
+خمسة في عشرة تكيب خمسة في عشرة تكيب خمسة في عشرة
+
+225
+00:23:48,350 --> 00:23:54,260
+تكيب خمسة في عشرةقدرت اكتبه على الشكل اللي عندنا
+
+226
+00:23:54,260 --> 00:24:03,180
+هنا و من هنا بروح بقول له sir any positive integer
+
+227
+00:24:03,180 --> 00:24:13,700
+in can be written as
+
+228
+00:24:13,700 --> 00:24:17,980
+in
+
+229
+00:24:17,980 --> 00:24:19,600
+yourself
+
+230
+00:24:21,240 --> 00:24:33,240
+ه اي كي عشرة عوز كي زاد اي كي minus ال one عشرة
+
+231
+00:24:33,240 --> 00:24:39,500
+عوز كي minus ال one زاد نظل ماشي لغاية اي one في
+
+232
+00:24:39,500 --> 00:24:46,000
+عشرة زائد ال اي نور لإن نص تلاتة اتنين واحد صفر
+
+233
+00:24:46,000 --> 00:24:53,970
+بظل ينزلبدأنا بكتابة k-1,k-2,k-3 لغاية وصلنا ل10
+
+234
+00:24:53,970 --> 00:25:01,310
+وقص واحد زائد ا نول يبقى اي انتجات بقدر اكتبها على
+
+235
+00:25:01,310 --> 00:25:07,590
+شكل كثيرة الحدود اللي عندناها طيب الان بدنا نروح
+
+236
+00:25:07,590 --> 00:25:19,380
+لمثال رقم 7 مثل رقم 7بيقول مافي any integer in any
+
+237
+00:25:19,380 --> 00:25:27,960
+integer in with decimal representation with
+
+238
+00:25:27,960 --> 00:25:33,280
+decimal representation
+
+239
+00:25:33,280 --> 00:25:42,980
+with
+
+240
+00:25:42,980 --> 00:25:51,740
+decimal representationAK AK-L1 ونظر الماشيين لغاية
+
+241
+00:25:51,740 --> 00:26:01,740
+A1 ال E0 is divisible by
+
+242
+00:26:01,740 --> 00:26:16,620
+9 if and only if if and only if ال AK plusAK-L1
+
+243
+00:26:16,620 --> 00:26:27,960
+Plus Plus A1 Plus A0 Is Divisible By 9
+
+244
+00:26:53,860 --> 00:26:59,740
+قلب الارقام بيقولي انا عند اي انتجار جدرت اكتبه
+
+245
+00:26:59,740 --> 00:27:06,480
+على الشكل اللي عندنا دعيكي من الشكل بيقولي هذا ال
+
+246
+00:27:06,480 --> 00:27:12,040
+N بقدر اقول divisible by 9 if and only if مجموعة
+
+247
+00:27:12,040 --> 00:27:17,860
+هدول اللي هو الأرقام is divisible by 9 بقوله بسيطة
+
+248
+00:27:17,860 --> 00:27:34,830
+خالص الان let ال Na positive integer then ال n بده
+
+249
+00:27:34,830 --> 00:27:45,130
+يساوي a k عشرة اقصى k زائد a k minus ال one مضروب
+
+250
+00:27:45,130 --> 00:27:51,110
+في عشرة اقصى k minus ال one زائد زائد a one في
+
+251
+00:27:51,110 --> 00:27:58,960
+عشرة زائدA note حسب ما احنا كاتبين هنا تمام يبقى
+
+252
+00:27:58,960 --> 00:28:05,120
+فرضنا انه على الشكل اللي عندنا هذا طيب الان انا
+
+253
+00:28:05,120 --> 00:28:08,580
+فرضت هذه as a positive انتجة وكتبناها بالشكل اللي
+
+254
+00:28:08,580 --> 00:28:19,460
+قلتها من هذا الان define a homomorphism Phi من Z
+
+255
+00:28:19,460 --> 00:28:31,340
+إلى Z تسعةby five of x بده يساوي ال X modulo تسعة
+
+256
+00:28:31,340 --> 00:28:35,080
+نيجي
+
+257
+00:28:35,080 --> 00:28:40,760
+للنص اللي جاي ليه جاي ليه ان ال N اللي عنها ده is
+
+258
+00:28:40,760 --> 00:28:46,300
+divisible by تسعة if and only if هذا divisible by
+
+259
+00:28:46,300 --> 00:28:58,780
+تسعة يبقى بداجي اقوله ال N isdivisible by 9 if and
+
+260
+00:28:58,780 --> 00:29:06,900
+only if يعني لازم ألاجي رقم 10 اضربه في 9 يطلع مين
+
+261
+00:29:06,900 --> 00:29:20,640
+ال N يبقى ال N يساوي 9 M وال M موجودة في Z مصدور؟
+
+262
+00:29:20,640 --> 00:29:30,080
+طيبهذا الكلام صحيح if and only if ال 5 of M بدل
+
+263
+00:29:30,080 --> 00:29:36,920
+سوى ال 5 of 9 M هذا
+
+264
+00:29:36,920 --> 00:29:44,460
+الكلام صحيح if and only if ال 5 of M تسعة M
+
+265
+00:29:44,460 --> 00:29:46,840
+موديولو تسعة
+
+266
+00:29:51,440 --> 00:29:59,440
+0 ممتاز يبقى هذا الكلام صحيح if and only if فاي of
+
+267
+00:29:59,440 --> 00:30:08,780
+n بده يسوي 0 0 تبع 100 تبع 9 طيب هذا الكلام صحيح
+
+268
+00:30:08,780 --> 00:30:15,100
+if and only if فاي of وين ال n هاي هشيلها و اكتب
+
+269
+00:30:15,100 --> 00:30:24,100
+بدالها كثيرة الحدود هذه يبقى AKفي عشرة أُس K زائد
+
+270
+00:30:24,100 --> 00:30:31,400
+A K minus ال one عشرة أُس K minus ال one زائد زائد
+
+271
+00:30:31,400 --> 00:30:40,560
+A one في عشرة زائد ال A note كله بده يساوي زيه طيب
+
+272
+00:30:40,560 --> 00:30:46,680
+هذا الكلام صحيح if and only if الفا يشغلين عليه
+
+273
+00:30:46,680 --> 00:30:52,500
+احناHomomorphism يبقى بقدر أدخل الـ Phi على كل
+
+274
+00:30:52,500 --> 00:31:01,060
+term من هذه الtermات يبقى هذا Phi of AK في عشر عوص
+
+275
+00:31:01,060 --> 00:31:09,020
+K Phi of AK minus ال one عشر عوص K minus ال one
+
+276
+00:31:09,020 --> 00:31:20,310
+زاد زاد Phi of A1 في عشرة زاد Phi of A0هذا الكلام
+
+277
+00:31:20,310 --> 00:31:25,930
+كله بده يساوي قداش بده يساوي Zero هذا الكلام صحيح
+
+278
+00:31:25,930 --> 00:31:31,950
+if and only if هذول حاصل ضرب و ال Phi homomorphism
+
+279
+00:31:31,950 --> 00:31:37,070
+خاصية ثانية و خاصية بدخل ال Phi على كل واحد من هذه
+
+280
+00:31:37,070 --> 00:31:45,410
+ال terms يبقى Phi of AK Phi of عشر عوز K زائد Phi
+
+281
+00:31:45,410 --> 00:31:53,370
+of AK minus ال oneفي الـ Phi of عشرة plus K minus
+
+282
+00:31:53,370 --> 00:32:02,310
+الـ one زائد زائد Phi of A1 في Phi of عشرة زائد
+
+283
+00:32:02,310 --> 00:32:09,130
+Phi of A0. كل هذا الكلام يساوي زيلة. فهيبقى هذا
+
+284
+00:32:09,130 --> 00:32:18,100
+صحيح F and قللي F. Phi of AKالعشرة هذه في زيت تسعة
+
+285
+00:32:18,100 --> 00:32:24,660
+كداشه اعتبر المناطق؟ واحد صح؟ إذا ما بقدر أشيلها و
+
+286
+00:32:24,660 --> 00:32:30,880
+أحط مكانها واحد أس كدير واحد في واحد بقى جد ما
+
+287
+00:32:30,880 --> 00:32:39,880
+بديكي بواحد يبقى هذه صار five of one وهنا five of
+
+288
+00:32:39,880 --> 00:32:49,840
+a k minus one في five of oneوهنا Phi of A1 في Phi
+
+289
+00:32:49,840 --> 00:32:56,920
+of 1 وهنا Phi of A0 كله سيكون ساوي مين؟ سيكون ساوي
+
+290
+00:32:56,920 --> 00:33:04,680
+Zero طلعيني للتعريف هنا Phi of 1 كده شو ساوي؟
+
+291
+00:33:04,680 --> 00:33:06,480
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+292
+00:33:06,480 --> 00:33:07,980
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+293
+00:33:07,980 --> 00:33:12,180
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+294
+00:33:12,180 --> 00:33:12,680
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+295
+00:33:12,680 --> 00:33:12,720
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+296
+00:33:12,720 --> 00:33:13,550
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، وافي
+
+297
+00:33:13,550 --> 00:33:22,410
+five of a k يبقى f and only f five of a k زائد
+
+298
+00:33:22,410 --> 00:33:29,850
+five of a k minus ال one زائد زائد five of a one
+
+299
+00:33:29,850 --> 00:33:37,130
+زائد five of a naught بده يساوي zero هذا الكلام
+
+300
+00:33:37,130 --> 00:33:46,610
+because five of oneيساوي ال one modulo تسعة طيب
+
+301
+00:33:46,610 --> 00:33:54,550
+برجع لنفس المعادل five of a k جداش بتساوي a k
+
+302
+00:33:54,550 --> 00:34:01,010
+modulo تسعة five of a k minus one a k minus one و
+
+303
+00:34:01,010 --> 00:34:08,310
+هكذا يفجر هذا الكلام صحيح if and only if ال a k
+
+304
+00:34:08,840 --> 00:34:15,800
+زائد ال A K minus ال one زائد ال A one زائد ال A
+
+305
+00:34:15,800 --> 00:34:22,740
+naught كلهم بدو يساوي Zero صحيح ؟ طيب هذا الكلام
+
+306
+00:34:22,740 --> 00:34:29,480
+if and only if الحلم يكون مجموع هدول كلهم بدو
+
+307
+00:34:29,480 --> 00:34:36,390
+يساوي Zeroإيش معنى هذا الكلام؟ إنه هذا انقسم أو
+
+308
+00:34:36,390 --> 00:34:43,550
+ينقسم وسط التسعة بدون باقي يبقى هذا الكلام صحيح if
+
+309
+00:34:43,550 --> 00:34:50,190
+and only if ال A K plus A K minus ال one plus A
+
+310
+00:34:50,190 --> 00:34:55,690
+one plus A one is divisible by
+
+311
+00:35:22,450 --> 00:35:29,550
+بنجي الأن لأول نظرية موجودة في هذا الشرطة من
+
+312
+00:35:29,550 --> 00:35:37,930
+العنون .. من العنونها Beneficent Parties of Ring
+
+313
+00:35:37,930 --> 00:35:40,950
+Homomorphisms
+
+314
+00:35:40,950 --> 00:35:49,490
+النظرية بتقول ما يبتد في ايران Let
+
+315
+00:35:49,490 --> 00:36:00,380
+الـ Phiمن R إلى S بيه ring homomorphism بيه ring
+
+316
+00:36:00,380 --> 00:36:03,420
+homomorphism
+
+317
+00:36:03,420 --> 00:36:18,180
+لت ال A بيه sub ring لت ال A بيه sub ring of R and
+
+318
+00:36:18,180 --> 00:36:33,500
+ال B andideal of S then النقطة الأولى النقطة
+
+319
+00:36:33,500 --> 00:36:45,040
+الأولى for any or any R belongs to R and any
+
+320
+00:36:45,040 --> 00:36:49,780
+positive integer
+
+321
+00:36:56,010 --> 00:37:01,170
+وانتجر N نحن
+
+322
+00:37:01,170 --> 00:37:04,970
+لدينا
+
+323
+00:37:04,970 --> 00:37:17,450
+الـ Phi of N A يساوي الـ N في Phi of A و Phi of R
+
+324
+00:37:17,450 --> 00:37:24,690
+to the power N يساوي Phi of Rكله to the power of N
+
+325
+00:37:24,690 --> 00:37:34,270
+نمره اتنين five of A كل العناصر five of A وبحيث ال
+
+326
+00:37:34,270 --> 00:37:46,010
+A موجودة فيها ال Z هي sub ring of S يعني صورة ال
+
+327
+00:37:46,010 --> 00:37:59,890
+sub ring هي sub ring كذلك تلاتةFLA is an ideal of
+
+328
+00:37:59,890 --> 00:38:12,210
+A and الـ Phi is onto .. and ال Phi is onto S ..
+
+329
+00:38:12,210 --> 00:38:18,630
+onto S then
+
+330
+00:38:27,960 --> 00:38:42,780
+ثم الـ Phi of A is an ideal of S مفتاح
+
+331
+00:38:42,780 --> 00:38:53,040
+رابع Phi inverse of B اللي هو كل الـ R اللي موجودة
+
+332
+00:38:53,040 --> 00:39:01,700
+في Rsuch that فاي of أه موجود فيه بيه. if I'm
+
+333
+00:39:01,700 --> 00:39:14,280
+ideal of أه is I'm ideal of أه. يمر خمسة if الأرض
+
+334
+00:39:14,280 --> 00:39:22,280
+كم يتتف. if الأرض كم يتتف
+
+335
+00:39:24,020 --> 00:39:38,900
+then الـ five of R is commutative نمرى
+
+336
+00:39:38,900 --> 00:39:52,910
+ستة if الـ R has a unity if الـ R has a unityas
+
+337
+00:39:52,910 --> 00:40:01,850
+unity one والاسم لا تساوي ال zero and five is unto
+
+338
+00:40:01,850 --> 00:40:13,950
+and five is unto then five
+
+339
+00:40:13,950 --> 00:40:20,450
+of one five of one is the unity and
+
+340
+00:40:22,860 --> 00:40:29,460
+unity of S نقرأ
+
+341
+00:40:29,460 --> 00:40:37,540
+السابعة The Phi is an isomorphism Phi is an
+
+342
+00:40:37,540 --> 00:40:50,420
+isomorphism if and only if ال Phi is on top and
+
+343
+00:40:52,600 --> 00:41:00,760
+الكيرنيل للفاي اللي هو كل العناصر R اللي موجودة في
+
+344
+00:41:00,760 --> 00:41:09,540
+R such that فاي of R بدي ساوي Zero بدي ساوي Zero
+
+345
+00:41:09,540 --> 00:41:19,080
+هنا تمانية فاي is an isomorphism فاي is an
+
+346
+00:41:19,080 --> 00:41:21,180
+isomorphism
+
+347
+00:41:22,290 --> 00:41:27,230
+from R
+
+348
+00:41:27,230 --> 00:41:29,730
+on to H
+
+349
+00:42:22,570 --> 00:42:27,910
+طبعا لو نظرنا لهذه الخواصة seven يعني بنلاقي نفس
+
+350
+00:42:27,910 --> 00:42:32,270
+الخواصة اللي موجودة عالميا على ال groups مضبط
+
+351
+00:42:32,270 --> 00:42:38,860
+تمامابيقول لو كان 5 من R إلى S برا رنجوموفيزم with
+
+352
+00:42:38,860 --> 00:42:45,620
+A sub ring من R و ال B I دي في S بيقول أي عنصر R
+
+353
+00:42:45,620 --> 00:42:51,120
+موجود في R و أي positive integer N we have ف5 of N
+
+354
+00:42:51,120 --> 00:42:56,900
+R يساوي N برا في 5 of R و 5R to the power N بيساوي
+
+355
+00:42:56,900 --> 00:43:03,310
+5 of R كلها to the power Nنقطة ثانية فى لما تأثر
+
+356
+00:43:03,310 --> 00:43:09,970
+على ال ideal A بده تبقى صورته هي sub ring من مين؟
+
+357
+00:43:09,970 --> 00:43:18,010
+من S ال A هو subset من R صورته فى of A هي sub ring
+
+358
+00:43:18,010 --> 00:43:23,610
+من مين؟ من ال S تلاتة لو كان ال A ايديلي و بطل
+
+359
+00:43:23,610 --> 00:43:29,520
+يسير ياش؟ sub ring يبقى خلّين ال A ايديلوالـ Phi
+
+360
+00:43:29,520 --> 00:43:35,900
+كانت أنته يبقى صورته بتكون ideal من S يبقى قلنا
+
+361
+00:43:35,900 --> 00:43:40,660
+Phi أنته ال homomorphism صار أنته وفي نفس الوقت ال
+
+362
+00:43:40,660 --> 00:43:45,680
+A صار ideal يبقى صورة ال ideal هي ideal كذلك
+
+363
+00:43:45,680 --> 00:43:51,200
+فاهمين في ال S Phi inverse of B كل العلاقات ال R
+
+364
+00:43:51,200 --> 00:43:55,860
+في R بحيث Phi of R موجودة وين في B كأننا بنجيب ال
+
+365
+00:43:55,860 --> 00:44:01,010
+homomorphism المعكوساللي هو من S إلى R يبقى كمان
+
+366
+00:44:01,010 --> 00:44:07,250
+هذا ID لو كانت ال R commutative يبقى صورتها في S
+
+367
+00:44:07,250 --> 00:44:13,930
+كذلك بتكون commutative النقطة الثالثة لو كان ال R
+
+368
+00:44:13,930 --> 00:44:18,830
+فيها ال unity و ال S بالسويس ال zero و ال five is
+
+369
+00:44:18,830 --> 00:44:24,830
+unto يبقى ال five of one هو ال unity تابع ال Sفاي
+
+370
+00:44:24,830 --> 00:44:30,130
+isomorphism if and only if فاي is onto والكيرنل
+
+371
+00:44:30,130 --> 00:44:34,850
+كان يساوي ال zero نفسها كانت في حالة ال group
+
+372
+00:44:34,850 --> 00:44:39,910
+بالضبط تماما بس هناك بجينا نقول اللي هو الكيرنل
+
+373
+00:44:39,910 --> 00:44:45,230
+فاي بده يساوي ال identity تماما وهذا هو ال
+
+374
+00:44:45,230 --> 00:44:51,000
+identity بالنسبة لعملية الجامعة النقطة التانيةلو
+
+375
+00:44:51,000 --> 00:44:55,360
+كان الـ Phi إيزو مورفزم من الـ ring إلى تانية يبقى
+
+376
+00:44:55,360 --> 00:45:00,700
+Phi inverse بدي يكون كذلك إيزو مورفزم من الـ S إلى
+
+377
+00:45:00,700 --> 00:45:07,400
+R المرة القادمة إن شاء الله تعالى يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..14b59acaf45ba1139cd3c40515002658d7710b6f
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY.srt
@@ -0,0 +1,890 @@
+1
+00:00:20,910 --> 00:00:25,830
+بسم الله الرحمن الرحيم نكمل ما ابتدأنا به في الـ F
+
+2
+00:00:25,830 --> 00:00:33,530
+of X has a Z NF. السؤال الذي بدنا نسأله: طب لو غيرنا
+
+3
+00:00:33,530 --> 00:00:38,870
+الـ degree  تَبْعَتْ الـ F وكان أكبر من ثلاثة: أربعة، خمسة،
+
+4
+00:00:38,870 --> 00:00:44,370
+ستة، إلخ. تمام؟ هل تبقى النظرية صحيحة؟
+
+5
+00:00:44,370 --> 00:00:49,570
+الإجابة: لا، وهذا هو موضوع الـ note الذي  كتبناه
+
+6
+00:00:49,570 --> 00:00:53,720
+على اللوحة. يبقى الملاحظة التي عندنا هذه: The above
+
+7
+00:00:53,720 --> 00:00:58,940
+theorem تَبْعَتْ المرة الماضية need not be true. ليس
+
+8
+00:00:58,940 --> 00:01:04,980
+بالضرورة صحيحة عندما تكون degree الـ F أكبر من ثلاثة،
+
+9
+00:01:04,980 --> 00:01:11,040
+يعني أربعة فما فوق. for example، كمثال على ذلك لو
+
+10
+00:01:11,040 --> 00:01:16,580
+جئنا إلى الـ Q of X، الـ Q of X is a field، مظبوط؟ طيب،
+
+11
+00:01:16,580 --> 00:01:22,130
+بدنا نجي نأخذ polynomial، هي الـ main الـ F of X
+
+12
+00:01:22,130 --> 00:01:28,270
+يساوي X⁴ + 2X² + 1
+
+13
+00:01:28,270 --> 00:01:34,890
+تمام؟ بالنسبة لي، هل نقدر نحللها إلى عاملين؟
+
+14
+00:01:34,890 --> 00:01:42,530
+الإجابة: نعم، وهي أن X² + 1 في X²
+
+15
+00:01:42,530 --> 00:01:49,460
++ 1. يبقى صارت الـ F التي عندنا Reducible على
+
+16
+00:01:49,460 --> 00:01:57,520
+من؟ على الـ Q. يبقى هذا يعطينا أن الـ F of X is
+
+17
+00:01:57,520 --> 00:02:08,140
+Reducible over Q. طيب، ما علينا، السؤال هو: هل أي
+
+18
+00:02:08,140 --> 00:02:17,480
+واحدة من هذين لها حل في الـ Q؟ X² + 1 يساوي
+
+19
+00:02:17,480 --> 00:02:23,900
+صفر؟ إنها حالة غريبة. but is irreducible, but اللي هو
+
+20
+00:02:23,900 --> 00:02:33,080
+مثلاً، but الـ X² + 1 تساوي صفر. أو، دور
+
+21
+00:02:33,080 --> 00:02:43,540
+بلاش تساوي صفر، has no solution in Q. يعني لا يمكن
+
+22
+00:02:44,020 --> 00:02:50,120
+أن أجد الرقم في الـ Q يحقق هذه المعادلة. has no
+
+23
+00:02:50,120 --> 00:02:56,120
+solution أو has no zero حسب نص النظرية. F
+
+24
+00:02:56,120 --> 00:03:01,880
+فبقول: لازم تلاقي Zero للـ ... للـ ... للـ ... للـ
+
+25
+00:03:01,880 --> 00:03:06,460
+polynomial F (small) of X إذا كانت الـ degree اثنين
+
+26
+00:03:06,460 --> 00:03:10,800
+أو ثلاثة. لكن لما أصبحت أربعة، هي ما فيش لها حلول.
+
+27
+00:03:10,800 --> 00:03:18,230
+تمام؟ يبقى has no solution في Q. يبقى هذا يؤكد
+
+28
+00:03:18,230 --> 00:03:22,790
+أن النظرية هذه لو شِلتْ الـ condition التي عندنا هذه،
+
+29
+00:03:22,790 --> 00:03:29,710
+تصبح غير صحيحة. تمام؟ إذًا هذه الملاحظة التي كنا
+
+30
+00:03:29,710 --> 00:03:33,430
+نقُولها على النظرية المرة التي فاتت، ولم يكن هناك
+
+31
+00:03:33,430 --> 00:03:40,830
+وقت لنشير إليها. نجي نأخذ definition جديد.
+
+32
+00:03:42,090 --> 00:03:50,210
+definition يقول: ما هي the content of
+
+33
+00:03:50,210 --> 00:04:03,510
+a non-zero polynomial؟ a non-zero polynomial a<sub>n</sub>
+
+34
+00:04:03,510 --> 00:04:09,130
+x<sup>n</sup> + a<sub>n-1</sub>x<sup>n-1</sup>
+
+35
+00:04:09,130 --> 00:04:21,950
++...+ a<sub>1</sub>x + a<sub>0</sub> حيث الـ a هذه كلها
+
+36
+00:04:21,950 --> 00:04:31,150
+are integers، كلها أعداد صحيحة، is the greatest
+
+37
+00:04:31,150 --> 00:04:38,770
+common divisor، اللي هو is the greatest
+
+38
+00:04:45,920 --> 00:04:57,600
+common divisor is
+
+39
+00:04:57,600 --> 00:05:05,460
+the greatest common divisor of
+
+40
+00:05:05,460 --> 00:05:06,460
+the integers
+
+41
+00:05:16,290 --> 00:05:23,570
+هو الـ a<sub>n</sub>، والـ a<sub>n-1</sub>، والـ a<sub>1</sub>، والـ a<sub>0</sub>. كمان تعريف ثاني: definition: a primitive
+
+43
+00:05:31,610 --> 00:05:38,610
+polynomial. a primitive polynomial
+
+44
+00:05:46,640 --> 00:05:53,660
+is an element, is
+
+45
+00:05:53,660 --> 00:06:05,560
+an element of Z[X], Z[X] with
+
+46
+00:06:05,560 --> 00:06:08,600
+content
+
+47
+00:06:08,600 --> 00:06:18,150
+one. لما ننتهي، سنعمل two definitions. نقرأ من جديد ونحاول
+
+48
+00:06:18,150 --> 00:06:23,010
+نفهم ما هو المقصود بكل تعريف من هذين
+
+49
+00:06:23,010 --> 00:06:29,810
+التعريفين. نجي مع التعريف الأول: الـ content of a non-
+
+50
+00:06:29,810 --> 00:06:34,830
+zero polynomial. هي قدامي أنا: عندي non-zero
+
+51
+00:06:34,830 --> 00:06:39,170
+polynomial بالشكل هذا، ما هو الـ content تبعها؟
+
+52
+00:06:39,170 --> 00:06:45,030
+يقول لي: بحيث كل الـ a التي عندي عبارة عن integers،
+
+53
+00:06:45,390 --> 00:06:54,230
+يبقى a<sub>n</sub>، a<sub>n-1</sub>، a<sub>n-2</sub>، لغاية a<sub>2</sub>، a<sub>1</sub>، a<sub>0</sub>، كلها أعداد صحيحة.
+
+54
+00:06:54,230 --> 00:06:59,970
+تمام؟ يبقى الـ content لهذا polynomial هو الـ
+
+55
+00:06:59,970 --> 00:07:07,150
+greatest common divisor لمن؟ لهذه integers. طب، الـ
+
+56
+00:07:07,150 --> 00:07:11,170
+content يمكن يكون واحد، يمكن يكون اثنين، يمكن يكون
+
+57
+00:07:11,170 --> 00:07:15,080
+ثلاثة، يمكن يكون أربعة، ممكن يكون كثير. لأنه هو
+
+58
+00:07:15,080 --> 00:07:20,000
+integer، ليس مُمكنات. تمام؟ إذًا يا بنات،
+
+59
+00:07:20,000 --> 00:07:24,820
+المعاملات التي عندي في هذا الـ polynomial كلها عدد
+
+60
+00:07:24,820 --> 00:07:29,920
+صحيح. تمام؟ من هو الـ content لهذا الـ polynomial؟ هو الـ
+
+61
+00:07:29,920 --> 00:07:36,280
+greatest common divisor. يعني أعلى رقم يقسم كل هذه
+
+62
+00:07:36,280 --> 00:07:41,820
+المعاملات. فهمنا التعريف الأول. التعريف الثاني سيعتمد
+
+63
+00:07:41,820 --> 00:07:47,270
+على التعريف الأول. طبعاً، هو التعريف الثاني قال: الـ
+
+64
+00:07:47,270 --> 00:07:53,470
+primitive polynomial. كثيرة الحدود الأولية. كلمة
+
+65
+00:07:53,470 --> 00:07:58,890
+primitive جاءت من كلمة prime. prime عدد أول. يبقى
+
+66
+00:07:58,890 --> 00:08:02,790
+primitive أول. يبقى الـ polynomial، كثيرة الحدود،
+
+67
+00:08:02,790 --> 00:08:11,950
+الأولية is an element of Z[X]. يبقى هي كثيرة حدود
+
+68
+00:08:11,950 --> 00:08:17,950
+في Z[X]، والمعاملات تَبْعَتْها كلها أعداد صحيحة، بحيث
+
+69
+00:08:17,950 --> 00:08:22,430
+الـ content  لها يساوي من؟ يساوي الواحد الصحيح.
+
+70
+00:08:22,430 --> 00:08:28,790
+يبقى أي polynomial في Z[X]، الذي طلع للمعاملات
+
+71
+00:08:28,790 --> 00:08:32,190
+تَبْعَتْ هذه الـ polynomial، إذا كان الـ greatest common
+
+72
+00:08:32,190 --> 00:08:36,710
+divisor لها كلها بواحد، يبقى على طول نقول: الـ
+
+73
+00:08:36,710 --> 00:08:41,340
+polynomial هي primitive. كان اثنين، ثلاثة، أربعة،
+
+74
+00:08:41,340 --> 00:08:46,000
+خمسة، لا يكون primitive. يبقى التعريف
+
+75
+00:08:46,000 --> 00:08:50,420
+الثاني يعتمد على التعريف الأول. إذًا ممكن أنا أُصِغ التعريف الثاني:
+
+76
+00:08:50,420 --> 00:08:55,180
+بقول: هي primitive polynomial F(X)
+
+77
+00:08:55,180 --> 00:09:00,600
+التي موجودة في Z[X]، هي primitive إذا كان الـ
+
+78
+00:09:00,600 --> 00:09:06,360
+content الذي يساوي واحد. مفهوم؟ اه، الـ content
+
+79
+00:09:06,360 --> 00:09:13,100
+يساوي واحد. يبقى أي polynomial في Z[X]، الـ content
+
+80
+00:09:13,100 --> 00:09:17,720
+لها يساوي واحد، نقول عنها primitive polynomial. طب
+
+81
+00:09:17,720 --> 00:09:21,560
+كان الـ content لها يساوي اثنين، يعني الـ greatest
+
+82
+00:09:21,560 --> 00:09:25,780
+common divisor للمعاملات كلها يساوي اثنين، يبقى في
+
+83
+00:09:25,780 --> 00:09:30,260
+هذه الحالة لا نقدر نقول عليها primitive polynomial.
+
+84
+00:09:30,260 --> 00:09:37,040
+تمام؟ طيب، نعطي مثال توضيحي على ذلك. يبقى example:
+
+85
+00:09:45,140 --> 00:09:46,460
+يبقى هذا Polynomial.
+
+86
+00:09:50,640 --> 00:10:03,940
+F(X) التي تساوي 3X³ - 4X + 35. هل هذه primitive؟
+
+87
+00:10:03,940 --> 00:10:11,960
+ناقش. 3X³ - 4X + 35. هل هذه primitive؟
+
+88
+00:10:11,960 --> 00:10:20,930
+نعم.  لأ. لأ.
+
+89
+00:10:20,930 --> 00:10:27,050
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+90
+00:10:27,050 --> 00:10:29,790
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+91
+00:10:29,790 --> 00:10:29,810
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+92
+00:10:29,810 --> 00:10:36,050
+لأ لأ لأ لأ
+
+93
+00:10:36,050 --> 00:10:44,090
+لأ لأ
+
+94
+00:10:44,420 --> 00:10:50,000
+و الـ 35،  is one. يعني الـ content لها
+
+95
+00:10:50,000 --> 00:10:56,640
+يساوي واحد. that is its
+
+96
+00:10:56,640 --> 00:11:02,980
+content is
+
+97
+00:11:02,980 --> 00:11:07,060
+one. but the polynomial
+
+98
+00:11:15,250 --> 00:11:28,490
+مثلاً، G(X) يساوي 12X² + 6X - 3. هل هذه primitive؟ لأ. is not primitive. السبب
+
+100
+00:11:40,190 --> 00:11:41,550
+because
+
+101
+00:11:44,990 --> 00:11:51,470
+the greatest common divisor of 12، 6، و
+
+102
+00:11:51,470 --> 00:11:56,310
+-3، يبقى نقول الآن، الـ  polynomial الثاني G(X)
+
+103
+00:11:56,310 --> 00:12:01,510
+الذي 12X² + 6X - 3 is not
+
+104
+00:12:01,510 --> 00:12:05,510
+primitive. ما هو السبب؟ لأن الـ greatest common
+
+105
+00:12:05,510 --> 00:12:10,190
+divisor للمعاملات 12، والـ 6، والـ -3 هو
+
+106
+00:12:10,190 --> 00:12:14,980
+من؟ هو الثلاثة. يعني الـ content لهذه الـ polynomial
+
+107
+00:12:14,980 --> 00:12:22,900
+هو ثلاثة. ممتاز. نجي الآن يا بنات إلى حاجة نظرية اسمها
+
+108
+00:12:22,900 --> 00:12:33,080
+Gauss's lemma. يبقى بالتالي Gauss's lemma، نظرية
+
+109
+00:12:33,080 --> 00:12:40,340
+جاوس، تقول: ما يعني the product
+
+110
+00:12:42,390 --> 00:12:51,150
+of two primitive polynomials
+
+111
+00:12:51,150 --> 00:12:55,310
+is
+
+112
+00:12:55,310 --> 00:13:00,810
+a primitive polynomial.
+
+113
+00:13:00,810 --> 00:13:09,510
+primitive. let's
+
+114
+00:13:09,510 --> 00:13:09,730
+hope
+
+115
+00:13:14,030 --> 00:13:19,150
+أنا بدي أفترض أن عندي two polynomials، وكل واحدة
+
+116
+00:13:19,150 --> 00:13:23,990
+فيهم primitive. بعدين بدي أحاول أثبت أن حاصل الضرب
+
+117
+00:13:23,990 --> 00:13:34,070
+يكون primitive. بدي أقول: let f(x) و g(x)
+
+118
+00:13:34,070 --> 00:13:42,590
+الاثنان are primitive polynomials
+
+119
+00:13:47,480 --> 00:13:54,860
+in Z[x]. I
+
+120
+00:13:54,860 --> 00:13:59,220
+want to show أن
+
+121
+00:13:59,220 --> 00:14:06,400
+أحاول أن أبين أن الـ f(x) g(x) is a
+
+122
+00:14:06,400 --> 00:14:11,280
+primitive. that
+
+123
+00:14:11,280 --> 00:14:11,660
+is
+
+124
+00:14:16,250 --> 00:14:22,350
+want to show that
+
+125
+00:14:22,350 --> 00:14:29,770
+أن الـ content of
+
+126
+00:14:29,770 --> 00:14:42,110
+الـ f(x) في الـ g(x) بتساوي كم؟ بتساوي واحد. لأن
+
+127
+00:14:42,110 --> 00:14:44,410
+سأثبت هذا الكلام بالتناقض.
+
+128
+00:14:49,910 --> 00:15:02,170
+assume that أن الـ content of، أو نفترض أنهم في الأول
+
+129
+00:15:02,170 --> 00:15:07,310
+primitive وما إلى ذلك. أو، بيأخذ... اه، قلنا أولاً الـ
+
+130
+00:15:07,310 --> 00:15:11,150
+primitive. صحيح. one to show حاصل ضربهم أن
+
+131
+00:15:11,150 --> 00:15:15,880
+is one. to show that هذه الـ content. assume that the
+
+132
+00:15:15,880 --> 00:15:24,160
+content of الـ f(x) في الـ g(x) greater than one.
+
+133
+00:15:24,160 --> 00:15:30,900
+افترضي أن الـ content لحاصل الضرب هذا أكبر
+
+134
+00:15:30,900 --> 00:15:43,580
+من واحد. طيب، نعطي فرض آخر:  Let P be a positive
+
+135
+00:15:43,580 --> 00:15:44,340
+prime
+
+136
+00:15:46,640 --> 00:15:52,800
+be a prime divisor
+
+137
+00:15:52,800 --> 00:15:55,980
+of
+
+138
+00:15:55,980 --> 00:16:10,900
+الـ content of f(x) في الـ g(x). افترضت
+
+139
+00:16:10,900 --> 00:16:16,820
+أن في عندي رقم، وهذا الرقم prime number، ويقسم الـ
+
+140
+00:16:16,820 --> 00:16:20,740
+content تبع الـ f(x) في g(x)، اللي هو أكبر من
+
+141
+00:16:20,740 --> 00:16:26,300
+الواحد. يمكن اثنين، يمكن ثلاثة، يمكن
+
+142
+00:16:26,300 --> 00:16:30,420
+أربعة، يمكن، إن شاء الله يكون عشرة. في عندي prime بدي
+
+143
+00:16:30,420 --> 00:16:37,740
+يقسم هذا الـ content. تمام؟ طيب، بدنا نشغل
+
+144
+00:16:37,740 --> 00:16:47,880
+شغلة ثانية. بدي أقول: الـ  F̄(x) والـ Ḡ
+
+145
+00:16:47,880 --> 00:16:58,800
+(x)، و الـ F̄(x) في Ḡ(x)، اللي هي
+
+146
+00:16:58,800 --> 00:17:07,320
+بدها تساوي F(x) في G(x) ،الكل bar بـ
+
+147
+00:17:07,320 --> 00:17:09,540
+polynomials
+
+148
+00:17:16,830 --> 00:17:33,090
+obtained from اللي هو الـ F(x) والـ G(x)، و الـ
+
+149
+00:17:33,090 --> 00:17:42,530
+F(x) في الـ G(x) by reducing
+
+150
+00:17:46,100 --> 00:17:52,460
+the coefficients. coefficients
+
+151
+00:17:52,460 --> 00:17:59,080
+modulo p. لو p
+
+152
+00:17:59,080 --> 00:18:04,360
+شوية. بدنا نفهم الحكاية هذه كويس مرة ثانية. بنا
+
+153
+00:18:04,360 --> 00:18:11,260
+نفترض أن الـ content للـ F G  له قيمة أكبر من من؟ من
+
+154
+00:18:11,260 --> 00:18:17,130
+الواحد. طيب، آخذ P هو prime divisor للـ content
+
+155
+00:18:17,130 --> 00:18:23,470
+الـ  متوقع تبع الـ F(x) في مين؟ الـ G(x). هذه
+
+156
+00:18:23,470 --> 00:18:29,230
+الخطوة الأولى. الخطوة الثانية: عمل polynomials جديدة من
+
+157
+00:18:29,230 --> 00:18:34,150
+الـ polynomials الموجودة. من الـ polynomials الجديدة F̄
+
+158
+00:18:34,150 --> 00:18:41,380
+(x) و Ḡ(x)، وحاصل ضربهما هو  primitive أو
+
+159
+00:18:41,380 --> 00:18:43,840
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+160
+00:18:43,840 --> 00:18:45,320
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+161
+00:18:45,320 --> 00:18:49,700
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+162
+00:18:49,700 --> 00:18:49,860
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+163
+00:18:49,860 --> 00:19:01,580
+بي بي بي بي بي بي بي بي
+
+164
+00:19:08,920 --> 00:19:14,260
+by reducing their coefficients modulo p. يبقى رحت
+
+165
+00:19:14,260 --> 00:19:19,000
+على معاملات f(x) وعلى معاملات g(x)، وعلى معاملات
+
+166
+00:19:19,000 --> 00:19:24,800
+حاصل الضرب، وكتبتهم بـ modulo p. يبقى في بعضها
+
+167
+00:19:24,800 --> 00:19:30,340
+يصبح بصفر، وبعضها لا يصبح بصفر. ما علينا، مش مشكلة.
+
+168
+00:19:30,340 --> 00:19:35,900
+يبقى هذول صفاتهم كلها modulo p. السؤال هو: يبقى يا بنات،
+
+169
+00:19:35,900 --> 00:19:47,240
+F̄ و Ḡ أين موجودة؟ في Z<sub>p</sub>[X]، صح؟ نعم.
+
+170
+00:19:47,240 --> 00:19:48,620
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+171
+00:19:48,620 --> 00:19:49,180
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+172
+00:19:49,180 --> 00:19:50,160
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+173
+00:19:50,160 --> 00:19:52,320
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+174
+00:19:52,320 --> 00:19:53,480
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+175
+00:19:53,480 --> 00:19:58,900
+نعم، نعم، نعم،
+
+176
+00:19:58,900 --> 00:20:03,100
+نعم،
+
+177
+00:20:03,100 --> 00:20:13,850
+نلاحظ Z<sub>p</sub>[X] is an integral domain. صح؟ يبقى and Z<sub>p</sub>
+
+178
+00:20:13,850 --> 00:20:24,250
+[X] is an integral domain. و هذا أخذناه قبل ذلك
+
+179
+00:20:24,250 --> 00:20:31,550
+لأنه Z<sub>p</sub>، لأنه Z<sub>p</sub> is an integral domain.
+
+180
+00:20:35,960 --> 00:20:41,780
+مرتين جئت على F وجئت وحصل الضرب، حولت المعاملات
+
+181
+00:20:4
+
+223
+00:25:25,300 --> 00:25:33,040
+يبقى الآن بداية أقول: f bar of x في الـ g bar of x
+
+224
+00:25:33,040 --> 00:25:40,820
+بديهي سواء zero أن z في a of x اللي هو الانتقال دبي
+
+225
+00:25:40,820 --> 00:25:48,260
+يبقى هذا معناه أن الـ f bar of x بديهي سواء zero or
+
+226
+00:25:48,260 --> 00:25:56,450
+الـ g bar of x بديهي سواء zero. طيب تعالى نسألك السؤال
+
+227
+00:25:56,450 --> 00:26:03,310
+التالي، لما نقول F bar of X يساوي Zero يعني الـ F of
+
+228
+00:26:03,310 --> 00:26:10,370
+X ده كل معاملاتها سقطت بدلالة P، يعني معناته P
+
+229
+00:26:10,370 --> 00:26:17,610
+بتقسم كل معامل من معاملات F of X، صح ولا لا؟ يبقى
+
+230
+00:26:17,610 --> 00:26:27,020
+this means that this means that هذا يعني أن الـ P
+
+231
+00:26:27,020 --> 00:26:37,200
+divide each coefficient of
+
+232
+00:26:37,200 --> 00:26:49,040
+الـ F of X أو الـ P divide each coefficient of الـ G
+
+233
+00:26:49,040 --> 00:26:49,760
+of X
+
+234
+00:26:53,050 --> 00:27:00,330
+يبقى الـ P بتقسم كل معامل لـ F of X أو الـ P بتقسم كل
+
+235
+00:27:00,330 --> 00:27:06,450
+معامل لمين؟ لـ G of X. هذا يعني أن الـ F of X is
+
+236
+00:27:06,450 --> 00:27:15,150
+primitive، أو الثانية ماهياش primitive. يبقى فالـ F
+
+237
+00:27:15,150 --> 00:27:19,970
+of X is not primitive
+
+238
+00:27:22,670 --> 00:27:33,250
+أو الـ g of x is not primitive. إما
+
+239
+00:27:33,250 --> 00:27:37,510
+هذه ماهياش primitive أو هذه ماهياش primitive. إيش
+
+240
+00:27:37,510 --> 00:27:42,750
+رايحين؟ تناقض؟ لأن احنا من الرأس المثلجون ناخد
+
+241
+00:27:42,750 --> 00:27:47,670
+هدول على الـ primitive polynomial. يبقى وصلنا إلى
+
+242
+00:27:47,670 --> 00:27:48,690
+contradiction
+
+243
+00:27:50,910 --> 00:27:58,290
+وصلنا إلى contradiction. يبقى فرضي اللي أنا فرضته
+
+244
+00:27:58,290 --> 00:28:04,150
+هذا غلط، والله صح غلط، وعكسه هو الصح. يبقى الـ
+
+245
+00:28:04,150 --> 00:28:10,670
+content للـ F يجيب دي سواء جدال واحد صحيح. يبقى
+
+246
+00:28:10,670 --> 00:28:16,230
+Therefore، الـ
+
+247
+00:28:16,230 --> 00:28:17,430
+content of
+
+248
+00:28:21,130 --> 00:28:30,190
+الـ F of X في الـ G of X is one. هذا يعطيكي أن الـ
+
+249
+00:28:30,190 --> 00:28:41,270
+F of X في الـ G of X is a primitive polynomials.
+
+250
+00:28:41,270 --> 00:28:45,490
+من الآن فصاعدًا، الـ product of two primitive
+
+251
+00:28:45,490 --> 00:28:53,160
+polynomials is a primitive. وهذا الكلام صحيح في Z of
+
+252
+00:28:53,160 --> 00:28:59,720
+x اللي المعاملات كلها أعداد صحيحة. طيب ننتقل إلى
+
+253
+00:28:59,720 --> 00:29:06,120
+النظرية التي تليها، theorem
+
+254
+00:29:06,120 --> 00:29:12,120
+little
+
+255
+00:29:12,120 --> 00:29:23,360
+f of x موجودة في كافة Z of x if
+
+256
+00:29:23,360 --> 00:29:33,740
+الـ f of x is reducible if الـ f of x is reducible
+
+257
+00:29:33,740 --> 00:29:46,630
+over الـ Q then over الـ Q then الـ F of X is
+
+258
+00:29:46,630 --> 00:29:58,970
+reducible in Z. سؤال يقول: خد F of X في Z of X، شوفوا
+
+259
+00:29:58,970 --> 00:30:02,590
+شو النظرية بتقول. يبقى بيقول: لو كانت الـ F of X
+
+260
+00:30:02,590 --> 00:30:07,690
+reducible على الـ Q، هذا يتطلب أن تكون reducible على
+
+261
+00:30:07,690 --> 00:30:15,380
+مين؟ على Z. وكأن الـ reducibility على الـ Q بده ينسحب
+
+262
+00:30:15,380 --> 00:30:20,340
+عالميًا للـ reducibility على الـ Z. إيه بالبرهان
+
+263
+00:30:20,340 --> 00:30:26,520
+كالتالي: يجب بالدالي أقول: little f of X موجودة في
+
+264
+00:30:26,520 --> 00:30:38,240
+Z of X. بعد هيك، افترض أن الـ F of X is reducible
+
+265
+00:30:39,730 --> 00:30:44,110
+بعد ذلك
+
+266
+00:30:44,110 --> 00:30:48,530
+F of X يساوي
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e0c3c50e61fe1458a67265534edf19d36959fe89
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY_raw.json
@@ -0,0 +1 @@
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0.8515625}, {"start": 731.51, "end": 732.19, "word": " التلاتة", "probability": 0.8717041015625}], "temperature": 1.0}, {"id": 25, "seek": 76034, "start": 732.36, "end": 760.34, "text": "يعني ال content لهذه ال polynomial هو تلاتة ممتاز نيجي الآن يا بنات لحاجة نظرية اسمها Gauss's lemma يبقى بالتالي Gauss's lemma أرضية جاوس تقول ما يعني the product", "tokens": [40228, 22653, 2423, 2701, 46740, 24192, 2423, 26110, 31439, 6055, 1211, 9307, 3660, 3714, 2304, 2655, 31377, 8717, 1829, 7435, 1829, 6024, 48506, 35186, 4724, 8315, 2655, 5296, 5016, 26108, 3660, 8717, 19913, 2288, 10632, 24525, 2304, 11296, 10384, 2023, 311, 7495, 1696, 7251, 3555, 4587, 7578, 20666, 2655, 6027, 1829, 10384, 2023, 311, 7495, 1696, 5551, 43042, 10632, 10874, 995, 41779, 6055, 39648, 19446, 37495, 22653, 264, 1674], "avg_logprob": -0.2941964392151151, "compression_ratio": 1.3764044943820224, "no_speech_prob": 0.0, "words": [{"start": 732.36, "end": 732.86, "word": "يعني", "probability": 0.95166015625}, {"start": 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"word": " لحاجة", "probability": 0.943359375}, {"start": 740.76, "end": 741.72, "word": " نظرية", "probability": 0.97216796875}, {"start": 741.72, "end": 742.9, "word": " اسمها", "probability": 0.97607421875}, {"start": 742.9, "end": 743.84, "word": " Gauss's", "probability": 0.53277587890625}, {"start": 743.84, "end": 744.36, "word": " lemma", "probability": 0.82177734375}, {"start": 744.36, "end": 745.5, "word": " يبقى", "probability": 0.911376953125}, {"start": 745.5, "end": 746.42, "word": " بالتالي", "probability": 0.9212646484375}, {"start": 746.42, "end": 748.84, "word": " Gauss's", "probability": 0.7082926432291666}, {"start": 748.84, "end": 751.42, "word": " lemma", "probability": 0.90966796875}, {"start": 751.42, "end": 753.08, "word": " أرضية", "probability": 0.5371907552083334}, {"start": 753.08, "end": 753.8, "word": " جاوس", "probability": 0.7366536458333334}, {"start": 753.8, "end": 756.28, "word": " تقول", "probability": 0.590087890625}, {"start": 756.28, "end": 756.56, "word": " ما", "probability": 0.61279296875}, {"start": 756.56, "end": 757.0, "word": " يعني", "probability": 0.562744140625}, {"start": 757.0, "end": 758.4, "word": " the", "probability": 0.256103515625}, {"start": 758.4, "end": 760.34, "word": " product", "probability": 0.96044921875}], "temperature": 1.0}, {"id": 26, "seek": 78973, "start": 762.39, "end": 789.73, "text": "of two primitive polynomials the derivative of two primitive polynomials is a primitive let's hope", "tokens": [2670, 732, 28540, 22560, 12356, 264, 13760, 295, 732, 28540, 22560, 12356, 307, 257, 28540, 718, 311, 1454], "avg_logprob": -0.3797286309693989, "compression_ratio": 1.462686567164179, "no_speech_prob": 0.0, "words": [{"start": 762.39, "end": 763.09, "word": "of", "probability": 0.253662109375}, {"start": 763.09, "end": 764.45, "word": " two", "probability": 0.9033203125}, {"start": 764.45, "end": 766.31, "word": " primitive", "probability": 0.8935546875}, {"start": 766.31, "end": 771.15, "word": " polynomials", "probability": 0.826416015625}, {"start": 771.15, "end": 775.31, "word": " the", "probability": 0.302001953125}, {"start": 775.31, "end": 775.61, "word": " derivative", "probability": 0.83154296875}, {"start": 775.61, "end": 775.89, "word": " of", "probability": 0.9521484375}, {"start": 775.89, "end": 776.11, "word": " two", "probability": 0.90966796875}, {"start": 776.11, "end": 776.63, "word": " primitive", "probability": 0.94091796875}, {"start": 776.63, "end": 777.87, "word": " polynomials", "probability": 0.957275390625}, {"start": 777.87, "end": 779.21, "word": " is", "probability": 0.72119140625}, {"start": 779.21, "end": 780.81, "word": " a", "probability": 0.90478515625}, {"start": 780.81, "end": 781.51, "word": " primitive", "probability": 0.876953125}, {"start": 781.51, "end": 789.51, "word": " let's", "probability": 0.5372314453125}, {"start": 789.51, "end": 789.73, "word": " hope", "probability": 0.361572265625}], "temperature": 1.0}, {"id": 27, "seek": 82259, "start": 794.03, "end": 822.59, "text": "أنا بدي افترض ان عندي two polynomials وكل واحدة فيهم primitive بعدين بدي احاول اثبت ان حاصل الضرب يكون primitive بدي اقول let f of x و g of x الاتنين are primitive polynomials", "tokens": [10721, 8315, 4724, 16254, 1975, 5172, 2655, 43042, 16472, 18871, 16254, 732, 22560, 12356, 4032, 28820, 36764, 24401, 3660, 8978, 16095, 28540, 39182, 9957, 4724, 16254, 1975, 5016, 995, 12610, 1975, 12984, 3555, 2655, 16472, 11331, 33546, 1211, 6024, 114, 25513, 7251, 30544, 28540, 4724, 16254, 1975, 39648, 718, 283, 295, 2031, 4032, 290, 295, 2031, 2423, 9307, 1863, 9957, 366, 28540, 22560, 12356], "avg_logprob": -0.3141826923076923, "compression_ratio": 1.5120481927710843, "no_speech_prob": 0.0, "words": [{"start": 794.03, "end": 794.51, "word": "أنا", "probability": 0.4736328125}, {"start": 794.51, "end": 794.81, "word": " بدي", "probability": 0.367919921875}, {"start": 794.81, "end": 795.31, "word": " افترض", "probability": 0.8892822265625}, 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851.66, "word": " is", "probability": 0.9619140625}], "temperature": 1.0}, {"id": 29, "seek": 88441, "start": 856.25, "end": 884.41, "text": "want to show that ان ال content of ال F of X في ال G of X بتساوي كده؟ بتساوي واحد لان اثبت هذا الكلام بالتناقض", "tokens": [86, 394, 281, 855, 300, 16472, 2423, 2701, 295, 2423, 479, 295, 1783, 8978, 2423, 460, 295, 1783, 39894, 3794, 995, 45865, 9122, 3215, 3224, 22807, 39894, 3794, 995, 45865, 36764, 24401, 5296, 7649, 1975, 12984, 3555, 2655, 23758, 2423, 28820, 10943, 20666, 2655, 8315, 4587, 11242], "avg_logprob": -0.20605469029396772, "compression_ratio": 1.3225806451612903, "no_speech_prob": 0.0, "words": [{"start": 856.25, "end": 856.81, "word": "want", "probability": 0.5804443359375}, {"start": 856.81, "end": 857.15, "word": " to", "probability": 0.9794921875}, {"start": 857.15, "end": 857.71, "word": " show", "probability": 0.92431640625}, {"start": 857.71, "end": 862.35, "word": " that", "probability": 0.853515625}, {"start": 862.35, 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"end": 1608.8, "word": " ال", "probability": 0.4482421875}, {"start": 1608.8, "end": 1609.04, "word": " G", "probability": 0.912109375}, {"start": 1609.04, "end": 1609.4, "word": " of", "probability": 0.9384765625}, {"start": 1609.4, "end": 1609.76, "word": " X", "probability": 0.99609375}], "temperature": 1.0}, {"id": 55, "seek": 163997, "start": 1613.05, "end": 1639.97, "text": "يبقى ال P بتقسم كل معامل ل F of X او ال P بتقسم كل معامل لمين ل G of X هذا يعني ان ال F of X is primitive لأو التانية ماهياش primitive يبقى فال F of X is not primitive", "tokens": [1829, 3555, 4587, 7578, 2423, 430, 39894, 4587, 38251, 28242, 20449, 10943, 1211, 5296, 479, 295, 1783, 1975, 2407, 2423, 430, 39894, 4587, 38251, 28242, 20449, 10943, 1211, 32767, 9957, 5296, 460, 295, 1783, 23758, 37495, 22653, 16472, 2423, 479, 295, 1783, 307, 28540, 5296, 10721, 2407, 16712, 7649, 10632, 19446, 3224, 1829, 33599, 28540, 7251, 3555, 4587, 7578, 6156, 6027, 479, 295, 1783, 307, 406, 28540], "avg_logprob": 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1795.27, "word": " خد", "probability": 0.5677490234375}, {"start": 1795.27, "end": 1795.51, "word": " F", "probability": 0.89306640625}, {"start": 1795.51, "end": 1795.73, "word": " of", "probability": 0.9384765625}, {"start": 1795.73, "end": 1795.99, "word": " X", "probability": 0.99365234375}, {"start": 1795.99, "end": 1796.29, "word": " في", "probability": 0.86767578125}, {"start": 1796.29, "end": 1796.67, "word": " Z", "probability": 0.97998046875}, {"start": 1796.67, "end": 1797.27, "word": " of", "probability": 0.94580078125}, {"start": 1797.27, "end": 1797.87, "word": " X", "probability": 0.99609375}, {"start": 1797.87, "end": 1798.97, "word": " شوفوا", "probability": 0.85498046875}, {"start": 1798.97, "end": 1799.13, "word": " شو", "probability": 0.866455078125}, {"start": 1799.13, "end": 1799.67, "word": " النظرية", "probability": 0.9478759765625}, {"start": 1799.67, "end": 1800.21, "word": " بتقول", "probability": 0.971435546875}, {"start": 1800.21, "end": 1800.65, "word": " يبقى", "probability": 0.79510498046875}, {"start": 1800.65, "end": 1801.05, "word": " بيقول", "probability": 0.953125}, {"start": 1801.05, "end": 1801.29, "word": " لو", "probability": 0.91748046875}, {"start": 1801.29, "end": 1801.81, "word": " كانت", "probability": 0.5198974609375}, {"start": 1801.81, "end": 1801.93, "word": " ال", "probability": 0.6787109375}, {"start": 1801.93, "end": 1802.13, "word": " F", "probability": 0.85498046875}, {"start": 1802.13, "end": 1802.35, "word": " of", "probability": 0.97119140625}, {"start": 1802.35, "end": 1802.59, "word": " X", "probability": 0.994140625}, {"start": 1802.59, "end": 1803.59, "word": " reducible", "probability": 0.7415771484375}, {"start": 1803.59, "end": 1804.01, "word": " على", "probability": 0.66845703125}, {"start": 1804.01, "end": 1804.25, "word": " ال", "probability": 0.8251953125}, {"start": 1804.25, "end": 1804.75, "word": " Q", "probability": 0.29052734375}, {"start": 1804.75, "end": 1805.65, "word": " هذا", "probability": 0.7001953125}, {"start": 1805.65, "end": 1806.37, "word": " يتطلب", "probability": 0.942138671875}, {"start": 1806.37, "end": 1806.55, "word": " ان", "probability": 0.720703125}, {"start": 1806.55, "end": 1806.87, "word": " تكون", "probability": 0.867919921875}, {"start": 1806.87, "end": 1807.39, "word": " reducible", "probability": 0.8134765625}, {"start": 1807.39, "end": 1807.69, "word": " على", "probability": 0.72216796875}, {"start": 1807.69, "end": 1808.67, "word": " مين؟", "probability": 0.6917317708333334}, {"start": 1808.67, "end": 1808.99, "word": " على", "probability": 0.79296875}, {"start": 1808.99, "end": 1809.31, "word": " Z", "probability": 0.916015625}], "temperature": 1.0}, {"id": 62, "seek": 183824, "start": 1810.16, "end": 1838.24, "text": "وكأن ال reducibility على ال Eq بده ينسحب عالميا لل reducibility على ال Z إيه بالبرهان كالتالي يجب بالدالي أقوله little f of X موجودة في Z of X بعد هيك SU افترض ان ال F of X is reducible", "tokens": [2407, 4117, 33456, 2423, 2783, 537, 39802, 15844, 2423, 462, 80, 47525, 3224, 7251, 1863, 3794, 5016, 3555, 6225, 45340, 25528, 24976, 2783, 537, 39802, 15844, 2423, 1176, 11933, 1829, 3224, 20666, 26890, 3224, 7649, 9122, 6027, 2655, 6027, 1829, 7251, 7435, 3555, 20666, 3215, 6027, 1829, 5551, 39648, 3224, 707, 283, 295, 1783, 3714, 29245, 23328, 3660, 8978, 1176, 295, 1783, 39182, 39896, 4117, 9872, 1975, 5172, 2655, 43042, 16472, 2423, 479, 295, 1783, 307, 2783, 32128], "avg_logprob": -0.3633307090288476, "compression_ratio": 1.5166666666666666, "no_speech_prob": 0.0, "words": [{"start": 1810.16, "end": 1810.8, "word": "وكأن", "probability": 0.73095703125}, {"start": 1810.8, "end": 1810.98, "word": " ال", "probability": 0.73876953125}, {"start": 1810.98, "end": 1812.64, "word": " reducibility", "probability": 0.7574869791666666}, {"start": 1812.64, "end": 1813.2, "word": " على", "probability": 0.64013671875}, {"start": 1813.2, "end": 1813.48, "word": " ال", "probability": 0.8095703125}, {"start": 1813.48, "end": 1813.98, "word": " Eq", "probability": 0.3568115234375}, {"start": 1813.98, "end": 1814.68, "word": " بده", "probability": 0.29010009765625}, {"start": 1814.68, "end": 1815.38, "word": " ينسحب", "probability": 0.96875}, {"start": 1815.38, "end": 1816.0, "word": " عالميا", "probability": 0.8528645833333334}, {"start": 1816.0, "end": 1816.54, "word": " لل", "probability": 0.50537109375}, {"start": 1816.54, "end": 1817.48, "word": " reducibility", "probability": 0.9083658854166666}, {"start": 1817.48, "end": 1818.2, "word": " على", "probability": 0.84716796875}, {"start": 1818.2, "end": 1818.5, "word": " ال", "probability": 0.623046875}, {"start": 1818.5, "end": 1818.74, "word": " Z", "probability": 0.63916015625}, {"start": 1818.74, "end": 1819.62, "word": " إيه", "probability": 0.7650553385416666}, {"start": 1819.62, "end": 1820.34, "word": " بالبرهان", "probability": 0.855224609375}, {"start": 1820.34, "end": 1821.34, "word": " كالتالي", "probability": 0.84951171875}, {"start": 1821.34, "end": 1822.1, "word": " يجب", "probability": 0.431640625}, {"start": 1822.1, "end": 1822.62, "word": " بالدالي", "probability": 0.5673828125}, {"start": 1822.62, "end": 1823.24, "word": " أقوله", "probability": 0.5513916015625}, {"start": 1823.24, "end": 1823.58, "word": " little", "probability": 0.55224609375}, {"start": 1823.58, "end": 1824.18, "word": " f", "probability": 0.9267578125}, {"start": 1824.18, "end": 1824.58, "word": " of", "probability": 0.70361328125}, {"start": 1824.58, "end": 1825.0, "word": " X", "probability": 0.390869140625}, {"start": 1825.0, "end": 1826.18, "word": " موجودة", "probability": 0.966064453125}, {"start": 1826.18, "end": 1826.52, "word": " في", "probability": 0.962890625}, {"start": 1826.52, "end": 1827.42, "word": " Z", "probability": 0.8857421875}, {"start": 1827.42, "end": 1827.88, "word": " of", "probability": 0.92138671875}, {"start": 1827.88, "end": 1828.24, "word": " X", "probability": 0.9931640625}, {"start": 1828.24, "end": 1829.32, "word": " بعد", "probability": 0.7080078125}, {"start": 1829.32, "end": 1829.78, "word": " هيك", "probability": 0.6568603515625}, {"start": 1829.78, "end": 1830.68, "word": " SU", "probability": 0.2459716796875}, {"start": 1830.68, "end": 1832.4, "word": " افترض", "probability": 0.9078369140625}, {"start": 1832.4, "end": 1833.3, "word": " ان", "probability": 0.453369140625}, {"start": 1833.3, "end": 1833.66, "word": " ال", "probability": 0.85986328125}, {"start": 1833.66, "end": 1834.0, "word": " F", "probability": 0.76806640625}, {"start": 1834.0, "end": 1834.4, "word": " of", "probability": 0.9453125}, {"start": 1834.4, "end": 1834.98, "word": " X", "probability": 0.99462890625}, {"start": 1834.98, "end": 1836.12, "word": " is", "probability": 0.93017578125}, {"start": 1836.12, "end": 1838.24, "word": " reducible", "probability": 0.8408203125}], "temperature": 1.0}, {"id": 63, "seek": 184853, "start": 1839.73, "end": 1848.53, "text": "بعد ذلك F of X يساوي", "tokens": [3555, 22488, 29910, 23275, 479, 295, 1783, 7251, 3794, 995, 45865], "avg_logprob": -0.8723958482344946, "compression_ratio": 0.7380952380952381, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1839.73, "end": 1840.81, "word": "بعد", "probability": 0.181884765625}, {"start": 1840.81, "end": 1844.11, "word": " ذلك", "probability": 0.6573486328125}, {"start": 1844.11, "end": 1846.79, "word": " F", "probability": 0.2017822265625}, {"start": 1846.79, "end": 1847.13, "word": " of", "probability": 0.20556640625}, {"start": 1847.13, "end": 1847.61, "word": " X", "probability": 0.80126953125}, {"start": 1847.61, "end": 1848.53, "word": " يساوي", "probability": 0.58123779296875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1850.653625, "duration_after_vad": 1743.0806249999953}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..03e8a133887f769e4a51399694806997861fef9c
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/nlY3MqIVnWY_raw.srt
@@ -0,0 +1,1112 @@
+1
+00:00:20,910 --> 00:00:25,830
+بسم الله الرحمن الرحيم نكمل ما ابتدأنا بيه في ال F
+
+2
+00:00:25,830 --> 00:00:33,530
+of X has a Z NF السؤال اللي بدنا نسأله طب لو غيرنا
+
+3
+00:00:33,530 --> 00:00:38,870
+ال degree تبعت ال F وكان أكبر من تلاتة أربع، خمسة،
+
+4
+00:00:38,870 --> 00:00:44,370
+ستة، اللي بدكي ايه؟ تمام هل تبقى نظرية صحيحة؟
+
+5
+00:00:44,370 --> 00:00:49,570
+الإجابة لا وهذا هو موضوع ال note اللي احنا كاتبينه
+
+6
+00:00:49,570 --> 00:00:53,720
+على اللوحةيبقى الملاحظة اللي عندنا هذه The above
+
+7
+00:00:53,720 --> 00:00:58,940
+theorem تبعت المرة الماضية need not be true ليس
+
+8
+00:00:58,940 --> 00:01:04,980
+بالضرورة صحيحة عندما تكون ضرر ال F أكبر من ثلاثة
+
+9
+00:01:04,980 --> 00:01:11,040
+يعني أربعة ثم فوق for example كمثال على ذلك لو
+
+10
+00:01:11,040 --> 00:01:16,580
+جينا ال Q of X ال Q of X is a field، مظبوط؟ طيب،
+
+11
+00:01:16,580 --> 00:01:22,130
+بدنا نجي ناخد بلانوميل اللي هي mainالـ F of X
+
+12
+00:01:22,130 --> 00:01:28,270
+يساوي X أُص أربعة زائد اتنين X تربية زائد واحد
+
+13
+00:01:28,270 --> 00:01:34,890
+تمام؟ بالنسبالي هل بنقدر نحللها إلى عاملين؟
+
+14
+00:01:34,890 --> 00:01:42,530
+الإجابة نعم وهي ان X تربية زائد واحد في X تربية
+
+15
+00:01:42,530 --> 00:01:49,460
+زائد واحديبقى صارت ال F اللي عندنا Reducible على
+
+16
+00:01:49,460 --> 00:01:57,520
+مين على ال Q يبقى هذا بدي يعطينا ان ال F of X is
+
+17
+00:01:57,520 --> 00:02:08,140
+Reducible over Q طيب ما علينا السؤال هو هل اي
+
+18
+00:02:08,140 --> 00:02:17,480
+واحدة من هدول لها حل في ال QX تربيه زائد واحد يسوى
+
+19
+00:02:17,480 --> 00:02:23,900
+صفر انها حالة اينا but is irreducible but اللي هو
+
+20
+00:02:23,900 --> 00:02:33,080
+مثلا but ال X تربيه زائد واحد تساوي zero أو دور
+
+21
+00:02:33,080 --> 00:02:43,540
+بلاش تساوي zero has no solution in AQ يعني لا يمكن
+
+22
+00:02:44,020 --> 00:02:50,120
+ألاقي الرقم في الـ Q يحقق هذه المعادلة has no
+
+23
+00:02:50,120 --> 00:02:56,120
+solution أو has no zero حسب نص من نص النظرية F
+
+24
+00:02:56,120 --> 00:03:01,880
+فبقول لازم تلاقي Zero لل .. لل .. لل .. لل
+
+25
+00:03:01,880 --> 00:03:06,460
+polynomial F small of X إذا كانت ال degree اتنين
+
+26
+00:03:06,460 --> 00:03:10,800
+أو تلاتة لكن لما انصرت أربعة هي مافيش أنزح حلول
+
+27
+00:03:10,800 --> 00:03:18,230
+تمام؟يبقى has no solution في ليكيوم يبقى هذا يؤكد
+
+28
+00:03:18,230 --> 00:03:22,790
+ان النظرية هذا لو شيلت ال condition اللي عندنا هذا
+
+29
+00:03:22,790 --> 00:03:29,710
+بصير غير صحيحة تمام؟ إذا هذه الملاحظة اللي كنا
+
+30
+00:03:29,710 --> 00:03:33,430
+بنقولها على النظرية المرة اللي فاتت ولم يكن هناك
+
+31
+00:03:33,430 --> 00:03:40,830
+وقت لأن نشيرة إليها نجي ناخد definition جديد
+
+32
+00:03:42,090 --> 00:03:50,210
+definition بيقول ما هي the content of
+
+33
+00:03:50,210 --> 00:04:03,510
+a non zero polynomial of a non zero polynomial a n
+
+34
+00:04:03,510 --> 00:04:09,130
+x to the power n a minus one x to the power n
+
+35
+00:04:09,130 --> 00:04:21,950
+minus oneplus a1x plus a0 where حيث ال a هدول كلهم
+
+36
+00:04:21,950 --> 00:04:31,150
+are integers كلهم أعداد صحيحة is the greatest
+
+37
+00:04:31,150 --> 00:04:38,770
+common divisor اللي هو is that greatest
+
+38
+00:04:45,920 --> 00:04:57,600
+common divisor is
+
+39
+00:04:57,600 --> 00:05:05,460
+the greatest common divisor of
+
+40
+00:05:05,460 --> 00:05:06,460
+the integers
+
+41
+00:05:16,290 --> 00:05:23,570
+هو الـ a n و ال a m minus ال one و ال a one و ال a
+
+42
+00:05:23,570 --> 00:05:31,610
+naught كمان تعريف تاني definition a primitive
+
+43
+00:05:31,610 --> 00:05:38,610
+polynomial a primitive polynomial
+
+44
+00:05:46,640 --> 00:05:53,660
+is an element is
+
+45
+00:05:53,660 --> 00:06:05,560
+an element of capital Z of X capital Z of X with
+
+46
+00:06:05,560 --> 00:06:08,600
+content
+
+47
+00:06:08,600 --> 00:06:18,150
+one لما بنقف هعمل two definitionsنقرأ من جديد و
+
+48
+00:06:18,150 --> 00:06:23,010
+نحاول نفهم ما هو المقصود بكل تعريف من هذين
+
+49
+00:06:23,010 --> 00:06:29,810
+التعريفين نجي مع التعريف الأول ال content of a non
+
+50
+00:06:29,810 --> 00:06:34,830
+-zero polynomial هي قدامي انا عند non-zero
+
+51
+00:06:34,830 --> 00:06:39,170
+polynomial بالشكل هذا ما هو ال content تبعها؟
+
+52
+00:06:39,170 --> 00:06:45,030
+بيقول لي بحيث كل ال إيهات اللي عندي عبارة عن انتجة
+
+53
+00:06:45,390 --> 00:06:54,230
+يبقى AN AN-1 AN-2 لغاية A2 A1 A0 كلهم أعداد صحيحة
+
+54
+00:06:54,230 --> 00:06:59,970
+تمام يبقى ال content للبرنامج الهادي هو ال
+
+55
+00:06:59,970 --> 00:07:07,150
+greatest common divisor لمين لهذه الانتجارة طب ال
+
+56
+00:07:07,150 --> 00:07:11,170
+content يمكن يكون واحد يمكن يكون اتنين يمكن يكون
+
+57
+00:07:11,170 --> 00:07:15,080
+تلاتة يمكن يكون اربع ممكن يكون كثيرلأ لأنه نور
+
+58
+00:07:15,080 --> 00:07:20,000
+انتجاز لأ نور انتجاز مش همكانية تمام اذا يا بنات
+
+59
+00:07:20,000 --> 00:07:24,820
+المعاملات اللي عندى فى هذه ال polynomial كلها عدد
+
+60
+00:07:24,820 --> 00:07:29,920
+صحيح تمام من هو ال content لهذه ال polynomial هو
+
+61
+00:07:29,920 --> 00:07:36,280
+ال grays common divisor يعني اعلى رقم بيقسم كل هذه
+
+62
+00:07:36,280 --> 00:07:41,820
+المعاملة فهمنا التعريف الاول التعريف التانى سيعتمد
+
+63
+00:07:41,820 --> 00:07:47,270
+على التعريف الاولطبعا هي التعريف التاني قال ال
+
+64
+00:07:47,270 --> 00:07:53,470
+primitive polynomial كثيرة الحدود الأولية كلمة
+
+65
+00:07:53,470 --> 00:07:58,890
+primitive جاء من كلمة prime prime عدد أول يبقى
+
+66
+00:07:58,890 --> 00:08:02,790
+primitive أول يبقى ال polynomial كثيرة الحدود
+
+67
+00:08:02,790 --> 00:08:11,950
+الأولية is an element of z of x يبقى هي كثيرة حدود
+
+68
+00:08:11,950 --> 00:08:17,950
+في z of xوالمعاملات تبعتها كلها أعداد صحيحة بحيث
+
+69
+00:08:17,950 --> 00:08:22,430
+ال content إلها يساوي مين؟ يساوي الواحد الصحية
+
+70
+00:08:22,430 --> 00:08:28,790
+يبقى أي polynomial في Z of X اللي طلع للمعاملات
+
+71
+00:08:28,790 --> 00:08:32,190
+تبعت هذه ال polynomial إذا كان الجريسيس common
+
+72
+00:08:32,190 --> 00:08:36,710
+divisor إلها كلها بواحد يبقى على طول الخطب يقول ال
+
+73
+00:08:36,710 --> 00:08:41,340
+polynomial هي primitiveكان اتنين، تلتة، اربعة،
+
+74
+00:08:41,340 --> 00:08:46,000
+خمسة جنة يكوني جنات الـ Primitive يبقى التعريف
+
+75
+00:08:46,000 --> 00:08:50,420
+الثاني يعتمد على التعريف الأول إذا ممكن أنا أصيه
+
+76
+00:08:50,420 --> 00:08:55,180
+التعريف الثاني بقول هي Primitive Polynomial F of X
+
+77
+00:08:55,180 --> 00:09:00,600
+اللي موجودة في Z of X هي Primitive إذا كان ال
+
+78
+00:09:00,600 --> 00:09:06,360
+content اللي هيساوي واحد مجروح؟ اه ال content
+
+79
+00:09:06,360 --> 00:09:13,100
+يساوي واحديبقى any polynomial في z of x ال content
+
+80
+00:09:13,100 --> 00:09:17,720
+لها يساوي واحد بقول عنها primitive polynomial طب
+
+81
+00:09:17,720 --> 00:09:21,560
+كان ال content لها يساوي اتنين يعني ال classes
+
+82
+00:09:21,560 --> 00:09:25,780
+common divisor للمعاملات كلها يساوي اتنين يبقى في
+
+83
+00:09:25,780 --> 00:09:30,260
+هذه الحالة بقدرش اقول عليها primitive polynomial
+
+84
+00:09:30,260 --> 00:09:37,040
+تمام طيب نعطي مثال توضيحي على ذلك يبقى example
+
+85
+00:09:45,140 --> 00:09:46,460
+يبقى ده polynomial.
+
+86
+00:09:50,640 --> 00:10:03,940
+F of X التي تساوي تلاتة X تربيع او تلاتة X تكيب
+
+87
+00:10:03,940 --> 00:10:11,960
+اناقش اربع X زائد خمسة وثلاثين. هل هذه قيمة
+
+88
+00:10:11,960 --> 00:10:20,930
+بيمنعك؟primitive؟ لأ لأ
+
+89
+00:10:20,930 --> 00:10:27,050
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+90
+00:10:27,050 --> 00:10:29,790
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+91
+00:10:29,790 --> 00:10:29,790
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+92
+00:10:29,790 --> 00:10:29,790
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+93
+00:10:29,790 --> 00:10:29,810
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+94
+00:10:29,810 --> 00:10:29,810
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+95
+00:10:29,810 --> 00:10:36,050
+لأ لأ لأ لأ
+
+96
+00:10:36,050 --> 00:10:44,090
+لأ لأ
+
+97
+00:10:44,420 --> 00:10:50,000
+and الخمسة وتلاتين is one يعني ال content إلها
+
+98
+00:10:50,000 --> 00:10:56,640
+يسوى واحد that is its
+
+99
+00:10:56,640 --> 00:11:02,980
+content is
+
+100
+00:11:02,980 --> 00:11:07,060
+one but the polynomial
+
+101
+00:11:15,250 --> 00:11:28,490
+مثلا Ge of X يساوى 12 X ترابيع زائد ستة X ناقص
+
+102
+00:11:28,490 --> 00:11:40,190
+ثلاثة هل هذه primitive؟ لأ is not primitive السبب
+
+103
+00:11:40,190 --> 00:11:41,550
+because
+
+104
+00:11:44,990 --> 00:11:51,470
+the greatest common divisor of الاطناش، نهيت كمان
+
+105
+00:11:51,470 --> 00:11:56,310
+مرة، تبقى فأقول الآن ال pronominant تاني g of x
+
+106
+00:11:56,310 --> 00:12:01,510
+اللي اتناشر x ثميه زي الستة x ناقص تلاتة is not
+
+107
+00:12:01,510 --> 00:12:05,510
+primitive ما هو السبب؟ لإن ال greatest common
+
+108
+00:12:05,510 --> 00:12:10,190
+divisor للمعاملة الاطناش والستة والناقص تلاتة هو
+
+109
+00:12:10,190 --> 00:12:14,980
+مين؟ هو التلاتةيعني ال content لهذه ال polynomial
+
+110
+00:12:14,980 --> 00:12:22,900
+هو تلاتة ممتاز نيجي الآن يا بنات لحاجة نظرية اسمها
+
+111
+00:12:22,900 --> 00:12:33,080
+Gauss's lemma يبقى بالتالي Gauss's lemma أرضية
+
+112
+00:12:33,080 --> 00:12:40,340
+جاوس تقول ما يعني the product
+
+113
+00:12:42,390 --> 00:12:51,150
+of two primitive polynomials
+
+114
+00:12:51,150 --> 00:12:55,310
+the
+
+115
+00:12:55,310 --> 00:13:00,810
+derivative of two primitive polynomials is a
+
+116
+00:13:00,810 --> 00:13:09,510
+primitive let's
+
+117
+00:13:09,510 --> 00:13:09,730
+hope
+
+118
+00:13:14,030 --> 00:13:19,150
+أنا بدي افترض ان عندي two polynomials وكل واحدة
+
+119
+00:13:19,150 --> 00:13:23,990
+فيهم primitive بعدين بدي احاول اثبت ان حاصل الضرب
+
+120
+00:13:23,990 --> 00:13:34,070
+يكون primitive بدي اقول let f of x و g of x
+
+121
+00:13:34,070 --> 00:13:42,590
+الاتنين are primitive polynomials
+
+122
+00:13:47,480 --> 00:13:54,860
+m z of x I
+
+123
+00:13:54,860 --> 00:13:59,220
+want to show ان
+
+124
+00:13:59,220 --> 00:14:06,400
+احاول ان بيبين ان ال f of x ال g of x is a
+
+125
+00:14:06,400 --> 00:14:11,280
+primitive that
+
+126
+00:14:11,280 --> 00:14:11,660
+is
+
+127
+00:14:16,250 --> 00:14:22,350
+want to show that
+
+128
+00:14:22,350 --> 00:14:29,770
+ان ال content of
+
+129
+00:14:29,770 --> 00:14:42,110
+ال F of X في ال G of X بتساوي كده؟ بتساوي واحد لان
+
+130
+00:14:42,110 --> 00:14:44,410
+اثبت هذا الكلام بالتناقض
+
+131
+00:14:49,910 --> 00:15:02,170
+assume that ان ال content of او نفرض انهم في الأول
+
+132
+00:15:02,170 --> 00:15:07,310
+ال primitive وما إلى ذلك او بيخد أه قلنا أولي ال
+
+133
+00:15:07,310 --> 00:15:11,150
+primitive صحيح one to show حاصر الطربي لبنان that
+
+134
+00:15:11,150 --> 00:15:15,880
+is one to show that هذي ال content assume thatthe
+
+135
+00:15:15,880 --> 00:15:24,160
+content of ال F of X في ال G of X greater than one
+
+136
+00:15:24,160 --> 00:15:30,900
+افترضي ان ال content اللي حصل الدرب هذا معناه اكبر
+
+137
+00:15:30,900 --> 00:15:43,580
+من واحد طيب نعطي فرض اخر لف ال P ب A positive ولا
+
+138
+00:15:43,580 --> 00:15:44,340
+prime
+
+139
+00:15:46,640 --> 00:15:52,800
+با prime divisor
+
+140
+00:15:52,800 --> 00:15:55,980
+of
+
+141
+00:15:55,980 --> 00:16:10,900
+ال content of f of x في ال main of g of x افترضت
+
+142
+00:16:10,900 --> 00:16:16,820
+ان في عندى رقم و الرقم هذا prime numberوبيقسم ال
+
+143
+00:16:16,820 --> 00:16:20,740
+content تبع ال f of x في g of x اللي هو main له
+
+144
+00:16:20,740 --> 00:16:26,300
+أكبر من main من الواحد يمكن اتنين يمكن تلاتة يمكن
+
+145
+00:16:26,300 --> 00:16:30,420
+اربعة قدمك ان شاء الله يكون عشرة فى عندى prime بدي
+
+146
+00:16:30,420 --> 00:16:37,740
+يقسم هذا main هذا ال content تمام طيب بدنا نشغل
+
+147
+00:16:37,740 --> 00:16:47,880
+كمان شغلة شغلة تانية بدي أقولالـ F bar of X والـ G
+
+148
+00:16:47,880 --> 00:16:58,800
+bar of X and الـ F bar في الـ G bar of X اللي هي
+
+149
+00:16:58,800 --> 00:17:07,320
+بدها تساوي F of X في الـ G of X اللي كل bar بـ
+
+150
+00:17:07,320 --> 00:17:09,540
+Pronomials
+
+151
+00:17:16,830 --> 00:17:33,090
+obtained from اللي هو ال F of X وال G of X and ال
+
+152
+00:17:33,090 --> 00:17:42,530
+F of X في ال G of X by reducing
+
+153
+00:17:46,100 --> 00:17:52,460
+the coefficients coefficients
+
+154
+00:17:52,460 --> 00:17:59,080
+of u لو p فبستنى
+
+155
+00:17:59,080 --> 00:18:04,360
+شوية بدنا نفهم الحكاية هذا كويس مرة تانية بنا
+
+156
+00:18:04,360 --> 00:18:11,260
+نفترض إن ال content لل FG ليه سواء أكبر من مين؟ من
+
+157
+00:18:11,260 --> 00:18:17,130
+الواحدطيب اخد P هو prime divisor لل content
+
+158
+00:18:17,130 --> 00:18:23,470
+المتوقع تبع ال F of X في مين ال D of G of X هاي
+
+159
+00:18:23,470 --> 00:18:29,230
+الفتوى الأولى فتوى الثاني عمل polynomials جديدة من
+
+160
+00:18:29,230 --> 00:18:34,150
+polynomials موجودة من ال polynomials الجديدة F
+
+161
+00:18:34,150 --> 00:18:41,380
+prime of X وG prime of X وحاصل ضربهما primeأو با
+
+162
+00:18:41,380 --> 00:18:43,840
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+163
+00:18:43,840 --> 00:18:45,320
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+164
+00:18:45,320 --> 00:18:49,700
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+165
+00:18:49,700 --> 00:18:49,700
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+166
+00:18:49,700 --> 00:18:49,860
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+167
+00:18:49,860 --> 00:18:49,860
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+168
+00:18:49,860 --> 00:19:01,580
+بي بي بي بي بي بي بي بي
+
+169
+00:19:08,920 --> 00:19:14,260
+by reducing their coefficients modulo p يبقى روحت
+
+170
+00:19:14,260 --> 00:19:19,000
+على معاملة f of x وعلى معاملة g of x وعلى معاملة
+
+171
+00:19:19,000 --> 00:19:24,800
+حصل الضرب وكتبتهم بيه modulo p يبقى في اشي بعضهم
+
+172
+00:19:24,800 --> 00:19:30,340
+حصير ب zero وبعضهم بصيرش ب zero ما علينا مش مشكلة
+
+173
+00:19:30,340 --> 00:19:35,900
+يبقى هذول اصفاتهم كله modulo p السؤال هويبقى بنات
+
+174
+00:19:35,900 --> 00:19:47,240
+F bar وG bar وين موجودة؟ في Z P of X، صح؟ نعم،
+
+175
+00:19:47,240 --> 00:19:48,620
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+176
+00:19:48,620 --> 00:19:49,180
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+177
+00:19:49,180 --> 00:19:50,160
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+178
+00:19:50,160 --> 00:19:52,320
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+179
+00:19:52,320 --> 00:19:52,320
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+180
+00:19:52,320 --> 00:19:53,480
+نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم، نعم،
+
+181
+00:19:53,480 --> 00:19:58,900
+نعم، نعم، نعم،
+
+182
+00:19:58,900 --> 00:20:03,100
+نعم،
+
+183
+00:20:03,100 --> 00:20:13,850
+نطب ZP of X is an integral domain صح يبقى and ZP
+
+184
+00:20:13,850 --> 00:20:24,250
+of X is an integral domain وده أخدناها قبل ذلك
+
+185
+00:20:24,250 --> 00:20:31,550
+لإنه ZP لإنه ZP is an integral domain
+
+186
+00:20:35,960 --> 00:20:41,780
+مرتين جيت على F وجيه وحصل الضرر حولت المعاملات
+
+187
+00:20:41,780 --> 00:20:47,420
+كلها مديونو P يبقى حصلت على polynomials جديدة اللي
+
+188
+00:20:47,420 --> 00:20:52,460
+حطيت عليها الشرطة فوق وتنطق F bar of X G bar of X
+
+189
+00:20:52,460 --> 00:20:58,040
+F of X في G of X الكل بار ممتاز يبقى كل واحدة منهم
+
+190
+00:20:58,040 --> 00:21:07,230
+موجودة وين بيزدد مش هجدك و بس انيالـ F bar of X
+
+191
+00:21:07,230 --> 00:21:15,350
+مضروبة في الـ G bar of X اللي هي الـ F of X في الـ
+
+192
+00:21:15,350 --> 00:21:20,810
+G of X في الكل bar أنا أزعم أنها الـ zero تبعي الـ
+
+193
+00:21:20,810 --> 00:21:24,750
+ZP معقول؟
+
+194
+00:21:24,750 --> 00:21:30,190
+معقول؟ الله أعلم شو السبب؟ because
+
+195
+00:21:57,520 --> 00:22:07,780
+مفهوم هذا اكيد افوت يعنيمش مفهومة انا عارف 90%
+
+196
+00:22:07,780 --> 00:22:13,520
+منكم على الأقل ان كنت متواضع مش فاهمين هذا هنفهمها
+
+197
+00:22:13,520 --> 00:22:19,820
+لكم في سطرين صغار تمام تعالوا نفهمها احنا بنقول ال
+
+198
+00:22:19,820 --> 00:22:25,340
+content هنا ماله؟ بدأ افترض ال content رقم يبقى
+
+199
+00:22:25,340 --> 00:22:30,340
+بدأ افترض ال content يساوي key تمام؟ فلو جيت في
+
+200
+00:22:30,340 --> 00:22:41,100
+الها مش هيك بذلك ال contentتبع ال F في G S K تمام؟
+
+201
+00:22:41,100 --> 00:22:48,280
+إيش يعني؟ لو أخدت أي element من حاصل المعامل تبع
+
+202
+00:22:48,280 --> 00:22:57,160
+حاصل ضرب لأي واحدة يوم تروح تسميته S مش يساوي ال
+
+203
+00:22:57,160 --> 00:23:02,300
+content اللي هو K في S Prime مثلا
+
+204
+00:23:05,350 --> 00:23:10,030
+مش فيه حصل الضرب F في G جيت على أي عنصر من حصل
+
+205
+00:23:10,030 --> 00:23:14,490
+الضرب Polynomial طويلة أو عريضة أخد عنصر منها
+
+206
+00:23:14,490 --> 00:23:19,230
+Element مضروب في X تربية ولا في X تكيب ولا في X
+
+207
+00:23:19,230 --> 00:23:24,390
+أربعة اللي بدكيا روحت أخدت المعامل تبعه تبع حصل
+
+208
+00:23:24,390 --> 00:23:31,930
+الضرب سميته AS يبقى هذا AS هو ال content مضروب في
+
+209
+00:23:31,930 --> 00:23:38,740
+element تاني مناللي هو من الفيديو اللي عندنا، صحيح
+
+210
+00:23:38,740 --> 00:23:46,100
+ولا لا؟ مش ال content هو ناقص خارج قسمة كل العوامل
+
+211
+00:23:46,100 --> 00:23:50,220
+أو المعاملات اللي عندي تبعتي ال polynomial، مش هذا
+
+212
+00:23:50,220 --> 00:23:55,140
+تعريف ال content فرضته كي يبقى أي واحد فيه عبارة
+
+213
+00:23:55,140 --> 00:24:01,000
+عن K في element A، مظبوط ولا لا؟ طيبإيش أنا جايل
+
+214
+00:24:01,000 --> 00:24:07,920
+هنا خد ال P prime divisor لل content يعني ال P بدي
+
+215
+00:24:07,920 --> 00:24:14,300
+يقسم ال K صح ولا لأ؟ يبقى أنا عندي كمان ال P بدي
+
+216
+00:24:14,300 --> 00:24:23,640
+يقسم ال K هذا يعني إنه K تساوي P في T شيل ال K هذه
+
+217
+00:24:23,640 --> 00:24:32,480
+اللي فوق و بدي أحط بدالهااس يساوي كيله PT في S
+
+218
+00:24:32,480 --> 00:24:40,200
+فراعي يبقى كل معامل داخل ال polynomial قدرت أكتب
+
+219
+00:24:40,200 --> 00:24:45,240
+دلالة ال P يبقى لما نقصدته جداش مدي يكون Zero،
+
+220
+00:24:45,240 --> 00:24:48,000
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+221
+00:24:48,000 --> 00:24:48,000
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+222
+00:24:48,000 --> 00:24:48,660
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+223
+00:24:48,660 --> 00:24:52,500
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+224
+00:24:52,500 --> 00:24:52,500
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+225
+00:24:52,500 --> 00:24:54,700
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+226
+00:24:54,700 --> 00:24:54,700
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+227
+00:24:54,700 --> 00:24:54,700
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+228
+00:24:54,700 --> 00:24:54,700
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+229
+00:24:54,700 --> 00:24:54,700
+Zero، Zero، Zero، Zero، Zero، Zero، Zero، Zero،
+
+230
+00:24:54,700 --> 00:25:00,090
+Zero،يبقى هاي حاصل الضرب يساوي zero because each
+
+231
+00:25:00,090 --> 00:25:07,150
+coefficient of هذه is a multiple of P طيب تعالوا
+
+232
+00:25:07,150 --> 00:25:13,270
+نستفيد شغل تاني حاصل الضرب يساوي zero واحنا بنشتغل
+
+233
+00:25:13,270 --> 00:25:20,050
+وين؟ في الول انتجرال الماني يبقى هذا الكلام مش
+
+234
+00:25:20,050 --> 00:25:24,770
+صحيح إلا إذا كان يا الأول ب zero يا التاني ب zero
+
+235
+00:25:25,300 --> 00:25:33,040
+يبقى الآن بداية أقوله f bar of x في ال g bar of x
+
+236
+00:25:33,040 --> 00:25:40,820
+بديه سوى zero ان z في a of x اللي هو الانتقال دبي
+
+237
+00:25:40,820 --> 00:25:48,260
+يبقى هذا معناه ان ال f bar of x بديه سوى zero or
+
+238
+00:25:48,260 --> 00:25:56,450
+ال g bar of x بديه سوى zeroطيب تعالى نسألك السؤال
+
+239
+00:25:56,450 --> 00:26:03,310
+التالف لما نقول F bar of X يساوي Zero يعني ال F of
+
+240
+00:26:03,310 --> 00:26:10,370
+X ده كل معاملاتها سقطت بدلالة P يعني معناته P
+
+241
+00:26:10,370 --> 00:26:17,610
+بتقسم كل معامل من معاملات F of X صح ولا لا؟ يبقى
+
+242
+00:26:17,610 --> 00:26:27,020
+this means that this meansthat هذا يعني ان ال P
+
+243
+00:26:27,020 --> 00:26:37,200
+divide each coefficient of
+
+244
+00:26:37,200 --> 00:26:49,040
+ال F of X او ال P divide each coefficient of ال G
+
+245
+00:26:49,040 --> 00:26:49,760
+of X
+
+246
+00:26:53,050 --> 00:27:00,330
+يبقى ال P بتقسم كل معامل ل F of X او ال P بتقسم كل
+
+247
+00:27:00,330 --> 00:27:06,450
+معامل لمين ل G of X هذا يعني ان ال F of X is
+
+248
+00:27:06,450 --> 00:27:15,150
+primitive لأو التانية ماهياش primitive يبقى فال F
+
+249
+00:27:15,150 --> 00:27:19,970
+of X is not primitive
+
+250
+00:27:22,670 --> 00:27:33,250
+أو الـ g of x is not primitive إما
+
+251
+00:27:33,250 --> 00:27:37,510
+هذه ماهياشي primitive أو هذه ماهياشي primitive إيش
+
+252
+00:27:37,510 --> 00:27:42,750
+رايحين؟ تناقض؟ لإن احنا من الرأس المثلجون ناخد
+
+253
+00:27:42,750 --> 00:27:47,670
+هدول ع ال primitive polynomial يبقى وصلنا إلى
+
+254
+00:27:47,670 --> 00:27:48,690
+contraction
+
+255
+00:27:50,910 --> 00:27:58,290
+وصلنا إلى Contradiction يبقى فرضي اللي أنا فرضته
+
+256
+00:27:58,290 --> 00:28:04,150
+هذا غلط و الله صح غلط و عكسه هو الصح يبقى ال
+
+257
+00:28:04,150 --> 00:28:10,670
+content لل F يجيب دي سواء جدال واحد صحيح يبقى
+
+258
+00:28:10,670 --> 00:28:16,230
+Therefore ال
+
+259
+00:28:16,230 --> 00:28:17,430
+content of
+
+260
+00:28:21,130 --> 00:28:30,190
+الـ F of X فى الـ G of X is one هذا يعطيكي ان الـ
+
+261
+00:28:30,190 --> 00:28:41,270
+F of X فى الـ G of X is a primitive البيانات
+
+262
+00:28:41,270 --> 00:28:45,490
+من الآن فصاعدة ال product of two primitive
+
+263
+00:28:45,490 --> 00:28:53,160
+polynomials is a primitiveوهذا الكلام صحيح في z of
+
+264
+00:28:53,160 --> 00:28:59,720
+x اللي المعاملات كلها أعداد صحيح طيب ننتقل إلى
+
+265
+00:28:59,720 --> 00:29:06,120
+النظرية التي تليها theorem
+
+266
+00:29:06,120 --> 00:29:12,120
+little
+
+267
+00:29:12,120 --> 00:29:23,360
+f of xموجودة في كافة z of x if
+
+268
+00:29:23,360 --> 00:29:33,740
+ال f of x is reducible if ال f of x is reducible
+
+269
+00:29:33,740 --> 00:29:46,630
+over ال Q then over ال Q thenالـ F of X is
+
+270
+00:29:46,630 --> 00:29:58,970
+reducible of Z سؤال يقول خد F of X في Z of X شوفوا
+
+271
+00:29:58,970 --> 00:30:02,590
+شو النظرية بتقول يبقى بيقول لو كانت ال F of X
+
+272
+00:30:02,590 --> 00:30:07,690
+reducible على ال Q هذا يتطلب ان تكون reducible على
+
+273
+00:30:07,690 --> 00:30:15,380
+مين؟ على Zوكأن ال reducibility على ال Eq بده ينسحب
+
+274
+00:30:15,380 --> 00:30:20,340
+عالميا لل reducibility على ال Z إيه بالبرهان
+
+275
+00:30:20,340 --> 00:30:26,520
+كالتالي يجب بالدالي أقوله little f of X موجودة في
+
+276
+00:30:26,520 --> 00:30:38,240
+Z of X بعد هيك SU افترض ان ال F of X is reducible
+
+277
+00:30:39,730 --> 00:30:44,110
+بعد ذلك
+
+278
+00:30:44,110 --> 00:30:48,530
+F of X يساوي
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/ny5FbQZurwU_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/ny5FbQZurwU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..619f97be09f44509b81638f8016fa6e8125001d4
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/ny5FbQZurwU_postprocess.srt
@@ -0,0 +1,1900 @@
+1
+00:00:21,530 --> 00:00:26,610
+بسم الله الرحمن الرحيم عودنا على بدء نرجع لنفس ال
+
+2
+00:00:26,610 --> 00:00:31,270
+chapter اللي معانا اللي هو ال integral domain أخر
+
+3
+00:00:31,270 --> 00:00:35,450
+حاجة عرفناها المرة اللي فاتت ال characteristic لل
+
+4
+00:00:35,450 --> 00:00:40,830
+ring هو أصغر
+
+5
+00:00:40,830 --> 00:00:47,370
+عدد صحيح موجب بضربه في جميع عناصر ال ring بيعطيني
+
+6
+00:00:47,370 --> 00:00:54,870
+ال zero elementطيب في عندنا نظرية هنا او اكثر من
+
+7
+00:00:54,870 --> 00:00:59,430
+نظرية نأتي الى النظرية الاولى بتقول little rb a
+
+8
+00:00:59,430 --> 00:01:05,210
+ring with unity one اخدنا ال unity اللي هو الواحد
+
+9
+00:01:05,210 --> 00:01:11,070
+if ال unity has infinite or dot under addition
+
+10
+00:01:11,070 --> 00:01:16,430
+يبقى ان حدث ذلك يبقى ال characteristic لهذه ال
+
+11
+00:01:16,430 --> 00:01:20,840
+ring هو عبارة عن ال zeroطبعا احنا في التعريف أخدنا
+
+12
+00:01:20,840 --> 00:01:25,080
+المرة اللي فاتت إذا ما جدرناش اللي لاجي هذا العدد
+
+13
+00:01:25,080 --> 00:01:28,680
+اللي لو ضربته في جميع عناصر ال ring بده يعطينا
+
+14
+00:01:28,680 --> 00:01:33,340
+zero بنقول يبقى ال characteristic ل يسوى مين يسوى
+
+15
+00:01:33,340 --> 00:01:39,900
+zero إذا كان الواحد has finite order و ليكن N تحت
+
+16
+00:01:39,900 --> 00:01:43,760
+عملية الجامعة يبقى ال characteristic لل ring بده
+
+17
+00:01:43,760 --> 00:01:49,520
+يسوى مين ال Mخلينا نرجع بالذاكره قليلا الى الوراق
+
+18
+00:01:49,520 --> 00:01:53,880
+قبل ما نبرهن كيف نرجع بالذاكره قليلا الى الوراق
+
+19
+00:01:53,880 --> 00:01:59,620
+طبعا order لل element في ال group نقولنا هو أصغر
+
+20
+00:01:59,620 --> 00:02:04,580
+عدد صحيح موجب بحط أس لل element بيعطينا ال
+
+21
+00:02:04,580 --> 00:02:08,780
+identity طبعا لكن احنا عندنا هنا على ring two
+
+22
+00:02:08,780 --> 00:02:13,600
+operations بكلامنا محدود بالنسبة لعملية الجمع وليس
+
+23
+00:02:13,600 --> 00:02:19,510
+بعملية الضغطيبقى الواحد لو كان has infinite order
+
+24
+00:02:19,510 --> 00:02:24,290
+يبقى ال characteristic لغينه ساوى zero و بعد ذلك
+
+25
+00:02:24,290 --> 00:02:28,890
+لو كان finite وليكن N بدي أثبت ان ال
+
+26
+00:02:28,890 --> 00:02:35,970
+characteristic يساوى مين؟ يساوى ال M يبقى هنا ال Y
+
+27
+00:02:35,970 --> 00:02:44,040
+موجود في ال واحد او ال unity موجود في R andI
+
+28
+00:02:44,040 --> 00:02:54,340
+assume أننا نفترض أن الواحد has infinite order
+
+29
+00:02:54,340 --> 00:03:01,020
+يعني under addition
+
+30
+00:03:01,020 --> 00:03:05,320
+مدام
+
+31
+00:03:05,320 --> 00:03:11,900
+infinite يعني ليس ممكن أن أجد عدد M أضربه فيه و
+
+32
+00:03:11,900 --> 00:03:18,770
+يطلع الناتجالعادى مش العادى انت زيرو تبقى لتعريف
+
+33
+00:03:18,770 --> 00:03:28,570
+ال characteristics مظبوط يبقى then there is no
+
+34
+00:03:28,570 --> 00:03:39,790
+integer in such that ال n في واحد بده يساوي زيرو
+
+35
+00:03:39,790 --> 00:03:44,020
+مش هقدر ألاقيمن تعريف المرة اللى فترة كتبناها في
+
+36
+00:03:44,020 --> 00:03:47,840
+نهاية المحاضرة يبقى ال .. ال ring هذه ال
+
+37
+00:03:47,840 --> 00:03:53,320
+characteristic تبعي يساوي جدير zero هذا بده يعطينا
+
+38
+00:03:53,320 --> 00:04:02,120
+انه ال characteristic لل R is zero طيب هي النقطة
+
+39
+00:04:02,120 --> 00:04:10,980
+الأولى بدهاجى الآن للنقطة الثانية يبقى assume that
+
+40
+00:04:12,360 --> 00:04:23,440
+الواحد اللى موجود في R has finite order that is
+
+41
+00:04:23,440 --> 00:04:31,740
+under addition برضه تحت عملية الجمع under addition
+
+42
+00:04:31,740 --> 00:04:40,840
+تحت عملية الجمع يعني هذا إيش معناه؟ معناه إن ال N
+
+43
+00:04:41,290 --> 00:04:50,010
+فى الواحد يساوي زيرو بدا أحاول أثبت أن ال N هذه هي
+
+44
+00:04:50,010 --> 00:04:55,170
+ال characteristic تبع مين ال ring R لذلك هذه N فى
+
+45
+00:04:55,170 --> 00:05:01,190
+واحد يساوي زيرو ماذا عن بقية عناصر ال ring اللى
+
+46
+00:05:01,190 --> 00:05:10,290
+عندنا فبدا فى أقول له let ال X be any element
+
+47
+00:05:11,950 --> 00:05:19,150
+يعني A افترض هذا ال X هو عبارة عن أي عنصر في A نجي
+
+48
+00:05:19,150 --> 00:05:26,910
+نشوف هذا الكلام إيش بده يساوي then زي شوف هل ال N
+
+49
+00:05:26,910 --> 00:05:32,310
+في X بدها تساوي Zero ولا لأ؟ طب ال X أخدته عشوائي
+
+50
+00:05:32,310 --> 00:05:37,010
+يعني انطبق على أي عنصر من عناصر ال ring اللي عندها
+
+51
+00:05:37,010 --> 00:05:45,880
+يتجه ال N Xكأن الـ X مجموعة مع نفسها N من المرات
+
+52
+00:05:45,880 --> 00:05:55,080
+يبقى هذه كأنها X زائد X زائد زائد X كم مرة؟ N
+
+53
+00:05:55,080 --> 00:06:03,320
+times يبقى هذه N من المرات طيب، أليست هذه بالضبط؟
+
+54
+00:06:03,320 --> 00:06:12,980
+هي واحد في X زائد واحد في Xزائد واحد في X كمان in
+
+55
+00:06:12,980 --> 00:06:19,820
+times مظبوط؟ طب لو جيت على ال distributive law
+
+56
+00:06:19,820 --> 00:06:24,760
+يبقى ال in X يساوي حسب ال distributive اللي هو
+
+57
+00:06:24,760 --> 00:06:34,180
+واحد زائد واحد زائد واحد كله في X تمام؟ ودول كدهش؟
+
+58
+00:06:34,180 --> 00:06:44,250
+in times كذلكيبقى هذا معناه ان N مضروبة في واحد
+
+59
+00:06:44,250 --> 00:06:51,270
+كله في X اللي برا طبعا عندي هنا N واحد بقداش Zero
+
+60
+00:06:51,270 --> 00:06:58,910
+يبقى هذا الكلام يساوي Zero في X يساوي Zero يبقى
+
+61
+00:06:58,910 --> 00:07:04,750
+صار ال N في X بيساوي Zero لكل ال X اللي موجودة في
+
+62
+00:07:04,750 --> 00:07:10,860
+R هذا الكلام صحيحلكل ال X اللي موجود في R إيش
+
+63
+00:07:10,860 --> 00:07:15,480
+تفسيرنا لهذه العبارة إن ال N هو ال characteristic
+
+64
+00:07:15,480 --> 00:07:22,140
+لمن؟ لل ring R هذا بده يعطينا إن ال characteristic
+
+65
+00:07:22,140 --> 00:07:27,500
+لل A بده يسوى ال N وهو المفروض
+
+66
+00:07:30,530 --> 00:07:35,810
+ال .. ال ring اللي فيها unity ال characteristic
+
+67
+00:07:35,810 --> 00:07:43,770
+تبعها يا إما zero يا إما in رقم قدر يطلع الله أعلى
+
+68
+00:07:43,770 --> 00:07:51,530
+طيب في نظرية ثانية مرتبطة بها تماما لأن كمان نظرية
+
+69
+00:07:51,530 --> 00:07:59,230
+أخرى وهي أخر نظرية موجودة في هذا section بتقولthe
+
+70
+00:07:59,230 --> 00:08:08,710
+characteristic of
+
+71
+00:08:08,710 --> 00:08:23,870
+an integral domain is an integral domain R is zero
+
+72
+00:08:23,870 --> 00:08:25,790
+or prime
+
+73
+00:08:48,340 --> 00:08:53,320
+النظرية اللى فوق بتقول لو عندى ring with unity
+
+74
+00:08:53,320 --> 00:08:57,520
+يبقى احد امرين يا اما ال characteristic اللى يساوي
+
+75
+00:08:57,520 --> 00:09:01,480
+zero يا اما ال characteristic اللى يساوي عدد
+
+76
+00:09:25,700 --> 00:09:32,870
+ماذا يعني معناه ال unit موجودة في ال R؟يبقى
+
+77
+00:09:32,870 --> 00:09:46,410
+implies ان ال R has a unity وليكن one same ويبقى
+
+78
+00:09:46,410 --> 00:09:50,890
+حصار ال R فيها ال unity يبقى بالنظرية اللي فوق ال
+
+79
+00:09:50,890 --> 00:09:59,310
+characteristic إلها يا إما zero يا إما N by the
+
+80
+00:09:59,310 --> 00:10:00,870
+above
+
+81
+00:10:06,870 --> 00:10:17,590
+الكاركترستيك للـ R is 0 or
+
+82
+00:10:17,590 --> 00:10:23,230
+N طب
+
+83
+00:10:23,230 --> 00:10:27,910
+نظريتنا إيش بتقول؟ يا إما Zero يا إما Prideإذا
+
+84
+00:10:27,910 --> 00:10:32,550
+إحنا لو أثبتنا إن ال in is a prime بتبقى المطلوب
+
+85
+00:10:32,550 --> 00:10:44,850
+صح؟ يبقى if we show that إن ال in is a prime then
+
+86
+00:10:44,850 --> 00:10:54,110
+we have the result يبقى
+
+87
+00:10:54,110 --> 00:10:59,520
+بيكون حصلنا على النتيجة المطلوبةيبقى ما علينا باقي
+
+88
+00:10:59,520 --> 00:11:06,480
+لنثبت إيش ان ال N is a prime تمام؟ إيش N is a
+
+89
+00:11:06,480 --> 00:11:12,220
+prime؟ يعني لا يقسم إلا على نفسه وعلى الواحد
+
+90
+00:11:12,220 --> 00:11:17,980
+الصحيح أنا بدي أمشي بالعكس بدي أفترض أن ال N بقدر
+
+91
+00:11:17,980 --> 00:11:23,900
+أحللها إلى حاصل ضرب رقمين والرقمين أكبر من الواحد
+
+92
+00:11:23,900 --> 00:11:31,470
+وأصغر من ال Nوشوف وين بيتوجه الدنيا طبعا الان احنا
+
+93
+00:11:31,470 --> 00:11:36,650
+بالنظرية الأولانية لفوق هذه قلنا الها ال
+
+94
+00:11:36,650 --> 00:11:42,630
+characteristic zero يا اما مين يا اما ال N طبعا
+
+95
+00:11:42,630 --> 00:11:48,630
+طيب يبقى احنا بنقول هنا لو طبعا ال zero هو اللي
+
+96
+00:11:48,630 --> 00:11:53,000
+مطلوب ان انا اقول ال zero يا اما primeيبقى Zero هو
+
+97
+00:11:53,000 --> 00:11:59,200
+Zero ضلي عليه بس ال N أثبتها ياش انه هي Prime يبقى
+
+98
+00:11:59,200 --> 00:12:09,560
+بده أروح أضله لت ال N بدها تساوي مثلا S في T وكل
+
+99
+00:12:09,560 --> 00:12:16,640
+من ال S و ال T أكبر من الواحد و أقل من ال N
+
+100
+00:12:20,000 --> 00:12:25,700
+يبقى دول كل واحد فيهم اكبر من واحد و اقل من ال N
+
+101
+00:12:25,700 --> 00:12:34,140
+تمام؟ طيب هنا احنا قلنا ان ال characteristic ليها
+
+102
+00:12:34,140 --> 00:12:41,340
+اما Zero يا اما N هذه ايش N ال characteristic يبقى
+
+103
+00:12:41,340 --> 00:12:47,660
+ال N في X بده يساوي Zero للكل صح ولا لأ او ال N في
+
+104
+00:12:47,660 --> 00:12:53,640
+واحدبدها تساوي مين؟ بدها تساوي 0 للكل يفجأة باجي
+
+105
+00:12:53,640 --> 00:13:05,820
+بقول since the characteristic is n we have ان ال n
+
+106
+00:13:05,820 --> 00:13:12,020
+في واحد بده ساوي 0 طيب
+
+107
+00:13:12,020 --> 00:13:20,870
+يعني 0 بده ساوي ال n في واحدقداش فرض ال N S في T
+
+108
+00:13:20,870 --> 00:13:31,090
+يبقى هذا S T في واحد اللي بقدر أكتبها S في واحد في
+
+109
+00:13:31,090 --> 00:13:39,550
+T في واحد يبقى قدرت أكتب N في واحد عليه شكل S واحد
+
+110
+00:13:39,550 --> 00:13:44,030
+T واحد يبقى هذا عنصر و هذا عنصر تاني حاصل ضربه ما
+
+111
+00:13:44,030 --> 00:13:50,760
+يساوي قداش Zeroهل هذا كلام صحيح إلا إذا .. هالكلام
+
+112
+00:13:50,760 --> 00:13:56,720
+هذا مش صحيح إلا إذا كان الأول ب zero أو الثاني ب
+
+113
+00:13:56,720 --> 00:14:01,860
+zero لإيش عندنا integral domain يبقى هذا بدي
+
+114
+00:14:01,860 --> 00:14:10,960
+يعطينا ميادة ان ال S في واحد بدي يسوي zero or T في
+
+115
+00:14:10,960 --> 00:14:22,370
+واحد بدي يسوي zero لأنالـ R is an integral domain
+
+116
+00:14:22,370 --> 00:14:27,110
+ايش يعني integral domain يعني he has no zero
+
+117
+00:14:27,110 --> 00:14:32,210
+divisors ماعندوش zero divisors الا zero يبقى يا
+
+118
+00:14:32,210 --> 00:14:36,750
+اما هذا في zero يا اما هذا في zero طيب تعالوا نقف
+
+119
+00:14:36,750 --> 00:14:40,990
+مع كل واحدة من هدول احنا قداشي قولنا ال
+
+120
+00:14:40,990 --> 00:14:49,140
+characteristic لارين N صح؟مين هو ال N هو أصغر عدد
+
+121
+00:14:49,140 --> 00:14:54,020
+بضربه في الواحد بيعطينا الناتج يساوي صفر لجأتي
+
+122
+00:14:54,020 --> 00:15:01,920
+أصغر منه صح؟ يبقى هذا الكلام مش ممكن إلا إذا كان
+
+123
+00:15:01,920 --> 00:15:06,500
+الأول بيساوي ال N أو التاني بيساوي ال N يبقى هنا
+
+124
+00:15:06,500 --> 00:15:14,540
+بقوله but ولكن ال N is the smallest
+
+125
+00:15:18,510 --> 00:15:23,590
+positive انتجار such
+
+126
+00:15:23,590 --> 00:15:31,870
+that ال N في ال واحد بده يساوي زيرو لقيت S في واحد
+
+127
+00:15:31,870 --> 00:15:36,530
+بده يساوي زيرو او T في واحد بده يساوي زيرو وهو
+
+128
+00:15:36,530 --> 00:15:42,670
+اصغر منه يبقى هذا الكلام مايمكن ان يكون صحيحا الا
+
+129
+00:15:42,670 --> 00:15:50,630
+اذا كان S في واحد هو مينال N تمام أو ال T في واحد
+
+130
+00:15:50,630 --> 00:16:04,930
+هو مين هو ال N يبقى this is a true only if ال N
+
+131
+00:16:04,930 --> 00:16:13,230
+بدها تساوي ال S or ال N بدها تساوي T مدام هي
+
+132
+00:16:13,230 --> 00:16:19,940
+كمانات يعني هل ال Nبقدر أحللها إلى حصر ضرب رقمين
+
+133
+00:16:19,940 --> 00:16:24,980
+أكبر من الواحد وأصغر من ال N لأ يبقى معناته فرض
+
+134
+00:16:24,980 --> 00:16:32,220
+اللي أنا فرضته في الأول خطأ وعكسه هو الصح يبقى so
+
+135
+00:16:32,220 --> 00:16:43,960
+ال N cannot be factored into
+
+136
+00:16:45,850 --> 00:16:49,890
+product of
+
+137
+00:16:49,890 --> 00:17:00,330
+smallest integers ماقدرش أحلله وده ماقدرش أحلله
+
+138
+00:17:00,330 --> 00:17:08,690
+ويبقى ال N إيش معناه ال إفرايه يبقى ضاص وهكذا ال N
+
+139
+00:17:08,690 --> 00:17:15,080
+is a primeيبقى بياد بلات من ال alpha صعدا بديك
+
+140
+00:17:15,080 --> 00:17:19,280
+تفهم الحجم يقولك integral domain يبقى ال
+
+141
+00:17:19,280 --> 00:17:23,880
+characteristic أحد أمرين يا إما zero يا إما عدد
+
+142
+00:17:23,880 --> 00:17:30,300
+أولي على طول الخط يعني ماعنديش عدد أولي زوجي إلا
+
+143
+00:17:30,300 --> 00:17:35,440
+اتنين وبالتالي لا يمكن ال characteristic يكون عدد
+
+144
+00:17:35,440 --> 00:17:39,180
+زوجي لل integral domain غير اتنين اما تقوللي اربع
+
+145
+00:17:39,180 --> 00:17:45,410
+ستة تمانية هذا معنىكل كلام مستبعد مالوش وجود لحد
+
+146
+00:17:45,410 --> 00:17:50,130
+هنا انتهى الجزء النظري تبع ال section لكن راح أحط
+
+147
+00:17:50,130 --> 00:17:55,870
+بعض الأشياء النظرية في مسائل التدريب يبدأ احنا
+
+148
+00:17:55,870 --> 00:17:59,990
+بدنا نروح نحطها في نهاية هذا ال section و ناخد
+
+149
+00:17:59,990 --> 00:18:06,410
+عليها بعض الأمثلة وبالتالي بصير مضحكا لهذا ال
+
+150
+00:18:06,410 --> 00:18:13,000
+sectionللأشياء الملحقة تعريفين ودول التعريفين ما
+
+151
+00:18:13,000 --> 00:18:18,380
+شوفناهم مش قبل ذلك التعريف الأول بيقول ما ياتي
+
+152
+00:18:18,380 --> 00:18:24,200
+little a bearing
+
+153
+00:18:24,200 --> 00:18:32,400
+with unity little
+
+154
+00:18:32,400 --> 00:18:43,110
+a أو littleالـ A belongs to R if ال A N بده ساوي
+
+155
+00:18:43,110 --> 00:18:51,570
+Zero for some positive integer
+
+156
+00:18:51,570 --> 00:18:56,290
+N
+
+157
+00:18:56,290 --> 00:19:06,530
+for some positive integer M then ال Ais called an
+
+158
+00:19:06,530 --> 00:19:17,770
+important and important element التعريف
+
+159
+00:19:17,770 --> 00:19:30,090
+الثاني هو let ال A belong to hearing A
+
+160
+00:19:35,830 --> 00:19:49,590
+إذا كان الـ A تربيع بيساوي الـ A، فالـ A يُسمى كـ
+
+161
+00:19:49,590 --> 00:19:55,270
+Idempotent
+
+162
+00:19:55,270 --> 00:20:04,730
+Element Idempotent
+
+163
+00:20:06,480 --> 00:20:13,940
+مثال واحد مثال
+
+164
+00:20:13,940 --> 00:20:23,160
+واحد المسؤال أربع تاشر من الكتاب بيقول show that
+
+165
+00:20:23,160 --> 00:20:33,580
+the set of the important elements are not potent
+
+166
+00:20:34,740 --> 00:20:46,500
+Elements of a commutative ring R of a commutative
+
+167
+00:20:46,500 --> 00:20:53,860
+ring R form
+
+168
+00:20:53,860 --> 00:20:56,600
+a sub ring of R
+
+169
+00:21:29,360 --> 00:21:34,480
+مرة تانية نحاول نفهم التعريفين مشان نبدأ نحل
+
+170
+00:21:34,480 --> 00:21:39,060
+مجموعة من الأمثلة عليهم والأمثلة بإن نجيبهم من
+
+171
+00:21:39,060 --> 00:21:44,340
+أسئلتي التمرين التعريف الأول بيقول يخلق R ring
+
+172
+00:21:44,340 --> 00:21:48,920
+with unit هو اللي عنصر موجود في Rإذا والله العنصر
+
+173
+00:21:48,920 --> 00:21:55,100
+هذا رفعته لعدد صحيح موجب كأس إله يعطاني zero
+
+174
+00:21:55,100 --> 00:22:01,700
+وشايفه قال لي for some مش for all يعني عدد صحيح
+
+175
+00:22:01,700 --> 00:22:07,260
+رفعته كأس إله اها then ال L عطاني zero then ال A
+
+176
+00:22:07,260 --> 00:22:11,000
+is called any potent element يبقى any potent
+
+177
+00:22:11,000 --> 00:22:16,350
+element هو عنصر من ال ring Rرفعته لأُس اللي هو
+
+178
+00:22:16,350 --> 00:22:22,370
+الأس عدد صحيح موجب أعطاني الـ 0 إن حدث ذلك يبقى في
+
+179
+00:22:22,370 --> 00:22:27,390
+هذه الحالة بسمي هذا ال element Nilpotent element
+
+180
+00:22:27,390 --> 00:22:32,570
+نيجي للتعريف التاني اللي هو ال idempotent element
+
+181
+00:22:32,570 --> 00:22:37,370
+فباجي بقول ال element A اللي موجود في ال ring R
+
+182
+00:22:37,370 --> 00:22:44,280
+بسميه idempotent لو ربعته أو ضربته في نفسهبدي
+
+183
+00:22:44,280 --> 00:22:48,880
+يعطيني مين؟ بدي يعطيني نفس العنصر يبقى الـ
+
+184
+00:22:48,880 --> 00:22:55,480
+idempotent element هو مين؟ اللي كان A تربعي سوية A
+
+185
+00:22:55,480 --> 00:22:59,580
+بقى الـ A بسمي مين؟ idempotent بدي ناخد بعض
+
+186
+00:22:59,580 --> 00:23:05,300
+الأمثلة على هذين التعريفين المثل الأول سؤال 14 من
+
+187
+00:23:05,300 --> 00:23:09,360
+الكتاب بيقول بيبينلي أن الست من ال potent elements
+
+188
+00:23:09,360 --> 00:23:15,200
+of B هي commutative ring Aبيطوللي ال sub ring من
+
+189
+00:23:15,200 --> 00:23:22,600
+ال a يبقى بالده دي افترض انه عندي S و ال S subset
+
+190
+00:23:22,600 --> 00:23:30,560
+من a where هدى اعرف مين هى ال S هدى يبقى ال S هي
+
+191
+00:23:30,560 --> 00:23:38,100
+the sixth of all elements a such that ال a n بدى
+
+192
+00:23:38,100 --> 00:23:49,720
+ساوي zero for somepositive or some positive انتجار
+
+193
+00:23:49,720 --> 00:24:00,880
+N أو الـ N موجودة في Zero طب السؤال إيه N يسوى
+
+194
+00:24:00,880 --> 00:24:07,180
+Zero لو لقيتني ال potent element آخر B بيكون ال B
+
+195
+00:24:07,180 --> 00:24:14,730
+أس N يسوى Zero والله بي أس رقم آخرمش رقم اخر لجالي
+
+196
+00:24:14,730 --> 00:24:20,350
+for some مجاليش for ال يعني مش كلهم لهم نفس الرقم
+
+197
+00:24:20,350 --> 00:24:26,870
+في واحد يوم عنصر A تكحيب يساوي Zero عنصر تاني بيقص
+
+198
+00:24:26,870 --> 00:24:31,910
+سبعة يساوي Zero واحد ال C يساوي عشرين يساوي Zero
+
+199
+00:24:31,910 --> 00:24:38,850
+يبقى كلهم هدول ال potent elements يبقى الأس هذا مش
+
+200
+00:24:38,850 --> 00:24:44,580
+ثابت يا بنات الأسيختلف من عنصرين إلى آخر طب احنا
+
+201
+00:24:44,580 --> 00:24:54,420
+بنثبت هذه ال suffering يبقى one to show that ان ال
+
+202
+00:24:54,420 --> 00:25:03,760
+S is a suffering of R مشان أثبت ال suffering يبقى
+
+203
+00:25:03,760 --> 00:25:12,090
+بدي أثبت ثلاث نقاط النقطة الأولى ان ال Sis non
+
+204
+00:25:12,090 --> 00:25:17,950
+-empty بنقدر نجيب عنصر موجود في S يا بنات يعني
+
+205
+00:25:17,950 --> 00:25:25,030
+عنصر أعفر للـS إن يبقى هناك شخصية لهمين Zero is
+
+206
+00:25:25,030 --> 00:25:31,870
+non-empty since Zero to the power N بده يسوى Zero
+
+207
+00:25:31,870 --> 00:25:40,220
+هذا معناه إن Zero موجود في الـS Why؟يبقى هنا من
+
+208
+00:25:40,220 --> 00:25:45,940
+النقطة الأولى بروح للنقطة الثانية بدي أخد عنصرين A
+
+209
+00:25:45,940 --> 00:25:53,060
+و B موجودات في ال S يبقى بروح بقوله then ال A to
+
+210
+00:25:53,060 --> 00:26:00,340
+the power N يسوى Zero and ال B to the power M يسوى
+
+211
+00:26:00,340 --> 00:26:11,370
+Zero for some N و Mاللي موجودة في Z plus يعني
+
+212
+00:26:11,370 --> 00:26:19,510
+أعداد صحيحة موجبة طبعا طيب الآن على فرض عددين
+
+213
+00:26:19,510 --> 00:26:25,090
+موجودات في S بدي أثبت أن الفرق بينما بينهما موجود
+
+214
+00:26:25,090 --> 00:26:33,910
+في S إذا بدي أخد ال A ناقص ال B و أرفعها لأس ما
+
+215
+00:26:33,910 --> 00:26:41,090
+الله أعلم منهبدى الناتج يساوي Z إضافى إيش تقترحوا
+
+216
+00:26:41,090 --> 00:26:45,210
+هذا الأس يكون؟
+
+217
+00:26:45,210 --> 00:26:57,750
+إيش يكون؟ N في M و الله N زائد M نعم N زائد M لإن
+
+218
+00:26:57,750 --> 00:27:07,000
+لو جيت قلت N زائد Mوالله إذا طلع هذا الكلب بيزيره،
+
+219
+00:27:07,000 --> 00:27:11,460
+بيقول خلاصنا الحمد لله، بص يهدن القوت المحتل.
+
+220
+00:27:11,720 --> 00:27:19,360
+السؤال هو بنقدر نفك القوس هذا؟ كيف؟
+
+221
+00:27:19,360 --> 00:27:26,360
+صحيح؟ ممتاز،
+
+222
+00:27:26,360 --> 00:27:31,280
+يعني إيش بنسمي المفكوك هذا؟لما كنت أقول في ثانوية
+
+223
+00:27:31,280 --> 00:27:38,800
+sin زائد ألف لكل أسنون إيش بجينا نسميها هذه نظرية
+
+224
+00:27:38,800 --> 00:27:46,120
+ذات الحدين ال binomial ذات الحدين يبقى بجينا نقول
+
+225
+00:27:46,120 --> 00:27:50,760
+بذكركوا تذكر بالثانوية بجينا نقول sin زائد ألف كل
+
+226
+00:27:50,760 --> 00:27:57,560
+أسنونيسوي سين أسنون زائد نون قاف واحد يعني توفيق
+
+227
+00:27:57,560 --> 00:28:03,140
+نوم للأشياء مقودة واحد واحد سين أسنون ناقص واحد
+
+228
+00:28:03,140 --> 00:28:09,120
+ألف زائد نون قاف اتنين سين أسنون ناقص اتنين ألف
+
+229
+00:28:09,120 --> 00:28:14,240
+تربيع السين الأستبعها بينقص والألف الأستبعها
+
+230
+00:28:14,240 --> 00:28:20,220
+بيزداد لغاية ما نوصل إلى ألف أسنونيبقى هنا بدنا
+
+231
+00:28:20,220 --> 00:28:24,280
+نمشي بنفس التكتيك تبع الشيء اللي اتعلمناه في
+
+232
+00:28:24,280 --> 00:28:29,800
+الثانوية حد فيكوا أخدت احتمالات؟ أخدنا احتمالات طب
+
+233
+00:28:29,800 --> 00:28:33,320
+في عندك .. في أخدتوها تلت حدين تبعهم في
+
+234
+00:28:33,320 --> 00:28:37,520
+الاحتمالات، مظبوط؟ يبقى تبع هذه معلومات طازة أجد
+
+235
+00:28:37,520 --> 00:28:42,780
+من مين من الثانوية العامة يبقى لو جينا بروح بنقول
+
+236
+00:28:42,780 --> 00:28:50,420
+هذه A أس N زائد Mلو الإشارة هذه زائد كله بيكون
+
+237
+00:28:50,420 --> 00:28:54,580
+زائد لكن مدام الإشارة هذه ناقص وصير حد موجب وحد
+
+238
+00:28:54,580 --> 00:29:03,700
+سالب يبقى بده يصير ناقص N زائد M one يعني توفيق N
+
+239
+00:29:03,700 --> 00:29:10,280
+زائد M من الأشياء مقودة واحد واحد اذا نجي لل A قص
+
+240
+00:29:10,280 --> 00:29:19,190
+N زائد M فنطح منها واحد في B قص واحداللي بعدها
+
+241
+00:29:19,190 --> 00:29:29,950
+بالموجة زائد N زائد M توفيق اتنين A أس N زائد M
+
+242
+00:29:29,950 --> 00:29:39,730
+نقص اتنين ب تربيع وانظر نمشي لغاية ما نصل الى الى
+
+243
+00:29:39,730 --> 00:29:48,990
+مين N زائد M M توفيق N زائد M لشام أخوها M Mبس
+
+244
+00:29:48,990 --> 00:29:54,050
+ضايل علينا مين ضايل علينا الإشارة يا رجال يبقى هذه
+
+245
+00:29:54,050 --> 00:30:04,170
+زادت و هنا ناقص واحد أس M تمام في A أس N تبقى ال M
+
+246
+00:30:04,170 --> 00:30:09,010
+مين خلصت ناقص اتنين ناقص تلاتة ناقص أربع خلصت
+
+247
+00:30:09,010 --> 00:30:14,950
+وصلنا إلى A أس N في هذه الحالة B زادت حتى وصلت إلى
+
+248
+00:30:14,950 --> 00:30:23,540
+مين إلى M تمامالان زائد زائد
+
+249
+00:30:23,540 --> 00:30:30,880
+مين؟ زائد ناقص واحد to the power M زائد واحد
+
+250
+00:30:30,880 --> 00:30:37,640
+الإشارة الأوس تبقى بزيد واحد يبقى هنا N زائد M و
+
+251
+00:30:37,640 --> 00:30:47,520
+هنا M زائد واحد في ال A أس N ناقص واحد B أس M زائد
+
+252
+00:30:47,520 --> 00:30:52,060
+واحدالـ A الأس تبعها بينقص واحد والـ M الأس تبعها
+
+253
+00:30:52,060 --> 00:30:59,980
+بيزيد واحد هنظل ناشين لغاية ما نصل إلى آخر حد آخر
+
+254
+00:30:59,980 --> 00:31:10,460
+حد بيكون ناقص واحد أس N زائد M في B أس N زائد M
+
+255
+00:31:10,460 --> 00:31:18,220
+وبتبقى صار A أس Zero اللي هو بواحد طيبكداش هدا
+
+256
+00:31:18,220 --> 00:31:23,060
+الكلام مساوي اقص
+
+257
+00:31:23,060 --> 00:31:31,660
+n في اقص m اقص n ب zero فهدا zero و هدا zero و هدا
+
+258
+00:31:31,660 --> 00:31:37,840
+zero و هدا zero need you to learn it better هذا مش
+
+259
+00:31:37,840 --> 00:31:43,160
+zero لكن هذا بيقص m في بيقص واحد بيقص m ب zero
+
+260
+00:31:43,160 --> 00:31:49,550
+يبقى هذا zeroهذا بيوسم في بيوسم بيوسم بزيرو يبقى
+
+261
+00:31:49,550 --> 00:31:57,910
+هذا كله بده يساوي زيرو زا ناقص زيرو زائد زيرو ناقص
+
+262
+00:31:57,910 --> 00:32:06,770
+مش عارف مين زائد ناقص واحد أس او ناقص واحد أس ام
+
+263
+00:32:06,770 --> 00:32:13,530
+زائد انف زيرو جد ما يكون يبقى النتج كله جد زيرو
+
+264
+00:32:13,530 --> 00:32:19,860
+مدام زيرويبقى بروح بقول ال sol E ناقص ال A ناقص B
+
+265
+00:32:19,860 --> 00:32:32,100
+ال A نل potent نل potent element مدام نل potent
+
+266
+00:32:32,100 --> 00:32:37,720
+element يعني معناته ان ال A ناقص ال B موجود وين في
+
+267
+00:32:37,720 --> 00:32:44,020
+S إذا احنا هنا أخدنا عنصرين موجودات في Sلجينا
+
+268
+00:32:44,020 --> 00:32:49,580
+الفرق فيما بينهما موجود في S بقيت علينا النقطة
+
+269
+00:32:49,580 --> 00:32:55,380
+الأخيرة ايش النقطة الأخيرة؟ بتقول افترض ان ال A و
+
+270
+00:32:55,380 --> 00:33:01,620
+ال B موجودات في S then ال A أُس M بده يساوي Zero
+
+271
+00:33:01,620 --> 00:33:07,680
+and ال B أُس M بده يساوي Zero بدي أثبت انه حاصل
+
+272
+00:33:07,680 --> 00:33:14,940
+دار بيهماموجود في S يساوي Zero لو رفعته لأس معين
+
+273
+00:33:14,940 --> 00:33:21,880
+خد الرقم اللي بديك أن حبيتي N ماشي حبيتي M ماشي
+
+274
+00:33:21,880 --> 00:33:28,540
+ولا داعي لمجموعهما أو حاصل ضربهما صح؟ يبقى لو جيت
+
+275
+00:33:28,540 --> 00:33:35,480
+قل مثلا أس M ايه واحدة ثانية أخدت أس N صح ميا ميا
+
+276
+00:33:35,920 --> 00:33:43,300
+يبقى هذا a أُس m في b أُس m هذا الكلام صحيح لأن ال
+
+277
+00:33:43,300 --> 00:33:47,160
+R is commutative لكن لو ماكنتش commutative هذا
+
+278
+00:33:47,160 --> 00:33:51,300
+كلام نهار غلط هو في المثلة قال ال R is commutative
+
+279
+00:33:51,300 --> 00:33:57,660
+هذا الكلام بده يسوى a أُس m في zero بده يسوى zero
+
+280
+00:33:57,660 --> 00:34:01,860
+هذا بده يعطينا أن a في b is
+
+281
+00:34:04,000 --> 00:34:10,260
+four ten L هذا
+
+282
+00:34:10,260 --> 00:34:17,920
+بيقول ان ال A في B موجود في S إذا انتقلت الشروط
+
+283
+00:34:17,920 --> 00:34:25,020
+التلاتة يبقى لنا علينا S is a suffering يبقى لص ال
+
+284
+00:34:25,020 --> 00:34:31,740
+S is a suffering of A
+
+285
+00:34:34,430 --> 00:34:39,870
+البتالي الثاني البتالي
+
+286
+00:34:39,870 --> 00:34:46,990
+الثاني له سؤال تمانتاشر سؤال ستاشر من الكتاب سؤال
+
+287
+00:34:46,990 --> 00:34:54,630
+ستاشر بقول prove that prove that the only
+
+288
+00:34:54,630 --> 00:35:02,090
+idempotence the only idempotence
+
+289
+00:35:04,090 --> 00:35:13,810
+the only are the importance in an integral domain
+
+290
+00:35:13,810 --> 00:35:22,970
+in integral domain are the zero and الواحد
+
+291
+00:35:33,450 --> 00:35:38,870
+يقولي اثبتلي انه في ال integral domain ماعنديش
+
+292
+00:35:38,870 --> 00:35:44,970
+idempotency اللي اتنين فقط لغير اللي هم من؟ ال
+
+293
+00:35:44,970 --> 00:35:51,030
+zero و ال واحد تمام؟ الان انا عندي integral domain
+
+294
+00:35:51,030 --> 00:35:57,230
+يبقى هو commutative ring with unit صح؟ يبقى ال ا
+
+295
+00:35:57,230 --> 00:36:09,470
+او assume لالـ R is an integral domain Assume الـ
+
+296
+00:36:09,470 --> 00:36:18,610
+R is an integral domain then الـ R has a unit
+
+297
+00:36:18,610 --> 00:36:28,230
+مثلاً 1 على سبيل المثال طيب
+
+298
+00:36:28,230 --> 00:36:38,390
+الآن لماذاالـ A دي الـ idemportant
+
+299
+00:36:38,390 --> 00:36:47,070
+in A صرت أن A عنصر موجود في A وهذا idemportant
+
+300
+00:36:47,070 --> 00:36:54,950
+يبقى then الـ A ترابيع تساوي الـ A حسب تعريف الـ
+
+301
+00:36:54,950 --> 00:37:00,430
+idemportant قبض لفريق رايكوا نعملها معادلة صفرية
+
+302
+00:37:00,800 --> 00:37:06,940
+إذا إيه تربية ناقص إيه بده يساوي زيه طيب من ال
+
+303
+00:37:06,940 --> 00:37:11,940
+distributive law إيه في إيه ناقص واحد يساوي زيه
+
+304
+00:37:11,940 --> 00:37:18,860
+العملية ده بقدر أعملها لو ال R فيهاش unity ده
+
+305
+00:37:18,860 --> 00:37:22,580
+بقدرش لكن هذا علشان ال integral domain و ال
+
+306
+00:37:22,580 --> 00:37:26,280
+commutative ring و ال unity يعني ال unity اللي
+
+307
+00:37:26,280 --> 00:37:30,730
+واحد موجود فيها إذا جدرتأستخدم الـ distributive
+
+308
+00:37:30,730 --> 00:37:38,710
+law طيب هذا بده يعطيني ان ال a تساوي 0 or ال a
+
+309
+00:37:38,710 --> 00:37:45,450
+ناقص واحد بده ساوي 0 هل هذا كلام صحيح في أي ring؟
+
+310
+00:37:45,450 --> 00:37:50,490
+لا مش صحيح لكن صحيح في من؟ ال integral و ال
+
+311
+00:37:50,490 --> 00:37:53,490
+integral domain و ال integral domain مافيش فيه
+
+312
+00:37:53,490 --> 00:38:02,600
+zero divisor يبقى هنا هذاbecause الارض
+
+313
+00:38:02,600 --> 00:38:11,320
+ليس لديها قطعين لا زرع يعني إيش؟ لو وجدت حاصل ضرب
+
+314
+00:38:11,320 --> 00:38:16,580
+كميتين بيكون بزيرو، بيكون الأولى بزيرو أو الثانية
+
+315
+00:38:16,580 --> 00:38:23,640
+بزيرو هذا بدّي يعطينا إن ال a تساوي zero أو ال a
+
+316
+00:38:23,640 --> 00:38:30,450
+تساوي واحد صحيحتمام؟ يبقى الـIdempotent Element
+
+317
+00:38:30,450 --> 00:38:34,150
+اللي عندنا طلع مين؟ طلع الـ Zero و الواحد، في
+
+318
+00:38:34,150 --> 00:38:40,950
+غيرهم؟ مش غيرهم، يبقى في حالة الـIntegral Domain،
+
+319
+00:38:40,950 --> 00:38:47,970
+the only idempotent element is Zero and the only,
+
+320
+00:38:48,350 --> 00:38:50,750
+غيرهم يبعد الله
+
+321
+00:38:56,210 --> 00:39:06,970
+طيب، هذا كان سؤال ستاشر مثال رقم تلاتة .. تلاتة
+
+322
+00:39:06,970 --> 00:39:16,270
+في سؤال فمانتاشر من الكتاب بيقول الـ F الـ R بـ A
+
+323
+00:39:16,270 --> 00:39:25,330
+ring F الـ A الموجود في R is add
+
+324
+00:39:29,700 --> 00:39:38,740
+idempotent idempotent then ال a n بده يساوي ال a
+
+325
+00:39:38,740 --> 00:39:49,740
+for all for all positive integers ان اللي موجودة
+
+326
+00:39:49,740 --> 00:39:50,820
+في z plus
+
+327
+00:40:10,550 --> 00:40:15,270
+أخد عنصر موجود فيها والعنصر كان هدا I important،
+
+328
+00:40:15,270 --> 00:40:20,870
+إيش يعني؟ A تربيع بده ساوي ال A، جال يبينلي إن ال
+
+329
+00:40:20,870 --> 00:40:27,310
+A N بده ساوي ال A لكل ال N اللي موجودة في Z plus،
+
+330
+00:40:27,310 --> 00:40:32,900
+يعنيو ال n is a positive .. او for all n و ال n is
+
+331
+00:40:32,900 --> 00:40:38,520
+a positive integer بقوله بسيطة الحلقة التالية احنا
+
+332
+00:40:38,520 --> 00:40:43,640
+عندنا معتقد ان ال a is important صح يبقى بالي
+
+333
+00:40:43,640 --> 00:40:52,860
+بقوله ال a ترافية بده يساوي ال a طيب بدنا نثبت ان
+
+334
+00:40:52,860 --> 00:40:59,720
+ال a to the power n تساوي ال aيبقى باجي بقوله want
+
+335
+00:40:59,720 --> 00:41:02,860
+فشاء
+
+336
+00:41:02,860 --> 00:41:12,320
+ان ال a n بده ساوي ال a لكل ال n اللي موجودة في
+
+337
+00:41:12,320 --> 00:41:17,020
+ذات ال plus بتحاول
+
+338
+00:41:17,020 --> 00:41:22,680
+أثبت هذا بواصفة السينتاج الرياضي ال induction عشان
+
+339
+00:41:22,680 --> 00:41:28,030
+تاخدوا ثلاث طرق أو ثلاث طرق للبراهينأحدهم نفس
+
+340
+00:41:28,030 --> 00:41:33,930
+التجارب الرياضية ال induction طيب السؤال هو قداش
+
+341
+00:41:33,930 --> 00:41:40,950
+أقل عدد صحيح موجة بيحقق هذه العلاقات؟ واحد اتنين
+
+342
+00:41:40,950 --> 00:41:46,870
+اتنين مش هانا it's important يبقى أقل واحد صحيح هو
+
+343
+00:41:46,870 --> 00:41:50,930
+اتنين سميلي هذه ال statement stop
+
+344
+00:41:53,580 --> 00:42:04,880
+تبقى باجي بقوله النقطة الأولى the statement is a
+
+345
+00:42:04,880 --> 00:42:17,200
+true at in يساوي اتنين السبب because ان ال a is an
+
+346
+00:42:17,200 --> 00:42:20,300
+idempotent
+
+347
+00:42:20,800 --> 00:42:27,300
+يعني ايش؟ يعني الـ A تربيه أو بدل هذه لو قلتلي
+
+348
+00:42:27,300 --> 00:42:30,820
+because الـ A تربيه سوى A plus الكلام اللي هو صحيح
+
+349
+00:42:30,820 --> 00:42:39,800
+طيب يبقى العبارة صحيحة عند أقل قيمة من ال N بتحقق
+
+350
+00:42:39,800 --> 00:42:46,860
+هذه المعادلة وهي 2 بدي أفترض أنها صحيحة عند رقم و
+
+351
+00:42:46,860 --> 00:42:55,860
+أثبت صحتها عند الرقم زي 1يبقى هنا assume that
+
+352
+00:42:55,860 --> 00:42:59,420
+equation
+
+353
+00:42:59,420 --> 00:43:14,800
+a star is a true at n تساوي m that is ان ال a أُس
+
+354
+00:43:14,800 --> 00:43:25,980
+m بدي ساوي aوروح بدي أخد consider A أُس M ذائد
+
+355
+00:43:25,980 --> 00:43:32,060
+واحد أشوف هل هذه العبارة صحيحة عندها ولا لا يبقى
+
+356
+00:43:32,060 --> 00:43:39,160
+هذا بقدر أقول A أُس M في ال AEOSM مابيبقى داشر
+
+357
+00:43:39,160 --> 00:43:44,820
+يبقى A يبقى بده يساوي A في A و A في A مابيبقى داشر
+
+358
+00:43:44,820 --> 00:43:50,840
+ايه تربية و ايه تربية ايه
+
+359
+00:43:50,840 --> 00:43:51,640
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+360
+00:43:51,640 --> 00:43:52,620
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+361
+00:43:52,620 --> 00:43:54,560
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+362
+00:43:54,560 --> 00:43:54,980
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+363
+00:43:54,980 --> 00:44:02,240
+ايه ايه ايه ايه ايه ايه
+
+364
+00:44:02,240 --> 00:44:05,340
+ايه
+
+365
+00:44:05,530 --> 00:44:13,490
+لكل الـ N اللي موجودة في الأعداد الصحيحة الموجب
+
+366
+00:44:13,490 --> 00:44:18,710
+يبقى المعلومة يا بنات استفدناها وسنستخدمها بعد ذلك
+
+367
+00:44:18,710 --> 00:44:23,330
+المعلومة أيش بتقول؟ بتقول إن لو كان عندي ID
+
+368
+00:44:23,330 --> 00:44:28,310
+important يبقى هذا ال element لو رفعته لأ الصحيح
+
+369
+00:44:28,310 --> 00:44:34,370
+موجبمن اتنين فصاعدا بدي يكون النتج يعطيني الـA
+
+370
+00:44:34,370 --> 00:44:42,990
+أتسن طيب أروح للسؤال الراجع السؤال الراجع اللي هو
+
+371
+00:44:42,990 --> 00:44:49,390
+سؤال تسعتاش من البيتار ايش بيقول بيقول determine
+
+372
+00:44:49,390 --> 00:44:55,830
+ordering elements determine ordering
+
+373
+00:44:55,830 --> 00:44:58,810
+elements
+
+374
+00:44:59,780 --> 00:45:05,780
+تحدد لك كل العناصر اللي في ال ring that are both
+
+375
+00:45:05,780 --> 00:45:14,160
+that are both و اللي بتكون that are both
+
+376
+00:45:14,160 --> 00:45:19,800
+Nilpotents Nilpotents
+
+377
+00:45:19,800 --> 00:45:24,140
+and Idipotents
+
+378
+00:45:33,160 --> 00:45:38,260
+مدمنين العناصر اللي بتكون في ال ring اللي بنفع
+
+379
+00:45:38,260 --> 00:45:45,280
+تكون Neil Potent و Idem Potent في نفس الوقت معقول
+
+380
+00:45:45,280 --> 00:45:51,200
+يا رناتي تكون العناصر Neil Potent و Idem Potent في
+
+381
+00:45:51,200 --> 00:45:56,990
+أهل واحد؟ ممكن تجيبولي ولا عنصر واحدالـ Zero Zero
+
+382
+00:45:56,990 --> 00:45:59,810
+to the power of N بـ Zero و Zero ترميع بـ Zero
+
+383
+00:45:59,810 --> 00:46:04,590
+تبقى يبقى Zero is an idempotent element يبقى يتعرف
+
+384
+00:46:04,590 --> 00:46:08,710
+عليها بيشوف فيه غيره و الله مافيش من خلال
+
+385
+00:46:08,710 --> 00:46:14,410
+المعلومات اللي عنده يبقى بيقول حددني كل عناصر ال
+
+386
+00:46:14,410 --> 00:46:18,770
+ring اللي بيكون nil potent و idempotent في نفس
+
+387
+00:46:18,770 --> 00:46:28,580
+الوقت يبقى الحل كالتالي solution لأA belongs في R
+
+388
+00:46:28,580 --> 00:46:40,320
+و R is a ring تمام such that بحيث ان null potent
+
+389
+00:46:40,320 --> 00:46:50,360
+يعني ال A أُس N بده يساوي Zero for some N
+
+390
+00:46:50,360 --> 00:47:02,290
+اللي موجود في Z plusand الـA ترابيع يساوي الـA I
+
+391
+00:47:02,290 --> 00:47:06,330
+important نيه ال important السؤال اللي بيجيبله إيش
+
+392
+00:47:06,330 --> 00:47:12,030
+بيقول بيقول لو كان ال element I important يبقى ال
+
+393
+00:47:12,030 --> 00:47:19,750
+A to the power M بيساوي ال A صح طيب هذا إيش معناه
+
+394
+00:47:19,750 --> 00:47:27,750
+I importantيبقى هذا معناه ان ال a to the power n
+
+395
+00:47:27,750 --> 00:47:35,410
+بتساوي ال a اللي هو example example
+
+396
+00:47:35,410 --> 00:47:42,790
+three اللي فوق above يبقى مثل ثلاثة اللي فوق
+
+397
+00:47:42,790 --> 00:47:50,660
+وعندنا هنا ال a أُس n بتساوي zeroطب من الاتنين
+
+398
+00:47:50,660 --> 00:47:55,460
+هذول مع بعض ايش بنستنتج بقى الطرف الشمال هو الطرف
+
+399
+00:47:55,460 --> 00:48:00,440
+الشمال إذا الطرف اليمين هو الطرف اليمين هذا بدي
+
+400
+00:48:00,440 --> 00:48:07,120
+أعطيك أنه A تساوي Zero يبقى Zero هو ال only null
+
+401
+00:48:07,120 --> 00:48:13,880
+potent and idempotent element يبقى هنا هذا بدي
+
+402
+00:48:13,880 --> 00:48:18,400
+يعطينا Zero as the only
+
+403
+00:48:33,590 --> 00:48:41,830
+سؤال شفته في الكتاب بيقوله تقدر تجيبولي ring و ال
+
+404
+00:48:41,830 --> 00:48:48,030
+ring هذه فيها element له unit و له zero divisor
+
+405
+00:48:51,120 --> 00:48:56,160
+هنجيب عنصر في ring العنصر هذا لا هو unit ولا هو
+
+406
+00:48:56,160 --> 00:49:05,220
+zero divisor 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
+
+407
+00:49:05,220 --> 00:49:06,400
+6 6 6 6 6 6 6 6 6 6 6
+
+408
+00:49:20,240 --> 00:49:23,820
+كم unit فيها؟ الواحد بيستغل الواحد مية المية اتنين
+
+409
+00:49:23,820 --> 00:49:28,680
+فيها units في الآخر طب فيها zero division؟ لأ لأ
+
+410
+00:49:28,680 --> 00:49:33,500
+يعني بدبر الاقي رقمين فيها حصل ضرهم يساوي zero لأ
+
+411
+00:49:33,500 --> 00:49:38,400
+يبقى ينسى الموضوع مفيش او مثال بسيط التلاتة موجود
+
+412
+00:49:38,400 --> 00:49:44,920
+في z والتلاتة له unit وله zero division صح؟ يبقى
+
+413
+00:49:44,920 --> 00:49:51,990
+hiringوفيها عناصر ليهم units وليهم zero divisors
+
+414
+00:49:51,990 --> 00:50:02,070
+طيب عندك هنا exercises خمسة من أسئلة التوريط بيقول
+
+415
+00:50:02,070 --> 00:50:17,510
+لي every element of ZN is a unit ofA0 Divider
+
+416
+00:50:17,510 --> 00:50:22,170
+Solution
+
+417
+00:50:22,170 --> 00:50:26,970
+كل
+
+418
+00:50:26,970 --> 00:50:32,110
+أنص في هذه ال ring أحد ال ring يا إما unit يا إما
+
+419
+00:50:32,110 --> 00:50:39,970
+every non-zero element every non-zero element of
+
+420
+00:50:39,970 --> 00:50:45,800
+ZIN is A unit or A0 Dividerيبقى بتقول خدلي K
+
+421
+00:50:45,800 --> 00:50:53,160
+موجودة في ZN such that و بحيث ال K above or equal
+
+422
+00:50:53,160 --> 00:50:58,940
+to Z بدي أثبت هذا ال K يا إما unit يا إما zero
+
+423
+00:50:58,940 --> 00:51:06,000
+divisor طب الآن في عندي حالتين احتمال انه ل
+
+424
+00:51:06,000 --> 00:51:12,800
+grasses common divisor لمن لل K و لل N يسوى واحد
+
+425
+00:51:13,730 --> 00:51:22,030
+ممكن زد ستة يبقى الستة و الخمسة مش الخمسة موجودة
+
+426
+00:51:22,030 --> 00:51:27,150
+في زد ستة اتنين are relatively prime صح يعني ال
+
+427
+00:51:27,150 --> 00:51:31,490
+classes common divisor قلهم جدير مثلا سيبقى من
+
+428
+00:51:31,490 --> 00:51:36,090
+الخمسة التلاتة موجودة في زد ستة ال classes common
+
+429
+00:51:36,090 --> 00:51:42,600
+divisor تلاتة مش الحل بطل يصير واحديبقى هنا f
+
+430
+00:51:42,600 --> 00:51:46,980
+لجريس ال common divisor اتنين اتنين f لجريس ال
+
+431
+00:51:46,980 --> 00:51:50,600
+common divisor اتنين اتنين f لجريس ال common
+
+432
+00:51:50,600 --> 00:51:53,460
+divisor اتنين اتنين f لجريس ال common divisor
+
+433
+00:51:53,460 --> 00:51:57,040
+اتنين اتنين f لجريس ال common divisor اتنين f
+
+434
+00:51:57,040 --> 00:51:59,040
+divisor اتنين f لجريس ال common divisor اتنين f
+
+435
+00:51:59,040 --> 00:52:05,360
+لجريس ال common divisor اتنين f لجريس ال common
+
+436
+00:52:05,360 --> 00:52:06,540
+divis
+
+437
+00:52:11,210 --> 00:52:22,990
+S وT موجودة في Z such that بحيث ان K بS زائد M في
+
+438
+00:52:22,990 --> 00:52:31,850
+T يسوى واحد طب هذه كلها بنى كم مضاعفات M في Z N
+
+439
+00:52:31,850 --> 00:52:38,950
+كم؟ Zero كم؟ Zero خايفين ليش؟ Zero يبقى هذه كلها ب
+
+440
+00:52:38,950 --> 00:52:45,330
+Zeroيبقى بيطلع هنا مين؟ K في S يساوي ال one حاصل
+
+441
+00:52:45,330 --> 00:52:50,050
+ضربته elements يساوي ال unity يبقى كل واحد فيهم is
+
+442
+00:52:50,050 --> 00:52:57,650
+a unit يبقى هذا يبدو يعطينا ان ال A is a unit
+
+443
+00:52:57,650 --> 00:53:06,710
+تمام؟ يبقى العنصر اللي جيبناه في ZN وافترضنا ان K
+
+444
+00:53:06,710 --> 00:53:13,190
+طلع unitقد يكون zero divisor يبقى بده اروح اخد
+
+445
+00:53:13,190 --> 00:53:20,630
+الحالة التانية F لجريس ال common divisor لل N او
+
+446
+00:53:20,630 --> 00:53:31,230
+لل K و ال N بده يساوي D مثلا و ال D هذه اكبر من
+
+447
+00:53:31,230 --> 00:53:38,330
+الواحد رقم اكبر من من الواحدطيب بده اشوف معنى هذا
+
+448
+00:53:38,330 --> 00:53:45,570
+الكلام ان ال A مضاعفة ال D صح ولا لأ يبقى هذا
+
+449
+00:53:45,570 --> 00:53:52,070
+الكلام بده يعطينا ال there exists M موجود في Z
+
+450
+00:53:52,070 --> 00:54:03,840
+plus such that بحيث ان ال A بده يساوي M في Dطبعا
+
+451
+00:54:03,840 --> 00:54:08,620
+يبقى الكهة ده اللي class is called divisor لديه مع
+
+452
+00:54:08,620 --> 00:54:15,760
+ان يساوي D بدل غضب ورقم مضروب في دي بدي احاول اثبت
+
+453
+00:54:15,760 --> 00:54:22,820
+ان الكهة ده هو zero divisor لذلك بقول لو جربت اضرب
+
+454
+00:54:22,820 --> 00:54:33,960
+K في N على D سؤال هوهل N على D يساوي Zero؟ لأ لأ
+
+455
+00:54:33,960 --> 00:54:39,300
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+456
+00:54:39,300 --> 00:54:39,640
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+457
+00:54:39,640 --> 00:54:39,760
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+458
+00:54:39,760 --> 00:54:39,800
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+459
+00:54:39,800 --> 00:54:40,740
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+460
+00:54:40,740 --> 00:54:54,960
+لأ
+
+461
+00:54:54,960 --> 00:55:01,060
+لأ ليبقى مضاعفات ال N بقداش ب Zero يبقى هذا الناتج
+
+462
+00:55:01,060 --> 00:55:08,240
+يساوي Zero يبقى صار ال K is a Zero divisor لإن ال
+
+463
+00:55:08,240 --> 00:55:14,500
+K لا يساوي Zero وال N على D لا يساوي Zero هذا
+
+464
+00:55:14,500 --> 00:55:23,590
+معناه إن ال K is a Zero divisorيبقى كل عنصر في Z
+
+465
+00:55:23,590 --> 00:55:28,630
+in يا إما unit يا إما zero divisor لكن هذا الكلام
+
+466
+00:55:28,630 --> 00:55:34,450
+على أي ring؟ لأ مش على Z in لأن طبعا سألتوا سؤال
+
+467
+00:55:34,450 --> 00:55:39,610
+أخدنا Z لاجئنا فيها فيش إلا toilets ومافيش فيها
+
+468
+00:55:39,610 --> 00:55:44,350
+zero divisor يالا في الوقت اتمرنوا في الأسئلة
+
+469
+00:55:44,350 --> 00:55:52,690
+التالية يبقى exercises على شطر 13ساعة خمسة هيو
+
+470
+00:55:52,690 --> 00:56:00,930
+حلناها خمسة و تمانية و عشر و عشرين و واحد و عشرين
+
+471
+00:56:00,930 --> 00:56:11,050
+و اربعة و عشرين و واحد و ثلاثين و اتنين و تلاتين و
+
+472
+00:56:11,050 --> 00:56:19,490
+اربعين و اتنين و اربعين و ستة و اربعين و اتنين و
+
+473
+00:56:19,490 --> 00:56:20,550
+خمسين
+
+474
+00:56:25,020 --> 00:56:35,580
+نين و خمسين و تلاتة و خمسين و ستة و خمسين و تمانية
+
+475
+00:56:35,580 --> 00:56:36,840
+و خمسين
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/qpWTrM9voc4_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/qpWTrM9voc4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..be34642bdc696fc7ad70946b6a744279ee3bad04
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/qpWTrM9voc4_postprocess.srt
@@ -0,0 +1,1800 @@
+1
+00:00:20,920 --> 00:00:26,160
+بسم الله الرحمن الرحيم نكمل ما اتدناه في المحاضرة
+
+2
+00:00:26,160 --> 00:00:34,400
+الماضية ولازلنا مع الـ Factor Rings مثاله رقم خمسة
+
+3
+00:00:34,400 --> 00:00:40,220
+بيقول يستخدم الـ R of X تمثل Ring of polynomials
+
+4
+00:00:40,220 --> 00:00:46,480
+كثيرات الحدود with real coefficientsيبقى المعاملات
+
+5
+00:00:46,480 --> 00:00:53,700
+تبعد كثيرات الحدود هي كلها أعداد حقيقية ناخد الـ
+
+6
+00:00:53,700 --> 00:00:57,080
+Principle Ideal Generated by X تربيه زايد واحد
+
+7
+00:00:57,080 --> 00:01:01,160
+اللي هو كل العناصر F of X اللي مضروبة في X تربيه
+
+8
+00:01:01,160 --> 00:01:05,960
+زايد واحد في هذه الـ F of X موجودة في R of X بذكرك
+
+9
+00:01:05,960 --> 00:01:10,800
+بجينا نقول الـ Principle Ideal Generated by A هو
+
+10
+00:01:10,800 --> 00:01:17,450
+كل العناصر على الشكل R في Aبحيث الـ R موجودة في R
+
+11
+00:01:17,450 --> 00:01:21,470
+يبقى نفس التعريف الـ R اللي موجودة في R هي
+
+12
+00:01:21,470 --> 00:01:26,130
+function والـ A اللي موجود في ال principle اللي هو
+
+13
+00:01:26,130 --> 00:01:30,110
+X تربية زائد واحد يبقى هذا التعريف السابق اللي
+
+14
+00:01:30,110 --> 00:01:34,470
+أخدناه لمين لل principle ideal generated by A هو
+
+15
+00:01:34,470 --> 00:01:39,730
+ال principle ideal generated by X تربية زائد واحد
+
+16
+00:01:40,320 --> 00:01:44,140
+يبقى في هذه الحالة نكوّل الـ Factoring الـ
+
+17
+00:01:44,140 --> 00:01:50,520
+Factoring لـ R of X modulo X تربية زائد واحد من
+
+18
+00:01:50,520 --> 00:01:55,120
+عناصرها عنصر من G زائد الـ principle ideal
+
+19
+00:01:55,120 --> 00:02:01,100
+generated by X تربية زائد واحد عنصر من R of X هو G
+
+20
+00:02:01,100 --> 00:02:07,910
+of X زائد الـ ideal اللي عندنا هذا أنا أزعمإن هذا
+
+21
+00:02:07,910 --> 00:02:13,170
+بيكون على الشكل ax زائد b يعني معادلة من الدرجة
+
+22
+00:02:13,170 --> 00:02:17,410
+الأولى زائد ال x تربيه زائد واحد وبعدها ال a و ال
+
+23
+00:02:17,410 --> 00:02:24,750
+b أعدادا حقيقي طب تعالوا نتفهم الآن ال g of x
+
+24
+00:02:24,750 --> 00:02:32,190
+موجودة وين؟ ال R of xاروبكس هي pronomial من الدرجة
+
+25
+00:02:32,190 --> 00:02:35,810
+الأولى و الله ممكن الأولى و التانية و التالتة و
+
+26
+00:02:35,810 --> 00:02:41,490
+العشرة و النونية و ما إلى ذلك أيوة يبقى هنا عندي
+
+27
+00:02:41,490 --> 00:02:45,170
+من أي درجة ان شاء الله يكون من الدرجة الخمسمية
+
+28
+00:02:45,170 --> 00:02:51,330
+تمام لكن انا ازعم اني بقدر اكتبها على الشكل معادلة
+
+29
+00:02:51,330 --> 00:02:55,510
+من الدرجة الأولى زي ال principle ideal generated
+
+30
+00:02:55,510 --> 00:03:02,860
+by X تربية زي الواحدةبقول هذه الصيغة صحيحة this is
+
+31
+00:03:02,860 --> 00:03:07,760
+true because لو كانت الـG of X موجودة في الـR of X
+
+32
+00:03:07,760 --> 00:03:15,800
+then شوف يا الكتابة هذه تبعت الـG of X بقدر أكتبها
+
+33
+00:03:15,800 --> 00:03:24,460
+على شكل دالة في X EQ of X مضروبة في X تربية زائد
+
+34
+00:03:24,460 --> 00:03:34,860
+واحد زائد R of Xو ال R of X يا إما بتتساوي Zero يا
+
+35
+00:03:34,860 --> 00:03:44,860
+إما ال degree لل R of X أقل من إثنين إيش اللاتيني
+
+36
+00:03:44,860 --> 00:03:49,800
+هذا؟ بدنا نفهم، من أين جاي بهذا الكلام؟ نجحنا فرضا
+
+37
+00:03:49,800 --> 00:03:55,140
+أنها AX؟ بصوا برا عليها شويةالان انا ماخد g of x
+
+38
+00:03:55,140 --> 00:04:00,680
+موجودة في ال polynomial الاصلية r of x يبقى هذه
+
+39
+00:04:00,680 --> 00:04:04,460
+الدرجة يمكن التالتة يمكن الرابعة الخامسة جد ما
+
+40
+00:04:04,460 --> 00:04:11,720
+يكون انا ازعم ان بقدر احطها على شكل معدن من الدرجة
+
+41
+00:04:11,720 --> 00:04:18,270
+الأولى نفترض انه كانت من الدرجة العشرة g of xيبقى
+
+42
+00:04:18,270 --> 00:04:24,550
+ليش بضروح أعمل بضروح أجسم جسمة مطولة على مين على X
+
+43
+00:04:24,550 --> 00:04:29,650
+تربية زائد واحد يبقى ال Ge of X اللي من الدرجة
+
+44
+00:04:29,650 --> 00:04:34,530
+العاشرة بدي أجسمها على ال polynomial X تربية زائد
+
+45
+00:04:34,530 --> 00:04:40,950
+واحد اللي من الدرجة الثانية بضل أجسم لغاية الدرجة
+
+46
+00:04:40,950 --> 00:04:46,320
+الصينية أقل من الدرجة الثانيةيعني أقل من درجة X
+
+47
+00:04:46,320 --> 00:04:51,900
+تربية وزايد واحد مظبوط يبقى بطل عندنا خارج القسمة
+
+48
+00:04:51,900 --> 00:04:57,400
+و بضل عندنا تحت باقي الباقي هذا قد يكون صفر زي ما
+
+49
+00:04:57,400 --> 00:05:02,200
+تجسمي مثلا اي عدد على عدد اذا ما تقولي تمانية على
+
+50
+00:05:02,200 --> 00:05:08,160
+اتنين يبقى اربع عدد صحيح ماضلش عندي باقي تمام لكن
+
+51
+00:05:08,160 --> 00:05:16,270
+لو قلنا جسمنا تسعة على اتنينبظل أربع و لسه بزيد
+
+52
+00:05:16,270 --> 00:05:21,390
+واحد بدنا نقسمه على اتنين مظبوط ولا لا يبقى هذا
+
+53
+00:05:21,390 --> 00:05:27,150
+اللي هو الباقي اللي بده يسميه R of X يبقى ال Q of
+
+54
+00:05:27,150 --> 00:05:33,270
+X تعتبر عددا صحيحا يعني بلغتنا في السوء ال
+
+55
+00:05:33,270 --> 00:05:38,950
+polynomialمضروبة في المقسوم عليه له X تربية زائد
+
+56
+00:05:38,950 --> 00:05:43,870
+واحد زائد الـ remainder الباقي اللي عندنا هو R of
+
+57
+00:05:43,870 --> 00:05:49,510
+X إذاً الـG of X حطيتها على الشكل اللي عندنا هذا
+
+58
+00:05:49,510 --> 00:05:56,310
+والـR of X قد تكون Zero بتكون Zero إذا تقسم G of X
+
+59
+00:05:56,310 --> 00:06:01,330
+على X تربية زائد واحد بدون باقي لو قسمت بدون باقي
+
+60
+00:06:01,330 --> 00:06:07,370
+يبقى R of X بقداش ب Zeroطيب إذا جسمته بقي عندنا
+
+61
+00:06:07,370 --> 00:06:13,430
+الباقي بظلمين R of X R of X درجته أقل من اتنين
+
+62
+00:06:13,430 --> 00:06:19,350
+يعني أقل من درجة X تربيه زي واحد لإن بنقول إذا
+
+63
+00:06:19,350 --> 00:06:23,890
+درجة البصر أكبر من درجة المقام أو درجة البصر جت
+
+64
+00:06:23,890 --> 00:06:29,530
+درجة المقام بنجسم جسمة متولة لها يتمصير درجة البصر
+
+65
+00:06:29,530 --> 00:06:34,370
+أقل من درجة المقام مظبوطمش هيك في القسمة المطولة
+
+66
+00:06:34,370 --> 00:06:41,030
+العادية تماما هنا تماما جسمنا الـG of X على الـX
+
+67
+00:06:41,030 --> 00:06:47,890
+تربية زي 1 طلع النتيجة Q of X وزال دلة اسمها R of
+
+68
+00:06:47,890 --> 00:06:53,050
+X إذا الـG of X يسبق Q of X في الـX تربية زي 1 زي
+
+69
+00:06:53,050 --> 00:06:59,130
+R of X R of X كان مضلش شيء يبقى R of X بـ0 ضلت دلة
+
+70
+00:06:59,130 --> 00:07:06,270
+بنقولها R of Xاللي درجتها أقل من درجة المقسوم عليه
+
+71
+00:07:06,270 --> 00:07:12,990
+أقل من اتنين يعني كده؟ واحد، مظبوط ولا لأ يعني ايش
+
+72
+00:07:12,990 --> 00:07:20,570
+بيصير؟ بيصير ax زائد b معادلة من الدرجة الأولى
+
+73
+00:07:20,570 --> 00:07:27,010
+وإذا طلعت F0 بيظل constant Bيبقى in general نقول
+
+74
+00:07:27,010 --> 00:07:32,210
+ax زايد بقدر ما تطلع ايه تطلع وقدر ما تطلع بيه
+
+75
+00:07:32,210 --> 00:07:37,350
+تطلع ماعناه مشكلة يبقى بناء عليه لمن قد يقول يا
+
+76
+00:07:37,350 --> 00:07:46,090
+بناتي g of x زايد principle ideal generated by x
+
+77
+00:07:46,090 --> 00:07:52,810
+تربيه زايد واحد مش بده يساوي بده يساوي هي ال q of
+
+78
+00:07:52,810 --> 00:08:01,860
+xU of X في X تربيع زائد واحد زائد R of X زائد
+
+79
+00:08:01,860 --> 00:08:05,720
+reference principle ideal generated by X تربيع
+
+80
+00:08:05,720 --> 00:08:11,540
+زائد واحد السؤال هو إيش رايك هذه مع reference
+
+81
+00:08:11,540 --> 00:08:16,960
+principle ideal إيش هذه موجودة هنا إذا حسب الكلام
+
+82
+00:08:16,960 --> 00:08:23,240
+اللي إحنا بنقوله هذه R of Xزائد لـPrincipal Ideal
+
+83
+00:08:23,240 --> 00:08:29,060
+Generated By X تربية زائد واحد تبقى Renovix أقل من
+
+84
+00:08:29,060 --> 00:08:35,180
+الدرجة الثانية بمقدار واحد أو مقدار اتنين يبقى
+
+85
+00:08:35,180 --> 00:08:43,180
+بناخد الأكبر وهذه تساوي AX زائد B زائد لPrincipal
+
+86
+00:08:43,180 --> 00:08:48,810
+Ideal Generated By X تربية زائد واحديبقى كلامنا
+
+87
+00:08:48,810 --> 00:08:55,510
+اللي قلناه صحيح ولا لا يبقى اي polynomial في جي او
+
+88
+00:08:55,510 --> 00:09:00,750
+اي polynomial في ال R of X الأصلية بقدر اكتبها على
+
+89
+00:09:00,750 --> 00:09:04,970
+سيط polynomial من الدرجة الأولى زاد ال principle
+
+90
+00:09:04,970 --> 00:09:10,450
+ideal generated by X تربيع زاد وعدها يورناك كيف
+
+91
+00:09:10,450 --> 00:09:15,470
+حصلنا عليها طب السؤال الأول طب احنا لو عندنا two
+
+92
+00:09:15,470 --> 00:09:19,700
+elements كيف بتضرمهم؟لأنها هتطلع معادل من الدرجة
+
+93
+00:09:19,700 --> 00:09:23,060
+التانية صحيح ولا لأ؟ يقول معادل من الدرجة الأولى
+
+94
+00:09:23,060 --> 00:09:26,400
+وهم الدرجة اللى ضربناهم تطلع معادل من الدرجة
+
+95
+00:09:26,400 --> 00:09:30,580
+التانية كيف سوى في هذه الحلقة نقولك القصة فسيطة
+
+96
+00:09:30,580 --> 00:09:37,580
+جدا كيف فسيطة جدا تعالى شوفى باياتك الان note that
+
+97
+00:09:37,580 --> 00:09:41,140
+لاحظي
+
+98
+00:09:41,140 --> 00:09:50,120
+باياتك الان يا بنات لو جيت قلتx تربيع زائد واحد زي
+
+99
+00:09:50,120 --> 00:09:55,600
+ال principle ideal generated by x تربيع زائد واحد
+
+100
+00:09:55,600 --> 00:10:02,740
+هداش بيعطيني ال principle ideal generated by x
+
+101
+00:10:02,740 --> 00:10:08,080
+تربيع زائد واحد لأن هذا عنصر موجود فيه صحيح ولا لأ
+
+102
+00:10:08,080 --> 00:10:14,550
+طب بنفع اقول هذا بنفع zeroزاد ال principle ideal
+
+103
+00:10:14,550 --> 00:10:20,310
+generated by one صحيح ولا لا؟ إذا البناء النعلي
+
+104
+00:10:20,310 --> 00:10:29,410
+بصير عند X تربية زائد واحد بده ساوي zero طبعا؟ طيب
+
+105
+00:10:29,410 --> 00:10:35,670
+معناه هذا الكلام إن ال X تربية بده ساوي كده؟ بده
+
+106
+00:10:35,670 --> 00:10:45,970
+ساوي سالف واحد طبعا؟إذا داخل هذه ال ring ها تشوف
+
+107
+00:10:45,970 --> 00:10:50,930
+تعد لمخك أيوة داري بارك هم مشغولش على ال real line
+
+108
+00:10:50,930 --> 00:10:57,110
+هم نشغل داخل مين؟ داخل ال ring R of X وإلا لو كان
+
+109
+00:10:57,110 --> 00:11:01,490
+على ال real line هذه المعادلة عندى ملهاش حل صح ولا
+
+110
+00:11:01,490 --> 00:11:07,630
+لا؟ لأنه لا يمكن لمجموع كميتين كميتين مربعات أو
+
+111
+00:11:07,630 --> 00:11:13,360
+كميتين موجبتينإن يكون صفر فالكلام مش ممكن إلا إذا
+
+112
+00:11:13,360 --> 00:11:18,580
+كانت كل واحدة فيهم صفر لكن إحنا عنا X تربية بدأت
+
+113
+00:11:18,580 --> 00:11:24,640
+ساوي سالب واحد على ال pronomials هدول وليس على ال
+
+114
+00:11:24,640 --> 00:11:29,340
+.. يعني داخل ال ring اللي عندنا طيب ان وريكي لهم
+
+115
+00:11:29,340 --> 00:11:34,720
+كيف الحسابات بصير داخل هذه ال ring لو بدي أضرب
+
+116
+00:11:34,720 --> 00:11:41,240
+مثلًا بدي أضرب عنصرين هتيليمعادلة خطية يالا صمي
+
+117
+00:11:41,240 --> 00:11:46,080
+يعني يعني زي اكس من طريقة الأولى معادلة عادية حط
+
+118
+00:11:46,080 --> 00:11:52,000
+الرقم الي عادي ثلاثة اكس زائد اتنين اتنين ممتاز
+
+119
+00:11:52,000 --> 00:11:58,160
+جدا يبقى انا عندي تلاتة اكس زائد اتنين زائد ال
+
+120
+00:11:58,160 --> 00:12:04,360
+principle ideal generated by one بدي اضربه فاهمين
+
+121
+00:12:04,910 --> 00:12:13,250
+هاتي لـ polynomial تانية غير هذه 5x
+
+122
+00:12:13,250 --> 00:12:19,830
+-3 يبقى عندى 5x-3 زائد لـ principal ideal
+
+123
+00:12:19,830 --> 00:12:26,390
+generated by one هذه المناطق لما أضربها بدأت تسوى
+
+124
+00:12:26,390 --> 00:12:36,600
+3x زائد 2 في 5x-3وهنا زائد لـ principal ideal
+
+125
+00:12:36,600 --> 00:12:41,640
+generated by x تربيع minus ال one يبقى هذه بدي
+
+126
+00:12:41,640 --> 00:12:47,560
+أضرب الآن بدي أفك حاصل ضربي فتلاتة في خمسة بخمس
+
+127
+00:12:47,560 --> 00:12:55,180
+طعشر x تربيع تمام و تلاتة x في ناقص تلاتة بناقص
+
+128
+00:12:55,180 --> 00:13:04,520
+تسعة x ناقص تسعة x وزائد عشرة xوزائد عشر عليه
+
+129
+00:13:04,520 --> 00:13:10,780
+وناقص التوزيع لـPrincipal Ideal Generated by X
+
+130
+00:13:10,780 --> 00:13:15,620
+تربية plus one.الحين يا بنات ال X تربية هنا مقداش؟
+
+131
+00:13:15,620 --> 00:13:20,880
+سالب واحد، إذا هشيل ال X تربية وحط مكانها سالب
+
+132
+00:13:20,880 --> 00:13:26,840
+واحد. هذا الكلام بدي يصير خمستاشر في سالب واحد.
+
+133
+00:13:27,200 --> 00:13:34,980
+عندك ناقص تسعة X وزائد عشرة X بظل زائد X وهنا ناقص
+
+134
+00:13:34,980 --> 00:13:40,140
+ستة زائد ال principle ideal generated by X ترمية
+
+135
+00:13:40,140 --> 00:13:47,180
+plus one طبعا هنا ناقص خمس عشان ناقص ستة ناقص
+
+136
+00:13:47,180 --> 00:13:54,150
+واحدة وعشرين إذا صارت عندي X ناقص واحدة وعشرينزايد
+
+137
+00:13:54,150 --> 00:13:59,110
+ال principle ideal generated by one X تربيع زايد
+
+138
+00:13:59,110 --> 00:14:04,690
+by one تمام؟ يبقى هذه عملية الضرفياني من حد مضرب
+
+139
+00:14:04,690 --> 00:14:08,810
+عنصرين هيطلع عند X تربيع وين طلعت ال X تربيع؟
+
+140
+00:14:08,810 --> 00:14:15,190
+بشيلها بحفظ بدلها سالب واحد وبالتالي بتعود البعود
+
+141
+00:14:15,190 --> 00:14:19,090
+العنصر إلى معادلة من الدرجة الأولى زايد ال
+
+142
+00:14:19,090 --> 00:14:24,610
+principle ideal generatedby x تربيع زائد واحد
+
+143
+00:14:24,610 --> 00:14:30,630
+تمام؟ إذا هذه عملية الضرب داخل من؟ داخل ال ring
+
+144
+00:14:30,630 --> 00:14:37,090
+اللي عملناه ننتقل الآن إلى تعريف جديد يبقى
+
+145
+00:14:37,090 --> 00:14:43,030
+definition احنا من أول ال section هنا و احنا عرفنا
+
+146
+00:14:43,030 --> 00:14:49,230
+ال idealواخدنا منه الـ Trivial Ideal اللي هو الـ
+
+147
+00:14:49,230 --> 00:14:54,450
+Zero اللي لا يحتوي على الـ Zero وسمناه الـ Ideal
+
+148
+00:14:54,450 --> 00:14:59,990
+البديهي أو الـ Ideal التغفر لأن أي واحد بيجيبه فيه
+
+149
+00:14:59,990 --> 00:15:05,250
+مشكلة لكن بدنا نيجي لحالات خاصة من ال Ideals حاجة
+
+150
+00:15:05,250 --> 00:15:12,320
+بنسميها Prime Ideal و Maximal Idealبنعطي تعريف لكل
+
+151
+00:15:12,320 --> 00:15:18,260
+منهما ثم نذهب الى أمثلة على ذلك الـ Definition
+
+152
+00:15:18,260 --> 00:15:31,140
+الأول A prime ID A of a commutative ring R
+
+153
+00:15:40,480 --> 00:15:51,120
+is a proper ideal is a proper ideal is a proper
+
+154
+00:15:51,120 --> 00:16:05,440
+ideal of R such that بحيث أن such that if
+
+155
+00:16:05,440 --> 00:16:18,860
+ال A و ال Bموجودة في a and ال a بي موجود في a then
+
+156
+00:16:18,860 --> 00:16:29,720
+ال a موجود في a هو ال b موجود فيه تعريف التاني
+
+157
+00:16:29,720 --> 00:16:43,380
+maximal id هي maximal id ايه ايه maximumأيديل A of
+
+158
+00:16:43,380 --> 00:16:50,140
+a commutative in
+
+159
+00:16:50,140 --> 00:17:04,400
+R is a proper ideal of R is a proper ideal of R
+
+160
+00:17:04,400 --> 00:17:14,290
+such thatبحيث ان الله دي ما صادش ده whenever
+
+161
+00:17:14,290 --> 00:17:18,550
+whenever
+
+162
+00:17:18,550 --> 00:17:35,990
+B is an id of A and ال A صاب ستة أو تسعة و ال B
+
+163
+00:17:36,610 --> 00:17:46,930
+subset أو تساوي الـR then الـB بديو يساوي الـA
+
+164
+00:17:46,930 --> 00:17:54,750
+الـB بديو يساوي الـAR الـD بديو يساوي الـD بديو
+
+165
+00:17:54,750 --> 00:18:02,490
+يساوي الـR example one
+
+166
+00:18:02,490 --> 00:18:12,660
+لو السؤال تسعةمن الكتاب هو ليلات الان اكبر من
+
+167
+00:18:12,660 --> 00:18:18,000
+الواحد بانتجر
+
+168
+00:18:18,000 --> 00:18:29,160
+عدد صحيح بانتجر then in
+
+169
+00:18:29,160 --> 00:18:34,300
+the rain زاد
+
+170
+00:18:35,170 --> 00:18:45,230
+I think that ال .. the ideal in
+
+171
+00:18:45,230 --> 00:18:52,270
+the is prime is
+
+172
+00:18:52,270 --> 00:19:02,410
+a prime if and only if if and only if ال N is a
+
+173
+00:19:02,410 --> 00:19:02,850
+prime
+
+174
+00:19:09,090 --> 00:19:15,050
+بنرجع للتعريفين اللي احنا كتبينه الـPrime Ideal ثم
+
+175
+00:19:15,050 --> 00:19:19,870
+الـMaximal Ideal يقول الـPrime Ideal ايه؟ Of a
+
+176
+00:19:19,870 --> 00:19:25,050
+commutative ring A is a proper ideal. يبقى الشرط
+
+177
+00:19:25,050 --> 00:19:29,110
+الأول الذي يجب ان يتحقق في الـIdeal حتى يكون
+
+178
+00:19:29,110 --> 00:19:31,870
+الـPrime هو؟ ماذا يعني proper?
+
+179
+00:19:35,240 --> 00:19:41,220
+ماشي معناه proper ideal يعني؟ يعني مايسويش ال ring
+
+180
+00:19:41,220 --> 00:19:49,180
+الأصلية أقل منها، subset منها، تمام؟ يبقى هذا الـ
+
+181
+00:19:49,180 --> 00:19:55,440
+improper بده يساويها، تمام؟ يبقى proper ideal
+
+182
+00:19:55,440 --> 00:20:02,330
+الشرق الأول، وبحيث ان لو كانت عنصرينموجودات في ال
+
+183
+00:20:02,330 --> 00:20:08,210
+ring R وحاصل ضاربهما موجود في ال ideal A يبقى يا
+
+184
+00:20:08,210 --> 00:20:14,310
+إما ال A بيكون في A يا إما ال B بيكون في A إن حدث
+
+185
+00:20:14,310 --> 00:20:20,170
+ذلك بقول ال A هو prime ideal يبقى إذا قال لي أثبت
+
+186
+00:20:20,170 --> 00:20:26,630
+أن هذا ال ideal هو prime بفترض أن عندي عنصرين في
+
+187
+00:20:26,630 --> 00:20:34,180
+ال ring R وحاصل ضاربهما وين موجودفي الـ ID ان حدث
+
+188
+00:20:34,180 --> 00:20:40,560
+ذلك يبقى بتروح اثبت ان احد العنصرين موجود وين؟ في
+
+189
+00:20:40,560 --> 00:20:46,340
+ال ID يبقى يا اما ايه موجود في ايه او ال ايه موجود
+
+190
+00:20:46,340 --> 00:20:52,440
+فيه تعالى نشوف معنى ال maximum ال ID maximum جاي
+
+191
+00:20:52,440 --> 00:20:57,870
+من maximum ايش يعني maximum اكبر ما يمكنوهذا
+
+192
+00:20:57,870 --> 00:21:04,050
+المقصود يبقى أكبر ما يمكن كيف؟ تعالوا نشوف يبقى ال
+
+193
+00:21:04,050 --> 00:21:08,910
+maximum ideal من الكميوتر ت bring هو يبقى ال
+
+194
+00:21:08,910 --> 00:21:13,810
+proper ideal of our يبقى زي مين؟ زي ال prime يبقى
+
+195
+00:21:13,810 --> 00:21:18,830
+ال prime و .. و ال maximum الأتنين are ال proper
+
+196
+00:21:18,830 --> 00:21:26,520
+ideal و بحيث أن لو كان عنديB هو ideal آخر من ال
+
+197
+00:21:26,520 --> 00:21:32,080
+ring R وكان ال ideal اللي أنا بتدعي انه maximal
+
+198
+00:21:32,080 --> 00:21:37,660
+subset من B و ال B subset من R يبقى هناك أحد
+
+199
+00:21:37,660 --> 00:21:44,060
+احتمالين يا إما ال A و ال B يتساووا يا إما ال B و
+
+200
+00:21:44,060 --> 00:21:50,140
+ال R يتساووا يبقى هذه هي الطريقة المثلاء لإثبات أن
+
+201
+00:21:50,140 --> 00:21:54,830
+ال A هو maximal ideal من Rيبقى في حالة الـ Prime
+
+202
+00:21:54,830 --> 00:21:59,850
+بتروح للعناصر، في حالة الـ Maximal بتروح أجيب
+
+203
+00:21:59,850 --> 00:22:05,190
+Ideal تاني، بحيث الـ Ideal اللي عندي ال subset منه
+
+204
+00:22:05,190 --> 00:22:10,430
+و ال Ideal هذا subset من ال ring R، بدي أثير، يا
+
+205
+00:22:10,430 --> 00:22:14,610
+إما A تساوي بيه، يا إما B تساوي منه، تساوية.
+
+206
+00:22:15,170 --> 00:22:19,090
+تعالوا ناخد أمثلة مختلفة على الـ Prime Ideals والـ
+
+207
+00:22:19,090 --> 00:22:24,040
+Maximal Ideals.كون الـ prime ideal هو التعريف
+
+208
+00:22:24,040 --> 00:22:29,180
+الأول إذا هناخد السؤال الأول أو المثال الأول على
+
+209
+00:22:29,180 --> 00:22:34,020
+الـ prime ideal قال خذ ال N أكبر من واحد نين تلاتة
+
+210
+00:22:34,020 --> 00:22:39,180
+أربعة خمسة زي ما بدك P an integer then in the ring
+
+211
+00:22:39,180 --> 00:22:46,440
+Z ال NZ هو عبارة عن ideal هأثبتنا طبعا سابقا Z
+
+212
+00:22:46,440 --> 00:22:51,910
+ideal و كذلك sub ringيبقى الانزد هذا بيكون a prime
+
+213
+00:22:51,910 --> 00:22:58,630
+if and only if الان is a prime تمام؟ يبقى القرآن
+
+214
+00:22:58,630 --> 00:23:04,870
+ده صير وين؟ اتجاه الان يبقى بدي اخد الاتجاه الأول
+
+215
+00:23:04,870 --> 00:23:09,230
+assume that
+
+216
+00:23:09,230 --> 00:23:13,870
+ان الان is a prime
+
+217
+00:23:18,720 --> 00:23:26,740
+want to show that
+
+218
+00:23:26,740 --> 00:23:41,440
+ان ال NZ is a prime ID طيب
+
+219
+00:23:41,440 --> 00:23:55,260
+we know thatWe know that احنا بنعرف ان الـNZ is a
+
+220
+00:23:55,260 --> 00:24:05,520
+proper ideal of مجموعة الأعداد الصحيحة اللي هي Z
+
+221
+00:24:05,520 --> 00:24:12,760
+أثبتناها سابقاً طيب الان بدي امشي حسب التحريك بدي
+
+222
+00:24:12,760 --> 00:24:19,290
+افترضإن في عندي عنصرين من ال ring Z حاصل ضربيهم
+
+223
+00:24:19,290 --> 00:24:28,550
+موجود وين؟ موجود في ال NZ يبقى بدأت أقول له let ال
+
+224
+00:24:28,550 --> 00:24:38,090
+A و ال B موجودة في Z such that بحيث أن ال A في ال
+
+225
+00:24:38,090 --> 00:24:41,430
+B موجودة في ال NZ
+
+226
+00:24:44,850 --> 00:24:50,350
+اخدت عنصرين من ال ring الأصلية A وB وافترضت ان
+
+227
+00:24:50,350 --> 00:24:55,590
+حاصل ضربهما موجود في ال ID اللي عندي ال ID المي
+
+228
+00:24:55,590 --> 00:25:03,490
+اللي عندي مين؟ NZ طبعا يفجأة صار حاصل ضربهما موجود
+
+229
+00:25:03,490 --> 00:25:10,130
+في ال NZ ممتاز جدا طب مدام حاصل ضربهما موجود في ال
+
+230
+00:25:10,130 --> 00:25:19,680
+NZإذا شكل حاصل الضرب A في B بديساو ال N في X for
+
+231
+00:25:19,680 --> 00:25:27,940
+some X اللي موجودة في Z صحيح ولا مناقش؟ حاصل الضرب
+
+232
+00:25:27,940 --> 00:25:34,180
+موجود هنا شكل العنصر هنا هو N في أي element أو في
+
+233
+00:25:34,180 --> 00:25:40,760
+some element من Z يبقى ال A بيه بديساو ال N X
+
+234
+00:25:41,230 --> 00:25:46,810
+طلعيلي هذه المعادلة الـ X و الـ N و الـ B و الـ A
+
+235
+00:25:46,810 --> 00:25:53,090
+كلهم integers أعداد صحيحة نرجع بالذاكرة إلى الوراق
+
+236
+00:25:53,090 --> 00:25:58,950
+أليس معنى هذه المعادلة أن الـ N بتقسم الـ A بـ B
+
+237
+00:25:58,950 --> 00:26:06,250
+تمام تمام يبقى هذا معناه أن الـ N divides الـ A في
+
+238
+00:26:06,250 --> 00:26:14,060
+Bهذا معناه ان ال N بيقسم ال A أو ال N بيقسم ال B
+
+239
+00:26:14,060 --> 00:26:23,060
+يا إما ال N بتقسم ال A يا إما ال N بتقسم ال B مدام
+
+240
+00:26:23,060 --> 00:26:34,100
+بتقسم ال A يبقى ال A بدها تساوي N M for some M
+
+241
+00:26:34,100 --> 00:26:44,170
+اللي موجودة في Zمظبوط يا جابانان or ال B تساوي N
+
+242
+00:26:44,170 --> 00:26:52,650
+كفار صمك اللي موجودة في ذلك صحيح؟
+
+243
+00:26:52,650 --> 00:27:01,710
+طيب مدان هيك ال A يساوي N في M ال M هي ال element
+
+244
+00:27:01,710 --> 00:27:07,040
+هذا الثابتو ال M موجودة في Z معناه هذا الكلام ان
+
+245
+00:27:07,040 --> 00:27:14,460
+ال A موجود وين؟ في ال N Z يبقى معناه هذا الكلام ان
+
+246
+00:27:14,460 --> 00:27:27,820
+ال A موجودة في ال N Z او ال B موجودة في ال N Z ليش
+
+247
+00:27:27,820 --> 00:27:34,320
+ان ال K في Z و M في Z؟ اظن ان هو المطلوب؟إذا وصلنا
+
+248
+00:27:34,320 --> 00:27:40,880
+و أحنا مش دارين يبقى هذا معناه إيش؟ معناته إن NZ
+
+249
+00:27:40,880 --> 00:27:48,740
+is a prime ideal طبقا لل definition اللي عندنا هذا
+
+250
+00:27:48,740 --> 00:27:53,360
+الاتجاه الأول بنا نمشي لاتجاه الثاني يبقى بضروح
+
+251
+00:27:53,360 --> 00:28:06,570
+أقوله conversely assume that إن ال Nz is a prime
+
+252
+00:28:06,570 --> 00:28:16,490
+ideal هش اللي بدنا ياه want to show بدنا نروح نبين
+
+253
+00:28:16,490 --> 00:28:24,770
+ان ال N is a prime because we noticed ان هذا عدد
+
+254
+00:28:24,770 --> 00:28:30,090
+صحيح أولي طيب هروح أقول suppose not
+
+255
+00:28:33,640 --> 00:28:40,460
+يعني إيش؟ يعني ما هواش عدد أول، ده ما هواش عدد
+
+256
+00:28:40,460 --> 00:28:46,440
+أول، إذا بقدر أحلله إلى حاصل ضرب عددين، صحيح ولا
+
+257
+00:28:46,440 --> 00:28:53,840
+لا؟ يبقى suppose not then الـN هذا بده يساوي حاصل
+
+258
+00:28:53,840 --> 00:29:00,370
+ضرب SVT، كونه عدد ما هواش عدد أوليبقدر أقول بحاصل
+
+259
+00:29:00,370 --> 00:29:07,450
+ضرب S في T وفي المقابل S وT أصغر من أنه أكبر من
+
+260
+00:29:07,450 --> 00:29:15,010
+الواحد الصحيح مظبوط إيه الان أنا أدعي أنه ليس عددا
+
+261
+00:29:15,010 --> 00:29:20,730
+أولية مدام ليس عددا أولية إذا بقدر أحلله على صيغة
+
+262
+00:29:20,730 --> 00:29:26,390
+حاصل ضرب عددين الواحد فيهم أكبر من الواحد الصحيح
+
+263
+00:29:26,390 --> 00:29:36,380
+كل واحد فيهموأقل من N طيب الان يا بناتي ال N موجود
+
+264
+00:29:36,380 --> 00:29:44,880
+في ال NZ أكيد لأن
+
+265
+00:29:44,880 --> 00:29:49,700
+ال واحد موجود في ال Z إذا ال N بقدر أقول عليها N
+
+266
+00:29:49,700 --> 00:29:55,520
+وافي واحد يبقى صلة ال N موجود في ال NZ جيب جدش بده
+
+267
+00:29:55,520 --> 00:30:05,870
+يعطينا جدش ال Nالـ S T موجودة في الـ N Z يعني معنى
+
+268
+00:30:05,870 --> 00:30:16,450
+هذا الكلام ان الـ S T هتساوي N في Y مثلا for some
+
+269
+00:30:16,450 --> 00:30:24,970
+Y اللي موجودة في Z طيب، بدنا نجي تفسير رياضي لهذه
+
+270
+00:30:24,970 --> 00:30:34,600
+المعادلةأليست N تقسم ال S T؟ يبقى هنا ساعة ال N
+
+271
+00:30:34,600 --> 00:30:43,680
+divides ال S T هذا معناه ان ال N divides ال S or
+
+272
+00:30:43,680 --> 00:30:49,840
+ال N divides ال T شو رأيكوا الكلام؟ اه صح والله
+
+273
+00:30:51,470 --> 00:30:57,890
+غلط، غلط ليش؟ لإن هذا أقل من N كيف ال N اللي هو
+
+274
+00:30:57,890 --> 00:31:02,090
+الكبير بدي يقسم لصغير؟ هذا كلام غير مضطر، بس لو
+
+275
+00:31:02,090 --> 00:31:05,970
+كان العدد صغير ممكن أن يقسم عدد كبير، لكن العدد
+
+276
+00:31:05,970 --> 00:31:09,690
+الكبير يقسم العدد اللي أصغر منه؟ هذا كلام غير
+
+277
+00:31:09,690 --> 00:31:16,230
+وارد، إذا هذا كلام ما له؟ Impossible، هذا الكلام
+
+278
+00:31:16,230 --> 00:31:17,810
+Impossible
+
+279
+00:31:20,630 --> 00:31:26,990
+هذا كلام غير ممكن طيب شوفي بنفسك تقول الفرض الخطأ
+
+280
+00:31:26,990 --> 00:31:32,630
+ده وين جد؟ قولنا suppose not يعني افترض ان العدد
+
+281
+00:31:32,630 --> 00:31:39,350
+ان ما هوش prime قعدنا الى خطأ أيه؟ دي فرض دي صح
+
+282
+00:31:39,350 --> 00:31:47,090
+ولا غلط؟ غلط وعكسه هو الصحيح يبقى هنا ال .. ال ..
+
+283
+00:31:47,090 --> 00:31:49,090
+ال .. ال prime
+
+284
+00:31:53,180 --> 00:32:04,060
+طب ننتقل الان الى المثال الثاني رامبل تيك
+
+285
+00:32:04,060 --> 00:32:08,220
+مقول
+
+286
+00:32:08,220 --> 00:32:13,320
+FLR is an integral thing و الله قبل المثال الثاني
+
+287
+00:32:13,320 --> 00:32:17,900
+خديلك هالملاحظة Note that
+
+288
+00:32:25,350 --> 00:32:43,190
+هل يومنات الـ zero is a prime ideal in the ..
+
+289
+00:32:43,190 --> 00:32:48,990
+احنا بندعي هيك لكن كل ادعاء بده إيه؟ بده إثبات
+
+290
+00:32:48,990 --> 00:32:52,090
+يبقى بادي بقوله because
+
+291
+00:32:56,780 --> 00:33:06,560
+If الـ A و الـ B موجودة في الـ Z and حاصل ضربهما
+
+292
+00:33:06,560 --> 00:33:15,780
+الـ A في B موجود في الـ Zero طلع ماشي مع التعريف
+
+293
+00:33:15,780 --> 00:33:19,480
+بالضبط و الـ Zero proper لأنه أصغر من الـ ring
+
+294
+00:33:19,480 --> 00:33:21,320
+الأصلي اللي هو الـ Z
+
+295
+00:33:25,270 --> 00:33:30,730
+الـ A و B يبدو يساوي Zero لأنه مافيش فيه إلا عنصر
+
+296
+00:33:30,730 --> 00:33:35,310
+واحد هو العنصري الصفري طب الـ A و الـ B انتجارز
+
+297
+00:33:35,310 --> 00:33:41,970
+صح؟ هل يُعقل إنه حصل ضرب 2 انتجار يساوي Zero؟ ليه
+
+298
+00:33:41,970 --> 00:33:49,330
+معقول إلا إذا كان أحدهم يساوي Zero؟ يبقى هذا معناه
+
+299
+00:33:49,330 --> 00:33:58,440
+إن الـ A يبدو يساوي ZeroOr الـ B يبدو يساوي 0 صح ؟
+
+300
+00:33:58,440 --> 00:34:05,880
+طب لو كان ال A يساوي 0 إذا ال A موجود في ال 0 Or
+
+301
+00:34:05,880 --> 00:34:16,620
+ال B موجود في ال 6 اللي هي 0 انطبخ التعريف يبقى
+
+302
+00:34:16,620 --> 00:34:26,130
+صار ال 0 عبارة عن ال prime ideal in Zالـ zero is
+
+303
+00:34:26,130 --> 00:34:37,670
+prime ideal الست اللي عندنا هذه and Z طيب
+
+304
+00:34:37,670 --> 00:34:44,410
+Z هذه ring واحدة مافيش غيرها فلو روحنا و قولنا ..
+
+305
+00:34:44,410 --> 00:34:51,930
+قولنا بدنا ناخد أكثر من ring يعني ممكنالكلام هذا
+
+306
+00:34:51,930 --> 00:34:56,930
+يحصل لمجموعة من الرمز والله مافيش غير هذا الكلام
+
+307
+00:34:56,930 --> 00:35:04,350
+للـ Z هذا السؤال اللي بدنا نجاوز عليه بالمثال رقم
+
+308
+00:35:04,350 --> 00:35:14,670
+اتنين example اتنين يقول ما يتلف ال R is an
+
+309
+00:35:14,670 --> 00:35:18,570
+integral domain
+
+310
+00:35:20,700 --> 00:35:28,040
+لو كان الـR integral domain then الـ zero is a
+
+311
+00:35:28,040 --> 00:35:41,240
+prime ID is a prime ID of R solution
+
+312
+00:35:41,240 --> 00:35:46,180
+عندنا
+
+313
+00:35:46,180 --> 00:35:55,450
+R integral domain يبقى assumeأفترضه أن الـR is an
+
+314
+00:35:55,450 --> 00:36:03,310
+integral domain يعني مافيش فيها قواسم لصفر إلا
+
+315
+00:36:03,310 --> 00:36:11,570
+الصفر نفسه، مظبوط؟ طيب، بدي أخد عنصرين في R،
+
+316
+00:36:11,570 --> 00:36:16,990
+فهتحاصل ضربه موجود وين؟ في الـ0، يبقى بدالي أقوله
+
+317
+00:36:16,990 --> 00:36:26,220
+let الـA و الـBموجودات في R such that ال A في ال B
+
+318
+00:36:26,220 --> 00:36:35,860
+موجود في Zero يبقى then ال A في ال B بتساوي Zero
+
+319
+00:36:35,860 --> 00:36:44,120
+بقى وجود اغاناط هذا يعني ان ال A تساوي ZeroAll الـ
+
+320
+00:36:44,120 --> 00:36:49,720
+P تساوي Zero؟ طيب ليه؟ لأن الـ R Integral Domain
+
+321
+00:36:49,720 --> 00:36:55,240
+لو ماكنش Integral Domain كلامي هذا غلط تمام يبقى
+
+322
+00:36:55,240 --> 00:37:05,940
+هذا .. هذا because because الـ R is an Integral
+
+323
+00:37:05,940 --> 00:37:13,560
+Domain هذا الكلام صحيحلشان هذا integral الدولي
+
+324
+00:37:13,560 --> 00:37:21,260
+مدام هات هذا يعني ان ال a موجود في ال ideal اللي
+
+325
+00:37:21,260 --> 00:37:28,340
+هو ال zero او ال b موجود في ال zero هذا بدي
+
+326
+00:37:28,340 --> 00:37:39,560
+اعطيكوا ان ال zero is a prime ideal in R يبقى ايضا
+
+327
+00:37:39,560 --> 00:37:46,580
+صحيح انك شغلتينالشغل الأولى انه ال ideal zero هو
+
+328
+00:37:46,580 --> 00:37:51,080
+prime ideal في ال six of integers من الملاحظة اللي
+
+329
+00:37:51,080 --> 00:37:56,820
+هناك و بعد هيك كمان ال zero is a prime ideal في ال
+
+330
+00:37:56,820 --> 00:38:03,740
+integrant domain طيب بدنا نروح لك لمثال آخر تمام؟
+
+331
+00:38:03,740 --> 00:38:12,060
+و هذا يكون ثالثثلاثة بنات اللي هو سؤال خمس تاشر من
+
+332
+00:38:12,060 --> 00:38:27,860
+الكتاب بيقولت الـ A B A ring with unity in one if
+
+333
+00:38:27,860 --> 00:38:43,570
+ال A is an ideaلو كان ال A عبارة عن ID of R and ال
+
+334
+00:38:43,570 --> 00:38:53,690
+F الواحد موجود في ال A موجود في ال A then ال A
+
+335
+00:38:53,690 --> 00:39:00,730
+تساوي R سؤال
+
+336
+00:39:00,730 --> 00:39:08,220
+مرتينعندنا الـ ring of unity هي الواحد قال ال إيه
+
+337
+00:39:08,220 --> 00:39:13,280
+ال ideal؟ الواحد اللي هو ال unity موجود في ال
+
+338
+00:39:13,280 --> 00:39:19,140
+ideal فلإن حد دلوقتي يبقى ال ideal إيه؟ بده يسوي
+
+339
+00:39:19,140 --> 00:39:24,680
+ال ring كلها ال ring كلها؟ أه ال ring كلها طب
+
+340
+00:39:24,680 --> 00:39:29,150
+خليني أسأل سؤال في مبادئ الرياضياتكيف بجينا الناس
+
+341
+00:39:29,150 --> 00:39:37,630
+تثبت ان two sets are equal يعني كل واحدة فيهم
+
+342
+00:39:37,630 --> 00:39:41,990
+subset من التانية يعني في الاتجاهين ان حدث ذلك
+
+343
+00:39:41,990 --> 00:39:48,070
+بقول له two sets are equal طيب تمام يبقى solution
+
+344
+00:39:48,070 --> 00:39:55,450
+بدي اكتب اول معادلة و اشوف ايش رأيكوا فيها صح هذا
+
+345
+00:39:55,450 --> 00:40:05,590
+بناnon-ideally proper يعني أجال من R تمام يبقى هذه
+
+346
+00:40:05,590 --> 00:40:12,330
+المعادلة رقم واحد إذا كنت أثبت أنها subset من A
+
+347
+00:40:12,330 --> 00:40:16,350
+بكون جبت الاتجاه الثاني وبالثاني بصير ال A تساوي
+
+348
+00:40:16,350 --> 00:40:24,030
+مين؟ تساوي ال R طيب الآن بدي أقول خد لل R موجودة
+
+349
+00:40:24,030 --> 00:40:31,110
+في A عشوائيةلتحاول اثبت ان ال R هذه موجودة في ايه؟
+
+350
+00:40:31,110 --> 00:40:43,110
+موجودة في ايه؟ then ال R تساوم واحد في R، صح؟ طيب،
+
+351
+00:40:43,110 --> 00:40:53,010
+تساوم R في واحد، مظبوط؟ انا ادعي ان هذه موجودة في
+
+352
+00:40:53,010 --> 00:40:55,230
+ايه؟ اكيد؟
+
+353
+00:40:56,980 --> 00:41:00,800
+عشان ال I دي ال واحد عشان ال A ال واحد في A وال A
+
+354
+00:41:00,800 --> 00:41:05,940
+I دي يبقى لو جبت اي element من الأرض ضربته في هذا
+
+355
+00:41:05,940 --> 00:41:10,940
+الواحد بيكون موجود في A صح ولا لا؟ ممتاز جدا يبقى
+
+356
+00:41:10,940 --> 00:41:18,380
+هذا موجود في السبب because ان الواحد موجود في A
+
+357
+00:41:18,380 --> 00:41:28,560
+and ال A is an I Dطيب يبقى العلم الـ R اللي موجود
+
+358
+00:41:28,560 --> 00:41:34,940
+في R لقيته موجود وين؟ ايش تفسيركم لهذا الكلام؟ R
+
+359
+00:41:34,940 --> 00:41:44,680
+صبست من A يبقى هنا R صبست من A و هذه العناقة رقم 2
+
+360
+00:41:44,680 --> 00:41:54,720
+اروح بقوله هنا from واحد و اتنين we haveيبقى بده
+
+361
+00:41:54,720 --> 00:42:02,900
+يصير الـA تساوي A يبقى يا بنات من الآن فصاعدا لو
+
+362
+00:42:02,900 --> 00:42:08,560
+قدرت أثبت ان ال unity موجود في ال ideal يبقى ال
+
+363
+00:42:08,560 --> 00:42:13,100
+ideal بده يساوي مين؟ بده يساوي ال ring الأصلية
+
+364
+00:42:13,100 --> 00:42:21,180
+تمام تمام طيب هذا كان مثال ثلاثة بدنا نروح لمثال
+
+365
+00:42:21,180 --> 00:42:21,980
+أربع
+
+366
+00:42:25,420 --> 00:42:34,000
+مثال أربع نعطيكم مثال عادلين أعتقد أن هذا سهل
+
+367
+00:42:34,000 --> 00:42:43,440
+بالنسبة لكم لأن وقته مثل فيه الظروف طيب
+
+368
+00:42:43,440 --> 00:42:53,060
+المثال بيقول ما يعني يبقى example أربع بيقول ايه
+
+369
+00:42:53,060 --> 00:43:03,580
+little aمثل A تساوي Z ده اتناشى then the only
+
+370
+00:43:03,580 --> 00:43:14,320
+ideals then the only ideals ideals
+
+371
+00:43:14,320 --> 00:43:22,840
+of AA قالوا
+
+372
+00:43:22,840 --> 00:43:28,910
+لكم Z ده اتناشىفيها مجموعة من ال ideals بدنا
+
+373
+00:43:28,910 --> 00:43:37,130
+نعرفهم تقدروا تجيبولي أسفل الأتنين ال zero وين؟
+
+374
+00:43:37,130 --> 00:43:45,050
+و الأرض؟ صح مش هيجيل من نفسها يبقى هدول قدفة حاجة
+
+375
+00:43:45,050 --> 00:43:48,650
+اللي لازم كل واحد حتى لو ماجريش جبر يكون عارفه
+
+376
+00:43:48,650 --> 00:43:55,540
+يبقى هنا ال zero اللي هو ال trivial idealوزد اتناش
+
+377
+00:43:55,540 --> 00:44:02,440
+it's ال تمام ومين كمان ال principle ideal
+
+378
+00:44:02,440 --> 00:44:09,360
+generated by اتنين مين عناسره؟ Zero, اتنين, اربع,
+
+379
+00:44:09,540 --> 00:44:17,540
+ستة, تمانية, اهاشران كفي أليس هذا هو اتنين زد
+
+380
+00:44:17,540 --> 00:44:25,790
+اتناش؟ صح؟ طيبلو قلت ال principle ideal generated
+
+381
+00:44:25,790 --> 00:44:33,770
+by تلاتة، Zero، تلاتة، ستة، تسعة، أليس هو ال ideal
+
+382
+00:44:33,770 --> 00:44:42,590
+اللي هو تلاتة زي اتناش؟ طيب، الأربع ال principle
+
+383
+00:44:42,590 --> 00:44:50,820
+ideal generated by أربع اللي هو أربع زي اتناشالـ
+
+384
+00:44:50,820 --> 00:44:56,040
+principle ideal generated by ستة، Zero وستة، فيش
+
+385
+00:44:56,040 --> 00:45:04,760
+غيرهم؟ يبقى هذا ستة زد اتناش.في غيرهم؟ مش عارفين،
+
+386
+00:45:04,760 --> 00:45:11,540
+يمكن يكون فيه. يمكن يكون فيه الله أعلم.ش اسم كنت
+
+387
+00:45:11,540 --> 00:45:25,080
+قاعد؟ ملك اشطة رفعيبقى ملكتات داعي أنها لا تملك كل
+
+388
+00:45:25,080 --> 00:45:32,980
+هذه الـ Ideal على هذه الرنجة نشوف الموافقين على
+
+389
+00:45:32,980 --> 00:45:36,220
+رأيها، والله مش الموافقين تعالوا نشوف.
+
+390
+00:45:39,140 --> 00:45:43,780
+الآن أنا عند اتنين، تلاتة، اربعة، خمسة، مش اتنين،
+
+391
+00:45:43,780 --> 00:45:48,860
+تلاتة، اربعة، ستة، الخمسة مش موجودة.والسبعة مش
+
+392
+00:45:48,860 --> 00:45:53,460
+موجودة والتمانية والتسعة والعشرة كلهم مش موجودات
+
+393
+00:45:53,460 --> 00:45:57,540
+والاحداشة كمان مع ال principle ideal generated by
+
+394
+00:45:57,540 --> 00:46:04,420
+احداشة طبعا طيب يبقى اللي مش موجودات هدول بدهم
+
+395
+00:46:04,420 --> 00:46:10,880
+يساووا كل واحد اسئلة واحد من هاللي موجودة ولا لا
+
+396
+00:46:10,880 --> 00:46:17,100
+بس مش كل واحد هو البعض ليس بالضرورة الكل شوفوا كده
+
+397
+00:46:17,670 --> 00:46:27,510
+مثلا لو جيتك وقلت بدأ أخد عشرة زد اتناش عشرة زد
+
+398
+00:46:27,510 --> 00:46:32,350
+اتناش اللي مش موجودة هنا هذه بدها تساوي عشرة في
+
+399
+00:46:32,350 --> 00:46:38,950
+zero في zero عشرة في واحد يبقى عشرة عشرة في اتنين
+
+400
+00:46:38,950 --> 00:46:47,100
+تمامية ممتاز عشرة في تلاتةتلاتين، شيلي أربعة
+
+401
+00:46:47,100 --> 00:46:53,320
+وعشرين، بيظل ستة، عشرة في أربعة، بيظل اربعين،
+
+402
+00:46:53,320 --> 00:46:57,280
+تلاتة في اتناشر، بيظل ستة وتلاتين، بيظل اربعة،
+
+403
+00:46:57,280 --> 00:47:02,300
+عشرة في خمسة، بيظل خمسين، شيلي أربعة في اتناشر،
+
+404
+00:47:02,300 --> 00:47:13,020
+بيظل اتنين، عشرة في ستة، ستين، ستين، فلسنا، يبقى
+
+405
+00:47:13,020 --> 00:47:22,830
+رجالفيش غيرهم أليس هذا هو هذا حرفيا يبقى هذا بده
+
+406
+00:47:22,830 --> 00:47:32,290
+يساوي اتنين زي اتناش بنفس الطريقة هنا في عندنا من؟
+
+407
+00:47:32,290 --> 00:47:39,630
+في عندنا بالعشرة زي اتناش التمانية والتسعة زي
+
+408
+00:47:39,630 --> 00:47:47,570
+اتناش التسعة زي اتناشبدي ساوي تلاتة زد اتناش
+
+409
+00:47:47,570 --> 00:47:56,270
+وزيادة على ذلك and التمانية زد اتناش بدي ساوي
+
+410
+00:47:56,270 --> 00:48:05,070
+الأربعة زد اتناش يبقى هدول التسعة والتمانية مظهروش
+
+411
+00:48:05,070 --> 00:48:10,890
+إلي هنا لأنهم موجوداتهم مش داري هذا ال principle
+
+412
+00:48:10,890 --> 00:48:15,060
+ideal generated by أربعةوهذا ال principle ideal
+
+413
+00:48:15,060 --> 00:48:18,940
+generated by تلاتة وهذا ال principle ideal
+
+414
+00:48:18,940 --> 00:48:25,460
+generated by اتنين وحداشر
+
+415
+00:48:25,460 --> 00:48:37,280
+ماشي انا ادعي الان انا ادعي مياتي ان خمسة زي اتناش
+
+416
+00:48:37,280 --> 00:48:45,830
+تساوي سبعة زي اتناشتساوي 11 زد 12 تساوي زد 12
+
+417
+00:48:45,830 --> 00:48:50,830
+itself جاربعة ده الكل هم ال prize الخمسة و السبعة
+
+418
+00:48:50,830 --> 00:48:54,910
+و الأحداشر عدد أوليها اضرب في كل أنصر هيطلع عندك
+
+419
+00:48:54,910 --> 00:49:03,010
+مين؟ زد 12 itself تمام؟ إذا بدنا نروح نعمل شبكية
+
+420
+00:49:03,010 --> 00:49:11,550
+لبين لل ideals هدول اه يبقى هنا بروح بقولهThe
+
+421
+00:49:11,550 --> 00:49:26,010
+lattice of ideals in Z12 is ببدأ من ات اللي هو Z12
+
+422
+00:49:26,010 --> 00:49:34,450
+الول امام بدي اتفرع منها two ideals ال ideal الأول
+
+423
+00:49:34,450 --> 00:49:44,040
+اتنين Z12الأيديل التاني ثلاثة زد اتناش في بينهم
+
+424
+00:49:44,040 --> 00:49:53,020
+تقاطع و لا عنصر تمام؟ هذه بدي يجي منها مين؟ أربعة
+
+425
+00:49:53,020 --> 00:50:00,520
+زد اتناش لإن الأربعة زد اتناش صاب ست والأربعة زد
+
+426
+00:50:00,520 --> 00:50:08,220
+اتناش هي صاب ست من الاتنين تمام؟ هذه ستة زد اتناشو
+
+427
+00:50:08,220 --> 00:50:16,340
+هذه صبست من مين؟ ستة زد اتنين صبست من تلاتة هذه
+
+428
+00:50:16,340 --> 00:50:24,300
+الستة وهذه التلاتة مش عاجزاكم بس و ستة هذه صبست من
+
+429
+00:50:24,300 --> 00:50:33,520
+اتنين ولا لا؟ طيب هنا ال zero صبست من هذه و صبست
+
+430
+00:50:33,520 --> 00:50:39,540
+من هذه ولا لا؟يبقى هيه مننا شبكية لل sub-ideals
+
+431
+00:50:39,540 --> 00:50:43,720
+اللي عندنا تمام؟ كله يبقى هذي بيسميها اللي هي
+
+432
+00:50:43,720 --> 00:50:49,900
+lattice لل ideals ليزد اتناش السؤال هو وين ال
+
+433
+00:50:49,900 --> 00:50:59,000
+maximum ideal هنا؟ proper ولا يوجد اكبر منها اتنين
+
+434
+00:50:59,000 --> 00:51:05,110
+زد اتناش و تلاتة زد اتناشيبقى هنا بروح بقوله from
+
+435
+00:51:05,110 --> 00:51:17,330
+this lattice the maximum ideals
+
+436
+00:51:17,330 --> 00:51:30,410
+are اتنين زد اتناش and تلاتة زد اتناش ولا يوجد
+
+437
+00:51:30,410 --> 00:51:39,720
+غيرهم maximumطبعا؟ طيب سؤال الأخير وبيسألوني هذه
+
+438
+00:51:39,720 --> 00:51:47,720
+المحاضرة في واحد فيهم من ال ideals هدود اللي
+
+439
+00:51:47,720 --> 00:51:52,340
+تركناهم اللي هو الخمسة والسبعة والإحدى عشر بيكون
+
+440
+00:51:52,340 --> 00:51:58,680
+maximum ideal أو ال prime ideal السبعة
+
+441
+00:51:58,680 --> 00:52:03,450
+من الستة أنا بتكلم عن السبعةوالخمسة والإحدى عشر
+
+442
+00:52:03,450 --> 00:52:09,410
+زدها اتنين. هذا طبعا كله يستوي من ال ring الأصلي؟
+
+443
+00:52:09,410 --> 00:52:15,870
+إذا بنفع يكون ideal او maximal ideal؟ ليش ان الشرط
+
+444
+00:52:15,870 --> 00:52:21,690
+الأول لا يتحقق و هو انه proper ideal. لذا بروح
+
+445
+00:52:21,690 --> 00:52:34,640
+بقول not that. Not that ان خمسةزد اتناش وسبع زد
+
+446
+00:52:34,640 --> 00:52:49,260
+اتناش and احداشر زد اتناش are not a prime and not
+
+447
+00:52:49,260 --> 00:52:57,780
+maximal ideals
+
+448
+00:52:59,650 --> 00:53:06,110
+because they
+
+449
+00:53:06,110 --> 00:53:13,330
+are not
+
+450
+00:53:13,330 --> 00:53:22,310
+proper or because they are improper دعواتك كلها
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/rOLyumgAtE4_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/rOLyumgAtE4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..812752e27d497fddd08fc2e0a653e124395f6b86
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/rOLyumgAtE4_postprocess.srt
@@ -0,0 +1,1768 @@
+1
+00:00:21,130 --> 00:00:25,950
+بالله الرحمن الرحيم انتهينا الآن من ال three
+
+2
+00:00:25,950 --> 00:00:30,250
+chapters و الان نمشي لل chapter الرابع اللي بتحدث
+
+3
+00:00:30,250 --> 00:00:35,850
+عن ال ring homomorphism لنعطي تعريف لل ring
+
+4
+00:00:35,850 --> 00:00:40,770
+homomorphism و نشوف وجه الاختلاف بينه و بين ال
+
+5
+00:00:40,770 --> 00:00:47,030
+group homomorphism بقول لو عندى two rings R و S
+
+6
+00:00:47,350 --> 00:00:53,670
+وعندي Phi هي mapping من R إلى S يبقى الـ Phi بقول
+
+7
+00:00:53,670 --> 00:00:58,690
+عنها Ring Homomorphism كلمة Homomorphism هختصرها
+
+8
+00:00:58,690 --> 00:01:02,650
+خلال الكتابة إلى Homo يبقى الـ Phi بسميها
+
+9
+00:01:02,650 --> 00:01:08,090
+Homomorphism إذا كان لجميع عناصر A وB اللي موجودة
+
+10
+00:01:08,090 --> 00:01:13,350
+في R We have condition الأول Phi of A زائد B بساوي
+
+11
+00:01:13,350 --> 00:01:18,060
+Phi of A زائد Phi of Bوالـ Condition التاني Phi of
+
+12
+00:01:18,060 --> 00:01:25,120
+A في B بيكون Phi of A مضروب في Phi of B لجميع قيم
+
+13
+00:01:25,120 --> 00:01:32,320
+A وB الموجودة في R يبدأ إذا Phi حققت هذين الشرتين
+
+14
+00:01:32,320 --> 00:01:38,380
+بقول عن Phi Homomorphism إذا حصل زيادة على ذلك ما
+
+15
+00:01:38,380 --> 00:01:43,020
+هي هذه الزيادة؟ كانت الـ Function Phi هي one to
+
+16
+00:01:43,020 --> 00:01:50,340
+one and untoنبقى الخيب ده سميها isomorphism كلمة
+
+17
+00:01:50,340 --> 00:01:54,720
+homomorphism أخدتوها في ال groups وكان معناها
+
+18
+00:01:54,720 --> 00:02:01,920
+التشاكل لكن isomorphism التشاكل النماطي إيش يعني
+
+19
+00:02:01,920 --> 00:02:05,460
+التشاكل النماطي هي ترجمة عربية، عربية أنا بدي
+
+20
+00:02:05,460 --> 00:02:10,680
+المعنى الرياضي لها ف homomorphism في علاقة ما بين
+
+21
+00:02:10,680 --> 00:02:15,580
+ring و ring أخرىبتحقق الشرطين هذول أكتر من هيك
+
+22
+00:02:15,580 --> 00:02:20,360
+ماعنديش لكن إذا isomorphism يبقى عدد العناصر في ال
+
+23
+00:02:20,360 --> 00:02:24,640
+ring الأولى جد عدد العناصر في ال ring الثانية هنا
+
+24
+00:02:24,640 --> 00:02:32,060
+إذا فيها على سبيل المثال أربعة عناصر ال order اللي
+
+25
+00:02:32,060 --> 00:02:35,720
+يساوي خمسة يبقى هذه فيها أربعة عناصر ال order فيها
+
+26
+00:02:35,720 --> 00:02:39,620
+اللي يساوي خمسة إذا فيها هذه unity يبقى ال ring
+
+27
+00:02:39,620 --> 00:02:45,810
+التانية فيها unity وباختصارجميع الخواص على ال ring
+
+28
+00:02:45,810 --> 00:02:51,330
+الأولى لها مناظر جميع نفس الخواص على ال ring
+
+29
+00:02:51,330 --> 00:02:55,930
+الثاني هذا معنى ال isomorphism لكن رياضيا مشان
+
+30
+00:02:55,930 --> 00:03:00,110
+أثبت ذلك بدي أثبت ال two conditions اللي عندنا و
+
+31
+00:03:00,110 --> 00:03:05,230
+بدي أثبت ان five is one to one and unto بدي ناخد
+
+32
+00:03:05,230 --> 00:03:10,540
+مجموعة من الأمثلة على ذلكالمثال الأول قال اعرف لـ
+
+33
+00:03:10,540 --> 00:03:17,200
+Phi من Z إلى ZL By Phi of K يسوى K Modulo M الـ K
+
+34
+00:03:17,200 --> 00:03:22,840
+هذه موجودة وين؟ في الـ Z و K Modulo N موجودة في ZM
+
+35
+00:03:22,840 --> 00:03:27,400
+قال يبقى Phi في هذه الحالة is a homomorphism
+
+36
+00:03:27,400 --> 00:03:32,300
+because بدالي ال two conditions اللي عندنا هذول
+
+37
+00:03:32,300 --> 00:03:41,600
+أروح أشوفهم تفعل يبقى Phi ofبدأ ياخد K زائد ال M
+
+38
+00:03:41,600 --> 00:03:47,020
+مثلا حسب ال definition اللي احنا حاطينه يبقى K
+
+39
+00:03:47,020 --> 00:03:55,660
+زائد ال M موديولو مين؟ موديولو N هذا الكلام بده
+
+40
+00:03:55,660 --> 00:04:08,790
+ساوي K موديولو N زائد M M موديولو Nهذا هنا هو
+
+41
+00:04:08,790 --> 00:04:15,630
+عمارة من مين؟ Phi of K يبقى هذا بيطيني Phi of K و
+
+42
+00:04:15,630 --> 00:04:24,610
+هذا Phi of M الكلام هذا صحيح لكل K و M اللي موجودة
+
+43
+00:04:24,610 --> 00:04:29,750
+في set of integers اللي هي مين اللي هي Z اللي
+
+44
+00:04:29,750 --> 00:04:34,570
+عندنا لخطر أسأل سؤال قبل ما أروح أجيب ال condition
+
+45
+00:04:34,570 --> 00:04:40,480
+الثانيالزائد اللي عندنا يا بنات هي نفس الزائد هذه
+
+46
+00:04:40,480 --> 00:04:48,800
+نفسها تماما، نفس ال operation لأ بتخلف، بتخلف ليش؟
+
+47
+00:04:48,800 --> 00:04:55,320
+لإن الزائد هذه معرفة على مين؟ على ring Z يبقى هذا
+
+48
+00:04:55,320 --> 00:05:00,880
+جمع الأعداد الصحيحة العادية يعني جمعة the usual
+
+49
+00:05:00,880 --> 00:05:08,430
+additionلكن في Z إن الجمع هذا جمع modulo N يبقى ال
+
+50
+00:05:08,430 --> 00:05:13,270
+condition هذا بنات الجمع هذا غير الجمع هذا هذا
+
+51
+00:05:13,270 --> 00:05:19,370
+العملية المعرفة على Z أو على ال ring R وهذه
+
+52
+00:05:19,370 --> 00:05:23,250
+العملية الزائدة الجمع المعرفة على ال ring بين S
+
+53
+00:05:23,250 --> 00:05:28,990
+يبقى two are different operationsتنتهي المختلفات
+
+54
+00:05:28,990 --> 00:05:34,110
+تماما لكن ممكن يكون اتنين نفس الشيء إذا كان من ال
+
+55
+00:05:34,110 --> 00:05:38,890
+ring إلى نفسها إذا من ال ring إلى نفسها يبقى بيصير
+
+56
+00:05:38,890 --> 00:05:42,510
+نفس العملية مش نفس ال ring تاني يبقى الجامعه على
+
+57
+00:05:42,510 --> 00:05:45,550
+ال ring التاني بيختلف عن الجامعه عالميا على ال
+
+58
+00:05:45,550 --> 00:05:48,790
+ring الأولى و لا كده و نفس الكلام اللي قلته
+
+59
+00:05:48,790 --> 00:05:53,270
+بالنسبة لعملية الضرب يبقى لو راجعنا لل group كان
+
+60
+00:05:53,270 --> 00:05:57,490
+عندي ال condition واحد مافيش غير هذاإذا العملية
+
+61
+00:05:57,490 --> 00:06:02,510
+عملية ضرب أو إذا العملية عملية جمع لكن في ال ring
+
+62
+00:06:02,510 --> 00:06:08,290
+بديت two conditions في آن واحد ومن هنا زدنا شرط عن
+
+63
+00:06:08,290 --> 00:06:12,810
+ما كان في حالة نين في حالة ال groups زي ما ال ring
+
+64
+00:06:12,810 --> 00:06:17,470
+أعرفنا عليها two operations بس ال group كانت one
+
+65
+00:06:17,470 --> 00:06:21,730
+operation أو one binary operation طيب ال
+
+66
+00:06:21,730 --> 00:06:30,240
+conditioning التانيفاي of K في M حسب التعريف يبقى
+
+67
+00:06:30,240 --> 00:06:38,080
+K في M موديولو N من ال number three يبقى ده K
+
+68
+00:06:38,080 --> 00:06:48,300
+موديولو N مضروب في M موديولو N ال K موديولو N هي
+
+69
+00:06:48,300 --> 00:06:57,290
+ديمين فاي of Kوالتانية Phi of M صحيح هذا الكلام
+
+70
+00:06:57,290 --> 00:07:04,130
+لكل ال K و M اللي موجودة وين اللي موجودة في Z يبقى
+
+71
+00:07:04,130 --> 00:07:12,570
+NSA Phi is a homomorphism كما طلب مني واحد في
+
+72
+00:07:12,570 --> 00:07:19,370
+المثل هذا يعتبر مثال بصير ومباشر ومافيش فيه تفكير
+
+73
+00:07:19,930 --> 00:07:27,510
+ننتقل إلى مثال آخر example two بيقول define a
+
+74
+00:07:27,510 --> 00:07:34,190
+function define a function Phi من ال set of
+
+75
+00:07:34,190 --> 00:07:39,390
+complex numbers إلى ال set of complex numbers
+
+76
+00:07:39,390 --> 00:07:48,890
+نفسها by Phi of ال a زائد ال b في ال I يساوي ال a
+
+77
+00:07:49,210 --> 00:08:01,130
+نقص الـP في الـI then I is hearing isomorphism
+
+78
+00:08:01,130 --> 00:08:05,750
+كلمة
+
+79
+00:08:05,750 --> 00:08:12,170
+isomorphism هختصرها ISO ISO هحط نقطة يبقى تفهميني
+
+80
+00:08:12,170 --> 00:08:18,100
+ان هذا isomorphism يبقى عجلة عن homomorphismحقق ال
+
+81
+00:08:18,100 --> 00:08:23,820
+two conditions وزيادة على ذلك وانتوا وانتوا وانتوا
+
+82
+00:08:23,820 --> 00:08:26,880
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+83
+00:08:26,880 --> 00:08:27,760
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+84
+00:08:27,760 --> 00:08:28,760
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+85
+00:08:28,760 --> 00:08:30,460
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+86
+00:08:30,460 --> 00:08:31,220
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+87
+00:08:31,220 --> 00:08:36,880
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+88
+00:08:36,880 --> 00:08:45,880
+وانتوا
+
+89
+00:08:45,880 --> 00:08:53,850
+وانيبقى بقوله let الـA زائد الـBI والـC زائد الـDI
+
+90
+00:08:53,850 --> 00:09:00,810
+موجودة في set of complex numbers then بتاجر أخد
+
+91
+00:09:00,810 --> 00:09:10,010
+فايل مجموعهما A زائد BI زائد C زائد DI
+
+92
+00:09:12,270 --> 00:09:17,210
+هذا الكلام يُسبب حسب ال complex number إذا جمعنا
+
+93
+00:09:17,210 --> 00:09:23,290
+جزء الحقيقي مع الحقيقي والتخيّلي مع التخيّلي يبقى
+
+94
+00:09:23,290 --> 00:09:35,090
+هذا A زائد C الحقيقي زائد B زائد D في I يبقى هذا
+
+95
+00:09:35,090 --> 00:09:39,490
+صار كله element واحد في set of complex number
+
+96
+00:09:39,490 --> 00:09:43,870
+جمعنا two complex numberطالع عندي one complex
+
+97
+00:09:43,870 --> 00:09:50,750
+number بتطلع عليه تعريف تعريف بيقول ايه؟ five of a
+
+98
+00:09:50,750 --> 00:09:56,390
+زي ال bi يسوى ال a ناقص bi اللي بدأ أسأله، في حق
+
+99
+00:09:56,390 --> 00:10:01,790
+واحدة ضارس complex number؟ كلكم؟ و الله شغالين
+
+100
+00:10:01,790 --> 00:10:06,610
+الحين؟ ممتاز، اللي خدتها و اللي شغالها الحين ممتاز
+
+101
+00:10:06,610 --> 00:10:10,510
+يبقى خليني أسأل السؤال التالي، مدام أنتم ماخدينها
+
+102
+00:10:10,820 --> 00:10:16,040
+هذا العنصر ايش بسميه بالنسبة للعنصر هذا المرافق ال
+
+103
+00:10:16,040 --> 00:10:21,500
+conjugate المرافق تبع هذا العنصر يبقى if I لو أثرت
+
+104
+00:10:21,500 --> 00:10:27,280
+على عنصر بتعطيني مرافق هذا العنصر اللي هو كمان
+
+105
+00:10:27,280 --> 00:10:32,620
+element موجود في set of complex number طيب يبقى
+
+106
+00:10:32,620 --> 00:10:38,820
+الأن بتجه طبقا لهذا التعريف يبقى بقول الجزء
+
+107
+00:10:38,820 --> 00:10:50,370
+الحقيقيناقص الجزء التخيلي B زائد D كله في I هذا
+
+108
+00:10:50,370 --> 00:10:56,310
+بقدر اكتبه كمجموع two elements يبقى بقدر اقول هذا
+
+109
+00:10:56,310 --> 00:11:06,250
+A ناقص B I العنصر الأول زائد C ناقص D في I اللي هو
+
+110
+00:11:06,250 --> 00:11:11,590
+العنصر التالفيبقى هذا العنصر استطعت كتابته على
+
+111
+00:11:11,590 --> 00:11:16,110
+مجموع عنصرين بمعنى لو جمعنا هذول اتنين بتطلع مين؟
+
+112
+00:11:16,110 --> 00:11:23,770
+بتطلع الأول طيب هذا الكلام يساوي يساوي
+
+113
+00:11:23,770 --> 00:11:28,230
+يبقى هذا العنصر طيب العنصر الأول هذا من هو؟ Phi of
+
+114
+00:11:28,230 --> 00:11:36,930
+A زي بي I يبقى هذا أصبح Phi of A زي بي I والتاني
+
+115
+00:11:37,430 --> 00:11:45,130
+فاي او C زائد D I يتحقق ال condition الأول من ال
+
+116
+00:11:45,130 --> 00:11:49,550
+two conditions تبعات ال homomorphism نذهب لل
+
+117
+00:11:49,550 --> 00:11:58,810
+condition التاني N فاي او A زائد بي I مضروب في C
+
+118
+00:11:58,810 --> 00:12:06,840
+زائد D Iبدي أخليه عنصر واحد حتى أقدر أدخل الـ Phi
+
+119
+00:12:06,840 --> 00:12:11,100
+عليه لذلك بدي أروح أضرب ال two elements في بعض
+
+120
+00:12:11,100 --> 00:12:19,380
+يبقى هذا الكلام بدي أساوي Phi of A في C الآن تعالى
+
+121
+00:12:19,380 --> 00:12:26,140
+B في DU و I في I و I ترميله بسالب واحد يبقى سالب
+
+122
+00:12:26,140 --> 00:12:34,900
+BD هذا الجزء الحقيقيبنا نيجي للجزء التشيولى زائد
+
+123
+00:12:34,900 --> 00:12:44,260
+الامين A D زائد B C كله في الامين في ال I وهي
+
+124
+00:12:44,260 --> 00:12:52,660
+الفرق صار هذا كله اللى هو الجزء الحقيقي وهذا هو
+
+125
+00:12:52,660 --> 00:12:57,580
+الجزء التشيولى يبقى صورة هذا العصر هو الكنجج
+
+126
+00:12:57,580 --> 00:13:04,520
+التابعيجى ال conjugate التابع هو عبارة عن a c ناقص
+
+127
+00:13:04,520 --> 00:13:14,940
+b d كله ال conjugate ناقص ال a d زائد ال b c كله
+
+128
+00:13:14,940 --> 00:13:23,900
+في ال I تمام هذا الكلام يساوي هل بقدر اكتب العصر
+
+129
+00:13:23,900 --> 00:13:29,890
+هذاعلى صيغة حاصل ضرب two elements إن جدرنا بيكون
+
+130
+00:13:29,890 --> 00:13:35,210
+حلت مشكلتنا ما جدرنا بيكون المشكلة قاعدة طيب
+
+131
+00:13:35,210 --> 00:13:44,210
+اتطلعوا لهك هل هذا هو ايه ناقص ال D I مضروب في C
+
+132
+00:13:44,210 --> 00:13:52,570
+ناقص ال D I تعالوا نضرب هذول ما هم هذول هاي لا بس
+
+133
+00:13:52,570 --> 00:13:58,310
+هم السابقفالله هنا a c بالموجة بغيرها الآن سالف في
+
+134
+00:13:58,310 --> 00:14:04,030
+سالف الموجة بي في دي اي في اي بناقص واحد تبقى سالف
+
+135
+00:14:04,030 --> 00:14:10,270
+بي في دي اي تقرينا من هنا هذا الان اللي هو بي سي
+
+136
+00:14:10,270 --> 00:14:15,810
+بالسالف في اي وهذه اي دي بالسالف في اي يبقى كلام
+
+137
+00:14:15,810 --> 00:14:21,950
+مظبوط إذا ال element هذا حطيته على صيغة حاصل ضرب
+
+138
+00:14:21,950 --> 00:14:28,180
+two elementsالـ Element الأول هذا ال conjugate شو
+
+139
+00:14:28,180 --> 00:14:38,060
+أصله؟ Phi of A زائد B I يبقى Phi of A زائد B I
+
+140
+00:14:38,060 --> 00:14:46,140
+والتاني Phi of C زائد D I يبقى اتحقق ال condition
+
+141
+00:14:46,140 --> 00:14:54,050
+التاني صح؟ يبقى Phi is homomorphicيبقى there فوق
+
+142
+00:14:54,050 --> 00:15:03,710
+ولهذا الـ Phi is a homomorphism الآن بدالي الـ Phi
+
+143
+00:15:03,710 --> 00:15:13,450
+is on as if Phi is one to one one to one بدنا نثبت
+
+144
+00:15:13,450 --> 00:15:18,090
+صحة هذا الكلام مشان نثبت صحة هذا الكلام بدنا ناخد
+
+145
+00:15:18,090 --> 00:15:23,930
+عنصرينمختلفة انه اثبت ان صورهم مختلفة او العملية
+
+146
+00:15:23,930 --> 00:15:29,490
+العكسية بدي اخد صورتين متساويتين و اثبت ان اصلهم
+
+147
+00:15:29,490 --> 00:15:35,690
+متساويتين ان حدث ذلك يبقى مصير الفاي is one point
+
+148
+00:15:35,690 --> 00:15:44,850
+يبقى باجي بقوله SU افترض ان الفاي of A زائد ال BI
+
+149
+00:15:44,850 --> 00:15:52,340
+بدي ساوي الفاي of C زائد ال DFيبقى حتة صورتين
+
+150
+00:15:52,340 --> 00:15:58,800
+متساويتين إذا جدلت أثبت أن ال A زيدي ال B I يسوي C
+
+151
+00:15:58,800 --> 00:16:03,340
+زيدي ال D I مصير الفاي is one to one وخلصنا من
+
+152
+00:16:03,340 --> 00:16:08,300
+الموضوع بقول كويس طيب هذا ال element اللي أخدته
+
+153
+00:16:08,300 --> 00:16:13,040
+الصورة مش عبارة عن نتيجتها هو ال conjugate element
+
+154
+00:16:13,040 --> 00:16:20,130
+أه يبقى هذا معناه أن ال A ناقص B I بالزاويةوالـ
+
+155
+00:16:20,130 --> 00:16:27,610
+Conjugate لهذه اللي هو C ذات الـ D I خيار A ناقص D
+
+156
+00:16:27,610 --> 00:16:34,350
+I A C ناقص D I كمان درسنا في ال complex لما يكون
+
+157
+00:16:34,350 --> 00:16:38,290
+complex number بيسوي complex number يبقى الجزء
+
+158
+00:16:38,290 --> 00:16:43,310
+الحقيقي بيسوي الجزء الحقيقي والتخيلي بيسوي التخيلي
+
+159
+00:16:43,310 --> 00:16:49,840
+إذا بناء عليه بقدر أقول ال A بيسوي ال Cوفي نفس
+
+160
+00:16:49,840 --> 00:16:58,260
+الوقت السالب B بدر يساوي سالب D يبقى هذا معناه ان
+
+161
+00:16:58,260 --> 00:17:05,740
+ال A بدر يساوي CL لو ضربت هنا في سالب 1 بصير ال B
+
+162
+00:17:05,740 --> 00:17:12,800
+بدر يساوي من ال D هذا معناه ان ال A زائد ال B I
+
+163
+00:17:12,800 --> 00:17:21,500
+يساوي ال A من هنا Cيبقى C والـ B من هنا D I وهو
+
+164
+00:17:21,500 --> 00:17:27,180
+المطلوب يبقى خات صوتين متساويتين طلع ان الاصل
+
+165
+00:17:27,180 --> 00:17:33,180
+تبعهم هي متساوي مش هانهيك الـ Phi is one to one.
+
+166
+00:17:33,880 --> 00:17:39,180
+هذا مباشر Direct Pro.يعني لا فيه لا لف ولا دوران
+
+167
+00:17:39,180 --> 00:17:44,020
+ولا فكرة. الآن بدنا نيجي لمين؟ لـ Phi is one to
+
+168
+00:17:44,020 --> 00:17:53,210
+one.يبقى في is on to ليش يعني معناه في is on to
+
+169
+00:17:53,210 --> 00:17:59,510
+بعلم الرياضية التابعنا بالبلد هيك الدول العربية
+
+170
+00:17:59,510 --> 00:18:06,430
+بقول في is on to يعني في دالة فوقية او اقتران فوقي
+
+171
+00:18:06,430 --> 00:18:12,330
+ايش يعني اقتران فوقي يعني غطى جميع أنصر ال code
+
+172
+00:18:12,330 --> 00:18:18,560
+domainيعني الـ Range هو الـ Codomain بالضبط تماماً
+
+173
+00:18:18,560 --> 00:18:23,480
+طب مشان أثبت أن الـ Phi is on to بتروح أخد Element
+
+174
+00:18:23,480 --> 00:18:30,140
+من الـ Codomain عشوائي و أثبت أنه أصل في ال domain
+
+175
+00:18:30,140 --> 00:18:35,860
+إن حدث ذلك يبقى Phi بصير on to يبقى إحنا عندنا Phi
+
+176
+00:18:35,860 --> 00:18:42,490
+من C إلى C بتاخد أي Element في ال Codomainو حاول
+
+177
+00:18:42,490 --> 00:18:48,210
+أثبت إنه إله أصل في ال domain إن جدرنا خلاص بصير
+
+178
+00:18:48,210 --> 00:18:53,870
+ال five as one و بالتالي ال five بصير isomorphism
+
+179
+00:18:53,870 --> 00:19:03,290
+طيب بداجي أقوله الآن ال a زائد ال bi موجود في ال
+
+180
+00:19:03,290 --> 00:19:08,830
+code من الوست of complex numbers هذا بده يعطينا
+
+181
+00:19:08,830 --> 00:19:19,140
+مين؟إن الـ A زائد ال V عارف ممكن أكتبه بطريقة أخرى
+
+182
+00:19:19,140 --> 00:19:27,680
+و هي ال A سالب سالب V عارف سالب في سالب الوجه دي
+
+183
+00:19:27,680 --> 00:19:34,140
+احنا ماسويناش اشي طيب لو رجعت لset of complex
+
+184
+00:19:34,140 --> 00:19:40,760
+numberالـA والـB الـreal number صح ولا لأ يبقى
+
+185
+00:19:40,760 --> 00:19:45,780
+السلب موجود والموجب موجود ماعنده مشكلة إذا هذا
+
+186
+00:19:45,780 --> 00:19:52,620
+element سلب هذا يبقى هذا conjugateت لمن ل element
+
+187
+00:19:52,620 --> 00:19:59,880
+تاني صح ولا لأ يعني هذا ههه هو عبارة عن صورة من
+
+188
+00:19:59,880 --> 00:20:09,160
+صورة الـA الذات الناقص بيه في الأرضأه حسب ال
+
+189
+00:20:09,160 --> 00:20:12,420
+definition اللي احنا كاتبينه Phi of ال element
+
+190
+00:20:12,420 --> 00:20:16,980
+يسوى ال conjugate طيب انا بد ال conjugate لهذا ال
+
+191
+00:20:16,980 --> 00:20:20,200
+conjugate لهذا ان الإشارة اللي يبقى number كلها
+
+192
+00:20:20,200 --> 00:20:26,760
+لها بالزائد يبقى هذا الكلام اللي هو Phi of ال a
+
+193
+00:20:26,760 --> 00:20:33,900
+ناقص بيه في ال R يبقى اي element موجود في set of
+
+194
+00:20:33,900 --> 00:20:39,450
+complex numbersاللي جاتله أصل في ال set of complex
+
+195
+00:20:39,450 --> 00:20:47,150
+numbers هو a ناقص bi طيب لو أخدت ال a ناقص bi
+
+196
+00:20:47,150 --> 00:20:53,290
+هيطلع a زائد bi اللي هو ال phi of a زائد bi يبقى
+
+197
+00:20:53,290 --> 00:20:57,390
+احنا بي كانت موجب والله سالبي بالتمنيش element
+
+198
+00:20:57,390 --> 00:21:03,630
+موجب سالب سفر كله صحيح عندي تمامإذا بناء عليه صارت
+
+199
+00:21:03,630 --> 00:21:07,690
+الـ Phi is onto لإن ال element اللي موجود في ال
+
+200
+00:21:07,690 --> 00:21:12,490
+set of complex number لاجت له أصل في ال set of
+
+201
+00:21:12,490 --> 00:21:17,070
+complex number يبقى أي element في ال set of
+
+202
+00:21:17,070 --> 00:21:21,050
+complex number له أصل في ال set of complex number
+
+203
+00:21:21,050 --> 00:21:25,130
+يبقى Phi is onto يبقى Phi حققت ال two conditions
+
+204
+00:21:25,130 --> 00:21:29,850
+تبع ال homomorphism حققت ال one to oneحققت اللي
+
+205
+00:21:29,850 --> 00:21:39,230
+انتوا يبقى فاي isomorphism يبقى هنا فاي is an
+
+206
+00:21:39,230 --> 00:21:46,430
+isomorphism هذا هو المثال الثاني نروح للمثال
+
+207
+00:21:46,430 --> 00:21:53,390
+الثالث مثل رقم تلاتة بيقول define a map او a
+
+208
+00:21:53,390 --> 00:22:03,660
+function define a functionمن الـ set of all
+
+209
+00:22:03,660 --> 00:22:11,900
+polynomials with real coefficients لمين للأربعة by
+
+210
+00:22:11,900 --> 00:22:22,280
+فاي of ال F of X بالدي ساوي ال F of 1 show
+
+211
+00:22:22,280 --> 00:22:32,210
+that ان الفاي isفي homomorphism
+
+212
+00:22:32,210 --> 00:22:43,610
+Phi is homomorphism but not isomorphism لنثبت أن
+
+213
+00:22:43,610 --> 00:22:51,630
+هذه homomorphism لكنها ليست في الحقيقة isomorphism
+
+214
+00:22:51,630 --> 00:22:58,730
+يبقى يكفيني إيش؟ أني أثبت أنها homomorphismnot one
+
+215
+00:22:58,730 --> 00:23:02,890
+to one او not one to one او واحد من اتنين ليس
+
+216
+00:23:02,890 --> 00:23:07,550
+بالضرورة لكي تكون مهياش ايزو مورفزن لا تريد السبع
+
+217
+00:23:07,550 --> 00:23:11,610
+دي تلو conditions يكشيني ميه ايه اللي تقدر عليه
+
+218
+00:23:11,610 --> 00:23:15,190
+اثبت انه ماهياش one to one خلاص كفى الله المؤمنين
+
+219
+00:23:15,190 --> 00:23:19,430
+القتال اثبت ماهياش one to one يبقى خلاص أي واحدة
+
+220
+00:23:19,430 --> 00:23:27,090
+فيهم طيب الحلقة التالية solutionخلّينا نشوف
+
+221
+00:23:27,090 --> 00:23:33,170
+تعريفنا هذا معقول ولا لأ؟ هنا الـ functions كلها
+
+222
+00:23:33,170 --> 00:23:37,510
+polynomial with real coefficients يبقى ال F of X
+
+223
+00:23:37,510 --> 00:23:44,330
+أي polynomial كودية صورتها مين؟ F of 1 فعطيني رقم،
+
+224
+00:23:44,330 --> 00:23:49,050
+real number، صح؟ موجود وين؟ موجود في أرض التعريف
+
+225
+00:23:49,050 --> 00:23:53,670
+هذا مافي مشكلة، تعريفنا سليم، أخدت ال من ال domain
+
+226
+00:23:53,990 --> 00:23:59,730
+لقيت له صورة في ال code من يبقى function تمام طيب
+
+227
+00:23:59,730 --> 00:24:03,930
+الان هو قال لي function يعني انا مش لازم اللي اروح
+
+228
+00:24:03,930 --> 00:24:07,910
+ابحث هل هي function ولا ما هي function يبقى هو
+
+229
+00:24:07,910 --> 00:24:11,870
+اعطاني وقال لي slim هاي ها دي function عندك بس شوف
+
+230
+00:24:11,870 --> 00:24:17,990
+حالي homomorphism او isomorphism ام لا يبقى
+
+231
+00:24:17,990 --> 00:24:25,990
+بالدقاق ياخد الان file او fالـ F في الـ F of X
+
+232
+00:24:25,990 --> 00:24:29,030
+والـ
+
+233
+00:24:29,030 --> 00:24:38,670
+G of X موجودات في الـ R of X Then بتاخد تأثير الـ
+
+234
+00:24:38,670 --> 00:24:47,590
+Phi على مجموعهما F of X زائد الـ G of X نرجع للـ
+
+235
+00:24:47,590 --> 00:24:55,650
+Calculus أليس هذا يا بنات Phif زائد g كله تأثير
+
+236
+00:24:55,650 --> 00:25:01,210
+على x وهو هذا تعريف مجموعة functions في ال
+
+237
+00:25:01,210 --> 00:25:08,070
+calculus هذا الكلام يساوي يبقى احنا هنا صار ان
+
+238
+00:25:08,070 --> 00:25:14,130
+مجموعة functions هي function جديدة وكأن هذه كلها
+
+239
+00:25:14,130 --> 00:25:20,590
+function جديدة يبقى صورة تميل بدأت تكون f زائد g
+
+240
+00:25:20,660 --> 00:25:27,360
+الـ g كله as a function of one برجه نرجع لل
+
+241
+00:25:27,360 --> 00:25:34,240
+calculus يبقى هذه f of one زائد ال g of one ال f
+
+242
+00:25:34,240 --> 00:25:43,980
+of one يبقى هي فاي لل f of x زائد الفاي لل g of x
+
+243
+00:25:43,980 --> 00:25:49,060
+إذا انت حقق من ال condition الأول بده أروح لل
+
+244
+00:25:49,060 --> 00:25:58,950
+condition التانيفاية الـ F of X مضروبة في الـ G of
+
+245
+00:25:58,950 --> 00:26:04,330
+X نرجع للكلكله ثانية تعرف حاصل ضرب to function
+
+246
+00:26:04,330 --> 00:26:11,630
+يبقى فاية للـ F مضروبة في G as a function of X
+
+247
+00:26:11,630 --> 00:26:19,010
+يبقى حاصل الضرب نتج عند اقتران جديد او دالة جديدة
+
+248
+00:26:19,410 --> 00:26:26,110
+كلها دالة واحدة فاي للدالة هذه تأثيرها على X يساوي
+
+249
+00:26:26,110 --> 00:26:32,570
+بهذه الدالة تأثيرها على الواحد يبقى بده يساوي FG
+
+250
+00:26:32,570 --> 00:26:38,310
+of one حسب ال definition اللي فوق يبقى هذا الكلام
+
+251
+00:26:38,310 --> 00:26:44,790
+بده يساوي ال F of one في ال G of one ال F of one
+
+252
+00:26:45,230 --> 00:26:55,390
+هذه فاي لل F of X وهذه فاي لل G of X إذا انتحقق
+
+253
+00:26:55,390 --> 00:27:06,810
+الشرطان يبقى هنا So فاي is a homomorphism قال اثبت
+
+254
+00:27:06,810 --> 00:27:13,890
+انها homomorphism لكنها ليستإذا أثبتنا إن فاي is
+
+255
+00:27:13,890 --> 00:27:20,590
+not one to one تكون خلصنا من الموضوع إذا بيدروح
+
+256
+00:27:20,590 --> 00:27:28,690
+أخد عمصرين مختلفين و أثبت إن صورهم مختلفة يا إما
+
+257
+00:27:28,690 --> 00:27:34,950
+أو صورهم مختلفة مشان أثبتينها one to one إذا أنا
+
+258
+00:27:34,950 --> 00:27:42,510
+بقول not one to oneبتاخد عمصرين مختلفين بدي أثبت
+
+259
+00:27:42,510 --> 00:27:50,130
+أن صورهم متساوية أو بتاخد صورتين متساويتين و أثبت
+
+260
+00:27:50,130 --> 00:27:58,010
+أن أصلهم غير متساوي، مظبوط؟ طيب، يبقى الأن أنا
+
+261
+00:27:58,010 --> 00:28:03,050
+أزعم أن الـ5 is not one to one بتاخد عمصرين
+
+262
+00:28:03,050 --> 00:28:10,780
+مختلفين في من؟ في R of Xيبقى ماجي بقوله يعني كأنه
+
+263
+00:28:10,780 --> 00:28:16,500
+بدي أخد counter example يبقى لو روحته قولله خد لل
+
+264
+00:28:16,500 --> 00:28:28,940
+F of X مثلا يساوي ال X تكييب زائد مثلا واحد and ال
+
+265
+00:28:28,940 --> 00:28:36,620
+G of X يساوي ال X زائد واحد هل هدون اتنين متساوية؟
+
+266
+00:28:36,620 --> 00:28:41,660
+لأthen ال
+
+267
+00:28:41,660 --> 00:28:53,620
+F of X لا يساوي ال G of X بياخد عنصرين مختلفين but
+
+268
+00:28:53,620 --> 00:29:01,660
+ولكن ال F of واحد كده شو بتساوي يا ابنها؟ F of
+
+269
+00:29:01,660 --> 00:29:09,560
+واحد نهت و G of واحديعني طلع صورتين متساويتين، صح؟
+
+270
+00:29:09,560 --> 00:29:17,600
+يبقى F of واحد تساوي G of واحد يساوي اتنين، يبقى
+
+271
+00:29:17,600 --> 00:29:27,260
+عنصران مختلفان صورتان متساويتين، بنت هيكون one to
+
+272
+00:29:27,260 --> 00:29:34,800
+one؟ لأ، يبقى هذا بده يعطينا ان five is not one to
+
+273
+00:29:34,800 --> 00:29:45,140
+oneمشان هيك So Phi is not an isomorphism كنت عاش
+
+274
+00:29:45,140 --> 00:29:50,980
+أكون Phi isomorphism أروح للشرط الراجل؟ مش داعي
+
+275
+00:29:50,980 --> 00:29:55,820
+خمسين فالمية من الشروط ماظبطتش يبقى خلاص مش داعي
+
+276
+00:29:55,820 --> 00:30:02,080
+أروح لمين للباقي يبقى هذا كده مثال رقم تلاتة مثال
+
+277
+00:30:02,080 --> 00:30:13,330
+رقم أربعاربعة بيقولش show that show that بيقوللي
+
+278
+00:30:13,330 --> 00:30:27,910
+انه قال من من z أربعة الى z عشرة defined by
+
+279
+00:30:27,910 --> 00:30:39,970
+defined by والمعرفة ديfive of x يساوي خمسة x
+
+280
+00:30:39,970 --> 00:30:50,890
+موديولو عشرة is a ring homomorphism is a ring
+
+281
+00:30:50,890 --> 00:30:58,030
+homomorphism
+
+282
+00:30:58,030 --> 00:31:10,920
+but ولكنها not an isomorphismبقى منها isomorphism
+
+283
+00:31:10,920 --> 00:31:21,100
+ولكنها ليست isomorphism solution الجسال
+
+284
+00:31:21,100 --> 00:31:25,440
+اللي جامله أتفتنى homomorphism لكنها ليست
+
+285
+00:31:25,440 --> 00:31:30,120
+isomorphism هذا بنفس الطريقة بدي أثبت أن نفس ال
+
+286
+00:31:30,120 --> 00:31:35,530
+file معرفة هذه عبارة عن homomorphismلكنها ليست
+
+287
+00:31:35,530 --> 00:31:41,030
+isomorphism سؤال انت درست وجبار حديث واحد مع
+
+288
+00:31:41,030 --> 00:31:47,010
+الدكتور محمد صح؟ صح لما كنت بعرف ال co-function من
+
+289
+00:31:47,010 --> 00:31:53,870
+ال group مثلا Zn إلى Zmمش الخطوة الأولى بتثبتلكوا
+
+290
+00:31:53,870 --> 00:31:58,430
+أنه Phi is well defined و بعدين بروح يثبت هذا
+
+291
+00:31:58,430 --> 00:32:03,430
+الكلام مظبط إذا إحنا هنا بنفس الطريقة بدنا نثبت
+
+292
+00:32:03,430 --> 00:32:08,050
+أنه Phi is well defined إيش يعني well defined من
+
+293
+00:32:08,050 --> 00:32:14,590
+الناحية الرياضية يعني بدي أخد عنصرين متساوين من ال
+
+294
+00:32:14,590 --> 00:32:20,590
+ring الأولى أثبت أنه الصورتين متساويتين في ال ring
+
+295
+00:32:20,590 --> 00:32:24,850
+الثانيةيعني عكس مين؟ عكس ال one to one ال one to
+
+296
+00:32:24,850 --> 00:32:28,970
+one باخد صورتين متساويتين بثبت أنه أصل متساوي، لأ
+
+297
+00:32:28,970 --> 00:32:34,250
+هذي بدي أخد عنصرين في الأصل متساويتين لأثبت أن
+
+298
+00:32:34,250 --> 00:32:40,970
+صورتهم متساوية، إن حدث ذلك يبقى بقوله five is well
+
+299
+00:32:40,970 --> 00:32:45,950
+defined يبقى وين ما تشوفي two rings بهذا الشكل
+
+300
+00:32:45,950 --> 00:32:50,820
+الخطوة الأولى تثبت أنه five is well definedيبقى
+
+301
+00:32:50,820 --> 00:32:59,980
+باجب أقولهم Phi is well defined يعني Phi معظفة
+
+302
+00:32:59,980 --> 00:33:06,220
+تعريفها مصحية لذلك بدي أجيب و أقولك افترضي ان عندي
+
+303
+00:33:06,220 --> 00:33:17,540
+عنصرين ال X modulo 4 بدي ساوي ال Y modulo 4 تمام؟
+
+304
+00:33:17,540 --> 00:33:25,820
+طيب هذا معناه مين؟معناته ان ال X ناقص ال Y كل
+
+305
+00:33:25,820 --> 00:33:31,600
+موديوله أربعة بده يساوي ال Zero موديوله أربعة
+
+306
+00:33:31,600 --> 00:33:44,040
+مظبوط هيك؟ طيب هذا معناه ان ال X ناقص ال Y يساوي
+
+307
+00:33:44,040 --> 00:33:53,790
+مضاعفات الأربعةيبقى هذا أربعة K و ال K هذه موجودة
+
+308
+00:33:53,790 --> 00:34:03,790
+في Z طب أنا بدي أوصل للصور شو الصور F of X يسوى
+
+309
+00:34:03,790 --> 00:34:12,750
+خمسة X تمام؟ إذا لو روحت ضربت في خمسة بنفع؟ بنفع
+
+310
+00:34:12,750 --> 00:34:17,680
+ليش ماينفع؟ عشان عندك معادلة رياضية بضرب في خمسةلو
+
+311
+00:34:17,680 --> 00:34:25,100
+ضربنا فيه خمسة بيصير خمسة K X ناقص Y يسوى خمسة في
+
+312
+00:34:25,100 --> 00:34:33,160
+أربعة K طيب بدي أشتغل في Z عشرة فبقول له يبقى هذه
+
+313
+00:34:33,160 --> 00:34:43,400
+خمسة X ناقص خمسة Y موديولو عشرة تسوى عشرين K
+
+314
+00:34:43,400 --> 00:34:51,550
+موديولو عشرةكداش الـ 20K في mod في Z عشرة Zero
+
+315
+00:34:51,550 --> 00:35:02,330
+يبقى هذا الكلام بده ساوي Zero mod 10 يبقى هذه بصير
+
+316
+00:35:02,330 --> 00:35:13,990
+خمسة X mod 10 ناقص خمسة Y mod 10 بده ساوي Zero mod
+
+317
+00:35:13,990 --> 00:35:25,760
+10يبقى هذه كإن الخمسة X Modulo عشرة متساوي خمسة Y
+
+318
+00:35:25,760 --> 00:35:32,540
+Modulo عشرة يعني إيش ال Phi of X متساوي Phi of Y
+
+319
+00:35:32,540 --> 00:35:41,560
+يبقى هذا معناه إن ال Phi of X متساوي Phi of Y لذلك
+
+320
+00:35:41,560 --> 00:35:50,620
+أخدت عنصرين متساويينإثبت إن صورتهم متساوية صورة
+
+321
+00:35:50,620 --> 00:35:55,860
+الأول هي نفس صورة التاني لذلك الدالة معرفة تعريفا
+
+322
+00:35:55,860 --> 00:36:01,820
+سليما ماحدش إله أي ممسك عليها الآن بدي أخش في
+
+323
+00:36:01,820 --> 00:36:09,700
+الموضوع التبعنا بقول لهم Phi is a homomorphism بدي
+
+324
+00:36:09,700 --> 00:36:17,510
+أخد عنصرين موجودين وين في Z أربعإن لو جيت قلت له
+
+325
+00:36:17,510 --> 00:36:29,090
+لأ X وY موجودة في Z أربع then الـ Phi of X زائد ال
+
+326
+00:36:29,090 --> 00:36:36,230
+Y حسب ال definition اللي احنا كاتبينه هذا بده يسوى
+
+327
+00:36:36,230 --> 00:36:44,990
+خمسة في X زائد ال Y موديول و عشر هذا بده يسوى يا
+
+328
+00:36:44,990 --> 00:36:53,770
+بناتالو خمسة X زائد خمسة Y موديولو عشرة هذا بده
+
+329
+00:36:53,770 --> 00:37:04,170
+يسوى خمسة X موديولو عشرة زائد خمسة Y موديولو عشرة
+
+330
+00:37:04,170 --> 00:37:10,330
+هذا بده يسوى من أوله لمن؟ Phi of X والتاني يبقى
+
+331
+00:37:10,330 --> 00:37:19,170
+هذا Phi of Xزائد Phi of Y إذا انتحقق الشرط الأول
+
+332
+00:37:19,170 --> 00:37:25,530
+من شروط ال homomorphism وهو Phi of X زائد Y بسوية
+
+333
+00:37:25,530 --> 00:37:32,370
+Phi of X زائد Phi of Y إذا روحنا مين للشرط الثاني
+
+334
+00:37:32,370 --> 00:37:39,310
+Phi of
+
+335
+00:37:39,310 --> 00:37:49,130
+X Y حسب ال definitionيساوي خمسة X Modulo عشرة.
+
+336
+00:37:49,630 --> 00:37:50,890
+Modulo عشرة.
+
+337
+00:37:53,730 --> 00:38:01,650
+طبعا؟ يعني هذا خمسة X Modulo عشرة في Y Modulo
+
+338
+00:38:01,650 --> 00:38:10,070
+عشرة. يبقى not homomorphism ولا لا؟ أكيد؟
+
+339
+00:38:10,070 --> 00:38:11,530
+قولوا غيره يا بنات
+
+340
+00:38:16,140 --> 00:38:21,740
+ولو كده كمان خمسة يعني لو بدل الخمسة كانت خمسة
+
+341
+00:38:21,740 --> 00:38:26,720
+وعشرين كان ماشي بتقوم ورا. مظبوط؟ بقدروا خمسة X في
+
+342
+00:38:26,720 --> 00:38:31,980
+خمسة Y. صح؟ طب هو الخمسة وعشرين في زيد عشرة في
+
+343
+00:38:31,980 --> 00:38:39,940
+كتير. خمسة يعني هذه بيضبط هي نفسهااللي هو خمسة
+
+344
+00:38:39,940 --> 00:38:47,580
+وعشرين XY موديولو عشر لإن الخمسة وعشرين في زد عشرة
+
+345
+00:38:47,580 --> 00:38:52,880
+هي خمسة اللي هي هذه لأن هذه هي هذه بالضبط تماما
+
+346
+00:38:52,880 --> 00:39:02,060
+إذا بقدر أقول هذه هي خمسة X موديولو عشرة مضروبة في
+
+347
+00:39:02,060 --> 00:39:10,720
+خمسة Y موديولو عشر مظبوط إيه؟يعني هذه Phi of X في
+
+348
+00:39:10,720 --> 00:39:16,520
+Phi of Y هذه بس النقطة اللي كانت لغز في السؤال
+
+349
+00:39:16,520 --> 00:39:21,280
+والباقي الشغل مباشرة يعني هذه اللي فيها تفكير بسيط
+
+350
+00:39:21,280 --> 00:39:25,180
+كيف أطلع من المطابق اللي أنا وقالتيه لإنه قاللي
+
+351
+00:39:25,180 --> 00:39:29,280
+أثبتلي إنه هذه عبارة عن homomorphism يبقى رصد من
+
+352
+00:39:29,280 --> 00:39:33,020
+أنا وعنك بدأتكون homomorphism لإنه قاللي أثبتها
+
+353
+00:39:33,020 --> 00:39:37,310
+يعني بقوله لا أثبتها بقولش إن أنا أثبتهايبقى هنا
+
+354
+00:39:37,310 --> 00:39:45,130
+اثبت انها homomorphic يبقى هنا فاي از هي
+
+355
+00:39:45,130 --> 00:39:55,350
+homomorphic طيب قالتلي انها ماهي ايزو مارفيزيك
+
+356
+00:39:55,350 --> 00:40:02,450
+قلتلتلي طيب اثبتوا ان فاي ماهي اش وان دور يبقى
+
+357
+00:40:02,450 --> 00:40:10,840
+بقوله فاي ازنقص one to one بكفي نجيب
+
+358
+00:40:10,840 --> 00:40:16,660
+counterexample كيف؟ الهي لو سألتك قداش five of
+
+359
+00:40:16,660 --> 00:40:24,680
+zero zero مضيوله عشرة zero مضيوله عشرة و لو سألتك
+
+360
+00:40:24,680 --> 00:40:35,140
+قداش five of اتنين اتنين في خمسة عشرة في زد عشرة
+
+361
+00:40:35,620 --> 00:40:44,880
+zero يبقى هذه بدها تساوي عشرة modulo عشرة يعني
+
+362
+00:40:44,880 --> 00:40:51,920
+zero modulo عشرة يبقى معنى هذا الكلام ان ال five
+
+363
+00:40:51,920 --> 00:40:59,700
+or zero يساوي ال five of اتنين هاي صوتين متساويتين
+
+364
+00:40:59,700 --> 00:41:07,620
+butليه اتنين بتسويش زيرو او زيرو بتسويش اتنين يبقى
+
+365
+00:41:07,620 --> 00:41:15,100
+five is not one to one يبقى five is not on
+
+366
+00:41:15,100 --> 00:41:20,100
+isomorphism طب لو واحدة حابة تثبت انه five is not
+
+367
+00:41:20,100 --> 00:41:25,300
+on يعني انت في السؤال اللي فات اثبت انه five is
+
+368
+00:41:25,300 --> 00:41:31,160
+not one to one و سيبت الانت بتقدر تثبت الناس
+
+369
+00:41:35,340 --> 00:41:39,240
+العنصر من زد عشرة ليس صورة العنصر من زد عشرة ليس
+
+370
+00:41:39,240 --> 00:41:41,340
+صورة العنصر من زد عشرة ليس صورة العنصر من زد عشرة
+
+371
+00:41:41,340 --> 00:41:42,680
+ليس صورة العنصر من زد عشرة ليس صورة العنصر من زد
+
+372
+00:41:42,680 --> 00:41:43,740
+عشرة ليس صورة العنصر من زد عشرة ليس صورة العنصر من
+
+373
+00:41:43,740 --> 00:41:45,520
+زد عشرة ليس صورة العنصر من زد عشرة ليس صورة العنصر
+
+374
+00:41:45,520 --> 00:41:49,160
+من زد عشرة ليس صورة العنصر من زد عشرة ليس صورة
+
+375
+00:41:49,160 --> 00:41:52,160
+العنصر من زد عشرة ليس صورة العنصر من زد عشرة ليس
+
+376
+00:41:52,160 --> 00:41:55,980
+صورة العنصر من زد عشرة ليس صورة العنصر من زد عشرة
+
+377
+00:41:55,980 --> 00:42:02,780
+ليس صتسعة ثلاثة مثلًا؟ سبعة ايوة و واحدة كلهم عشرة
+
+378
+00:42:02,780 --> 00:42:17,140
+طيب بقدر اقوله هنا also five is not only لو
+
+379
+00:42:17,140 --> 00:42:25,280
+جدرس أثبت ان ال range لو جدرس أثبت ان ال range لا
+
+380
+00:42:25,280 --> 00:42:30,500
+يسوى جد عشرةمش بقول خلصنا؟ طب بدنا ندور على ال
+
+381
+00:42:30,500 --> 00:42:39,140
+range نشوف وقدرش ال range فبعيه الفائع يساوي؟ أيه
+
+382
+00:42:39,140 --> 00:42:45,920
+الفائع؟ X موجودة في Z أربع يعني بدي أخد five of
+
+383
+00:42:45,920 --> 00:42:49,520
+zero, five of واحد, five of اتنين, five of تلاتة
+
+384
+00:42:49,520 --> 00:42:53,680
+وشوهش بيعطينا؟ بيعطينا ال range صح ولا لا؟ احنا
+
+385
+00:42:53,680 --> 00:42:58,660
+بدي يعطينا أربع قيم وليس عشريبقى فاي ما هيش،
+
+386
+00:42:58,660 --> 00:43:03,140
+كنتوا، لكن أنا بالدبلي اللي هي رياضية ال ring تبع
+
+387
+00:43:03,140 --> 00:43:09,460
+الفاي، five of zero يسوي zero صح؟ و five of واحد
+
+388
+00:43:09,460 --> 00:43:17,260
+خمسة في واحد هي فامسة طب و five of اتنين هي five
+
+389
+00:43:17,260 --> 00:43:24,490
+of تلاتة خمسة هي five أربعة ماعندكفاي of اتنين
+
+390
+00:43:24,490 --> 00:43:28,590
+اللي هو zero فاي of تلاتة هو خمسة واربع ماعنديش
+
+391
+00:43:28,590 --> 00:43:35,230
+خلاص يبقى غير بس خمسة وزيره لا يسوى ال code من
+
+392
+00:43:35,230 --> 00:43:42,370
+اللي هو زت عشر يبقى فاي is not unto because قوليلي
+
+393
+00:43:42,370 --> 00:43:48,390
+هنا because ما هو معنى أنتوا أني بدي أغطي جميع
+
+394
+00:43:48,390 --> 00:43:54,080
+أنصر الزت عشرة بالاستثناء إن حد تداركبقول هذه five
+
+395
+00:43:54,080 --> 00:44:01,960
+is only هذا كان المثال رقم أربعة ونفس المثال رقم
+
+396
+00:44:01,960 --> 00:44:13,160
+خمسة مثال خمسة بيقول little r d a commutative ring
+
+397
+00:44:13,160 --> 00:44:16,280
+commutative
+
+398
+00:44:16,280 --> 00:44:19,840
+ring of characteristic two
+
+399
+00:44:22,460 --> 00:44:32,240
+characteristic two define a mapping define a
+
+400
+00:44:32,240 --> 00:44:38,480
+mapping بدنا
+
+401
+00:44:38,480 --> 00:44:47,220
+نعرف function والله ده ده five من ال R إلى نفسي من
+
+402
+00:44:47,220 --> 00:44:58,330
+ال ring لنفسها byفاي of A بده ساول A ترابيع لكل ال
+
+403
+00:44:58,330 --> 00:45:10,210
+A اللي موجودة في R show that show that فاي بيقوله
+
+404
+00:45:10,210 --> 00:45:18,750
+ان فاي is a homomorphism but not
+
+405
+00:45:21,270 --> 00:45:36,270
+Isomorphism لكنها ليست Isomorphism سؤال
+
+406
+00:45:36,270 --> 00:45:40,570
+مرة تانية في عندكم mutated brain ال characteristic
+
+407
+00:45:40,570 --> 00:45:45,750
+هي يساوي اتنين يعني لو ضربت اتنين في اي عنصر من
+
+408
+00:45:45,750 --> 00:45:52,330
+عناصرها بيطلع عنصر الصيفريجالي أعرف في من ال ring
+
+409
+00:45:52,330 --> 00:45:56,970
+إلى نفسها ب في of a و 7 a تربيع لكل ال a الموجودة
+
+410
+00:45:56,970 --> 00:46:02,650
+في R بيظهر أن في عبارة عن homomorphism لكنها ليست
+
+411
+00:46:02,650 --> 00:46:10,870
+isomorphism إذا بدي أخد ال a و ال b موجودة في R
+
+412
+00:46:10,870 --> 00:46:20,450
+عشوائية then بدي أخد تأثير ال في على مجموعهمايبقى
+
+413
+00:46:20,450 --> 00:46:28,470
+هذا الكلام بيصير a زائد b لكل ال R is commutative
+
+414
+00:46:28,470 --> 00:46:34,350
+يبقى لو commutative بدي أفك هذه بصير a تربية زائد
+
+415
+00:46:34,350 --> 00:46:41,110
+2ab زائد b تربية لكن لو ماكنتش commutative بدي
+
+416
+00:46:41,110 --> 00:46:47,250
+أقول لك a b زائد ba لكن لما كانت commutative يبقى
+
+417
+00:46:47,250 --> 00:46:48,530
+2ab
+
+418
+00:46:59,070 --> 00:47:06,190
+النتيجة تساوي A تربيع زائد B تربيع ال A تربيع حسب
+
+419
+00:47:06,190 --> 00:47:12,230
+ال definition هي Phi of A والتانية حسب ال
+
+420
+00:47:12,230 --> 00:47:19,840
+definition Phi of B5 of A زي 5 of B تحقق ال
+
+421
+00:47:19,840 --> 00:47:29,000
+condition الأول بدالي لل condition الثاني and 5 of
+
+422
+00:47:29,000 --> 00:47:38,740
+A في B بده يساوي ال A بيه كل تربية و يساوي هل هذا
+
+423
+00:47:38,740 --> 00:47:45,670
+الكلام يساوي A تربية B تربيةلا يسويه إلا إذا كان
+
+424
+00:47:45,670 --> 00:47:52,210
+ترمى commutative ماكانش commutative يبقى a, b, a,
+
+425
+00:47:52,330 --> 00:47:56,530
+b لكن نظرا إلى ان ال commutative ببدل زي ما بده
+
+426
+00:47:56,530 --> 00:48:02,450
+يبقى a تربية, b تربية ال a تربية هي Phi of a و ال
+
+427
+00:48:02,450 --> 00:48:08,490
+b تربية Phi of b يبقى تحقق ال two conditions يبقى
+
+428
+00:48:08,490 --> 00:48:17,150
+باجر بقوله so Phiis a homomorphism قال لي اثبتلي
+
+429
+00:48:17,150 --> 00:48:20,110
+ان هو homomorphism اثبتنا قال لي بس not
+
+430
+00:48:20,110 --> 00:48:29,510
+isomorphism بقوله ال phi is not isomorphism ليش؟
+
+431
+00:48:29,510 --> 00:48:34,610
+because اي عدد مستلبته بيديه نفسه لو أخدت منه phi
+
+432
+00:48:34,610 --> 00:48:43,930
+of a قداشه ساوي؟ a تربيهوخد فاى of ناقص اى الناقص
+
+433
+00:48:43,930 --> 00:48:49,870
+اى الكل ترجعله في قدر اى تربيع من الاتنين هدول
+
+434
+00:48:49,870 --> 00:48:57,230
+بدره يقول فاى of اى بده يساوي فاى of سالب اى يبقى
+
+435
+00:48:57,230 --> 00:49:08,030
+صورة تانى متساويه تانى but ولكن ال a لا تساوي سالب
+
+436
+00:49:08,030 --> 00:49:14,630
+اىماقالليش ماعنديش condition يقوللي انه ايه بده
+
+437
+00:49:14,630 --> 00:49:20,830
+تساوي سالب ايه يبقى بناء عليه الارابي علمه is not
+
+438
+00:49:20,830 --> 00:49:32,910
+one two يبقى هنا five is not and times of not لا
+
+439
+00:49:32,910 --> 00:49:39,410
+يزال هناك المزيد من الأمثلةومن ضمن الأمثلة القادمة
+
+440
+00:49:39,410 --> 00:49:45,770
+ان شاء الله بدنا نحسب أكم homomorphism عندما ال
+
+441
+00:49:45,770 --> 00:49:53,390
+ring إلى ring أخرى وهذا طبعا عملته في جبر حديث
+
+442
+00:49:53,390 --> 00:49:59,370
+واحد وبدنا نروح نعمل كذلك في جبر حديث اثنين
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/t5SjM3-XatY_postprocess.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/t5SjM3-XatY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f31db38ead2122264f20fc7b267312157f8bf4f2
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/t5SjM3-XatY_postprocess.srt
@@ -0,0 +1,1376 @@
+1
+00:02:15,810 --> 00:02:20,410
+بسم الله الرحمن الرحيم اليوم ان شاء الله نبدأ في
+
+2
+00:02:20,410 --> 00:02:26,670
+chapter 16 عنوانه polynomial rings يبقى كأنه احنا
+
+3
+00:02:26,670 --> 00:02:32,350
+فهو بدنا نيجي من كل ال rings ناخد حالة خاصة هي ال
+
+4
+00:02:32,350 --> 00:02:37,090
+ring اللي عناصرها كثيرات الحدود يبقى هذا معناه
+
+5
+00:02:37,090 --> 00:02:44,080
+polynomial rings بدنا نعطي تعريفين ومن ثمنجي
+
+6
+00:02:44,080 --> 00:02:48,620
+لعملية الجمع وعملية الضرب على مين على ال hologram
+
+7
+00:02:48,620 --> 00:02:54,640
+التعريف الأول بيقول ما يأتي Little RBA commutative
+
+8
+00:02:54,640 --> 00:03:01,800
+ring بدي أكون set جديدة بدي أسميها R of X هذه ال
+
+9
+00:03:01,800 --> 00:03:08,610
+set على أسرها كل عنصر فيها عبارة عن كثيرة حدودan x
+
+10
+00:03:08,610 --> 00:03:13,190
+to the power n plus an minus one x to the power n
+
+11
+00:03:13,190 --> 00:03:17,770
+minus one زائد زائد a one x زائد ال a node الأس
+
+12
+00:03:17,770 --> 00:03:23,330
+تبع ال x بينزل والباقي كله ثوابت الثوابت هذه ال a
+
+13
+00:03:23,330 --> 00:03:27,850
+a node و a one و a two و a three لغاية a من وين
+
+14
+00:03:27,850 --> 00:03:32,710
+جيبناها جيبناها من ال ring الأصلية اللي هي R فرح
+
+15
+00:03:32,710 --> 00:03:38,270
+قالليA I belongs to main in commutative ring اللي
+
+16
+00:03:38,270 --> 00:03:44,030
+هي A طب ال N is a non negative integer يعني ممكن
+
+17
+00:03:44,030 --> 00:03:49,950
+يكون positive و ممكن يكون zero فإن كانت ال N بيه
+
+18
+00:03:49,950 --> 00:03:54,170
+zero بصير ال polynomial بنسميها ال constant
+
+19
+00:03:54,170 --> 00:03:59,670
+polynomial ليش؟ لأن أي عدد مرفوع لل أس صفر واحد
+
+20
+00:03:59,670 --> 00:04:06,130
+بصير عندنا baseالـ F of X هي مين الـ A نود فيها
+
+21
+00:04:06,130 --> 00:04:12,010
+مقدار ثابت واحد فقط وهذا ما سنشير اليه بعد قليل
+
+22
+00:04:12,010 --> 00:04:17,870
+على أي حال كل الـ A هات هدول المعاملات تبعات الـ X
+
+23
+00:04:17,870 --> 00:04:23,050
+هم عناصر في ال set R أو في ال commutative ring R
+
+24
+00:04:23,050 --> 00:04:27,650
+الـ N نظم non negative integer هذه كلها ال set
+
+25
+00:04:27,860 --> 00:04:35,060
+بسميها a ring of polynomials حلقة كثيرات الحدود أو
+
+26
+00:04:35,060 --> 00:04:39,560
+polynomial ring سواء تسمي هذه والله هذه الاتنين
+
+27
+00:04:39,560 --> 00:04:45,120
+are the same over are in the indeterminate X يعني
+
+28
+00:04:45,120 --> 00:04:51,120
+في المجهول Xالـ which is commutative الـ ring هذه
+
+29
+00:04:51,120 --> 00:04:56,900
+للـ R of X commutative لأن R الأصلية commutative و
+
+30
+00:04:56,900 --> 00:05:02,360
+المعاملات كلهم من R و X تقبل commutes مع ال X
+
+31
+00:05:02,360 --> 00:05:07,560
+تربيع و X تكييب و X أربعة و X مية و هكذا تمام إذا
+
+32
+00:05:07,560 --> 00:05:11,240
+كل هذا ال ring commutative هذا هو ال definition
+
+33
+00:05:11,240 --> 00:05:16,380
+الأول ال definition التاني متى تتساوى two
+
+34
+00:05:16,380 --> 00:05:21,000
+polynomialsفبقول في عندي Polynomial وفي عندي
+
+35
+00:05:21,000 --> 00:05:26,040
+Polynomial تانية اتنين are equal if and only if ال
+
+36
+00:05:26,040 --> 00:05:31,360
+A I بتسوى B I لكل ال I زيروا واحد اتنين تلاتة الى
+
+37
+00:05:31,360 --> 00:05:38,000
+ما شاء الله يعني ايش قصده يقول قصده يقول ان A1 في
+
+38
+00:05:38,000 --> 00:05:41,260
+ال Polynomial الأولى يسوى B1 في ال Polynomial
+
+39
+00:05:41,260 --> 00:05:45,960
+الثانية A0 في ال Polynomial الأولى يسوى B0 في ال
+
+40
+00:05:45,960 --> 00:05:50,270
+Polynomial الثانيةA2 في ال polynomial الأولى يسوى
+
+41
+00:05:50,270 --> 00:05:55,470
+B2 في ال polynomial الثالثة وهكذا هذا بدي أطرح على
+
+42
+00:05:55,470 --> 00:06:01,290
+ما سامعكم أسوالي التالية هل ال polynomial الأولى و
+
+43
+00:06:01,290 --> 00:06:06,650
+ال polynomial التانية من نفس الدرجة يعني أكبر أس
+
+44
+00:06:06,650 --> 00:06:13,370
+لل X في الأولى زي أكبر أس لل X في الثانية؟ متأكدة؟
+
+45
+00:06:13,370 --> 00:06:19,670
+لأ مش صحيحوالله لو كان هيك لكان قلت X to the power
+
+46
+00:06:19,670 --> 00:06:25,430
+N لكن غير قلت X to the power M هل احنا قلنا ال N
+
+47
+00:06:25,430 --> 00:06:30,650
+بتساوي ال M؟ طيب خليني بدي ارجعكوا لشغل عامل
+
+48
+00:06:30,650 --> 00:06:35,550
+اشتغلته فيه Calculus B Calculus B؟ اه Calculus B
+
+49
+00:06:35,550 --> 00:06:41,410
+لما كنا نسوي partial fractions كسور جزئية ونقارن
+
+50
+00:06:41,410 --> 00:06:45,970
+المعاملات في الطرفين هلالمعادلة كانت على الطرف
+
+51
+00:06:45,970 --> 00:06:49,710
+اليمين زي المعادلة على الطرف الشمال؟ لأ طيب في
+
+52
+00:06:49,710 --> 00:06:54,110
+عندي هنا X تكعيب و هنا في شغال X تربيع وانزل يبقى
+
+53
+00:06:54,110 --> 00:07:00,350
+معامل X تكعيب دي سوى قداش؟ سوى صفر يبقى هذا معناه
+
+54
+00:07:00,350 --> 00:07:07,610
+ان التنتين ليست من نفس القصر لأ M و N two integers
+
+55
+00:07:07,610 --> 00:07:13,600
+و اتنين are different مختلفين على بعض تماماهو يوضح
+
+56
+00:07:13,600 --> 00:07:19,220
+لك الكلام هذا أكثر وقال لك حيث ال AI بده يساوي
+
+57
+00:07:19,220 --> 00:07:26,080
+Zero إذا كانت ال I أكبر من N نفترض ال N عاشرة ال M
+
+58
+00:07:26,080 --> 00:07:33,800
+كانت أتناشر يبقى رقم 11 ورقم 12 والكولوجيا الأولى
+
+59
+00:07:33,800 --> 00:07:40,650
+مش موجودين ال X أص 11 و X أص 12يبقى المعاملات الـ
+
+60
+00:07:40,650 --> 00:07:48,330
+A11 والـ A12 بأصفار، ماخدين بالك؟ هي الـ AI بساوي
+
+61
+00:07:48,330 --> 00:07:54,770
+Zero إذا كانت الـ I أكبر من N، A11 و A12 بيكون
+
+62
+00:07:54,770 --> 00:08:01,390
+بأصفار، لكن في التانية A11 و A12 بمعاملات، رموز
+
+63
+00:08:01,590 --> 00:08:05,010
+بقول يبقى الرمز الأول بده يساوي Zero والرمز التاني
+
+64
+00:08:05,010 --> 00:08:09,790
+بده يساوي Zero إن كانوا اتنين are equal بشرط
+
+65
+00:08:09,790 --> 00:08:14,150
+التساوي فروحنا قولناش قولنا two polynomials هدول
+
+66
+00:08:14,150 --> 00:08:19,530
+are equivalent only if ال AI بده يساوي ال BI لكل
+
+67
+00:08:19,530 --> 00:08:23,610
+ال I اللي بتساوي Zero واحد واثنين وتلاتة لآخر
+
+68
+00:08:23,610 --> 00:08:28,870
+الحدود اللي عندنا واضح كلامي؟يبقى بناة الأس تبع ال
+
+69
+00:08:28,870 --> 00:08:34,210
+X في الأولى ليس هو نفس الأس في الثانية قد يكون وقد
+
+70
+00:08:34,210 --> 00:08:39,390
+لا يكون يعني ممكن يحصل لكن in general لأ يا أصغر
+
+71
+00:08:39,390 --> 00:08:44,610
+منه يا ايه يا أكبر منه كما سنرى بعد قليل فعند أول
+
+72
+00:08:44,610 --> 00:08:49,810
+مثال بدنا ناخده طيب الآن احنا عرفنا ال polynomial
+
+73
+00:08:49,810 --> 00:08:56,220
+تمام وعرفنا هنا كثيرات حدودوالمعاملة تبعها من الـ
+
+74
+00:08:56,220 --> 00:09:00,420
+commutative ring R وعرفنا انها commutative ring
+
+75
+00:09:00,420 --> 00:09:07,360
+تمام كيف بنعمل عملية الجمع وعملية الضرب على هذه ال
+
+76
+00:09:07,360 --> 00:09:12,720
+polynomial فبقول ما ياتي بنجي وقول هاي F of X وهاي
+
+77
+00:09:12,720 --> 00:09:18,400
+G of X والاتنين هدول two elements في الستم او في
+
+78
+00:09:18,400 --> 00:09:24,670
+ال ring of all polynomials طيبودا جمع F of X زي G
+
+79
+00:09:24,670 --> 00:09:30,310
+of X يساوي A S زي B S في X و S S ماشي S هذه؟
+
+80
+00:09:30,310 --> 00:09:36,530
+ماعرفهاش لكن بدنا نعرفها زي A S minus one زي B S
+
+81
+00:09:36,530 --> 00:09:41,190
+minus في X و S S minus ال one زي زي A one B one في
+
+82
+00:09:41,190 --> 00:09:46,290
+X زي A naught B naught S هي أكبر رقم في الإتنين
+
+83
+00:09:46,290 --> 00:09:52,720
+يعني لو كان N هو الرقم الكبير يبقى S يبقى 12بإن لو
+
+84
+00:09:52,720 --> 00:09:59,300
+كان M هو الرقم الأكبر يبقى ال S تساوي M هيوغلب
+
+85
+00:09:59,300 --> 00:10:08,200
+Where حيث ال S is the maximum of M and N الرقم
+
+86
+00:10:08,200 --> 00:10:14,200
+الكبير فيهم بيكون هو مين؟ S في حالة الجمع وال AI
+
+87
+00:10:14,200 --> 00:10:17,940
+بيساوي Zero لل I اللي أكبر من N وال BI بيساوي Zero
+
+88
+00:10:17,940 --> 00:10:24,690
+لل I اللي أكبر من 100أكبر من ال M واضح كلامي هذا
+
+89
+00:10:24,690 --> 00:10:29,310
+لسه الجامعة الجامعة مش فيه مشكلة سهل المشكلة وين؟
+
+90
+00:10:29,310 --> 00:10:36,630
+فالطرف بيقول الآن ال F of X في ال G of X CM زائد N
+
+91
+00:10:36,630 --> 00:10:41,910
+X اصم زائد M CM زائد N minus one X to the power M
+
+92
+00:10:41,910 --> 00:10:46,370
+زائد N minus one ونظل ماشي لغة من وصل ل C one X
+
+93
+00:10:46,370 --> 00:10:52,150
+زائد C nonواللي بدنا نعرف مين هو CK يعني بدنا نعرف
+
+94
+00:10:52,150 --> 00:10:58,950
+مين C0 ومين C1 ومين C3 ومين C4 ومين C5 ومين C6
+
+95
+00:10:58,950 --> 00:11:01,410
+ومين C7 ومين C8 ومين C9 ومين C10 ومين C11 ومين C12
+
+96
+00:11:01,410 --> 00:11:01,890
+C18 ومين C19 ومين C20 ومين C21 ومين C22 ومين C22
+
+97
+00:11:01,890 --> 00:11:02,390
+ومين C22 ومين C22 ومين C22 ومين C22 ومين C22 ومين
+
+98
+00:11:02,390 --> 00:11:03,410
+C22 ومين C22 ومين C22 ومين C22 ومين C22 ومين C22
+
+99
+00:11:03,410 --> 00:11:12,270
+ومين C22 ومين C22 ومين C22 ومين C22 ومين C22 ومين
+
+100
+00:11:12,270 --> 00:11:15,350
+C22
+
+101
+00:11:15,350 --> 00:11:24,210
+ومين C22نضرب زي اتجاه عكسي المعامل xn مع ثابت تبع
+
+102
+00:11:24,210 --> 00:11:29,550
+ال polynomial التانية المعامل تبع x أُس n minus ال
+
+103
+00:11:29,550 --> 00:11:34,010
+one في المعامل تبع x لل polynomial التانية و هكذا
+
+104
+00:11:34,010 --> 00:11:38,810
+واحد برجع التانية بقدم لغاية ما نخلص نجمع هدول
+
+105
+00:11:38,810 --> 00:11:45,770
+بيكون المعامل تبع مين؟ تبع xk يبقى قولنا هيك ckهو
+
+106
+00:11:45,770 --> 00:11:56,330
+A K B نوت A K I A K ل A N في B نوت زائد A N minus
+
+107
+00:11:56,330 --> 00:12:01,570
+ال one في B one زائد A N minus ال two في B two
+
+108
+00:12:01,570 --> 00:12:08,270
+وهكذا هذه نازلة وهذه راجعة لغاية ايش ما نكمل طب
+
+109
+00:12:08,270 --> 00:12:13,370
+انت قلت ال M و ال N مش زي بعض اقول صحيحلغاية ما
+
+110
+00:12:13,370 --> 00:12:18,870
+لوصل ل M فيه زيادة بيكون المعاملات بأصفار لأنها
+
+111
+00:12:18,870 --> 00:12:25,870
+يجلل AI تسوية Zero من I أكبر من N هذا لو كانت ال N
+
+112
+00:12:25,870 --> 00:12:31,610
+هي الصورة و M هي الكبرى وهذا العكس لو كانت M هي
+
+113
+00:12:31,610 --> 00:12:35,770
+الكبرى و N هي الصورة يبقى كل الأرقام اللي بتيجي
+
+114
+00:12:35,770 --> 00:12:41,440
+بعدها بيكون كلها بأصفارالكلام اللى شفته بنروح نحطه
+
+115
+00:12:41,440 --> 00:12:47,360
+على أرض الواقع بمثال مشان نعرف كيف نشتغل هبقى جيب
+
+116
+00:12:47,360 --> 00:12:52,780
+اقول في الطريق انه عندي two polynomials في ZD3
+
+117
+00:12:52,780 --> 00:12:57,200
+يبقى ال ring اللى عندنا of polynomials جايبين
+
+118
+00:12:57,200 --> 00:13:03,880
+معاملات ثمنوية من ZD3 يبقى معناها ZD3 يا zero يا
+
+119
+00:13:03,880 --> 00:13:09,660
+واحد يا اتنين ما بزيد عن ذلكتطلع تتوفر لنا كله 2 و
+
+120
+00:13:09,660 --> 00:13:15,720
+1، مظبوط؟ و Zero، Zero ما هو هنا X تكيب طارت، لأنه
+
+121
+00:13:15,720 --> 00:13:19,640
+ما عاملها باشر، ب Zero. طيب، أخدت تنتين و أخدت
+
+122
+00:13:19,640 --> 00:13:20,960
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+123
+00:13:20,960 --> 00:13:21,180
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+124
+00:13:21,180 --> 00:13:23,800
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+125
+00:13:23,800 --> 00:13:26,140
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+126
+00:13:26,140 --> 00:13:26,180
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+127
+00:13:26,180 --> 00:13:35,270
+تنتين و تنتين و تنتينقداش أعلى أس ل X عندي تلاتة
+
+128
+00:13:35,270 --> 00:13:43,450
+ممتازة لما أضرب قداش أعلى أس ل X خمسة لأن X تربيع
+
+129
+00:13:43,450 --> 00:13:48,030
+في X تقريب X و أس خمسة إذا بدي أبدأ أعرف قداش A
+
+130
+00:13:48,030 --> 00:13:52,370
+خمسة و B خمسة و A أربعة و B أربعة و A تلاتة و B
+
+131
+00:13:52,370 --> 00:13:56,010
+تلاتة و A تلاتة و هكذا لغاية ما نخلص لإن اللي
+
+132
+00:13:56,010 --> 00:14:00,830
+بلزمنيش في الجبهة بلزمني وينفضرب يبقى خلينا نحطهم
+
+133
+00:14:00,830 --> 00:14:05,710
+في الأول قبل ما نبدأ الان لو جيت بلات قولتلك ايه
+
+134
+00:14:05,710 --> 00:14:13,710
+خمسة كداش عندنا هنا Zero طب و ايه أربعة؟ طب و ايه
+
+135
+00:14:13,710 --> 00:14:20,390
+تلاتة؟ اتنين يعني معملك سهل هو يساوي اتنين و ايه
+
+136
+00:14:20,390 --> 00:14:27,890
+اتنين؟ واحد و ايه واحد؟ اتنين و ايه نوت يساوي
+
+137
+00:14:27,890 --> 00:14:32,630
+اتنين؟هيحطيك المعاملات تبع ال polynomial الأولى
+
+138
+00:14:32,630 --> 00:14:36,870
+بتحط بنفس الطريقة المعاملات تبع ال polynomial
+
+139
+00:14:36,870 --> 00:14:43,450
+التالية ال بي خمسة بزيرو وال بي أربعة بزيرو وال بي
+
+140
+00:14:43,450 --> 00:14:48,310
+تلاتة بزيرو لإن هذا بتبدأ الاكس تربية يفجأ بإننا
+
+141
+00:14:48,310 --> 00:14:55,570
+نيجي لمين؟ لل بي اتنين بي اتنين يساوي اتنين و بي
+
+142
+00:14:55,570 --> 00:15:04,080
+واحديساوي اتنين و B node يساوي واحد طيب
+
+143
+00:15:04,080 --> 00:15:11,180
+ليش بدأت من عند الخمسة لإن حاصل الضرب بده يجيبلي X
+
+144
+00:15:11,180 --> 00:15:16,440
+أس خمسة واحنا قلنا حاصل الضرب بيبدأ من عند C M
+
+145
+00:15:16,440 --> 00:15:21,740
+زائد N يبقى لو جمعت الأسين بيطلع خمسة إذا بده يجيب
+
+146
+00:15:21,740 --> 00:15:26,450
+المعاملات من عند ال A خمسةبدي أجل المطلوب الأول
+
+147
+00:15:26,450 --> 00:15:34,270
+بدي أخد ال F of X زائد ال G of X الحين هدول
+
+148
+00:15:34,270 --> 00:15:40,310
+بالزموري لأ زموش اللي في عملية الجمع يبقى سيبورة
+
+149
+00:15:40,310 --> 00:15:45,430
+منهم عملية الجمع بتقول لي ما ياتي بتبقى تجمع
+
+150
+00:15:45,430 --> 00:15:54,280
+المعاملات المتناظرة X أوس خمسة X أوس اسمين Sالكبير
+
+151
+00:15:54,280 --> 00:16:00,560
+فيهم، مين الكبير يا بنات؟ X تكيب، إذا بتبدأ A3
+
+152
+00:16:00,560 --> 00:16:08,240
+زائد B3 في X تكيب يفجأ هذا، بده يساوي A3، وين عن
+
+153
+00:16:08,240 --> 00:16:19,060
+نهاي؟ A3 باتنين زائد B3 ب Zero في X تكيب زاد، اللي
+
+154
+00:16:19,060 --> 00:16:24,860
+بعده ال X تربيع، هاي ال X تربيعيبقى واحد زائد
+
+155
+00:16:24,860 --> 00:16:31,780
+اتنين يبقى واحد زائد اتنين في ال X تقعيد ال X
+
+156
+00:16:31,780 --> 00:16:36,520
+تربية زائد اتنين في ال X تقعيد ال X تربية زائد
+
+157
+00:16:36,520 --> 00:16:38,240
+اتنين في ال X تقعيد ال X تربية زائد اتنين في ال X
+
+158
+00:16:38,240 --> 00:16:42,360
+تربية زائد اتنين في ال X تربية زائد اتنين في ال X
+
+159
+00:16:42,360 --> 00:16:45,160
+تربية زائد اتنين في ال X تربية زائد اتنين في ال X
+
+160
+00:16:45,160 --> 00:16:49,440
+تربية زائد اتنين في ال X تربية زائد اتنين في ال X
+
+161
+00:16:49,440 --> 00:16:50,820
+تربية زائد اتنين في ال X تربية زائد اتنين في ال X
+
+162
+00:16:50,820 --> 00:16:56,640
+تربية زائد اتب2 X تك عيد التاني واحد زي اتنين
+
+163
+00:16:56,640 --> 00:17:05,080
+تلاتة في زي التلاتة Zero يبقى هذا Zero ب X تك
+
+164
+00:17:05,080 --> 00:17:12,280
+تربيع اللي بعده اتنين زي اتنين اربع في زي التلاتة
+
+165
+00:17:12,280 --> 00:17:19,040
+بواحد يبقى زائد X زائد X اللي يجي اللي بعده اتنين
+
+166
+00:17:19,040 --> 00:17:25,170
+زي اتنين واحدبتلاتة يبقى زائد زير يبقى صارت
+
+167
+00:17:25,170 --> 00:17:31,430
+النتيجة النهائية اتنين X تكيب زائد X فقط لا غير
+
+168
+00:17:31,430 --> 00:17:40,030
+هذا الجبهر نيجي للضرر بدي اخد ال F of X في ال G of
+
+169
+00:17:40,030 --> 00:17:50,040
+X يبقى بقدر بـCK لو CM زائد Mيبقى هذا بده يبدأ من
+
+170
+00:17:50,040 --> 00:17:55,220
+وين؟ من عند الخمسة لأنه حصل الضرب بده يجيب ليهكسوس
+
+171
+00:17:55,220 --> 00:18:05,880
+خمسة إذا a خمسة في b نوت a خمسة في b نوت a خمسة
+
+172
+00:18:05,880 --> 00:18:14,140
+اللي هو بزيرو b نوت اللي هو كده؟ بواحد زرع a أربعة
+
+173
+00:18:14,140 --> 00:18:28,920
+بزيروفي B1 اللي هو ب 2 زي A3 اللي هو ب 2 في 2 2
+
+174
+00:18:28,920 --> 00:18:39,640
+في 2 زي اللي بعده A2 اللي هو ب 1 في 8 في 0 خلاص
+
+175
+00:18:39,640 --> 00:18:48,120
+هاي 1 2 3 هاي 1 2 3 اه بجين ال 0يبقى v3 اللي هو f0
+
+176
+00:18:48,120 --> 00:18:59,960
+زائد a2 في 0 زائد 2 في 0 كل هذا في x أُس 5 زائد
+
+177
+00:18:59,960 --> 00:19:06,440
+تمام؟ بدنا نيجي لبعد اللي بعد يكون x main أربعة أس
+
+178
+00:19:06,440 --> 00:19:11,420
+أربعة يبقى هدول مالاش علاقة فيهم خلصنا منهم بدنا
+
+179
+00:19:11,420 --> 00:19:19,560
+نبدأ من عند ال a4يبقى زائد a4 اللي هو بزيرو في b
+
+180
+00:19:19,560 --> 00:19:27,440
+node اللي هو بواحد يبقى بواحد زائد a3 اللي هو
+
+181
+00:19:27,440 --> 00:19:35,420
+باتنين في مين؟ في b1 اللي هو باتنين زائد a2 اللي
+
+182
+00:19:35,420 --> 00:19:44,110
+هو بواحد في مين؟ في b2 اللي هو باتنين زائد a1اللي
+
+183
+00:19:44,110 --> 00:19:52,310
+هو بإتنين فمين في واحد اتنين تلاتة اربع يبقى واحد
+
+184
+00:19:52,310 --> 00:19:58,770
+اتنين تلاتة اربع اللي هو ب Zero ب Zero زائد اتنين
+
+185
+00:19:58,770 --> 00:20:05,430
+كمان Zero يبقى واحد اتنين تلاتة اربع خمسة ستة واحد
+
+186
+00:20:05,430 --> 00:20:11,390
+اتنين تلاتة اربع خمسة مضبوط كل هذا الكلام ب X أُس
+
+187
+00:20:11,390 --> 00:20:18,300
+4نجي لل X تكييب زرع ال X تكييب انتهينا من هدول
+
+188
+00:20:18,300 --> 00:20:24,520
+التنتيج تبقى بدي أبدأ من أنت A تلاتة A تلاتة اللي
+
+189
+00:20:24,520 --> 00:20:33,060
+هو اتنين في B يولد واحد زائد واحد في اتنين زائد
+
+190
+00:20:33,060 --> 00:20:43,640
+اتنين في اتنين زائد اتنين في جداش في زيرهذا ال X
+
+191
+00:20:43,640 --> 00:20:52,100
+تكيب زائد نهيده لل X تربيعه يبقى نهيده لل X تربيعه
+
+192
+00:20:52,100 --> 00:21:00,620
+هذا انتهينا منهم ملينا يبقى واحد في واحد يبقى واحد
+
+193
+00:21:00,620 --> 00:21:08,780
+في واحد زائد اتنين في اتنين زائد اتنين في اتنين
+
+194
+00:21:08,780 --> 00:21:16,730
+زائدإتنين في إتنين إتنين في إتنين كلها ده X تربيه
+
+195
+00:21:16,730 --> 00:21:22,350
+زائد تبعات ال X هدول انتهينا منهم يبقى اتنين في
+
+196
+00:21:22,350 --> 00:21:31,150
+واحد اتنين في واحد زائد اتنين في اتنين في X زائد
+
+197
+00:21:31,150 --> 00:21:36,530
+انتهينا من هدول يبقى اتنين في واحد اتنين في واحد
+
+198
+00:21:36,530 --> 00:21:39,450
+تمام؟
+
+199
+00:21:40,010 --> 00:21:48,650
+طيب نجي نجمع هذا الكلام يساوي Zero Zero هذي أربعة
+
+200
+00:21:48,650 --> 00:21:56,630
+و الفاق كله ب Zero أربعة في زي التلاتة كده؟ واحد
+
+201
+00:21:56,630 --> 00:22:03,770
+يبقى بضل عشان دي إلا X أس خمسة كما هي نجي لل X أس
+
+202
+00:22:03,770 --> 00:22:10,880
+أربعة هذا Zero أربعة و اتنينستة والباقية أصفر ستة
+
+203
+00:22:10,880 --> 00:22:19,660
+في زيت تلاتة Zero يبقى زائد Zero في X مصر أربع
+
+204
+00:22:19,660 --> 00:22:27,860
+نيجي لل X تكيب اتنين واتنين أربع واربع تمانية وهذا
+
+205
+00:22:27,860 --> 00:22:35,340
+ب Zero تمانية في زيت تلاتة باتنين يبقى زائد اتنين
+
+206
+00:22:35,340 --> 00:22:44,550
+X تكيبنجي للتربيع اربع واربع تمانية واحد تسعة في
+
+207
+00:22:44,550 --> 00:22:52,270
+زي التلاتة Zero يفجأ زائد Zero X تربيع نجي للإكس
+
+208
+00:22:52,270 --> 00:23:00,250
+أربع واتنين ستة في زي التلاتة Zero يفجأ Zero X
+
+209
+00:23:00,250 --> 00:23:07,740
+زائد اتنين يفجأ النتيجة تساوي X أُس خمسةهذا Zero
+
+210
+00:23:07,740 --> 00:23:15,140
+راح اتنين X تكيب زائد اتنين X تكيب هذا Zero مع
+
+211
+00:23:15,140 --> 00:23:22,360
+السلامة هذا Zero مع السلامة ضال زائد اتنين حد في
+
+212
+00:23:22,360 --> 00:23:28,480
+كل هاي تساؤل هنا سواء كان الجمع او الضرب وقيسي
+
+213
+00:23:28,480 --> 00:23:34,380
+عليها بعدها كل Ring أخرى من العاملها بنفس الطريقة
+
+214
+00:23:34,800 --> 00:23:43,840
+وخاصة عند إيجاد الأول هذا CK يعني C5 هذا C4، هذا
+
+215
+00:23:43,840 --> 00:23:52,620
+C3، هذا C2، هذا C1، هذا C نودة تمام؟ واضح كيف
+
+216
+00:23:52,620 --> 00:23:57,300
+الترتيب؟ يعمل نطلع ان شاء الله بدون خطأ خالص
+
+217
+00:24:21,590 --> 00:24:26,210
+طيب في عندنا three definitions اللي اتعرضنا لهو
+
+218
+00:24:26,210 --> 00:24:34,990
+الآن ال definition الأول بيقول if ال f of x يساوي
+
+219
+00:24:34,990 --> 00:24:40,830
+ال a in x to the power n a in minus ال one x to
+
+220
+00:24:40,830 --> 00:24:50,270
+the power n minus one زائد a one x زائد ال a نهر
+
+221
+00:24:52,070 --> 00:25:00,150
+and ال a n does not equal to zero then the integer
+
+222
+00:25:00,150 --> 00:25:08,950
+n then the integer n
+
+223
+00:25:08,950 --> 00:25:19,670
+العدد الصحيح is called is called the degree of the
+
+224
+00:25:19,670 --> 00:25:31,690
+polynomialof the polynomial and
+
+225
+00:25:31,690 --> 00:25:42,990
+ال AN and ال AN is called is
+
+226
+00:25:42,990 --> 00:25:44,630
+called the leading coefficient
+
+227
+00:25:55,130 --> 00:26:02,270
+the leading coefficient of the function او ال
+
+228
+00:26:02,270 --> 00:26:12,430
+polynomial f of x تعريف الثاني definition of the
+
+229
+00:26:12,430 --> 00:26:21,370
+leading coefficient ال
+
+230
+00:26:21,370 --> 00:26:35,410
+a nIt's the unity of R is the unity of R then ال F
+
+231
+00:26:35,410 --> 00:26:47,470
+of X then ال F of X is called .. is called a monic
+
+232
+00:26:47,470 --> 00:26:50,230
+polynomial.
+
+233
+00:27:02,430 --> 00:27:09,970
+يقولوا دي polynomial دي
+
+234
+00:27:09,970 --> 00:27:21,590
+polynomial F of X بدها تساوي Zero has no degree
+
+235
+00:27:21,590 --> 00:27:30,550
+has no degree Y دي polynomial Y دي
+
+236
+00:27:30,550 --> 00:27:31,290
+polynomial
+
+237
+00:27:36,030 --> 00:27:44,030
+بينما الـ polynomial f of x بدها تساوي الـ a ان هو
+
+238
+00:27:44,030 --> 00:27:48,610
+a squared هيكون
+
+239
+00:27:48,610 --> 00:27:49,710
+اصلا الـ polynomial
+
+240
+00:29:00,150 --> 00:29:05,890
+أحنا عندنا ثلاثة تعريف بدنا نجي نفهم كل تعريف من
+
+241
+00:29:05,890 --> 00:29:12,870
+التعريف الثلاثة الأولى بيعطيني شكل polynomial في
+
+242
+00:29:12,870 --> 00:29:19,450
+ال ring اللي R of X من A in XL لغاية ال A نور
+
+243
+00:29:19,450 --> 00:29:24,850
+بيقولي أن ال A in does not equal to zeroطب لو كانت
+
+244
+00:29:24,850 --> 00:29:30,470
+ب zero، ايش اللي بيحصل؟ ال degree تنزل بمقدار
+
+245
+00:29:30,470 --> 00:29:36,210
+واحد، يبقى هنا مقصود ال a ان لا تسوى zero حتى تبقى
+
+246
+00:29:36,210 --> 00:29:43,270
+الدرجة هي اللي هو ال أس تبع ال X اللي معامله ال aM
+
+247
+00:29:43,270 --> 00:29:47,650
+يبقى شرط أساسي ان ال aM does not equal to zero
+
+248
+00:29:47,650 --> 00:29:55,280
+يبقى الانتجار ان في هذه الحالةبقول عنه هو درجة هذه
+
+249
+00:29:55,280 --> 00:30:01,620
+ال polynomial طب والمعامل تبعها AN هذا اللي بسويش
+
+250
+00:30:01,620 --> 00:30:06,260
+ال zero بسميه leading coefficients يعني المعامل
+
+251
+00:30:06,260 --> 00:30:13,600
+القائد او المعامل الرئيسي تمام يبقى ال AN بسميه
+
+252
+00:30:13,600 --> 00:30:18,120
+leading coefficient المعامل الرئيسي او المعامل
+
+253
+00:30:18,120 --> 00:30:23,250
+القائد لل polynomial ليش؟لأن هذا إن كان لا يسوى
+
+254
+00:30:23,250 --> 00:30:30,190
+Zero يبقى ال X أُس N موجودة لكن لو كان يسوى Zero
+
+255
+00:30:30,190 --> 00:30:34,770
+بطيل ال X أُس وبالتالي تنقص درجة مين ال Polynome
+
+256
+00:30:34,770 --> 00:30:40,070
+اللي هو بالتالي وجوده يترتب عليه أن ال N بتكون
+
+257
+00:30:40,070 --> 00:30:46,270
+موجودة وبتبدأ تنزل الأسس تبع تمين تبع ال X لغاية
+
+258
+00:30:46,270 --> 00:30:53,240
+ما تنعدم تمامايبقى فيه انا شغلة مهمة جدا النقطة
+
+259
+00:30:53,240 --> 00:30:58,200
+الأولى ال N هو درجة ال polynomial وال A N بسميه
+
+260
+00:30:58,200 --> 00:31:02,900
+leading coefficients تعريف التاني بيقول ال leading
+
+261
+00:31:02,900 --> 00:31:08,300
+coefficients ال A N لو كان هو ال unity تبع ال R
+
+262
+00:31:08,300 --> 00:31:13,440
+مين ما يكون ال unity يكون هذا then ال F of X is
+
+263
+00:31:13,440 --> 00:31:19,120
+called a monic polynomialيبقى لو كان الان هذا هرط
+
+264
+00:31:19,120 --> 00:31:23,980
+ان كان ال unity هو الواحد كان بواحد كان رقم تاني
+
+265
+00:31:23,980 --> 00:31:28,060
+غير الواحد و اللي يكن غير الواحد يبقى في هذه
+
+266
+00:31:28,060 --> 00:31:33,340
+الحالة ال polynomial هذه بسميها مليك التعريف
+
+267
+00:31:33,340 --> 00:31:37,620
+التالت ال polynomial لو كان F of X يسوى Zero بيقول
+
+268
+00:31:37,620 --> 00:31:44,310
+مالهاش درجةلكن ال F of X تساوي أي رقم بسميها ال
+
+269
+00:31:44,310 --> 00:31:49,570
+constant polynomial سؤالي هو ال F of X تساوي zero
+
+270
+00:31:49,570 --> 00:31:53,790
+هي constant polynomial ؟ constant polynomial بس
+
+271
+00:31:53,790 --> 00:31:58,430
+has no degree طيب ال F of X يساوي خمسة constant
+
+272
+00:31:58,430 --> 00:32:05,690
+polynomial و الدرجة تبعتها صفر يبقى zero degree
+
+273
+00:32:06,230 --> 00:32:10,610
+يبقى لو كان صفر if of x يساوي صفر بقول مالهاش درجة
+
+274
+00:32:10,610 --> 00:32:16,050
+لكن لو كان if of x يساوي أي رقم غير الصفر بقول هذه
+
+275
+00:32:16,050 --> 00:32:21,010
+polynomial من الدرجة الصفرية from the zero degree
+
+276
+00:32:21,010 --> 00:32:27,730
+طيب بنجي لأول نظرية في هذا الموضوع وهي على الشكل
+
+277
+00:32:27,730 --> 00:32:29,510
+التالي DRM
+
+278
+00:32:36,180 --> 00:32:44,080
+تقول if D is an integral domain if capital D is an
+
+279
+00:32:44,080 --> 00:32:47,740
+is
+
+280
+00:32:47,740 --> 00:32:58,120
+an integral domain then
+
+281
+00:32:58,120 --> 00:33:01,260
+D
+
+282
+00:33:01,260 --> 00:33:10,730
+of X is an integral domainالـ Integral
+
+283
+00:33:10,730 --> 00:33:13,770
+domain
+
+284
+00:33:32,330 --> 00:33:35,870
+يقولوا لو كان دي Integral domain ماذا نقصد بال
+
+285
+00:33:35,870 --> 00:33:42,490
+Integral domain؟ community bring with unity مافيش
+
+286
+00:33:42,490 --> 00:33:47,350
+فيها Zero divisors إلا الصفر تمام؟ حط المعلومة هذه
+
+287
+00:33:47,350 --> 00:33:51,030
+في دماغنا و بدنا نبدأ نشتغل عليها إذا الخطوة
+
+288
+00:33:51,030 --> 00:33:59,630
+الأولى بدي أقوله let دي be an Integral domain
+
+289
+00:34:02,990 --> 00:34:07,930
+تمام then ال
+
+290
+00:34:07,930 --> 00:34:15,810
+D is a commutative ring
+
+291
+00:34:15,810 --> 00:34:19,410
+with
+
+292
+00:34:19,410 --> 00:34:31,550
+unity مثلا one say على سبيل المثال بواحد طيب احنا
+
+293
+00:34:31,550 --> 00:34:38,610
+بنثبتإن ال D of X هذه هي Integral دموعنا يبقى بدنا
+
+294
+00:34:38,610 --> 00:34:43,910
+هي أولا commutative ring with unity تمام يبقى باجي
+
+295
+00:34:43,910 --> 00:34:56,830
+بقوله ال D of X is commutative ring because
+
+296
+00:34:56,830 --> 00:35:13,460
+ال D نفسهاis a commutative ring يعني
+
+297
+00:35:13,460 --> 00:35:19,040
+المعاملات كلهم بيكونوا بتبدلوا مع بعض مافيش مشكلة
+
+298
+00:35:19,040 --> 00:35:24,200
+وال X بتبدل مع X تربيه و مع X تكيب ممكن نعمل يمين
+
+299
+00:35:24,200 --> 00:35:28,640
+او شمال ماتفرجش عندنا يبقى صحيح D of X is a
+
+300
+00:35:28,640 --> 00:35:37,470
+commutative ringبداجي اقوله if ال one is the unity
+
+301
+00:35:37,470 --> 00:35:49,050
+of D then ال F of X بده يساوي ال unity يعني ال
+
+302
+00:35:49,050 --> 00:35:54,890
+constant polynomial هذه بيساوي واحد is the unity
+
+303
+00:35:54,890 --> 00:35:56,970
+of
+
+304
+00:35:57,970 --> 00:36:09,710
+D of X سبب because ان ال G of X اضربيها ال F of X
+
+305
+00:36:09,710 --> 00:36:15,890
+تساوي واحد هي الواحد في ال G of X كده تساوي ال G
+
+306
+00:36:15,890 --> 00:36:24,110
+of X لكل ال G of X اللي موجودة وين؟ D of X
+
+307
+00:36:26,640 --> 00:36:31,340
+ده ليش صار على الـ Neverland ال D of X صارت
+
+308
+00:36:31,340 --> 00:36:37,140
+commutative ring with unity تمام؟ احنا ماثبتهاش
+
+309
+00:36:37,140 --> 00:36:44,440
+انها integral domain تمام؟ لشان هيك بدي اشوف حاصل
+
+310
+00:36:44,440 --> 00:36:52,320
+ضرب two elements و اثبت انه موجودفي او افضل انه
+
+311
+00:36:52,320 --> 00:36:56,920
+موجود في دي يبقى الاول في دي يا اما الثاني في دي
+
+312
+00:36:56,920 --> 00:37:07,460
+بس هنا سنثبت بطريقة شوية يعني انا بنتقل الشامع
+
+313
+00:37:07,460 --> 00:37:15,520
+واحدة تحت بس ايوة ال prime ideal ال prime ideal
+
+314
+00:37:15,520 --> 00:37:20,150
+بدي اخد حاصل ضرب two elements موجودات فيهو أثبت
+
+315
+00:37:20,150 --> 00:37:25,350
+إما الأول أو الثاني موجود فيه لأ هذه بدي أخد اللي
+
+316
+00:37:25,350 --> 00:37:31,770
+هو حاصل ضرب two elements بدي أثبت إنه حاصل الضرب
+
+317
+00:37:31,770 --> 00:37:38,970
+هذا المعاملات ولا واحد فيهم ب zero يعني مافيش zero
+
+318
+00:37:38,970 --> 00:37:44,570
+divisor ومصيره مثالي مصير integral domain صح؟ يبقى
+
+319
+00:37:44,570 --> 00:37:52,830
+بالداجة أقوله letالـ F of X اللي هو بده يساوي A N
+
+320
+00:37:52,830 --> 00:38:02,470
+X N A N minus ال 1 X N minus ال 1 زائد A 1 X زائد
+
+321
+00:38:02,470 --> 00:38:11,870
+ال A نوت وبالشرط ان ال A N لا يساوي Zero والتاني
+
+322
+00:38:11,870 --> 00:38:21,250
+ال G of Xبدي يساوي بي ام اكس ام بي ام ماينوس الوان
+
+323
+00:38:21,250 --> 00:38:29,350
+اكس ام ماينوس الوان زائد زائد بي وان اكس زائد بي
+
+324
+00:38:29,350 --> 00:38:38,450
+لات وال بي ام لا يساوي زيو اتنين هدول موجودات في D
+
+325
+00:38:38,450 --> 00:38:39,590
+of X
+
+326
+00:38:44,970 --> 00:38:56,090
+لو جيت ال leading factors then the leading then
+
+327
+00:38:56,090 --> 00:39:00,790
+the leading factors
+
+328
+00:39:00,790 --> 00:39:08,530
+ممكن
+
+329
+00:39:08,530 --> 00:39:16,030
+يساوي زيرو ؟ مش إمكانية يبقى لا يمكنإنه يساوي zero
+
+330
+00:39:16,030 --> 00:39:26,950
+السبب because ان ال a n لا يساوي zero و ال b m لا
+
+331
+00:39:26,950 --> 00:39:32,990
+يساوي zero اذا الحاصل ضربهم ليه يساوي zero طب
+
+332
+00:39:32,990 --> 00:39:38,730
+معقول حاصل ضربعنصرين مايسويش ال zero حتى لو كان كل
+
+333
+00:39:38,730 --> 00:39:44,550
+واحد فيهم لا يسوي zero لا ممكن يسوي zero بس في ال
+
+334
+00:39:44,550 --> 00:39:50,490
+integral domain لأ صح ولا لأ يبقى هنا هذا لأ لأ
+
+335
+00:39:50,490 --> 00:39:56,370
+because هذا لا يسوي زي مثلا زيد ستة زيد ستة اتنين
+
+336
+00:39:56,370 --> 00:40:01,090
+في تلاتة zero مبني اللي لا يسوي zero و هذا لا يسوي
+
+337
+00:40:01,090 --> 00:40:04,190
+zero طيب هذا لا يسوي zero و and
+
+338
+00:40:06,460 --> 00:40:19,040
+الـ D is an integral domain طب
+
+339
+00:40:19,040 --> 00:40:25,020
+هذا عنصر ولا عناصر كتيرة؟ أي اتنين نضربها في بعض
+
+340
+00:40:25,020 --> 00:40:29,160
+لا يمكن يساوي Zero يبقى في عندي Zero divisor؟ لا
+
+341
+00:40:29,160 --> 00:40:32,220
+يبقى مش Zero divisor يبقى خلصنا Integral domain
+
+342
+00:40:32,700 --> 00:40:43,820
+يبقى هذا بده يعطينا ان ال D of X has no zero
+
+343
+00:40:43,820 --> 00:40:59,000
+divisors يبقى دص و هكذا ال D of X is an integral
+
+344
+00:41:12,560 --> 00:41:15,180
+طيب، أعطيكم العافية المرجعة ان شاء الله
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/t5SjM3-XatY_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/t5SjM3-XatY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f2aeb6f0f23f401ac880b3673655ac065d53e81f
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/t5SjM3-XatY_raw.srt
@@ -0,0 +1,1388 @@
+1
+00:02:15,810 --> 00:02:20,410
+بسم الله الرحمن الرحيم اليوم ان شاء الله نبدأ في
+
+2
+00:02:20,410 --> 00:02:26,670
+chapter 16 عنوانه polynomial rings يبقى كأنه احنا
+
+3
+00:02:26,670 --> 00:02:32,350
+فهو بدنا نيجي من كل ال rings ناخد حالة خاصة هي ال
+
+4
+00:02:32,350 --> 00:02:37,090
+ring اللي عناصرها كثيرات الحدود يبقى هذا معناه
+
+5
+00:02:37,090 --> 00:02:44,080
+polynomial rings بدنا نعطي تعريفين ومن ثمنجي
+
+6
+00:02:44,080 --> 00:02:48,620
+لعملية الجمع وعملية الضرب على مين على ال hologram
+
+7
+00:02:48,620 --> 00:02:54,640
+التعريف الأول بيقول ما يأتي Little RBA commutative
+
+8
+00:02:54,640 --> 00:03:01,800
+ring بدي أكون set جديدة بدي أسميها R of X هذه ال
+
+9
+00:03:01,800 --> 00:03:08,610
+set على أسرها كل عنصر فيها عبارة عن كثيرة حدودan x
+
+10
+00:03:08,610 --> 00:03:13,190
+to the power n plus an minus one x to the power n
+
+11
+00:03:13,190 --> 00:03:17,770
+minus one زائد زائد a one x زائد ال a node الأس
+
+12
+00:03:17,770 --> 00:03:23,330
+تبع ال x بينزل والباقي كله ثوابت الثوابت هذه ال a
+
+13
+00:03:23,330 --> 00:03:27,850
+a node و a one و a two و a three لغاية a من وين
+
+14
+00:03:27,850 --> 00:03:32,710
+جيبناها جيبناها من ال ring الأصلية اللي هي R فرح
+
+15
+00:03:32,710 --> 00:03:38,270
+قالليA I belongs to main in commutative ring اللي
+
+16
+00:03:38,270 --> 00:03:44,030
+هي A طب ال N is a non negative integer يعني ممكن
+
+17
+00:03:44,030 --> 00:03:49,950
+يكون positive و ممكن يكون zero فإن كانت ال N بيه
+
+18
+00:03:49,950 --> 00:03:54,170
+zero بصير ال polynomial بنسميها ال constant
+
+19
+00:03:54,170 --> 00:03:59,670
+polynomial ليش؟ لأن أي عدد مرفوع لل أس صفر واحد
+
+20
+00:03:59,670 --> 00:04:06,130
+بصير عندنا baseالـ F of X هي مين الـ A نود فيها
+
+21
+00:04:06,130 --> 00:04:12,010
+مقدار ثابت واحد فقط وهذا ما سنشير اليه بعد قليل
+
+22
+00:04:12,010 --> 00:04:17,870
+على أي حال كل الـ A هات هدول المعاملات تبعات الـ X
+
+23
+00:04:17,870 --> 00:04:23,050
+هم عناصر في ال set R أو في ال commutative ring R
+
+24
+00:04:23,050 --> 00:04:27,650
+الـ N نظم non negative integer هذه كلها ال set
+
+25
+00:04:27,860 --> 00:04:35,060
+بسميها a ring of polynomials حلقة كثيرات الحدود أو
+
+26
+00:04:35,060 --> 00:04:39,560
+polynomial ring سواء تسمي هذه والله هذه الاتنين
+
+27
+00:04:39,560 --> 00:04:45,120
+are the same over are in the indeterminate X يعني
+
+28
+00:04:45,120 --> 00:04:51,120
+في المجهول Xالـ which is commutative الـ ring هذه
+
+29
+00:04:51,120 --> 00:04:56,900
+للـ R of X commutative لأن R الأصلية commutative و
+
+30
+00:04:56,900 --> 00:05:02,360
+المعاملات كلهم من R و X تقبل commutes مع ال X
+
+31
+00:05:02,360 --> 00:05:07,560
+تربيع و X تكييب و X أربعة و X مية و هكذا تمام إذا
+
+32
+00:05:07,560 --> 00:05:11,240
+كل هذا ال ring commutative هذا هو ال definition
+
+33
+00:05:11,240 --> 00:05:16,380
+الأول ال definition التاني متى تتساوى two
+
+34
+00:05:16,380 --> 00:05:21,000
+polynomialsفبقول في عندي Polynomial وفي عندي
+
+35
+00:05:21,000 --> 00:05:26,040
+Polynomial تانية اتنين are equal if and only if ال
+
+36
+00:05:26,040 --> 00:05:31,360
+A I بتسوى B I لكل ال I زيروا واحد اتنين تلاتة الى
+
+37
+00:05:31,360 --> 00:05:38,000
+ما شاء الله يعني ايش قصده يقول قصده يقول ان A1 في
+
+38
+00:05:38,000 --> 00:05:41,260
+ال Polynomial الأولى يسوى B1 في ال Polynomial
+
+39
+00:05:41,260 --> 00:05:45,960
+الثانية A0 في ال Polynomial الأولى يسوى B0 في ال
+
+40
+00:05:45,960 --> 00:05:50,270
+Polynomial الثانيةA2 في ال polynomial الأولى يسوى
+
+41
+00:05:50,270 --> 00:05:55,470
+B2 في ال polynomial الثالثة وهكذا هذا بدي أطرح على
+
+42
+00:05:55,470 --> 00:06:01,290
+ما سامعكم أسوالي التالية هل ال polynomial الأولى و
+
+43
+00:06:01,290 --> 00:06:06,650
+ال polynomial التانية من نفس الدرجة يعني أكبر أس
+
+44
+00:06:06,650 --> 00:06:13,370
+لل X في الأولى زي أكبر أس لل X في الثانية؟ متأكدة؟
+
+45
+00:06:13,370 --> 00:06:19,670
+لأ مش صحيحوالله لو كان هيك لكان قلت X to the power
+
+46
+00:06:19,670 --> 00:06:25,430
+N لكن غير قلت X to the power M هل احنا قلنا ال N
+
+47
+00:06:25,430 --> 00:06:30,650
+بتساوي ال M؟ طيب خليني بدي ارجعكوا لشغل عامل
+
+48
+00:06:30,650 --> 00:06:35,550
+اشتغلته فيه Calculus B Calculus B؟ اه Calculus B
+
+49
+00:06:35,550 --> 00:06:41,410
+لما كنا نسوي partial fractions كسور جزئية ونقارن
+
+50
+00:06:41,410 --> 00:06:45,970
+المعاملات في الطرفين هلالمعادلة كانت على الطرف
+
+51
+00:06:45,970 --> 00:06:49,710
+اليمين زي المعادلة على الطرف الشمال؟ لأ طيب في
+
+52
+00:06:49,710 --> 00:06:54,110
+عندي هنا X تكعيب و هنا في شغال X تربيع وانزل يبقى
+
+53
+00:06:54,110 --> 00:07:00,350
+معامل X تكعيب دي سوى قداش؟ سوى صفر يبقى هذا معناه
+
+54
+00:07:00,350 --> 00:07:07,610
+ان التنتين ليست من نفس القصر لأ M و N two integers
+
+55
+00:07:07,610 --> 00:07:13,600
+و اتنين are different مختلفين على بعض تماماهو يوضح
+
+56
+00:07:13,600 --> 00:07:19,220
+لك الكلام هذا أكثر وقال لك حيث ال AI بده يساوي
+
+57
+00:07:19,220 --> 00:07:26,080
+Zero إذا كانت ال I أكبر من N نفترض ال N عاشرة ال M
+
+58
+00:07:26,080 --> 00:07:33,800
+كانت أتناشر يبقى رقم 11 ورقم 12 والكولوجيا الأولى
+
+59
+00:07:33,800 --> 00:07:40,650
+مش موجودين ال X أص 11 و X أص 12يبقى المعاملات الـ
+
+60
+00:07:40,650 --> 00:07:48,330
+A11 والـ A12 بأصفار، ماخدين بالك؟ هي الـ AI بساوي
+
+61
+00:07:48,330 --> 00:07:54,770
+Zero إذا كانت الـ I أكبر من N، A11 و A12 بيكون
+
+62
+00:07:54,770 --> 00:08:01,390
+بأصفار، لكن في التانية A11 و A12 بمعاملات، رموز
+
+63
+00:08:01,590 --> 00:08:05,010
+بقول يبقى الرمز الأول بده يساوي Zero والرمز التاني
+
+64
+00:08:05,010 --> 00:08:09,790
+بده يساوي Zero إن كانوا اتنين are equal بشرط
+
+65
+00:08:09,790 --> 00:08:14,150
+التساوي فروحنا قولناش قولنا two polynomials هدول
+
+66
+00:08:14,150 --> 00:08:19,530
+are equivalent only if ال AI بده يساوي ال BI لكل
+
+67
+00:08:19,530 --> 00:08:23,610
+ال I اللي بتساوي Zero واحد واثنين وتلاتة لآخر
+
+68
+00:08:23,610 --> 00:08:28,870
+الحدود اللي عندنا واضح كلامي؟يبقى بناة الأس تبع ال
+
+69
+00:08:28,870 --> 00:08:34,210
+X في الأولى ليس هو نفس الأس في الثانية قد يكون وقد
+
+70
+00:08:34,210 --> 00:08:39,390
+لا يكون يعني ممكن يحصل لكن in general لأ يا أصغر
+
+71
+00:08:39,390 --> 00:08:44,610
+منه يا ايه يا أكبر منه كما سنرى بعد قليل فعند أول
+
+72
+00:08:44,610 --> 00:08:49,810
+مثال بدنا ناخده طيب الآن احنا عرفنا ال polynomial
+
+73
+00:08:49,810 --> 00:08:56,220
+تمام وعرفنا هنا كثيرات حدودوالمعاملة تبعها من الـ
+
+74
+00:08:56,220 --> 00:09:00,420
+commutative ring R وعرفنا انها commutative ring
+
+75
+00:09:00,420 --> 00:09:07,360
+تمام كيف بنعمل عملية الجمع وعملية الضرب على هذه ال
+
+76
+00:09:07,360 --> 00:09:12,720
+polynomial فبقول ما ياتي بنجي وقول هاي F of X وهاي
+
+77
+00:09:12,720 --> 00:09:18,400
+G of X والاتنين هدول two elements في الستم او في
+
+78
+00:09:18,400 --> 00:09:24,670
+ال ring of all polynomials طيبودا جمع F of X زي G
+
+79
+00:09:24,670 --> 00:09:30,310
+of X يساوي A S زي B S في X و S S ماشي S هذه؟
+
+80
+00:09:30,310 --> 00:09:36,530
+ماعرفهاش لكن بدنا نعرفها زي A S minus one زي B S
+
+81
+00:09:36,530 --> 00:09:41,190
+minus في X و S S minus ال one زي زي A one B one في
+
+82
+00:09:41,190 --> 00:09:46,290
+X زي A naught B naught S هي أكبر رقم في الإتنين
+
+83
+00:09:46,290 --> 00:09:52,720
+يعني لو كان N هو الرقم الكبير يبقى S يبقى 12بإن لو
+
+84
+00:09:52,720 --> 00:09:59,300
+كان M هو الرقم الأكبر يبقى ال S تساوي M هيوغلب
+
+85
+00:09:59,300 --> 00:10:08,200
+Where حيث ال S is the maximum of M and N الرقم
+
+86
+00:10:08,200 --> 00:10:14,200
+الكبير فيهم بيكون هو مين؟ S في حالة الجمع وال AI
+
+87
+00:10:14,200 --> 00:10:17,940
+بيساوي Zero لل I اللي أكبر من N وال BI بيساوي Zero
+
+88
+00:10:17,940 --> 00:10:24,690
+لل I اللي أكبر من 100أكبر من ال M واضح كلامي هذا
+
+89
+00:10:24,690 --> 00:10:29,310
+لسه الجامعة الجامعة مش فيه مشكلة سهل المشكلة وين؟
+
+90
+00:10:29,310 --> 00:10:36,630
+فالطرف بيقول الآن ال F of X في ال G of X CM زائد N
+
+91
+00:10:36,630 --> 00:10:41,910
+X اصم زائد M CM زائد N minus one X to the power M
+
+92
+00:10:41,910 --> 00:10:46,370
+زائد N minus one ونظل ماشي لغة من وصل ل C one X
+
+93
+00:10:46,370 --> 00:10:52,150
+زائد C nonواللي بدنا نعرف مين هو CK يعني بدنا نعرف
+
+94
+00:10:52,150 --> 00:10:58,950
+مين C0 ومين C1 ومين C3 ومين C4 ومين C5 ومين C6
+
+95
+00:10:58,950 --> 00:11:01,410
+ومين C7 ومين C8 ومين C9 ومين C10 ومين C11 ومين C12
+
+96
+00:11:01,410 --> 00:11:01,410
+ومين C13 ومين C14 ومين C15 ومين C16 ومين C17 ومين
+
+97
+00:11:01,410 --> 00:11:01,890
+C18 ومين C19 ومين C20 ومين C21 ومين C22 ومين C22
+
+98
+00:11:01,890 --> 00:11:02,390
+ومين C22 ومين C22 ومين C22 ومين C22 ومين C22 ومين
+
+99
+00:11:02,390 --> 00:11:03,410
+C22 ومين C22 ومين C22 ومين C22 ومين C22 ومين C22
+
+100
+00:11:03,410 --> 00:11:12,270
+ومين C22 ومين C22 ومين C22 ومين C22 ومين C22 ومين
+
+101
+00:11:12,270 --> 00:11:15,350
+C22
+
+102
+00:11:15,350 --> 00:11:24,210
+ومين C22نضرب زي اتجاه عكسي المعامل xn مع ثابت تبع
+
+103
+00:11:24,210 --> 00:11:29,550
+ال polynomial التانية المعامل تبع x أُس n minus ال
+
+104
+00:11:29,550 --> 00:11:34,010
+one في المعامل تبع x لل polynomial التانية و هكذا
+
+105
+00:11:34,010 --> 00:11:38,810
+واحد برجع التانية بقدم لغاية ما نخلص نجمع هدول
+
+106
+00:11:38,810 --> 00:11:45,770
+بيكون المعامل تبع مين؟ تبع xk يبقى قولنا هيك ckهو
+
+107
+00:11:45,770 --> 00:11:56,330
+A K B نوت A K I A K ل A N في B نوت زائد A N minus
+
+108
+00:11:56,330 --> 00:12:01,570
+ال one في B one زائد A N minus ال two في B two
+
+109
+00:12:01,570 --> 00:12:08,270
+وهكذا هذه نازلة وهذه راجعة لغاية ايش ما نكمل طب
+
+110
+00:12:08,270 --> 00:12:13,370
+انت قلت ال M و ال N مش زي بعض اقول صحيحلغاية ما
+
+111
+00:12:13,370 --> 00:12:18,870
+لوصل ل M فيه زيادة بيكون المعاملات بأصفار لأنها
+
+112
+00:12:18,870 --> 00:12:25,870
+يجلل AI تسوية Zero من I أكبر من N هذا لو كانت ال N
+
+113
+00:12:25,870 --> 00:12:31,610
+هي الصورة و M هي الكبرى وهذا العكس لو كانت M هي
+
+114
+00:12:31,610 --> 00:12:35,770
+الكبرى و N هي الصورة يبقى كل الأرقام اللي بتيجي
+
+115
+00:12:35,770 --> 00:12:41,440
+بعدها بيكون كلها بأصفارالكلام اللى شفته بنروح نحطه
+
+116
+00:12:41,440 --> 00:12:47,360
+على أرض الواقع بمثال مشان نعرف كيف نشتغل هبقى جيب
+
+117
+00:12:47,360 --> 00:12:52,780
+اقول في الطريق انه عندي two polynomials في ZD3
+
+118
+00:12:52,780 --> 00:12:57,200
+يبقى ال ring اللى عندنا of polynomials جايبين
+
+119
+00:12:57,200 --> 00:13:03,880
+معاملات ثمنوية من ZD3 يبقى معناها ZD3 يا zero يا
+
+120
+00:13:03,880 --> 00:13:09,660
+واحد يا اتنين ما بزيد عن ذلكتطلع تتوفر لنا كله 2 و
+
+121
+00:13:09,660 --> 00:13:15,720
+1، مظبوط؟ و Zero، Zero ما هو هنا X تكيب طارت، لأنه
+
+122
+00:13:15,720 --> 00:13:19,640
+ما عاملها باشر، ب Zero. طيب، أخدت تنتين و أخدت
+
+123
+00:13:19,640 --> 00:13:20,960
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+124
+00:13:20,960 --> 00:13:21,180
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+125
+00:13:21,180 --> 00:13:23,800
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+126
+00:13:23,800 --> 00:13:26,140
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+127
+00:13:26,140 --> 00:13:26,140
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+128
+00:13:26,140 --> 00:13:26,180
+تنتين و تنتين و تنتين و تنتين و تنتين و تنتين و
+
+129
+00:13:26,180 --> 00:13:35,270
+تنتين و تنتين و تنتينقداش أعلى أس ل X عندي تلاتة
+
+130
+00:13:35,270 --> 00:13:43,450
+ممتازة لما أضرب قداش أعلى أس ل X خمسة لأن X تربيع
+
+131
+00:13:43,450 --> 00:13:48,030
+في X تقريب X و أس خمسة إذا بدي أبدأ أعرف قداش A
+
+132
+00:13:48,030 --> 00:13:52,370
+خمسة و B خمسة و A أربعة و B أربعة و A تلاتة و B
+
+133
+00:13:52,370 --> 00:13:56,010
+تلاتة و A تلاتة و هكذا لغاية ما نخلص لإن اللي
+
+134
+00:13:56,010 --> 00:14:00,830
+بلزمنيش في الجبهة بلزمني وينفضرب يبقى خلينا نحطهم
+
+135
+00:14:00,830 --> 00:14:05,710
+في الأول قبل ما نبدأ الان لو جيت بلات قولتلك ايه
+
+136
+00:14:05,710 --> 00:14:13,710
+خمسة كداش عندنا هنا Zero طب و ايه أربعة؟ طب و ايه
+
+137
+00:14:13,710 --> 00:14:20,390
+تلاتة؟ اتنين يعني معملك سهل هو يساوي اتنين و ايه
+
+138
+00:14:20,390 --> 00:14:27,890
+اتنين؟ واحد و ايه واحد؟ اتنين و ايه نوت يساوي
+
+139
+00:14:27,890 --> 00:14:32,630
+اتنين؟هيحطيك المعاملات تبع ال polynomial الأولى
+
+140
+00:14:32,630 --> 00:14:36,870
+بتحط بنفس الطريقة المعاملات تبع ال polynomial
+
+141
+00:14:36,870 --> 00:14:43,450
+التالية ال بي خمسة بزيرو وال بي أربعة بزيرو وال بي
+
+142
+00:14:43,450 --> 00:14:48,310
+تلاتة بزيرو لإن هذا بتبدأ الاكس تربية يفجأ بإننا
+
+143
+00:14:48,310 --> 00:14:55,570
+نيجي لمين؟ لل بي اتنين بي اتنين يساوي اتنين و بي
+
+144
+00:14:55,570 --> 00:15:04,080
+واحديساوي اتنين و B node يساوي واحد طيب
+
+145
+00:15:04,080 --> 00:15:11,180
+ليش بدأت من عند الخمسة لإن حاصل الضرب بده يجيبلي X
+
+146
+00:15:11,180 --> 00:15:16,440
+أس خمسة واحنا قلنا حاصل الضرب بيبدأ من عند C M
+
+147
+00:15:16,440 --> 00:15:21,740
+زائد N يبقى لو جمعت الأسين بيطلع خمسة إذا بده يجيب
+
+148
+00:15:21,740 --> 00:15:26,450
+المعاملات من عند ال A خمسةبدي أجل المطلوب الأول
+
+149
+00:15:26,450 --> 00:15:34,270
+بدي أخد ال F of X زائد ال G of X الحين هدول
+
+150
+00:15:34,270 --> 00:15:40,310
+بالزموري لأ زموش اللي في عملية الجمع يبقى سيبورة
+
+151
+00:15:40,310 --> 00:15:45,430
+منهم عملية الجمع بتقول لي ما ياتي بتبقى تجمع
+
+152
+00:15:45,430 --> 00:15:54,280
+المعاملات المتناظرة X أوس خمسة X أوس اسمين Sالكبير
+
+153
+00:15:54,280 --> 00:16:00,560
+فيهم، مين الكبير يا بنات؟ X تكيب، إذا بتبدأ A3
+
+154
+00:16:00,560 --> 00:16:08,240
+زائد B3 في X تكيب يفجأ هذا، بده يساوي A3، وين عن
+
+155
+00:16:08,240 --> 00:16:19,060
+نهاي؟ A3 باتنين زائد B3 ب Zero في X تكيب زاد، اللي
+
+156
+00:16:19,060 --> 00:16:24,860
+بعده ال X تربيع، هاي ال X تربيعيبقى واحد زائد
+
+157
+00:16:24,860 --> 00:16:31,780
+اتنين يبقى واحد زائد اتنين في ال X تقعيد ال X
+
+158
+00:16:31,780 --> 00:16:36,520
+تربية زائد اتنين في ال X تقعيد ال X تربية زائد
+
+159
+00:16:36,520 --> 00:16:38,240
+اتنين في ال X تقعيد ال X تربية زائد اتنين في ال X
+
+160
+00:16:38,240 --> 00:16:42,360
+تربية زائد اتنين في ال X تربية زائد اتنين في ال X
+
+161
+00:16:42,360 --> 00:16:45,160
+تربية زائد اتنين في ال X تربية زائد اتنين في ال X
+
+162
+00:16:45,160 --> 00:16:49,440
+تربية زائد اتنين في ال X تربية زائد اتنين في ال X
+
+163
+00:16:49,440 --> 00:16:49,440
+تربية زائد اتنين في ال X تربية زائد اتنين في ال X
+
+164
+00:16:49,440 --> 00:16:50,820
+تربية زائد اتنين في ال X تربية زائد اتنين في ال X
+
+165
+00:16:50,820 --> 00:16:56,640
+تربية زائد اتب2 X تك عيد التاني واحد زي اتنين
+
+166
+00:16:56,640 --> 00:17:05,080
+تلاتة في زي التلاتة Zero يبقى هذا Zero ب X تك
+
+167
+00:17:05,080 --> 00:17:12,280
+تربيع اللي بعده اتنين زي اتنين اربع في زي التلاتة
+
+168
+00:17:12,280 --> 00:17:19,040
+بواحد يبقى زائد X زائد X اللي يجي اللي بعده اتنين
+
+169
+00:17:19,040 --> 00:17:25,170
+زي اتنين واحدبتلاتة يبقى زائد زير يبقى صارت
+
+170
+00:17:25,170 --> 00:17:31,430
+النتيجة النهائية اتنين X تكيب زائد X فقط لا غير
+
+171
+00:17:31,430 --> 00:17:40,030
+هذا الجبهر نيجي للضرر بدي اخد ال F of X في ال G of
+
+172
+00:17:40,030 --> 00:17:50,040
+X يبقى بقدر بـCK لو CM زائد Mيبقى هذا بده يبدأ من
+
+173
+00:17:50,040 --> 00:17:55,220
+وين؟ من عند الخمسة لأنه حصل الضرب بده يجيب ليهكسوس
+
+174
+00:17:55,220 --> 00:18:05,880
+خمسة إذا a خمسة في b نوت a خمسة في b نوت a خمسة
+
+175
+00:18:05,880 --> 00:18:14,140
+اللي هو بزيرو b نوت اللي هو كده؟ بواحد زرع a أربعة
+
+176
+00:18:14,140 --> 00:18:28,920
+بزيروفي B1 اللي هو ب 2 زي A3 اللي هو ب 2 في 2 2
+
+177
+00:18:28,920 --> 00:18:39,640
+في 2 زي اللي بعده A2 اللي هو ب 1 في 8 في 0 خلاص
+
+178
+00:18:39,640 --> 00:18:48,120
+هاي 1 2 3 هاي 1 2 3 اه بجين ال 0يبقى v3 اللي هو f0
+
+179
+00:18:48,120 --> 00:18:59,960
+زائد a2 في 0 زائد 2 في 0 كل هذا في x أُس 5 زائد
+
+180
+00:18:59,960 --> 00:19:06,440
+تمام؟ بدنا نيجي لبعد اللي بعد يكون x main أربعة أس
+
+181
+00:19:06,440 --> 00:19:11,420
+أربعة يبقى هدول مالاش علاقة فيهم خلصنا منهم بدنا
+
+182
+00:19:11,420 --> 00:19:19,560
+نبدأ من عند ال a4يبقى زائد a4 اللي هو بزيرو في b
+
+183
+00:19:19,560 --> 00:19:27,440
+node اللي هو بواحد يبقى بواحد زائد a3 اللي هو
+
+184
+00:19:27,440 --> 00:19:35,420
+باتنين في مين؟ في b1 اللي هو باتنين زائد a2 اللي
+
+185
+00:19:35,420 --> 00:19:44,110
+هو بواحد في مين؟ في b2 اللي هو باتنين زائد a1اللي
+
+186
+00:19:44,110 --> 00:19:52,310
+هو بإتنين فمين في واحد اتنين تلاتة اربع يبقى واحد
+
+187
+00:19:52,310 --> 00:19:58,770
+اتنين تلاتة اربع اللي هو ب Zero ب Zero زائد اتنين
+
+188
+00:19:58,770 --> 00:20:05,430
+كمان Zero يبقى واحد اتنين تلاتة اربع خمسة ستة واحد
+
+189
+00:20:05,430 --> 00:20:11,390
+اتنين تلاتة اربع خمسة مضبوط كل هذا الكلام ب X أُس
+
+190
+00:20:11,390 --> 00:20:18,300
+4نجي لل X تكييب زرع ال X تكييب انتهينا من هدول
+
+191
+00:20:18,300 --> 00:20:24,520
+التنتيج تبقى بدي أبدأ من أنت A تلاتة A تلاتة اللي
+
+192
+00:20:24,520 --> 00:20:33,060
+هو اتنين في B يولد واحد زائد واحد في اتنين زائد
+
+193
+00:20:33,060 --> 00:20:43,640
+اتنين في اتنين زائد اتنين في جداش في زيرهذا ال X
+
+194
+00:20:43,640 --> 00:20:52,100
+تكيب زائد نهيده لل X تربيعه يبقى نهيده لل X تربيعه
+
+195
+00:20:52,100 --> 00:21:00,620
+هذا انتهينا منهم ملينا يبقى واحد في واحد يبقى واحد
+
+196
+00:21:00,620 --> 00:21:08,780
+في واحد زائد اتنين في اتنين زائد اتنين في اتنين
+
+197
+00:21:08,780 --> 00:21:16,730
+زائدإتنين في إتنين إتنين في إتنين كلها ده X تربيه
+
+198
+00:21:16,730 --> 00:21:22,350
+زائد تبعات ال X هدول انتهينا منهم يبقى اتنين في
+
+199
+00:21:22,350 --> 00:21:31,150
+واحد اتنين في واحد زائد اتنين في اتنين في X زائد
+
+200
+00:21:31,150 --> 00:21:36,530
+انتهينا من هدول يبقى اتنين في واحد اتنين في واحد
+
+201
+00:21:36,530 --> 00:21:39,450
+تمام؟
+
+202
+00:21:40,010 --> 00:21:48,650
+طيب نجي نجمع هذا الكلام يساوي Zero Zero هذي أربعة
+
+203
+00:21:48,650 --> 00:21:56,630
+و الفاق كله ب Zero أربعة في زي التلاتة كده؟ واحد
+
+204
+00:21:56,630 --> 00:22:03,770
+يبقى بضل عشان دي إلا X أس خمسة كما هي نجي لل X أس
+
+205
+00:22:03,770 --> 00:22:10,880
+أربعة هذا Zero أربعة و اتنينستة والباقية أصفر ستة
+
+206
+00:22:10,880 --> 00:22:19,660
+في زيت تلاتة Zero يبقى زائد Zero في X مصر أربع
+
+207
+00:22:19,660 --> 00:22:27,860
+نيجي لل X تكيب اتنين واتنين أربع واربع تمانية وهذا
+
+208
+00:22:27,860 --> 00:22:35,340
+ب Zero تمانية في زيت تلاتة باتنين يبقى زائد اتنين
+
+209
+00:22:35,340 --> 00:22:44,550
+X تكيبنجي للتربيع اربع واربع تمانية واحد تسعة في
+
+210
+00:22:44,550 --> 00:22:52,270
+زي التلاتة Zero يفجأ زائد Zero X تربيع نجي للإكس
+
+211
+00:22:52,270 --> 00:23:00,250
+أربع واتنين ستة في زي التلاتة Zero يفجأ Zero X
+
+212
+00:23:00,250 --> 00:23:07,740
+زائد اتنين يفجأ النتيجة تساوي X أُس خمسةهذا Zero
+
+213
+00:23:07,740 --> 00:23:15,140
+راح اتنين X تكيب زائد اتنين X تكيب هذا Zero مع
+
+214
+00:23:15,140 --> 00:23:22,360
+السلامة هذا Zero مع السلامة ضال زائد اتنين حد في
+
+215
+00:23:22,360 --> 00:23:28,480
+كل هاي تساؤل هنا سواء كان الجمع او الضرب وقيسي
+
+216
+00:23:28,480 --> 00:23:34,380
+عليها بعدها كل Ring أخرى من العاملها بنفس الطريقة
+
+217
+00:23:34,800 --> 00:23:43,840
+وخاصة عند إيجاد الأول هذا CK يعني C5 هذا C4، هذا
+
+218
+00:23:43,840 --> 00:23:52,620
+C3، هذا C2، هذا C1، هذا C نودة تمام؟ واضح كيف
+
+219
+00:23:52,620 --> 00:23:57,300
+الترتيب؟ يعمل نطلع ان شاء الله بدون خطأ خالص
+
+220
+00:24:21,590 --> 00:24:26,210
+طيب في عندنا three definitions اللي اتعرضنا لهو
+
+221
+00:24:26,210 --> 00:24:34,990
+الآن ال definition الأول بيقول if ال f of x يساوي
+
+222
+00:24:34,990 --> 00:24:40,830
+ال a in x to the power n a in minus ال one x to
+
+223
+00:24:40,830 --> 00:24:50,270
+the power n minus one زائد a one x زائد ال a نهر
+
+224
+00:24:52,070 --> 00:25:00,150
+and ال a n does not equal to zero then the integer
+
+225
+00:25:00,150 --> 00:25:08,950
+n then the integer n
+
+226
+00:25:08,950 --> 00:25:19,670
+العدد الصحيح is called is called the degree of the
+
+227
+00:25:19,670 --> 00:25:31,690
+polynomialof the polynomial and
+
+228
+00:25:31,690 --> 00:25:42,990
+ال AN and ال AN is called is
+
+229
+00:25:42,990 --> 00:25:44,630
+called the leading coefficient
+
+230
+00:25:55,130 --> 00:26:02,270
+the leading coefficient of the function او ال
+
+231
+00:26:02,270 --> 00:26:12,430
+polynomial f of x تعريف الثاني definition of the
+
+232
+00:26:12,430 --> 00:26:21,370
+leading coefficient ال
+
+233
+00:26:21,370 --> 00:26:35,410
+a nIt's the unity of R is the unity of R then ال F
+
+234
+00:26:35,410 --> 00:26:47,470
+of X then ال F of X is called .. is called a monic
+
+235
+00:26:47,470 --> 00:26:50,230
+polynomial.
+
+236
+00:27:02,430 --> 00:27:09,970
+يقولوا دي polynomial دي
+
+237
+00:27:09,970 --> 00:27:21,590
+polynomial F of X بدها تساوي Zero has no degree
+
+238
+00:27:21,590 --> 00:27:30,550
+has no degree Y دي polynomial Y دي
+
+239
+00:27:30,550 --> 00:27:31,290
+polynomial
+
+240
+00:27:36,030 --> 00:27:44,030
+بينما الـ polynomial f of x بدها تساوي الـ a ان هو
+
+241
+00:27:44,030 --> 00:27:48,610
+a squared هيكون
+
+242
+00:27:48,610 --> 00:27:49,710
+اصلا الـ polynomial
+
+243
+00:29:00,150 --> 00:29:05,890
+أحنا عندنا ثلاثة تعريف بدنا نجي نفهم كل تعريف من
+
+244
+00:29:05,890 --> 00:29:12,870
+التعريف الثلاثة الأولى بيعطيني شكل polynomial في
+
+245
+00:29:12,870 --> 00:29:19,450
+ال ring اللي R of X من A in XL لغاية ال A نور
+
+246
+00:29:19,450 --> 00:29:24,850
+بيقولي أن ال A in does not equal to zeroطب لو كانت
+
+247
+00:29:24,850 --> 00:29:30,470
+ب zero، ايش اللي بيحصل؟ ال degree تنزل بمقدار
+
+248
+00:29:30,470 --> 00:29:36,210
+واحد، يبقى هنا مقصود ال a ان لا تسوى zero حتى تبقى
+
+249
+00:29:36,210 --> 00:29:43,270
+الدرجة هي اللي هو ال أس تبع ال X اللي معامله ال aM
+
+250
+00:29:43,270 --> 00:29:47,650
+يبقى شرط أساسي ان ال aM does not equal to zero
+
+251
+00:29:47,650 --> 00:29:55,280
+يبقى الانتجار ان في هذه الحالةبقول عنه هو درجة هذه
+
+252
+00:29:55,280 --> 00:30:01,620
+ال polynomial طب والمعامل تبعها AN هذا اللي بسويش
+
+253
+00:30:01,620 --> 00:30:06,260
+ال zero بسميه leading coefficients يعني المعامل
+
+254
+00:30:06,260 --> 00:30:13,600
+القائد او المعامل الرئيسي تمام يبقى ال AN بسميه
+
+255
+00:30:13,600 --> 00:30:18,120
+leading coefficient المعامل الرئيسي او المعامل
+
+256
+00:30:18,120 --> 00:30:23,250
+القائد لل polynomial ليش؟لأن هذا إن كان لا يسوى
+
+257
+00:30:23,250 --> 00:30:30,190
+Zero يبقى ال X أُس N موجودة لكن لو كان يسوى Zero
+
+258
+00:30:30,190 --> 00:30:34,770
+بطيل ال X أُس وبالتالي تنقص درجة مين ال Polynome
+
+259
+00:30:34,770 --> 00:30:40,070
+اللي هو بالتالي وجوده يترتب عليه أن ال N بتكون
+
+260
+00:30:40,070 --> 00:30:46,270
+موجودة وبتبدأ تنزل الأسس تبع تمين تبع ال X لغاية
+
+261
+00:30:46,270 --> 00:30:53,240
+ما تنعدم تمامايبقى فيه انا شغلة مهمة جدا النقطة
+
+262
+00:30:53,240 --> 00:30:58,200
+الأولى ال N هو درجة ال polynomial وال A N بسميه
+
+263
+00:30:58,200 --> 00:31:02,900
+leading coefficients تعريف التاني بيقول ال leading
+
+264
+00:31:02,900 --> 00:31:08,300
+coefficients ال A N لو كان هو ال unity تبع ال R
+
+265
+00:31:08,300 --> 00:31:13,440
+مين ما يكون ال unity يكون هذا then ال F of X is
+
+266
+00:31:13,440 --> 00:31:19,120
+called a monic polynomialيبقى لو كان الان هذا هرط
+
+267
+00:31:19,120 --> 00:31:23,980
+ان كان ال unity هو الواحد كان بواحد كان رقم تاني
+
+268
+00:31:23,980 --> 00:31:28,060
+غير الواحد و اللي يكن غير الواحد يبقى في هذه
+
+269
+00:31:28,060 --> 00:31:33,340
+الحالة ال polynomial هذه بسميها مليك التعريف
+
+270
+00:31:33,340 --> 00:31:37,620
+التالت ال polynomial لو كان F of X يسوى Zero بيقول
+
+271
+00:31:37,620 --> 00:31:44,310
+مالهاش درجةلكن ال F of X تساوي أي رقم بسميها ال
+
+272
+00:31:44,310 --> 00:31:49,570
+constant polynomial سؤالي هو ال F of X تساوي zero
+
+273
+00:31:49,570 --> 00:31:53,790
+هي constant polynomial ؟ constant polynomial بس
+
+274
+00:31:53,790 --> 00:31:58,430
+has no degree طيب ال F of X يساوي خمسة constant
+
+275
+00:31:58,430 --> 00:32:05,690
+polynomial و الدرجة تبعتها صفر يبقى zero degree
+
+276
+00:32:06,230 --> 00:32:10,610
+يبقى لو كان صفر if of x يساوي صفر بقول مالهاش درجة
+
+277
+00:32:10,610 --> 00:32:16,050
+لكن لو كان if of x يساوي أي رقم غير الصفر بقول هذه
+
+278
+00:32:16,050 --> 00:32:21,010
+polynomial من الدرجة الصفرية from the zero degree
+
+279
+00:32:21,010 --> 00:32:27,730
+طيب بنجي لأول نظرية في هذا الموضوع وهي على الشكل
+
+280
+00:32:27,730 --> 00:32:29,510
+التالي DRM
+
+281
+00:32:36,180 --> 00:32:44,080
+تقول if D is an integral domain if capital D is an
+
+282
+00:32:44,080 --> 00:32:47,740
+is
+
+283
+00:32:47,740 --> 00:32:58,120
+an integral domain then
+
+284
+00:32:58,120 --> 00:33:01,260
+D
+
+285
+00:33:01,260 --> 00:33:10,730
+of X is an integral domainالـ Integral
+
+286
+00:33:10,730 --> 00:33:13,770
+domain
+
+287
+00:33:32,330 --> 00:33:35,870
+يقولوا لو كان دي Integral domain ماذا نقصد بال
+
+288
+00:33:35,870 --> 00:33:42,490
+Integral domain؟ community bring with unity مافيش
+
+289
+00:33:42,490 --> 00:33:47,350
+فيها Zero divisors إلا الصفر تمام؟ حط المعلومة هذه
+
+290
+00:33:47,350 --> 00:33:51,030
+في دماغنا و بدنا نبدأ نشتغل عليها إذا الخطوة
+
+291
+00:33:51,030 --> 00:33:59,630
+الأولى بدي أقوله let دي be an Integral domain
+
+292
+00:34:02,990 --> 00:34:07,930
+تمام then ال
+
+293
+00:34:07,930 --> 00:34:15,810
+D is a commutative ring
+
+294
+00:34:15,810 --> 00:34:19,410
+with
+
+295
+00:34:19,410 --> 00:34:31,550
+unity مثلا one say على سبيل المثال بواحد طيب احنا
+
+296
+00:34:31,550 --> 00:34:38,610
+بنثبتإن ال D of X هذه هي Integral دموعنا يبقى بدنا
+
+297
+00:34:38,610 --> 00:34:43,910
+هي أولا commutative ring with unity تمام يبقى باجي
+
+298
+00:34:43,910 --> 00:34:56,830
+بقوله ال D of X is commutative ring because
+
+299
+00:34:56,830 --> 00:35:13,460
+ال D نفسهاis a commutative ring يعني
+
+300
+00:35:13,460 --> 00:35:19,040
+المعاملات كلهم بيكونوا بتبدلوا مع بعض مافيش مشكلة
+
+301
+00:35:19,040 --> 00:35:24,200
+وال X بتبدل مع X تربيه و مع X تكيب ممكن نعمل يمين
+
+302
+00:35:24,200 --> 00:35:28,640
+او شمال ماتفرجش عندنا يبقى صحيح D of X is a
+
+303
+00:35:28,640 --> 00:35:37,470
+commutative ringبداجي اقوله if ال one is the unity
+
+304
+00:35:37,470 --> 00:35:49,050
+of D then ال F of X بده يساوي ال unity يعني ال
+
+305
+00:35:49,050 --> 00:35:54,890
+constant polynomial هذه بيساوي واحد is the unity
+
+306
+00:35:54,890 --> 00:35:56,970
+of
+
+307
+00:35:57,970 --> 00:36:09,710
+D of X سبب because ان ال G of X اضربيها ال F of X
+
+308
+00:36:09,710 --> 00:36:15,890
+تساوي واحد هي الواحد في ال G of X كده تساوي ال G
+
+309
+00:36:15,890 --> 00:36:24,110
+of X لكل ال G of X اللي موجودة وين؟ D of X
+
+310
+00:36:26,640 --> 00:36:31,340
+ده ليش صار على الـ Neverland ال D of X صارت
+
+311
+00:36:31,340 --> 00:36:37,140
+commutative ring with unity تمام؟ احنا ماثبتهاش
+
+312
+00:36:37,140 --> 00:36:44,440
+انها integral domain تمام؟ لشان هيك بدي اشوف حاصل
+
+313
+00:36:44,440 --> 00:36:52,320
+ضرب two elements و اثبت انه موجودفي او افضل انه
+
+314
+00:36:52,320 --> 00:36:56,920
+موجود في دي يبقى الاول في دي يا اما الثاني في دي
+
+315
+00:36:56,920 --> 00:37:07,460
+بس هنا سنثبت بطريقة شوية يعني انا بنتقل الشامع
+
+316
+00:37:07,460 --> 00:37:15,520
+واحدة تحت بس ايوة ال prime ideal ال prime ideal
+
+317
+00:37:15,520 --> 00:37:20,150
+بدي اخد حاصل ضرب two elements موجودات فيهو أثبت
+
+318
+00:37:20,150 --> 00:37:25,350
+إما الأول أو الثاني موجود فيه لأ هذه بدي أخد اللي
+
+319
+00:37:25,350 --> 00:37:31,770
+هو حاصل ضرب two elements بدي أثبت إنه حاصل الضرب
+
+320
+00:37:31,770 --> 00:37:38,970
+هذا المعاملات ولا واحد فيهم ب zero يعني مافيش zero
+
+321
+00:37:38,970 --> 00:37:44,570
+divisor ومصيره مثالي مصير integral domain صح؟ يبقى
+
+322
+00:37:44,570 --> 00:37:52,830
+بالداجة أقوله letالـ F of X اللي هو بده يساوي A N
+
+323
+00:37:52,830 --> 00:38:02,470
+X N A N minus ال 1 X N minus ال 1 زائد A 1 X زائد
+
+324
+00:38:02,470 --> 00:38:11,870
+ال A نوت وبالشرط ان ال A N لا يساوي Zero والتاني
+
+325
+00:38:11,870 --> 00:38:21,250
+ال G of Xبدي يساوي بي ام اكس ام بي ام ماينوس الوان
+
+326
+00:38:21,250 --> 00:38:29,350
+اكس ام ماينوس الوان زائد زائد بي وان اكس زائد بي
+
+327
+00:38:29,350 --> 00:38:38,450
+لات وال بي ام لا يساوي زيو اتنين هدول موجودات في D
+
+328
+00:38:38,450 --> 00:38:39,590
+of X
+
+329
+00:38:44,970 --> 00:38:56,090
+لو جيت ال leading factors then the leading then
+
+330
+00:38:56,090 --> 00:39:00,790
+the leading factors
+
+331
+00:39:00,790 --> 00:39:08,530
+ممكن
+
+332
+00:39:08,530 --> 00:39:16,030
+يساوي زيرو ؟ مش إمكانية يبقى لا يمكنإنه يساوي zero
+
+333
+00:39:16,030 --> 00:39:26,950
+السبب because ان ال a n لا يساوي zero و ال b m لا
+
+334
+00:39:26,950 --> 00:39:32,990
+يساوي zero اذا الحاصل ضربهم ليه يساوي zero طب
+
+335
+00:39:32,990 --> 00:39:38,730
+معقول حاصل ضربعنصرين مايسويش ال zero حتى لو كان كل
+
+336
+00:39:38,730 --> 00:39:44,550
+واحد فيهم لا يسوي zero لا ممكن يسوي zero بس في ال
+
+337
+00:39:44,550 --> 00:39:50,490
+integral domain لأ صح ولا لأ يبقى هنا هذا لأ لأ
+
+338
+00:39:50,490 --> 00:39:56,370
+because هذا لا يسوي زي مثلا زيد ستة زيد ستة اتنين
+
+339
+00:39:56,370 --> 00:40:01,090
+في تلاتة zero مبني اللي لا يسوي zero و هذا لا يسوي
+
+340
+00:40:01,090 --> 00:40:04,190
+zero طيب هذا لا يسوي zero و and
+
+341
+00:40:06,460 --> 00:40:19,040
+الـ D is an integral domain طب
+
+342
+00:40:19,040 --> 00:40:25,020
+هذا عنصر ولا عناصر كتيرة؟ أي اتنين نضربها في بعض
+
+343
+00:40:25,020 --> 00:40:29,160
+لا يمكن يساوي Zero يبقى في عندي Zero divisor؟ لا
+
+344
+00:40:29,160 --> 00:40:32,220
+يبقى مش Zero divisor يبقى خلصنا Integral domain
+
+345
+00:40:32,700 --> 00:40:43,820
+يبقى هذا بده يعطينا ان ال D of X has no zero
+
+346
+00:40:43,820 --> 00:40:59,000
+divisors يبقى دص و هكذا ال D of X is an integral
+
+347
+00:41:12,560 --> 00:41:15,180
+طيب، أعطيكم العافية المرجعة ان شاء الله
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM_raw.json b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..dc15c973714b4a23facb4e72353dacd23d072249
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/tviGPuJtuBM_raw.json
@@ -0,0 +1 @@
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"temperature": 1.0}, {"id": 6, "seek": 18961, "start": 161.51, "end": 189.61, "text": "و كذلك if we show that إذا جدرنا نبين إن الواحد أو ال unity موجود في A then ال A is maximum مش هذا مثال سابق خدناه المحلقة الماضية إنه لو أخدت أي من ال ring R اللي بتبقى commutative ring with unity", "tokens": [2407, 9122, 8848, 23275, 498, 321, 855, 300, 11933, 15730, 10874, 3215, 2288, 8315, 8717, 3555, 9957, 36145, 2423, 14407, 24401, 34051, 2423, 18205, 3714, 29245, 23328, 8978, 316, 550, 2423, 316, 307, 6674, 37893, 23758, 50113, 6027, 8608, 16758, 4587, 16490, 3215, 8315, 3224, 9673, 5016, 1211, 28671, 9673, 46958, 10632, 36145, 3224, 45164, 5551, 9778, 3215, 2655, 36632, 9154, 2423, 4875, 497, 13672, 1829, 39894, 3555, 4587, 7578, 800, 325, 1166, 4875, 365, 18205], "avg_logprob": -0.19389204855089065, "compression_ratio": 1.4477611940298507, "no_speech_prob": 0.0, "words": [{"start": 161.51, "end": 161.87, "word": "و", "probability": 0.88330078125}, {"start": 161.87, "end": 162.55, "word": " 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عالنا R كمية ت bring with unity والـA ايديل في R يبقى بيقول الـR modulo A بتبقى integral domain إذا كان الـA prime ايديل", "tokens": [1211, 2407, 25961, 2423, 39184, 32, 2423, 39184, 30519, 1312, 6156, 995, 8717, 3615, 28480, 4724, 4587, 7578, 2423, 24793, 10632, 1975, 5016, 8315, 6225, 6027, 8315, 497, 9122, 2304, 10632, 6055, 1565, 365, 18205, 16070, 39184, 32, 1975, 1829, 16254, 1211, 8978, 497, 7251, 3555, 4587, 7578, 4724, 1829, 39648, 2423, 39184, 49, 1072, 13455, 316, 39894, 3555, 4587, 7578, 11573, 9274, 11933, 15730, 25961, 2423, 39184, 32, 5835, 1975, 1829, 16254, 1211], "avg_logprob": -0.4035416769981384, "compression_ratio": 1.4879518072289157, "no_speech_prob": 0.0, "words": [{"start": 1435.03, "end": 1435.43, "word": "لو", "probability": 0.6845703125}, {"start": 1435.43, "end": 1435.75, "word": " كان", "probability": 0.95068359375}, {"start": 1435.75, "end": 1436.25, "word": " الـA", "probability": 0.4964192708333333}, {"start": 1436.25, "end": 1443.93, "word": " 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One to show one to show that بدنا نحاول ندبد ان الـ R modulo A", "tokens": [20892, 2540, 300, 16472, 2423, 39184, 316, 307, 316, 6, 7348, 13, 1485, 281, 855, 472, 281, 855, 300, 47525, 8315, 8717, 5016, 995, 12610, 8717, 3215, 3555, 3215, 16472, 2423, 39184, 497, 1072, 13455, 316], "avg_logprob": -0.42567567567567566, "compression_ratio": 1.2747252747252746, "no_speech_prob": 0.0, "words": [{"start": 1695.2599999999998, "end": 1696.6599999999999, "word": "Assume", "probability": 0.6331787109375}, {"start": 1696.6599999999999, "end": 1698.06, "word": " that", "probability": 0.75927734375}, {"start": 1698.06, "end": 1699.34, "word": " ان", "probability": 0.54443359375}, {"start": 1699.34, "end": 1699.72, "word": " الـ", "probability": 0.8486328125}, {"start": 1699.72, "end": 1700.12, "word": " A", "probability": 0.435546875}, {"start": 1700.12, "end": 1700.88, "word": " is", "probability": 0.515625}, {"start": 1700.88, "end": 1701.54, "word": " A'", "probability": 0.420654296875}, 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{"start": 2159.02, "end": 2159.66, "word": " اقوله", "probability": 0.5562337239583334}, {"start": 2159.66, "end": 2160.34, "word": " left", "probability": 0.58984375}, {"start": 2160.34, "end": 2161.14, "word": " ال", "probability": 0.411865234375}, {"start": 2161.14, "end": 2161.56, "word": " a", "probability": 0.41943359375}, {"start": 2161.56, "end": 2162.42, "word": " موضوعه", "probability": 0.492626953125}, {"start": 2162.42, "end": 2162.86, "word": " a", "probability": 0.82373046875}, {"start": 2162.86, "end": 2163.74, "word": " a", "probability": 0.1842041015625}, {"start": 2163.74, "end": 2164.34, "word": " b", "probability": 0.26904296875}, {"start": 2164.34, "end": 2165.82, "word": " a", "probability": 0.6572265625}, {"start": 2165.82, "end": 2166.7, "word": " field", "probability": 0.94140625}, {"start": 2166.7, "end": 2168.14, "word": " يبقى", "probability": 0.952880859375}, {"start": 2168.14, "end": 2168.68, "word": " b", "probability": 0.451904296875}, {"start": 2168.68, "end": 2169.38, "word": " a", "probability": 0.96142578125}, {"start": 2169.38, "end": 2170.3, "word": " field", "probability": 0.95654296875}, {"start": 2170.3, "end": 2172.2, "word": " طبعا", "probability": 0.74066162109375}, {"start": 2172.2, "end": 2172.98, "word": " بدي", "probability": 0.6531982421875}, {"start": 2172.98, "end": 2173.4, "word": " اثبت", "probability": 0.89208984375}, {"start": 2173.4, "end": 2173.62, "word": " ان", "probability": 0.91943359375}, {"start": 2173.62, "end": 2173.84, "word": " ال", "probability": 0.95556640625}, {"start": 2173.84, "end": 2174.04, "word": " a", "probability": 0.943359375}, {"start": 2174.04, "end": 2174.58, "word": " باله", "probability": 0.6368408203125}, {"start": 2174.58, "end": 2175.34, "word": " is", "probability": 0.84375}, {"start": 2175.34, "end": 2176.16, "word": " maximum", "probability": 0.84912109375}, {"start": 2176.16, "end": 2177.56, "word": " يبقى", "probability": 0.987548828125}, {"start": 2177.56, "end": 2178.14, "word": " one", "probability": 0.8564453125}, {"start": 2178.14, "end": 2179.56, "word": " two", "probability": 0.8505859375}, {"start": 2179.56, "end": 2181.72, "word": " one", "probability": 0.8603515625}, {"start": 2181.72, "end": 2182.82, "word": " two", "probability": 0.951171875}, {"start": 2182.82, "end": 2184.12, "word": " show", "probability": 0.18017578125}, {"start": 2184.12, "end": 2185.78, "word": " that", "probability": 0.8837890625}], "temperature": 1.0}, {"id": 78, "seek": 221519, "start": 2186.69, "end": 2215.19, "text": "إن ال A is maximum يبدأ يقول افترض ان ال B بيكون ايديل او R بحيث ان ال A اللي عندنا", "tokens": [28814, 1863, 2423, 316, 307, 6674, 7251, 44510, 10721, 7251, 39648, 1975, 5172, 2655, 43042, 16472, 2423, 363, 4724, 1829, 30544, 1975, 1829, 16254, 1211, 1975, 2407, 497, 4724, 5016, 1829, 12984, 16472, 2423, 316, 13672, 1829, 43242, 8315], "avg_logprob": -0.4386718824505806, "compression_ratio": 1.2429906542056075, "no_speech_prob": 0.0, "words": 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"end": 2240.57, "word": " ان", "probability": 0.5458984375}, {"start": 2240.57, "end": 2240.87, "word": " الـ", "probability": 0.928955078125}, {"start": 2240.87, "end": 2241.05, "word": " A", "probability": 0.8212890625}, {"start": 2241.05, "end": 2241.79, "word": " maximum", "probability": 0.62255859375}, {"start": 2241.79, "end": 2242.41, "word": " لو", "probability": 0.370361328125}, {"start": 2242.41, "end": 2242.69, "word": " روحت", "probability": 0.9033203125}, {"start": 2242.69, "end": 2243.31, "word": " لتعريف", "probability": 0.953515625}, {"start": 2243.31, "end": 2243.49, "word": " ال", "probability": 0.88671875}, {"start": 2243.49, "end": 2243.99, "word": " maximum", "probability": 0.8154296875}], "temperature": 1.0}, {"id": 80, "seek": 227203, "start": 2244.31, "end": 2272.03, "text": "فرأت أنه عندي ideal تاني B بحيث الـA subset من B ولا يساوي و الـB subset من R. إذا أثبتوا إنه B يساوي الـR، بصير هذا الـMaximal أو إذا أثبتوا إن الـUnity هو الموجود في B، يبقى بصير الـA 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A", "probability": 0.91845703125}, {"start": 2744.25, "end": 2747.41, "word": " يبقى", "probability": 0.79766845703125}, {"start": 2747.41, "end": 2747.57, "word": " ال", "probability": 0.962890625}, {"start": 2747.57, "end": 2747.87, "word": " B", "probability": 0.958984375}, {"start": 2747.87, "end": 2748.45, "word": " مش", "probability": 0.9775390625}, {"start": 2748.45, "end": 2748.97, "word": " موجود", "probability": 0.99267578125}, {"start": 2748.97, "end": 2749.17, "word": " في", "probability": 0.9140625}, {"start": 2749.17, "end": 2749.33, "word": " ال", "probability": 0.9794921875}, {"start": 2749.33, "end": 2749.57, "word": " A", "probability": 0.98486328125}, {"start": 2749.57, "end": 2750.63, "word": " then", "probability": 0.365234375}, {"start": 2750.63, "end": 2753.65, "word": " ال", "probability": 0.93701171875}, {"start": 2753.65, "end": 2754.07, "word": " B", "probability": 0.94140625}, {"start": 2754.07, "end": 2755.27, "word": " زائد", "probability": 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modulo A مدام أنصر غير صفري", "tokens": [1829, 3555, 4587, 7578, 20193, 7251, 43020, 14739, 7251, 3794, 995, 45865, 1958, 7251, 3555, 4587, 7578, 2423, 363, 30767, 16373, 3215, 2423, 316, 307, 257, 2107, 12, 32226, 4478, 7251, 3555, 4587, 7578, 23758, 2423, 363, 30767, 16373, 3215, 2423, 316, 307, 257, 2107, 12, 32226, 4478, 2107, 12, 32226, 4478, 294, 497, 1072, 13455, 316, 3714, 3215, 10943, 14739, 9381, 2288, 32771, 13546, 20328, 5172, 16572], "avg_logprob": -0.295516318169193, "compression_ratio": 1.5492957746478873, "no_speech_prob": 0.0, "words": [{"start": 2760.82, "end": 2761.46, "word": "يبقى", "probability": 0.80279541015625}, {"start": 2761.46, "end": 2761.68, "word": " لا", "probability": 0.57861328125}, {"start": 2761.68, "end": 2762.46, "word": " يمكن", "probability": 0.871826171875}, {"start": 2762.46, "end": 2762.88, "word": " أن", "probability": 0.62841796875}, {"start": 2762.88, "end": 2763.56, "word": " يساوي", "probability": 0.8695068359375}, {"start": 2763.56, 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ان ال b زايد ال a is a unit خلصنا يبقى هذا بيكون ال b زايد ال a is a unit", "tokens": [9566, 3555, 1975, 1829, 8592, 6055, 36178, 13546, 4117, 14407, 24976, 3615, 3555, 9640, 3660, 29538, 22807, 1975, 3224, 11331, 33546, 1211, 48812, 25513, 18871, 9381, 2288, 9957, 7251, 3794, 995, 45865, 45595, 11536, 1829, 31371, 4724, 11622, 995, 25708, 2423, 257, 307, 257, 4985, 1975, 5016, 8315, 12174, 1211, 8315, 34105, 45164, 12174, 3215, 2288, 8315, 8717, 12984, 3555, 2655, 16472, 2423, 272, 30767, 995, 25708, 2423, 257, 307, 257, 4985, 16490, 1211, 9381, 8315, 7251, 3555, 4587, 7578, 23758, 4724, 1829, 30544, 2423, 272, 30767, 995, 25708, 2423, 257, 307, 257, 4985], "avg_logprob": -0.20493421742790624, "compression_ratio": 1.7916666666666667, "no_speech_prob": 0.0, "words": [{"start": 3340.17, "end": 3340.45, "word": "طب", "probability": 0.5723876953125}, {"start": 3340.45, "end": 3340.63, "word": " ايش", "probability": 0.6443277994791666}, {"start": 3340.63, "end": 3341.37, "word": " تفسيركوا", "probability": 0.802001953125}, {"start": 3341.37, "end": 3342.11, "word": " للعبارة", "probability": 0.969921875}, {"start": 3342.11, "end": 3343.67, "word": " هذه؟", "probability": 0.625244140625}, {"start": 3343.67, "end": 3344.41, "word": " اه", "probability": 0.53863525390625}, {"start": 3344.41, "end": 3345.29, "word": " حاصل", "probability": 0.8821614583333334}, {"start": 3345.29, "end": 3345.63, "word": " ضرب", "probability": 0.99462890625}, {"start": 3345.63, "end": 3346.33, "word": " عنصرين", "probability": 0.9595947265625}, {"start": 3346.33, "end": 3346.99, "word": " يساوي", "probability": 0.950439453125}, {"start": 3346.99, "end": 3348.45, "word": " اليونيتي", "probability": 0.67608642578125}, {"start": 3348.45, "end": 3349.67, "word": " بزايد", "probability": 0.70977783203125}, {"start": 3349.67, "end": 3349.93, "word": " ال", "probability": 0.77685546875}, {"start": 3349.93, "end": 3350.19, "word": " a", "probability": 0.401123046875}, {"start": 3350.19, "end": 3350.69, "word": " is", "probability": 0.6875}, {"start": 3350.69, "end": 3351.59, "word": " a", "probability": 0.8896484375}, {"start": 3351.59, "end": 3352.05, "word": " unit", "probability": 0.96826171875}, {"start": 3352.05, "end": 3352.85, "word": " احنا", "probability": 0.8792317708333334}, {"start": 3352.85, "end": 3353.33, "word": " قلنا", "probability": 0.88232421875}, {"start": 3353.33, "end": 3353.67, "word": " هنا", "probability": 0.94091796875}, {"start": 3353.67, "end": 3353.99, "word": " لو", "probability": 0.96142578125}, {"start": 3353.99, "end": 3354.75, "word": " قدرنا", "probability": 0.902099609375}, {"start": 3354.75, "end": 3355.47, "word": " نثبت", "probability": 0.993408203125}, {"start": 3355.47, "end": 3355.77, "word": " ان", "probability": 0.8515625}, {"start": 3355.77, "end": 3356.05, "word": " ال", "probability": 0.794921875}, {"start": 3356.05, "end": 3356.35, "word": " b", "probability": 0.5361328125}, {"start": 3356.35, "end": 3356.99, "word": " زايد", "probability": 0.9337565104166666}, {"start": 3356.99, "end": 3357.29, "word": " ال", "probability": 0.97900390625}, {"start": 3357.29, "end": 3357.49, "word": " a", "probability": 0.978515625}, {"start": 3357.49, "end": 3357.81, "word": " is", "probability": 0.87109375}, {"start": 3357.81, "end": 3358.07, "word": " a", "probability": 0.84033203125}, {"start": 3358.07, "end": 3358.37, "word": " unit", "probability": 0.96826171875}, {"start": 3358.37, "end": 3359.37, "word": " خلصنا", "probability": 0.9573974609375}, {"start": 3359.37, "end": 3360.45, "word": " يبقى", "probability": 0.9395751953125}, {"start": 3360.45, "end": 3360.77, "word": " هذا", "probability": 0.92138671875}, {"start": 3360.77, "end": 3361.53, "word": " بيكون", "probability": 0.8279622395833334}, {"start": 3361.53, "end": 3362.29, "word": " ال", "probability": 0.93408203125}, {"start": 3362.29, "end": 3362.79, "word": " b", "probability": 0.86474609375}, {"start": 3362.79, "end": 3363.63, "word": " زايد", "probability": 0.9602864583333334}, {"start": 3363.63, "end": 3363.97, "word": " ال", "probability": 0.98388671875}, {"start": 3363.97, "end": 3364.45, "word": " a", "probability": 0.98974609375}, {"start": 3364.45, "end": 3365.71, "word": " is", "probability": 0.89501953125}, {"start": 3365.71, "end": 3366.21, "word": " a", "probability": 0.97607421875}, {"start": 3366.21, "end": 3366.67, "word": " unit", "probability": 0.9619140625}], "temperature": 1.0}, {"id": 119, "seek": 339048, "start": 3367.1, "end": 3390.48, "text": "يبقى صار عندى any non zero element b plus a في ال R modulo a is a يعني يبقى ال R modulo a is a field هذا بيعطيلك ان ال R modulo a is a field تمام؟ وهو المطلوب", "tokens": [1829, 3555, 4587, 7578, 20328, 9640, 43242, 7578, 604, 2107, 4018, 4478, 272, 1804, 257, 8978, 2423, 497, 1072, 13455, 257, 307, 257, 37495, 22653, 7251, 3555, 4587, 7578, 2423, 497, 1072, 13455, 257, 307, 257, 2519, 23758, 4724, 40228, 9566, 1829, 23275, 16472, 2423, 497, 1072, 13455, 257, 307, 257, 2519, 46811, 10943, 22807, 37037, 2407, 9673, 9566, 1211, 37746], "avg_logprob": -0.24722781008289707, "compression_ratio": 1.4825174825174825, "no_speech_prob": 0.0, "words": [{"start": 3367.1, "end": 3367.62, "word": "يبقى", "probability": 0.88427734375}, {"start": 3367.62, "end": 3368.16, "word": " صار", "probability": 0.641845703125}, {"start": 3368.16, "end": 3368.8, "word": " عندى", "probability": 0.840087890625}, {"start": 3368.8, "end": 3369.2, "word": " any", "probability": 0.666015625}, {"start": 3369.2, "end": 3369.86, "word": " non", "probability": 0.8759765625}, {"start": 3369.86, "end": 3370.54, "word": " zero", "probability": 0.50439453125}, {"start": 3370.54, "end": 3371.34, "word": " element", "probability": 0.92724609375}, {"start": 3371.34, "end": 3371.82, "word": " b", "probability": 0.16455078125}, {"start": 3371.82, "end": 3372.26, "word": " plus", "probability": 0.23974609375}, {"start": 3372.26, "end": 3372.6, "word": " a", "probability": 0.9814453125}, {"start": 3372.6, "end": 3372.74, "word": " في", "probability": 0.475830078125}, {"start": 3372.74, "end": 3372.94, "word": " ال", "probability": 0.81640625}, {"start": 3372.94, "end": 3373.14, "word": " R", "probability": 0.49169921875}, {"start": 3373.14, "end": 3373.74, "word": " modulo", "probability": 0.67822265625}, {"start": 3373.74, "end": 3374.12, "word": " a", "probability": 0.76953125}, {"start": 3374.12, "end": 3374.68, "word": " is", "probability": 0.414794921875}, {"start": 3374.68, "end": 3375.04, "word": " a", "probability": 0.8994140625}, {"start": 3375.04, "end": 3375.3, "word": " يعني", "probability": 0.5538330078125}, {"start": 3375.3, "end": 3376.08, "word": " يبقى", "probability": 0.8968505859375}, {"start": 3376.08, "end": 3376.2, "word": " ال", "probability": 0.7900390625}, {"start": 3376.2, "end": 3376.46, "word": " R", "probability": 0.94677734375}, {"start": 3376.46, "end": 3377.04, "word": " modulo", "probability": 0.91015625}, {"start": 3377.04, "end": 3377.48, "word": " a", "probability": 0.97509765625}, {"start": 3377.48, "end": 3378.1, "word": " is", "probability": 0.7783203125}, {"start": 3378.1, "end": 3378.68, "word": " a", "probability": 0.96533203125}, {"start": 3378.68, "end": 3379.5, "word": " field", "probability": 0.80615234375}, {"start": 3379.5, "end": 3380.42, "word": " هذا", "probability": 0.7646484375}, {"start": 3380.42, "end": 3381.4, "word": " بيعطيلك", "probability": 0.883984375}, {"start": 3381.4, "end": 3381.92, "word": " ان", "probability": 0.72705078125}, {"start": 3381.92, "end": 3382.16, "word": " ال", "probability": 0.92529296875}, {"start": 3382.16, "end": 3382.52, "word": " R", "probability": 0.970703125}, {"start": 3382.52, "end": 3383.24, "word": " modulo", "probability": 0.941650390625}, {"start": 3383.24, "end": 3383.88, "word": " a", "probability": 0.982421875}, {"start": 3383.88, "end": 3384.5, "word": " is", "probability": 0.80810546875}, {"start": 3384.5, "end": 3385.2, "word": " a", "probability": 0.986328125}, {"start": 3385.2, "end": 3386.44, "word": " field", "probability": 0.93017578125}, {"start": 3386.44, "end": 3388.4, "word": " تمام؟", "probability": 0.747802734375}, {"start": 3388.4, "end": 3389.34, "word": " وهو", "probability": 0.7432861328125}, {"start": 3389.34, "end": 3390.48, "word": " المطلوب", "probability": 0.9376220703125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3393.201625, "duration_after_vad": 3293.437499999988}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/xVdNKWsk6Ew.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/xVdNKWsk6Ew.srt
new file mode 100644
index 0000000000000000000000000000000000000000..677dde1b10b9f56e5235664a65d98cbe9dbea010
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/xVdNKWsk6Ew.srt
@@ -0,0 +1,1454 @@
+1
+00:00:20,700 --> 00:00:24,800
+بسم الله الرحمن الرحيم، نكمل ما ابتدأناه في المرة
+
+2
+00:00:24,800 --> 00:00:30,660
+الماضية من حل المسائل على شاكلة خمسة عشر، طبعاً احنا
+
+3
+00:00:30,660 --> 00:00:36,980
+في المرة الماضية، على ما قلت، حلنا المسائل لثمانية
+
+4
+00:00:36,980 --> 00:00:42,520
+وعشرة، وثمانية، اللي أنا قلنا أربعة عشر، أربعة عشر
+
+5
+00:00:42,520 --> 00:00:47,580
+روتيني، بدي أعطيك الـ function أو الـ math وأنت لحالك
+
+6
+00:00:47,580 --> 00:00:51,580
+تفتيها هذه المرة، هذه لأن جاية واحدة زيها برضه
+
+7
+00:00:51,580 --> 00:00:56,980
+مصفوفة بعد قليل بنفس الطريقة أيضاً، السؤال الرابع عشر
+
+8
+00:00:56,980 --> 00:01:07,260
+هأقول لك كل فكرة فقط، اللي في المعرفة، من يهو الـ z of
+
+9
+00:01:07,260 --> 00:01:13,880
+جذر اتنين من الـ z of جذر اتنين، هي كل العناصر على
+
+10
+00:01:13,880 --> 00:01:21,690
+صيغة a زائد b جذر اتنين، بحيث الـ A والـ B belong to
+
+11
+00:01:21,690 --> 00:01:31,210
+Z، ماذا هذي؟ بدنا نثبت الـ isomorphic للـ H، والـ H هي
+
+12
+00:01:31,210 --> 00:01:39,890
+كل المصفوفات اللي على الصيغة A 2BBA، بحيث الـ A والـ B
+
+13
+00:01:39,890 --> 00:01:47,580
+كذلك موجودة في Z، قليلة الشهادات، فإذن الـ isomorphism الـ
+
+14
+00:01:47,580 --> 00:01:54,120
+Phi هذه، أنا بدي أعرفها على إنها Phi of A زائد B
+
+15
+00:01:54,120 --> 00:02:01,540
+جذر اتنين، فالمتأثر على هذا الـ element، الصورة
+
+16
+00:02:01,540 --> 00:02:07,040
+تبعته، بدي أخليها A 2BDA
+
+17
+00:02:07,040 --> 00:02:15,760
+بتثبت لي إن Phi isomorphism، شو ببين لي إن Phi
+
+18
+00:02:17,100 --> 00:02:20,200
+Isomorphism، طبعاً هو ما يعطيك الـ function، يعطيك
+
+19
+00:02:20,200 --> 00:02:24,200
+يقول لك فيه homomorphism من الـ ring الأولى للـ ring
+
+20
+00:02:24,200 --> 00:02:27,860
+الثانية، تثبت لي إنه isomorphism، احنا عطيناك الـ
+
+21
+00:02:27,860 --> 00:02:31,680
+function، ويقول لك يلا اتفضلي، زي ما سوينا كل الـ
+
+22
+00:02:31,680 --> 00:02:35,960
+functions قبل ذلك، تثبت لي إنه homomorphism، وتثبت
+
+23
+00:02:35,960 --> 00:02:40,400
+أنه one to one، أو one to one، هو كل شغل مباشر، لا
+
+24
+00:02:40,400 --> 00:02:45,400
+فيه لف ولا فيه دوران، مباشر، طيب ننتقل إلى السؤال
+
+25
+00:02:45,400 --> 00:02:52,080
+الذي يليه، وهو سؤال اثنين وعشرين، ثمانية عشر
+
+26
+00:02:52,080 --> 00:02:58,380
+ثمانية عشر، بيقول لي is the mapping من Z عشرة given by
+
+27
+00:02:58,380 --> 00:03:04,460
+is a ring homomorphism ولا لأ، تمام؟ قال لي هي
+
+28
+00:03:04,460 --> 00:03:16,790
+ثمانية عشر، هل الـ mapping من Z عشرة إلى Z عشرة، من Z عشرة
+
+29
+00:03:16,790 --> 00:03:27,810
+إلى Z عشرة defined by، defined by اللي هو five of x
+
+30
+00:03:27,810 --> 00:03:32,370
+يساوي 2x، هل هي ring homomorphism ولا لأ؟
+
+31
+00:03:32,370 --> 00:03:37,630
+الإجابة لأ، تبعت الجمع مظبوط مئة بالمئة، بس تبعت
+
+32
+00:03:37,630 --> 00:03:48,370
+الضرب لأ، يبقى الإجابة أنه because أنه five of الـ
+
+33
+00:03:48,370 --> 00:03:56,790
+X في Y يساوي 2XY، ليه ما يساوي 2X في 2Y
+
+34
+00:03:56,790 --> 00:04:02,450
+اللي هي five of X في five of Y، هذا الشرط الثاني من
+
+35
+00:04:02,450 --> 00:04:07,250
+شروط الـ homomorphism غير متحقق، يبقى هذا very easy
+
+36
+00:04:07,250 --> 00:04:15,390
+مش محتاج شغل، طيب، إذا بروح لسؤال 22، سؤال 22 بيقول
+
+37
+00:04:15,390 --> 00:04:25,390
+بده كل ring isomorphism من ZN إلى ZN، يبقى fine
+
+38
+00:04:25,390 --> 00:04:34,170
+بدنا نجيب الـ Phi اللي من ZN إلى ZN، بحيث تكون هذه
+
+39
+00:04:34,170 --> 00:04:41,890
+isomorphism، such that الـ Phi is isomorphism
+
+40
+00:04:41,890 --> 00:04:48,490
+solution، لو
+
+41
+00:04:48,490 --> 00:04:54,430
+رجعتوا إلى سؤال ثمانية، أول سؤال حلناه كان من Z n
+
+42
+00:04:54,430 --> 00:05:03,270
+إلى Z n، كان Phi of X يساوي AX، أثبتناه homomorphism
+
+43
+00:05:03,270 --> 00:05:07,820
+بظلت علينا قصة الـ one to one and onto، مظبوط؟
+
+44
+00:05:07,820 --> 00:05:13,960
+يبقى بقى دي بقول لك from exercises
+
+45
+00:05:13,960 --> 00:05:23,420
+8 اللي أحد قال مرة اللي فاتت، we have أن الـ 5 of x
+
+46
+00:05:23,420 --> 00:05:31,180
+بده يساوي AX is a homomorphism
+
+47
+00:05:35,730 --> 00:05:42,430
+طيب، احنا فرضنا هنا Phi ما هو isomorphism، طيب هذا
+
+48
+00:05:42,430 --> 00:05:48,510
+كان مع الشرط، إذا بتلقى إن الـ A تربيع يساوي الـ A
+
+49
+00:05:48,510 --> 00:05:56,090
+يعني معناته إن الـ A في الـ A بده يساوي الـ A، صح؟
+
+50
+00:05:56,090 --> 00:06:04,630
+يعني معناته إن Phi of A في الـ A بده يساوي Phi of A
+
+51
+00:06:05,140 --> 00:06:12,480
+يعني معناه إن الـ five of A في الـ five of A بده
+
+52
+00:06:12,480 --> 00:06:21,760
+يساوي الـ five of A، يعني معناه إن الـ five of one في
+
+53
+00:06:21,760 --> 00:06:31,780
+الـ five of one بده يساوي الـ five of one، أكيد؟ أكيد
+
+54
+00:06:31,780 --> 00:06:37,890
+يعني، طيب تعالى نرجع بالذاكرة قليلاً، هو بيقول الـ Phi
+
+55
+00:06:37,890 --> 00:06:45,490
+isomorphism، صح؟ مظبوط؟ صورة الـ identity element
+
+56
+00:06:45,490 --> 00:06:49,530
+بدها تروح لمين؟ للـ identity element، في حالة الـ
+
+57
+00:06:49,530 --> 00:06:56,810
+isomorphism، بقول لك but ولكن، اللي هو الـ Phi of one
+
+58
+00:06:56,810 --> 00:07:01,870
+بده يساوي الـ one، لأن الـ Phi عبارة عن isomorphism
+
+59
+00:07:02,350 --> 00:07:09,790
+بناء عليه، هذا الكلام بده يخلي إن الـ five of one
+
+60
+00:07:09,790 --> 00:07:17,810
+بده يساوي الـ one، طبعاً، طيب تعالى نشوف احنا عندنا
+
+61
+00:07:17,810 --> 00:07:24,570
+five of x بده يساوي AX، هذا بده يخلي لك إن الـ
+
+62
+00:07:24,570 --> 00:07:31,970
+five of one بده يساوي A في one، صحيح؟ يعني هذا
+
+63
+00:07:31,970 --> 00:07:40,150
+بده يخليه، لأنه Phi of one بده يساوي A، مظبوط؟
+
+64
+00:07:40,150 --> 00:07:46,790
+طيب، من الاثنين هدول مع بعض، إيش بتستنتجي؟ الـ A بده
+
+65
+00:07:46,790 --> 00:07:52,490
+يساوي واحد، هذا بيساوي هذا، يبقى الـ A بدها تساوي
+
+66
+00:07:52,490 --> 00:08:00,380
+واحد، يبقى صارت هذه الـ function الآن، Phi of x بدي
+
+67
+00:08:00,380 --> 00:08:07,020
+يساوي واحد في X، يبقى الـ Phi of X يساوي مين الـ
+
+68
+00:08:07,020 --> 00:08:12,480
+X؟ مين هي هذه يا بنات؟ شو اسمها في لغة الرياضيات؟
+
+69
+00:08:12,480 --> 00:08:16,780
+الـ identity function، مظبوط؟ طيب الـ identity
+
+70
+00:08:16,780 --> 00:08:23,820
+function one to one and onto؟ أي identity function
+
+71
+00:08:23,820 --> 00:08:31,810
+is one to one and onto، يبقى هذه،  و هي the
+
+72
+00:08:31,810 --> 00:08:37,430
+identity function
+
+73
+00:08:37,430 --> 00:08:45,810
+هذا بده يقول إنه مدام هي identity، يبقى Phi is one
+
+74
+00:08:45,810 --> 00:08:56,530
+to one and onto، and onto، so Phi is an isomorphism
+
+75
+00:08:58,130 --> 00:09:04,290
+يبقى يا بنات، لا يوجد عندي isomorphisms من الـ Zn
+
+76
+00:09:04,290 --> 00:09:10,570
+إلى الـ Zn إلا الـ identity function، دالة الوحدة
+
+77
+00:09:10,570 --> 00:09:15,870
+بنقول عليها Phi of X يساوي X، Phi of m يساوي m
+
+78
+00:09:15,870 --> 00:09:22,890
+Phi of Y تساوي Y، إلى آخره، تمام؟ يبقى هذا شكل الـ
+
+79
+00:09:22,890 --> 00:09:30,070
+function أو شكل الـ homomorphisms من الـ Zn إلى Zn
+
+80
+00:09:30,070 --> 00:09:42,030
+هذا سؤال اللي هو 22، سؤال 24 و 25 مع بعض، سؤال 25 في
+
+81
+00:09:42,030 --> 00:09:51,810
+الأول، بدنا الـ homomorphism من Z plus أو الـ direct
+
+82
+00:09:51,810 --> 00:09:57,960
+sum مع Z إلى Z direct sum مع Z.
+
+83
+00:10:00,500 --> 00:10:14,380
+تتوقعوا كم homomorphism؟ يلا، واحد، اثنين، خمسة عشر،
+
+84
+00:10:14,380 --> 00:10:20,560
+أيوة، يلا شوفوا القرقرة، مال النهاية مثلاً؟ One
+
+85
+00:10:20,560 --> 00:10:27,680
+dollar. أنت عندك هو قطر واحد، فأنت تسوي التبديلات
+
+86
+00:10:27,680 --> 00:10:36,300
+الممكنة، كده، يعني التبديلات؟ مش ثمانية؟
+
+87
+00:10:36,300 --> 00:10:39,940
+تسعة
+
+88
+00:10:39,940 --> 00:10:45,960
+homomorphisms، تعالى نشوف الـ homomorphisms
+
+89
+00:10:45,960 --> 00:10:54,840
+الممكنة، هي Phi of A و B، بدي آخذ عنصر من Z direct sum
+
+90
+00:10:54,840 --> 00:11:02,420
+مع Z، الاحتمال الأول إنه يطلع A و B، صح؟ آه، بالسالب
+
+91
+00:11:02,420 --> 00:11:05,920
+الموجب كمان، سبحان الله، يعني مهما يكون الرقم، يكون
+
+92
+00:11:05,920 --> 00:11:10,060
+سالب موجب، بصفر ما تفرقش عندي، خلاص أنا أخذت element
+
+93
+00:11:10,060 --> 00:11:15,740
+من الـ direct sum، الـ homomorphism الثانية، Phi of a
+
+94
+00:11:15,740 --> 00:11:27,160
+و B، ممكن يكون B و A، مظبوط؟ طيب، الثالث، Phi of A و B
+
+95
+00:11:27,160 --> 00:11:36,640
+ممكن يكون A و A، الرابع، Phi of A و B، ممكن يكون B و
+
+96
+00:11:36,640 --> 00:11:48,660
+B، Phi الخامس، Phi of A و B، ممكن يكون A و zero، Phi of
+
+97
+00:11:48,660 --> 00:11:59,720
+A و B، ممكن يكون zero و A، Phi of A و B، ممكن يكون
+
+98
+00:11:59,720 --> 00:12:15,900
+zero و B، Phi of A و B، ممكن يكون B و zero، Phi of
+
+99
+00:12:15,900 --> 00:12:19,910
+A و B، ممكن يكون B و zero، والذي هو الـ Zero Function.
+
+100
+00:12:20,770 --> 00:12:26,190
+الحين، كل واحد من هدول homomorphism، في غيره؟ لا يوجد
+
+101
+00:12:26,190 --> 00:12:32,630
+غيرهم، تسعة، مش أربعة ولا ثمانية ولا خمسة عشر زي ما
+
+102
+00:12:32,630 --> 00:12:36,490
+قلنا، ولا مالها، يبقى هم التسعة، لا يوجد غيرهم.
+
+103
+00:12:36,990 --> 00:12:41,490
+تقدر في الدائرة براحتك عشوائياً، حط يدك على أي واحد
+
+104
+00:12:41,490 --> 00:12:45,670
+من التسعة، وتثبته إنه homomorphism، تمام؟ نثبته بكل
+
+105
+00:12:45,670 --> 00:12:50,950
+سهولة، طيب بدنا نيجي نطبق سؤال 24، اللي هو سؤال
+
+106
+00:12:50,950 --> 00:12:58,030
+الواحد وعشرين، سؤال 24، جاي لي ما هي الاحتمالات الممكنة للـ
+
+107
+00:12:58,030 --> 00:13:02,550
+Phi of 1 و 0؟
+
+108
+00:13:02,550 --> 00:13:10,110
+موجودة، و بيبي zero، من الاحتمالات الممكنة، هلا بقول
+
+109
+00:13:10,110 --> 00:13:19,700
+ممكن تكون zero و zero، آخر واحد، صح؟ وممكن يكون واحد
+
+110
+00:13:19,700 --> 00:13:29,500
+و واحد، صح؟ وممكن يكون واحد و zero، اللي هو identity
+
+111
+00:13:29,500 --> 00:13:35,460
+وممكن يكون zero و واحد، في غير هيك؟ لأ، يبقى
+
+112
+00:13:35,460 --> 00:13:41,260
+ما عنديش إلا أربعة homomorphisms، لأ خامس لأ، هذا الـ
+
+113
+00:13:41,260 --> 00:13:46,820
+zero homomorphism، هذا اللي هو، وين هذا هو الـ
+
+114
+00:13:46,820 --> 00:13:51,240
+identity homomorphism، واثنين هدول هي الأربعة، لا
+
+115
+00:13:51,240 --> 00:13:55,520
+يوجد غيرها، رغم إن هو المتبادل من هدول، بيقول
+
+116
+00:13:55,520 --> 00:13:58,440
+الـ Z فيها مالها عدد مني العناصر، مالها نهاية من
+
+117
+00:13:58,440 --> 00:14:02,940
+العناصر، والـ Z direct sum Z فيها مريض، ممكن يكون مالها
+
+118
+00:14:02,940 --> 00:14:06,960
+نهاية ولا مالها نهاية، ولا حاجة، التبديلات الممكنة
+
+119
+00:14:06,960 --> 00:14:12,680
+للأربعة عناصر الموجودة فقط، لا ريحة، يبقى هذا أربعة، و
+
+120
+00:14:12,680 --> 00:14:16,880
+عشرين اللي كان مطلوب، وزيادة عليه سؤال خمسة و
+
+121
+00:14:16,880 --> 00:14:20,720
+عشرين، خمسة وعشرين، وبعدين كل سؤال اثنين وثلاثين
+
+122
+00:14:20,720 --> 00:14:27,700
+مش هاد اللي هو القسمة على الحادي عشر، يبقى بيجي لسؤال
+
+123
+00:14:27,700 --> 00:14:35,160
+اثنين وثلاثين، بيقول N positive integer، وأثبت
+
+124
+00:14:35,160 --> 00:14:46,890
+الـ proof أن N is divisible by 11 if and only if
+
+125
+00:14:46,890 --> 00:14:55,370
+if and only if الـ A9 ناقص الـ A1 زائد الـ A2 ناقص
+
+126
+00:14:55,370 --> 00:15:04,710
+زائد ناقص واحد to the power K للـ AK is divisible
+
+127
+00:15:04,710 --> 00:15:10,970
+by 11، تمام؟
+
+128
+00:15:11,810 --> 00:15:16,850
+طيب، احنا أخذنا سؤال تفعيل الـ Division، من بقى تسعة،
+
+129
+00:15:16,850 --> 00:15:22,830
+مظبوط؟ طيب، احنا هذا مش هنحله، هنعطيك المفتاح ونروح
+
+130
+00:15:22,830 --> 00:15:26,630
+لسؤال أربعة وثلاثين، اللي جاي سؤاله بيقول تسعة
+
+131
+00:15:26,630 --> 00:15:30,210
+وسؤاله بيقول أحد عشر، اثنين، بسؤال الواحد، بيقول
+
+132
+00:15:30,210 --> 00:15:36,250
+خلاصنا، وبنمُرنك كيفية عملية الحسابات من سؤال أربعة
+
+133
+00:15:36,250 --> 00:15:40,940
+وثلاثين، خلينا مع هذا، طيب هذا لما أخذنا إيه المثال
+
+134
+00:15:40,940 --> 00:15:45,040
+السابق، دي باسم البرتقال، كان كل العناصر هذه موجبة
+
+135
+00:15:45,040 --> 00:15:50,540
+صح؟ من أين أتت هذه السالبة؟ هذا اللي بدنا نجاوب
+
+136
+00:15:50,540 --> 00:15:55,800
+عليه؟ نقول بسيطة، مشان نثبت هذا الكلام، بدنا نعرف
+
+137
+00:15:55,800 --> 00:16:04,080
+في من Z إلى Z11، بالنيابة شرع الـ homomorphism اللي
+
+138
+00:16:04,080 --> 00:16:10,970
+على الشكل التالي، Phi of x بده يساوي x modulo
+
+139
+00:16:10,970 --> 00:16:15,390
+11، مش هذا الـ natural homomorphism اللي عرفناه في
+
+140
+00:16:15,390 --> 00:16:19,050
+حالة التسعة؟ ما جينا نقول Phi of x بيساوي x
+
+141
+00:16:19,050 --> 00:16:24,630
+modulo 9، هنا x modulo 11، أي integer n
+
+142
+00:16:24,630 --> 00:16:31,130
+حاطينه على الصيغة a ك، أقصى ك زائد a ك ماينص واحد
+
+143
+00:16:31,130 --> 00:16:36,270
+أقصى ك minus one، زائد زائد a one في عشرة زائد a node
+
+144
+00:16:36,600 --> 00:16:44,200
+تذكروا؟ آه، مظبوط، يفجأ  أي إن عندي هنا، بتعمله بنفس
+
+145
+00:16:44,200 --> 00:16:49,580
+الطريقة، مع ملاحظة ما يأتي، في Z عشرة، في Z أحد عشر، يا
+
+146
+00:16:49,580 --> 00:16:56,880
+بنات، الحادي عشر قداش تساوي  zero، يعني معنى هذا الكلام
+
+147
+00:16:56,880 --> 00:17:02,440
+إن العشرة تساوي قداش؟ يفجأ، الآن اللي حطيناها بده
+
+148
+00:17:02,440 --> 00:17:06,740
+يشيل كل عشرة ويحط مكانها سالب واحد، بيصير سالب واحد
+
+149
+00:17:06,740 --> 00:17:10,180
+قصة واحد، بسالب واحد، سالب واحد تربيع بالموجب، سالب
+
+150
+00:17:10,180 --> 00:17:13,980
+واحد تكعيب بالسالب، قصة أربعة موجب، قصة خمسة سالب، من
+
+151
+00:17:13,980 --> 00:17:18,940
+هنا سيظهر هذا سالب موجب، موجب سالب، إلى اثنين، عرفنا
+
+152
+00:17:18,940 --> 00:17:25,440
+من وين هذه بدأت تطلع، من هذه، طبعاً احنا قلنا سابقاً إن
+
+153
+00:17:25,440 --> 00:17:34,680
+الـ N تساوي a ك عشرة أوس ك زائد a ك ماينص واحد عشرة أوس
+
+154
+00:17:34,680 --> 00:17:40,600
+ك ماينص واحد، زائد a one في عشرة، زائد a node
+
+155
+00:17:40,600 --> 00:17:46,600
+تذكرون؟ طيب، ممتاز، لنا، بدي أشيل كل عشرة هذه وأحط
+
+156
+00:17:46,600 --> 00:17:51,440
+مكانها سالب واحد، بصير لنا سالب موجب، سالب موجب،
+
+157
+00:17:51,440 --> 00:17:52,900
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+158
+00:17:52,900 --> 00:17:55,280
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+159
+00:17:55,280 --> 00:17:56,340
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+160
+00:17:56,340 --> 00:17:57,300
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+161
+00:17:57,300 --> 00:18:01,080
+سالب، سالب، سالب،
+
+162
+00:18:02,410 --> 00:18:06,990
+مع السؤال اللي أخذناه في المحاضرة الثانية بسؤال واحد
+
+163
+00:18:06,990 --> 00:18:12,450
+وهو سؤال أربعة وثلاثين، يعني بدك تسوي الـ تفكيك
+
+164
+00:18:12,450 --> 00:18:17,570
+اللي هنا، بنات مثل المثال حرفياً، بس بده يشيل كل عشرة
+
+165
+00:18:17,570 --> 00:18:23,490
+ويحط مكانها سالب واحد، وبالتالي عرفنا طريقة القسمة
+
+166
+00:18:23,490 --> 00:18:28,830
+على مين؟ على الحادي عشر، سؤال أربعة وثلاثين بيقول ما
+
+167
+00:18:28,830 --> 00:18:35,330
+يقصد، سؤال أربعة وثلاثين، قولي show that the number
+
+168
+00:18:35,330 --> 00:18:43,490
+الـ number N اللي هو بده يساوي، بده يساوي
+
+223
+00:25:38,110 --> 00:25:41,370
+تسعة هذا الكلام is
+
+224
+00:25:43,710 --> 00:25:49,730
+divisible by 9 هذا الكلام يمكن أن تقوله إذا كتش
+
+225
+00:25:49,730 --> 00:25:57,390
+مجموعة هذه البنات تسعين، يبقى التسعين is divisible
+
+226
+00:25:57,390 --> 00:26:05,470
+by 9. طب هذه تقسم بالتسعة ولا لا؟ صح، يبقى بتقسم
+
+227
+00:26:05,470 --> 00:26:10,810
+والنتج يساوي عشرة، معناته أن الـ N هذه is divisible
+
+228
+00:26:10,810 --> 00:26:22,620
+by 9. يبقى so الـ N is divisible by 9. هذه رقم اثنين
+
+229
+00:26:22,620 --> 00:26:33,180
+وهذه رقم واحد. طيب إذا from واحد
+
+230
+00:26:33,180 --> 00:26:40,460
+and اثنين، الـ N is divisible
+
+231
+00:26:41,490 --> 00:26:51,390
+by both 11 and 9. تقسم بِهَذين الاثنين، يبقى تقسم بحاصل
+
+232
+00:26:51,390 --> 00:26:59,790
+ضربيهما. هذا بده يعطينا أن الـ N is divisible by
+
+233
+00:26:59,790 --> 00:27:06,690
+تسعة وتسعين، وانتهينا من المسألة. يبقى هذه المسألة
+
+234
+00:27:06,690 --> 00:27:11,080
+جبت القسمة على تسعة، وجبت القسمة على أحد عشر. نقسم على
+
+235
+00:27:11,080 --> 00:27:15,660
+تسعة. مثال في المحاضرة المرة قبل الماضية، والاحدى
+
+236
+00:27:15,660 --> 00:27:20,260
+عشرين في محاضرة اليوم. السؤال اثنين وثلاثين
+
+237
+00:27:20,260 --> 00:27:29,760
+سنطبقه على سؤال أربعة وثلاثين. بعد ذلك، نأتي لسؤال
+
+238
+00:27:29,760 --> 00:27:37,180
+اثنين وأربعين. جاءني كل ring homomorphism. سؤال اثنين
+
+239
+00:27:37,180 --> 00:27:38,100
+وأربعين
+
+240
+00:27:41,570 --> 00:27:49,130
+الـ ring homomorphisms. في من الـ six rational numbers
+
+241
+00:27:49,130 --> 00:27:57,590
+للستة rational numbers. تعرف من هم؟
+
+242
+00:27:57,590 --> 00:28:07,990
+من؟ هيا، أحدٌ حلّ فيكم السؤال؟ يعني
+
+243
+00:28:07,990 --> 00:28:12,020
+الـ identity function. بس بدنا نثبت أنها الـ identity
+
+244
+00:28:12,020 --> 00:28:17,660
+function. آه، أنا أظهرت، صحيح، أن كلامي مضبوط. هو الـ
+
+245
+00:28:17,660 --> 00:28:23,500
+identity function، ولا يوجد غيرها. كيف كالتالي؟ خلونا
+
+246
+00:28:23,500 --> 00:28:31,380
+نحلّ هكذا. solution milligrams
+
+247
+00:28:31,380 --> 00:28:37,820
+five of one بده يساوي الواحد، مضبوط؟ طيب الآن لو
+
+248
+00:28:37,820 --> 00:28:46,570
+جئت أخذت الـ N الموجودة في Z، والـ Z  صاحب 6 من 100 من
+
+249
+00:28:46,570 --> 00:28:55,650
+الـ Q، يبقى الـ N موجودة في الـ Q. ثم Phi of N أستطيع
+
+250
+00:28:55,650 --> 00:29:02,070
+أن أكتبها. Phi of واحد زائد واحد زائد واحد... كم مرة يا بنات؟
+
+251
+00:29:02,070 --> 00:29:11,970
+كم مرة في  N. طيب، الـ phi أنا أقول أنه homomorphism، طبعاً
+
+252
+00:29:11,970 --> 00:29:16,390
+وأنا افترضت أنه عبارة عن homomorphism، يبقى هذا
+
+253
+00:29:16,390 --> 00:29:22,030
+الكلام بده يساوي Phi of one زائد Phi of one زائد
+
+254
+00:29:22,030 --> 00:29:31,150
+زائد Phi of one. كم مرة؟ N times. يبقى هذا معناه
+
+255
+00:29:31,150 --> 00:29:40,600
+أن الـ Phi of N يساوي N في Phi of 1. فالـ Phi of 1 يبقى
+
+256
+00:29:40,600 --> 00:29:46,280
+واحد. يبقى هذا بده يعطينا أن Phi of N
+
+257
+00:29:46,280 --> 00:29:53,560
+يساوي الـ N في واحد. هذا بده يعطينا أن Phi of N بده
+
+258
+00:29:53,560 --> 00:30:02,300
+يساوي الـ N. بده يساوي الـ N. يبقى صارت هذه الـ identity
+
+259
+00:30:02,300 --> 00:30:09,600
+map. وهذه أيضاً هي الـ identity map. بس هؤلاء على من؟
+
+260
+00:30:09,600 --> 00:30:16,140
+على الأعداد الصحيحة. بدنا نشوف الأعداد الكسرية
+
+261
+00:30:16,140 --> 00:30:22,340
+التي تكون على شكل كسور اعتيادية. طبعاً نحن عندنا
+
+262
+00:30:22,340 --> 00:30:27,300
+set of rational numbers، AQ، كل الأعداد التي على
+
+263
+00:30:27,300 --> 00:30:34,010
+شكل M على N بحيث أن الـ M والـ N موجودة في الـ Z، والـ N
+
+264
+00:30:34,010 --> 00:30:46,670
+لا تساوي صفراً. يبقى
+
+265
+00:30:46,670 --> 00:30:51,090
+أثبتنا أن الـ homomorphisms على الأعداد الصحيحة هي
+
+266
+00:30:51,090 --> 00:30:55,690
+identity function. نأتي على الكسور التي ليست
+
+267
+00:30:55,690 --> 00:31:05,330
+أعداداً صحيحة. يبقى أنا آخذ Phi of M على N. أليست Phi
+
+268
+00:31:05,330 --> 00:31:17,150
+of M في N أس سالب واحد؟ صح؟ طيب، أليست هذه Phi of M
+
+269
+00:31:17,150 --> 00:31:28,210
+في Phi of N أس سالب واحد؟ صحيح. طيب، نرجع للـ groups
+
+270
+00:31:28,210 --> 00:31:36,150
+لو رجعنا للـ groups. هذه Phi of M في Phi of N أس
+
+271
+00:31:36,150 --> 00:31:44,270
+سالب واحد. طب، الـ Phi of M، أليست هي الـ M من العلاقة
+
+272
+00:31:44,270 --> 00:31:50,170
+التي عندنا؟ هذه لأنها integers. وهذه التي هي main
+
+273
+00:31:50,170 --> 00:31:57,270
+وهذه Phi of N التي هي الـ N أس سالب واحد. يبقى صارت
+
+274
+00:31:57,270 --> 00:32:05,880
+الـ M على N. يبقى Phi of M على N هي M على N. يبقى هنا
+
+275
+00:32:05,880 --> 00:32:15,720
+Phi of Q بدها تساوي الـ Q لكل Q الموجودة في
+
+276
+00:32:15,720 --> 00:32:21,600
+كل  Q. من هي الـ function هذه؟ الـ identity
+
+277
+00:32:21,600 --> 00:32:27,910
+function، كما زعمت زميلتكم قبل قليل. يبقى هذه الـ
+
+278
+00:32:27,910 --> 00:32:39,450
+Identity Map أو الـ Identity Homomorphism، طبعاً؟
+
+279
+00:32:39,450 --> 00:32:47,670
+إذا قبل قليل من ZN إلى ZN، لم نجد أي isomorphism إلا
+
+280
+00:32:47,670 --> 00:32:53,780
+الـ Identity Map. وهنا من الـ EQ إلى الـ EQ لم نجد إلا
+
+281
+00:32:53,780 --> 00:33:00,200
+الـ identity homomorphism. هذا سؤال اثنين وأربعين.
+
+282
+00:33:00,200 --> 00:33:04,620
+أظن كان معنا سبعة وأربعين؟ هذا محلول عندك في
+
+283
+00:33:04,620 --> 00:33:11,180
+الكتاب تفصيلياً. يبقى عليكِ أن تراجعيه وتكتبيه الآن.
+
+284
+00:33:11,180 --> 00:33:15,620
+أهم سؤال عندي، على جَدِّ اللِّواجِتْ. ضايل سؤال سته وستون
+
+285
+00:33:15,620 --> 00:33:24,420
+الذي هو خمسة مطالب، تمام، ويشمل الفكرة تبعت سؤال أربعة عشر
+
+286
+00:33:24,420 --> 00:33:29,900
+الذي تركناه، وقلنا لكِ سأجيب. إذا أردت أن أذهب إلى سؤال ٦٦
+
+287
+00:33:29,900 --> 00:33:33,160
+سؤال
+
+288
+00:33:33,160 --> 00:33:42,680
+٦٦ يقول: لماذا نحن ring؟ اعطِ كل المصفوفات التي على
+
+289
+00:33:42,680 --> 00:33:52,220
+الشكل a, b, b, a بحيث أن الـ A والـ B موجودتان في الستة
+
+290
+00:33:52,220 --> 00:34:03,000
+أعداد حقيقية. وعندنا Phi معرفة من A, B إلى D. A تساوي A
+
+291
+00:34:03,000 --> 00:34:12,140
+ناقص B. المطلوب الأول: نُبرهن على أن Phi is
+
+292
+00:34:12,140 --> 00:34:16,360
+homomorphism. والله، نُبرهن على أنها homomorphism.
+
+293
+00:34:20,790 --> 00:34:28,730
+خلّي بالكِ هنا. يبقى بدي آخذ الحالة الأولى وهي نصف
+
+294
+00:34:28,730 --> 00:34:33,570
+الأول من الـ homomorphism تبع الجمع. يبقى بدي آخذ
+
+295
+00:34:33,570 --> 00:34:42,970
+Phi of مجموع مصفوفتين موجودتين في R. وليكنتا A, B, B, A
+
+296
+00:34:42,970 --> 00:34:54,130
+زائد C, D, D, C. و نعرف جيداً، كيف نقوم بجمع المصفوفات.
+
+297
+00:34:54,130 --> 00:35:00,430
+حسب ما تعلمته في الجبر الخطي، كل عنصر يُجمع مع نظيره.
+
+298
+00:35:00,430 --> 00:35:09,590
+تُصبح المصفوفة التالية: A زائد C، B زائد D، B زائد D، A زائد C.  جُمعت مصفوفة
+
+299
+00:35:09,590 --> 00:35:18,690
+واحدة حسب الـ definition التي عندنا. بده يساوي A
+
+300
+00:35:18,690 --> 00:35:25,080
+ناقص B. ف هذا بده يساوي A زائد C ناقص
+
+301
+00:35:25,080 --> 00:35:32,360
+B زائد D. التي أستطيع أن أكتبها على الشكل التالي: A
+
+302
+00:35:32,360 --> 00:35:39,840
+ناقص B زائد C ناقص D. التي أستطيع أن أكتبها على الشكل التالي: A
+
+303
+00:35:39,840 --> 00:35:49,940
+ناقص B زائد C ناقص D. حسب الـ definition  فاي
+
+304
+00:35:49,940 --> 00:35:57,680
+of المصفوفة هذه. يبقى هذا فاي of المصفوفة A, B, B, A
+
+305
+00:35:57,680 --> 00:36:06,540
+زائد فاي of المصفوفة الثانية. فاي of ... الـ ...
+
+306
+00:36:06,540 --> 00:36:24,910
+الـ C, D, D, C. يبقى بالنسبة للجمع، مباشرة. لا يوجد لف ولا دوران ولا صعوبة. نأخذ
+
+307
+00:36:24,910 --> 00:36:30,370
+Phi of حاصل ضرب A, B, B, A في من؟ في C, D, D, C ويساوي
+
+308
+00:36:30,370 --> 00:36:40,290
+Phi of ضرب المصفوفتين. الصف الأول في العمود الأول لو
+
+309
+00:36:40,290 --> 00:36:47,540
+نجمع، يُعطينا العنصر الأول. يبقى AC زائد BD. يبقى AC
+
+310
+00:36:47,540 --> 00:36:57,120
+زائد BD. هذا العنصر الأول في العمود الأول. الصف
+
+311
+00:36:57,120 --> 00:37:04,300
+الأول في العمود الثاني يُعطينا العنصر الثاني. يبقى
+
+312
+00:37:04,300 --> 00:37:09,230
+AD زائد BC. يبقى AD زائد BC. الصف الثاني في العمود
+
+313
+00:37:09,230 --> 00:37:18,390
+الأول يُعطينا AD زائد BC. والعنصر الأخير AC زائد BD.
+
+314
+00:37:18,390 --> 00:37:28,210
+طيب، صارت كلها مصفوفة واحدة، ليست مصفوفتين. حسب التعريف
+
+315
+00:37:28,210 --> 00:37:35,310
+الذي عندنا. يبقى العنصر الذي في الصف الأول
+
+316
+00:37:35,310 --> 00:37:39,270
+ناقص العنصر الذي في الصف الثاني. يبقى هذا بده
+
+317
+00:37:39,270 --> 00:37:44,490
+يعطينا: AC زائد BD ناقص AD ناقص
+
+318
+00:37:44,490 --> 00:37:53,930
+BC. اعتبري هذه المعادلة رقم واحد. بدي آتي آخذ Phi
+
+319
+00:38:02,920 --> 00:38:12,400
+of A, B, B, A في Phi of C, D, D, C. by yourself. هذه يا
+
+320
+00:38:12,400 --> 00:38:20,340
+بنات التي هي: A ناقص B، وهذه C ناقص D.
+
+321
+00:38:20,340 --> 00:38:30,160
+بدي أضرب القوسين في بعض. يبقى هذه: AC ناقص
+
+322
+00:38:30,160 --> 00:38:44,210
+AD ناقص BC زائد BD. ناقص BD ناقص AD ناقص BC.
+
+323
+00:38:44,210 --> 00:38:53,270
+يطلع، يشوف، أيّة هي؟ ها هي بالحرف الواحد. يبقى
+
+324
+00:38:53,270 --> 00:39:03,210
+هذه اثنين. يبقى أقول هنا: from واحد واثنين. We
+
+325
+00:39:03,210 --> 00:39:10,370
+have أن الـ Phi of A, B, B, A
+
+326
+00:39:10,370 --> 00:39:25,750
+مضروبة في C, D, D, C تساوي Phi of A, B, B, A في Phi of C, D, D, C.
+
+327
+00:39:25,750 --> 00:39:29,450
+وبالتالي، Phi is a homomorphism.
+
+328
+00:39:45,400 --> 00:39:55,480
+المطلوب الثاني: خلصنا. أيش قال؟ بده find kernel
+
+329
+00:39:55,480 --> 00:40:05,520
+الـ phi. أقول له: kernel الـ phi هو كل المصفوفات A,
+
+330
+00:40:05,860 --> 00:40:11,120
+B, B, A
+
+331
+00:40:14,230 --> 00:40:20,890
+بحيث أن الـ phi of A, B, B, A بده يساوي صفر.
+
+332
+00:40:20,890 --> 00:40:28,290
+مضبوط؟ أليس هذا هو التعريف؟ طيب، هذا الكلام معناه ماذا؟
+
+333
+00:40:28,290 --> 00:40:36,350
+كل المصفوفات A, B, B, A بحيث أن صورة هذا العنصر هي A
+
+334
+00:40:36,350 --> 00:40:43,940
+ناقص B. يبقى A ناقص B بده يساوي صفر. يبقى
+
+335
+00:40:43,940 --> 00:40:51,700
+هذا الكلام: كل المصفوفات A, B, B, A such that A
+
+336
+00:40:51,700 --> 00:40:57,520
+تساوي B. إذا أنا هشيل كل B وأضع مكانها A، أو
+
+337
+00:40:57,520 --> 00:41:04,440
+أشيل كل A وأضع مكانها B. يبقى هذا الكلام بده يساوي
+
+338
+00:41:04,440 --> 00:41:11,820
+كل المصفوفات التي على الشكل A, A, A, A بحيث أن A موجود
+
+339
+00:41:11,820 --> 00:41:18,560
+في Z. يبقى kernel تابع هذه الـ function
+
+340
+00:41:18,560 --> 00:41:24,400
+كل المصفوفات التي نظامها اثنين في اثنين، والتي جميع
+
+341
+00:41:24,400 --> 00:41:30,220
+عناصرها متساوية. قال لي بعد ذلك، المطلوب الثالث.
+
+342
+00:41:30,220 --> 00:41:41,920
+نُبرهن على أن R modulo kernel  لـ Phi
+
+343
+00:41:42,290 --> 00:41:50,890
+Isomorphic إلى من؟ Isomorphic to Z. Solution.
+
+344
+00:41:50,890 --> 00:41:59,610
+هذه
+
+345
+00:41:59,610 --> 00:42:06,600
+مرت علينا في نظرية من نظريات خلال هذا الشهر. ما اسمها؟ الـ first isomorphism theorem. ممتاز جداً، يبقى أنا
+
+346
+00:42:06,600 --> 00:42:10,640
+أبدأ أذهب إلى الـ first isomorphism theorem، وأقارنها
+
+347
+00:42:10,640 --> 00:42:16,380
+مع من؟ مع المطلوب. يمكن أن تصدق، ويمكن أن لا تصدق. الله
+
+348
+00:42:16,380 --> 00:42:20,980
+أعلم. طب، أقول هنا: from أو قبل ذلك، we know
+
+349
+00:42:20,980 --> 00:42:27,600
+that
+
+350
+00:42:27,600 --> 00:42:28,240
+إنّ
+
+351
+00:42:31,630 --> 00:42:40,230
+الـ kernel الـ phi is an ideal of R. مضبوط يا
+
+352
+00:42:40,230 --> 00:42:46,150
+عزيزي؟ الـ kernel ideal. أثبتنا نظرية كذلك خلال
+
+353
+00:42:46,150 --> 00:42:56,010
+هذا الفصل. طيب، أذهب وأقول هنا: by the isomorphism
+
+354
+00:42:56,010 --> 00:43:05,590
+theorem. We have. واحدة يذكرها في Ego أن R modulo
+
+355
+00:43:05,590 --> 00:43:14,010
+الـ kernel لـ Phi isomorphic إلى ماذا؟ إلى Phi of R. Phi of R
+
+356
+00:43:14,010 --> 00:43:22,210
+طب، ما هو المطلوب؟ أثبت isomorphic to Z. نقول: إذا
+
+357
+00:43:22,210 --> 00:43:29,710
+قدرنا أن نثبت أن Phi of R isomorphic to Z، يتم المطلوب.
+
+358
+00:43:30,380 --> 00:43:35,980
+والأسهل من ذلك أن نثبت أن Phi of R هي Z
+
+359
+00:43:35,980 --> 00:43:41,680
+itself. إذا قدرنا أن نثبت هذا الكلام، يقول: خلصنا، تمام.
+
+360
+00:43:41,680 --> 00:43:50,400
+يبقى واجب أن أقول له: if we show that إذا قدرنا أن نثبت أن
+
+361
+00:43:50,400 --> 00:44:01,930
+Phi of R تساوي Z، يبقى then we have the result.
+
+362
+00:44:01,930 --> 00:44:08,730
+يكون خلصنا، حصلنا على النتيجة. لذلك، بدي أحاول أن أثبت
+
+363
+00:44:08,730 --> 00:44:14,090
+أن كل واحدة فيهما subset من التالية. يبقى أذهب
+
+364
+00:44:14,090 --> 00:44:23,370
+وأقول له: let x موجودة في Phi of R، تمام؟
+
+365
+00:44:23,370 --> 00:44:38,030
+then الـ x تساوي Phi of مصفوفة من R. ستكون A1, B1,
+
+366
+00:44:38,030 --> 00:44:45,650
+B1, A1. Phi
+
+367
+00:44:45,650 --> 00:44:51,210
+of هذه. x موجودة في Phi of  عنصر. x تساوي Phi of
+
+368
+00:44:51,210 --> 00:44:57,640
+عنصر من R. مهما كان، يكون. طيب، هذا شو عبارة عن؟
+
+369
+00:44:57,640 --> 00:45:04,080
+A1 ناقص B1. طب، A1 و B1 أين موجودتان؟ في Z.
+
+370
+00:45:04,080 --> 00:45:08,860
+الفرق بينهما موجود في Z لأن الفرق بين any two
+
+371
+00:45:08,860 --> 00:45:16,440
+integers is an integer. يبقى هذا موجود في Z. يبقى
+
+372
+00:45:16,440 --> 00:45:24,040
+x subset من من؟ subset من Z. نعمل
+
+373
+00:45:24,040 --> 00:45:32,500
+العملية العكسية. on the other hand, let
+
+374
+00:45:32,500 --> 00:45:40,320
+x موجودة في Z. إذا قدرنا أن نثبت أن الـ x موجودة في
+
+375
+00:45:40,320 --> 00:45:46,240
+Phi of R، يكون خلاص تم المطلوب، تمام؟ يبقى افترضنا أن
+
+376
+00:45:46,240 --> 00:45:56,000
+x موجودة في Z، then الـ x تساوي... أستطيع أن أضعها فرقاً بين
+
+377
+00:45:56,000 --> 00:46:02,460
+any two integers بدون مشاكل، حتى لو كانت صفر. أستطيع
+
+378
+00:46:02,460 --> 00:46:06,600
+أن أضعها صفر ناقص صفر. أستطيع أن أضعها خمسة ناقص خمسة. مائة
+
+379
+00:46:06,600 --> 00:46:11,980
+ناقص مائة. جداً. يبقى العنصر الذي أخذته أستطيع
+
+380
+00:46:11,980 --> 00:46:18,500
+أن أضعه كفرق بين two integers. يبقى then الـ x بده يكون
+
+381
+00:46:18,500 --> 00:46:27,490
+A ناقص B مثلاً.  أليس A ناقص B عبارة عن
+
+382
+00:46:27,490 --> 00:46:40,950
+Phi of A, B, B, A؟ وهذه موجودة في Phi of R، صح؟
+
+383
+00:46:40,950 --> 00:46:47,930
+فهذه موجودة في Phi of R. يبقى العنصر الذي أخذته
+
+384
+00:46:47,930 --> 00:46:56,250
+في Z، أين موجود؟ في Phi of R. يبقى هنا، التي
+
+385
+00:46:56,250 --> 00:47:06,670
+هي الـ Z subset من Phi of R. سمي هذه الأولى رقم واحد،
+
+386
+00:47:06,670 --> 00:47:14,450
+وسمي هذه رقم اثنين. فنذهب ونقول: from واحد واثنين،
+
+387
+00:47:14,450 --> 00:47:25,030
+we have أن Phi of R تساوي الـ Z itself.
+
+388
+00:47:25,030
+
+445
+00:53:59,320 --> 00:54:08,480
+هذا الكلام بدي يساوي 3003 زي الكيرن ألألفاية هل هذا
+
+446
+00:54:08,480 --> 00:54:16,980
+يساوي الكيرن ألألفاية؟ لا يساوي الكيرن ألألفاية يبقى
+
+447
+00:54:16,980 --> 00:54:24,520
+هذا أضمان a zero element يبقى هنا، ساعة اللي هو من
+
+448
+00:54:24,520 --> 00:54:27,480
+3003
+
+449
+00:54:27,930 --> 00:54:38,070
+زائد الكيرن ألألفاية is a non-zero n بدي أفرض
+
+450
+00:54:38,070 --> 00:54:46,190
+أنه له معكوس طبعاً، طيب لما له معكوس بدي أشوف هل
+
+451
+00:54:46,190 --> 00:54:52,670
+أصل إلى تناقض، والله بصير كلامي صحيح أنا فضّلي
+
+452
+00:54:52,670 --> 00:54:57,030
+بقول لهم as you want that
+
+453
+00:54:58,690 --> 00:55:09,050
+أنه ثلاثة 003 زائد كيرن للفاي مضروب A
+
+454
+00:55:09,050 --> 00:55:20,850
+B B A زائد كيرن للفاي كل هذا مضروب، هذا بده يساوي
+
+455
+00:55:20,850 --> 00:55:26,270
+الـ unity، من الـ unity واحد 001 اللي هو
+
+456
+00:55:26,270 --> 00:55:37,550
+موجود في A 1001 زائد الكيرن للـ 5 يبقى
+
+457
+00:55:37,550 --> 00:55:49,370
+هذا معناته يا بنات أن الثلاثة 003 في الـ A B B A
+
+458
+00:55:49,370 --> 00:56:01,420
+يساوي واحد 001 مضبوط؟ عشان أكتر، طيب هذا معناه هو
+
+459
+00:56:01,420 --> 00:56:06,920
+المضروب التالي، الصف الأول في العمود الأول ثلاثة A
+
+460
+00:56:06,920 --> 00:56:13,640
+و هنا ثلاثة B و هنا ثلاثة B و هنا ثلاثة A بدها
+
+461
+00:56:13,640 --> 00:56:20,100
+تساوي واحد 001 طيب هذا إيش معناه؟ أن ثلاثة A
+
+462
+00:56:20,100 --> 00:56:27,320
+بدها تساوي واحد، يعني إيه تساوي كده؟ هل التوتس موجود
+
+463
+00:56:27,320 --> 00:56:33,740
+في Z؟ يبقى هذا does not belong to Z يبقى الفرض اللي
+
+464
+00:56:33,740 --> 00:56:38,660
+فرضته هذا غلط ولا صح؟ غلط، يعني معناه أن العنصر هذا
+
+465
+00:56:38,660 --> 00:56:44,760
+ما له معكوس، عنصر غير صفري ما له معكوس يبقى لا يمكن
+
+466
+00:56:44,760 --> 00:56:49,840
+أن يكون هذا فيلد، لإن الفيلد كل عنصر غير صفري له
+
+467
+00:56:49,840 --> 00:56:59,630
+معكوس، طيب كويس، مش موجود في 6 الخمسة 2 2
+
+468
+00:56:59,630 --> 00:57:06,650
+خمسة زائد الكيرن اللي الـ five has no
+
+469
+00:57:06,650 --> 00:57:11,070
+multiplicative
+
+470
+00:57:11,070 --> 00:57:20,450
+inverse، هذا بده يعطينا أن الـ R Modular Kernel لـ
+
+471
+00:57:20,450 --> 00:57:29,150
+Phi is not a field، مدام ما هوش فيلد يبقى الـ Kernel
+
+472
+00:57:29,150 --> 00:57:38,610
+لـ Phi is not maximal، يبقى عندك طريقتين لإثبات
+
+473
+00:57:38,610 --> 00:57:44,110
+الـ Prime وعندك طريقتين لإثبات، نين لإثبات الـ
+
+474
+00:57:44,110 --> 00:57:47,510
+maximal، أعطيكم العافية
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/xVdNKWsk6Ew_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/xVdNKWsk6Ew_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e15f3a75fe91f6cbc4e59b625ac1a550be30ac8d
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/xVdNKWsk6Ew_raw.srt
@@ -0,0 +1,1896 @@
+1
+00:00:20,700 --> 00:00:24,800
+بسم الله الرحمن الرحيم نكمل ما ابتدأناه في المرة
+
+2
+00:00:24,800 --> 00:00:30,660
+الماضية من حل المسائل على شكتر خمستاشر طبعا احنا
+
+3
+00:00:30,660 --> 00:00:36,980
+في المرة الماضية على ما قلت حلنا المسائل له تمانية
+
+4
+00:00:36,980 --> 00:00:42,520
+وعشرة واثمانة اللي انا قلنا اربعتاشر اربعتاشر
+
+5
+00:00:42,520 --> 00:00:47,580
+روتيني بدي اعطيك ال function او ال math وانت لحالك
+
+6
+00:00:47,580 --> 00:00:51,580
+تفتيهاهذه المرة هذه لأنه جاي واحدة زيها برضه
+
+7
+00:00:51,580 --> 00:00:56,980
+مصفوفة بعد قليل بنفس الطريقة ايضا السؤال الاربعتاج
+
+8
+00:00:56,980 --> 00:01:07,260
+هاكيلك كل فكرة فقط اللي في المعرفة من يهو ال z of
+
+9
+00:01:07,260 --> 00:01:13,880
+جدر اتنين من ال z of جدر اتنين هي كل العناصر على
+
+10
+00:01:13,880 --> 00:01:21,690
+صيغة a زائد b جدر اتنينبحيث ال A و ال B belong to
+
+11
+00:01:21,690 --> 00:01:31,210
+Z ماذا هذي؟ بدنا نثبت ال isomorphic لل H و ال H هي
+
+12
+00:01:31,210 --> 00:01:39,890
+كل المصففة اللي على الصيغة A2BBA بحيث ال A و ال B
+
+13
+00:01:39,890 --> 00:01:47,580
+كذلك موجودة في Z قللي شهدات فاجز isomorphismالـ
+
+14
+00:01:47,580 --> 00:01:54,120
+Phi هذه أنا بدي أعزفها على إنها Phi of A زائد B
+
+15
+00:01:54,120 --> 00:02:01,540
+جانير اتنين فالمتأثر على هذا ال element الصورة
+
+16
+00:02:01,540 --> 00:02:07,040
+تبعته بدي أخليها A2BDA
+
+17
+00:02:07,040 --> 00:02:15,760
+بتبتيلي إن Phi isomorphism شو بينيلي إن Phi
+
+18
+00:02:17,100 --> 00:02:20,200
+Isomorphism طبعا هو ماعطكيش ال function يعطاك
+
+19
+00:02:20,200 --> 00:02:24,200
+يقالك فيه homomorphism من ال ring الأولى لل ring
+
+20
+00:02:24,200 --> 00:02:27,860
+التانية تثبت علي انه isomorphism احنا عطناك ال
+
+21
+00:02:27,860 --> 00:02:31,680
+function ويقولك يالله اتفضلي زي ما سوينا كل ال
+
+22
+00:02:31,680 --> 00:02:35,960
+functions قبل ذلك تثبتلي انه homomorphism و تثبت
+
+23
+00:02:35,960 --> 00:02:40,400
+انها one to one او one to one هو كل شغل مباشر لا
+
+24
+00:02:40,400 --> 00:02:45,400
+في لف ولا في دوران مباشر دورطيب ننتقل الى السؤال
+
+25
+00:02:45,400 --> 00:02:52,080
+الذى دالى يليه وهو سؤال يتنين وعشرين تمنتاشر
+
+26
+00:02:52,080 --> 00:02:58,380
+تمنتاشر بيقول لي is the mapping من Z عشرة given by
+
+27
+00:02:58,380 --> 00:03:04,460
+is a ring homomorphism ولا لأ تمام قال لي هاي
+
+28
+00:03:04,460 --> 00:03:16,790
+تمنتاشر هل كل الفاية من Z عشرةالى z عشرة من z عشرة
+
+29
+00:03:16,790 --> 00:03:27,810
+الى z عشرة defined by defined by اللي هو five of x
+
+30
+00:03:27,810 --> 00:03:32,370
+يسوى اتنين x هل هي ring homomorphism ولا لأ
+
+31
+00:03:32,370 --> 00:03:37,630
+الاجابة لأ تبعت الجمع مظبوط مية لمية بس تبعت
+
+32
+00:03:37,630 --> 00:03:48,370
+الضاربة لأيبقى الإجابة انه because انه five of ال
+
+33
+00:03:48,370 --> 00:03:56,790
+X في Y يسوى اتنين XY ليه يسوى اتنين X في اتنين Y
+
+34
+00:03:56,790 --> 00:04:02,450
+اللي هي five of X في five of A هذا الشرط الثاني من
+
+35
+00:04:02,450 --> 00:04:07,250
+شروط ال homomorphism غير متحقق يبقى هذا very easy
+
+36
+00:04:07,250 --> 00:04:15,390
+مش محتاج شغلطيب إذا بروح لسؤال 22 سؤال 22 بيقول
+
+37
+00:04:15,390 --> 00:04:25,390
+بده كل ring isomorphism من ZN إلى ZN يبقى fine
+
+38
+00:04:25,390 --> 00:04:34,170
+بدنا نجيه five اللي من ZN إلى ZN بحيث تكون هذه
+
+39
+00:04:34,170 --> 00:04:41,890
+isomorphism such thatالـ Phi is isomorphism
+
+40
+00:04:41,890 --> 00:04:48,490
+solution لو
+
+41
+00:04:48,490 --> 00:04:54,430
+رجعتوا الى سؤال تمانية أول سؤال حلناه كان من Z in
+
+42
+00:04:54,430 --> 00:05:03,270
+إلى Z in كان Phi of X يساوي A X أثبتناه همومورفيزم
+
+43
+00:05:03,270 --> 00:05:07,820
+بظلت علينا قصة ال one to one and one to oneمظبوط
+
+44
+00:05:07,820 --> 00:05:13,960
+يبقى بقى دي بقولك from exercises
+
+45
+00:05:13,960 --> 00:05:23,420
+8 اللي حد قال مرة اللي فاتت we have ان ال 5 of x
+
+46
+00:05:23,420 --> 00:05:31,180
+بده يساوي ax is a homomorphism
+
+47
+00:05:35,730 --> 00:05:42,430
+طيب احنا فرضين هنا Phi ما له isomorphism طيب هذا
+
+48
+00:05:42,430 --> 00:05:48,510
+كان مع الشرط إذا بتلقوا ان ال A ترابيع يساوي ال A
+
+49
+00:05:48,510 --> 00:05:56,090
+يعني معناته ان ال A في ال A بده يساوي ال A صح؟
+
+50
+00:05:56,090 --> 00:06:04,630
+يعني معناته ان Phi of A في ال A بده يساوي Phi of A
+
+51
+00:06:05,140 --> 00:06:12,480
+يعني معناه ان ال five of a في ال five of a بده
+
+52
+00:06:12,480 --> 00:06:21,760
+ساوي ال five of a يعني معناه ان ال five of one في
+
+53
+00:06:21,760 --> 00:06:31,780
+ال five of one بده ساوي ال five of one أكيد؟ أكيد
+
+54
+00:06:31,780 --> 00:06:37,890
+يعنيطيب تعالى نرجع بالذاكرة قليلا هو بيقول الـ Phi
+
+55
+00:06:37,890 --> 00:06:45,490
+isomorphism صح؟ مظبوط؟ صورة ال identity element
+
+56
+00:06:45,490 --> 00:06:49,530
+بدها تروح لمين؟ لل identity element في حالة ال
+
+57
+00:06:49,530 --> 00:06:56,810
+isomorphism بقوله but ولكن اللي هو ال Phi of one
+
+58
+00:06:56,810 --> 00:07:01,870
+بده يساوي ال one لأن ال Phi عبارة عن isomorphism
+
+59
+00:07:02,350 --> 00:07:09,790
+بناء عليه هذا الكلام بده يخللي ان ال five of one
+
+60
+00:07:09,790 --> 00:07:17,810
+بده يساوي ال one طبعا طيب تعالى نشوف احنا عندنا
+
+61
+00:07:17,810 --> 00:07:24,570
+five of x بده يساوي ال ax هذا بده يخليلك ان ال
+
+62
+00:07:24,570 --> 00:07:31,970
+five of one بده يساوي ال a في ال one صحيح؟يعني هذا
+
+63
+00:07:31,970 --> 00:07:40,150
+بده يخلّيه لإنه فاي of one بده يساوي ال a مظبوط؟
+
+64
+00:07:40,150 --> 00:07:46,790
+طيب من الإتنين هدول مع بعض إيش بتستنتجي؟ ال a بده
+
+65
+00:07:46,790 --> 00:07:52,490
+يساوي واحد هذا بيساوي هذا يبقى ال a بدها تساوي
+
+66
+00:07:52,490 --> 00:08:00,380
+واحد يبقى صارت هذه ال function الآن فاي of xبدي
+
+67
+00:08:00,380 --> 00:08:07,020
+يساوي الواحد في ال X يبقى ال Phi of X يساوي مين ال
+
+68
+00:08:07,020 --> 00:08:12,480
+X؟ مين هي هذه يا بنات؟ شو اسمها في لغة الرياضيات؟
+
+69
+00:08:12,480 --> 00:08:16,780
+ال identity function، مظبوط؟ طب ال identity
+
+70
+00:08:16,780 --> 00:08:23,820
+function one to one and unto؟ اي identity function
+
+71
+00:08:23,820 --> 00:08:31,810
+is one to one and unto يبقى هذه واتشis the
+
+72
+00:08:31,810 --> 00:08:37,430
+identity function
+
+73
+00:08:37,430 --> 00:08:45,810
+هذا بده يقيل انه مدام هال identity يبقى فاي is one
+
+74
+00:08:45,810 --> 00:08:56,530
+to one and unto and unto so فاي is an isomorphism
+
+75
+00:08:58,130 --> 00:09:04,290
+يبقى يا بنات لا يوجد عندى isomorphisms من الـZ in
+
+76
+00:09:04,290 --> 00:09:10,570
+إلى الـZ in إلا ال identity functions لدلة الوحدة
+
+77
+00:09:10,570 --> 00:09:15,870
+بقيتنا نقول عليها Phi of X يسوى X Phi of M يسوى M
+
+78
+00:09:15,870 --> 00:09:22,890
+Phi of Y تسوى Y إلى آخرى تمام؟ يبقى هذا شكل ال
+
+79
+00:09:22,890 --> 00:09:30,070
+function أو شكل ال homomorphisms من الـZن الى ز ان
+
+80
+00:09:30,070 --> 00:09:42,030
+هذا سؤال اللي هو 22 سؤال 24 و 25 مع بعض سؤال 25 في
+
+81
+00:09:42,030 --> 00:09:51,810
+الأول بدنا ال homomorphism من ز plus او ال direct
+
+82
+00:09:51,810 --> 00:09:57,960
+sum مع ز الى ز Direct sum مع زد.
+
+83
+00:10:00,500 --> 00:10:14,380
+تتوقعوا أكم همومورفزيوم؟ يلّا واحد، نين، خمساش،
+
+84
+00:10:14,380 --> 00:10:20,560
+أيوة، يلّا شوفوا القرقر، مال النهاية مثلًا؟ One
+
+85
+00:10:20,560 --> 00:10:27,680
+dollar.انت عندك هو قطير واحد فانت تسوي التبديلات
+
+86
+00:10:27,680 --> 00:10:36,300
+الممكنة كده يعني التبديلات؟ مش تمانية؟
+
+87
+00:10:36,300 --> 00:10:39,940
+تسعة
+
+88
+00:10:39,940 --> 00:10:45,960
+همومورفزيومز من هم تعالى نشوف الهمومورفزيومز
+
+89
+00:10:45,960 --> 00:10:54,840
+الممكنة هي Phi of A وBبدي اخد عنصر من z direct sum
+
+90
+00:10:54,840 --> 00:11:02,420
+ع z الاحتمال الاول انه يطلع a وb صح؟ اه بالسلب
+
+91
+00:11:02,420 --> 00:11:05,920
+الموجة كمان سبيكيم سلب يعني مين ما يكون الرقم يكون
+
+92
+00:11:05,920 --> 00:11:10,060
+سلب موجة بصفره مابتفرقش عندي خلاص انا خدت element
+
+93
+00:11:10,060 --> 00:11:15,740
+من ال direct sum الهكومة الفجرية التانية phi of a
+
+94
+00:11:15,740 --> 00:11:27,160
+وb ممكن يكون b وfمصبوح؟ طيب التالت Phi of A و B
+
+95
+00:11:27,160 --> 00:11:36,640
+ممكن يكون A و A الرابع Phi of A و B ممكن يكون B و
+
+96
+00:11:36,640 --> 00:11:48,660
+B Phi أربعة Phi of A و B ممكن يكون A و Zerofive of
+
+97
+00:11:48,660 --> 00:11:59,720
+a و b ممكن يكون zero و a five of a و b ممكن يكون
+
+98
+00:11:59,720 --> 00:12:15,900
+zero و b five of a و b ممكن يكون b و zero five of
+
+99
+00:12:15,900 --> 00:12:19,910
+a و b ممكن يكون b و zeroالذي هو الـ Zero Function.
+
+100
+00:12:20,770 --> 00:12:26,190
+الحين كل واحد من هذول همومورفزم، في غيره؟ لا يوجد
+
+101
+00:12:26,190 --> 00:12:32,630
+غيرهم، تسعة، مش أربع ولا تمانية ولا خمستاشر زي ما
+
+102
+00:12:32,630 --> 00:12:36,490
+قلنا ولا مالورية، يبقى هم التسعة لا يوجد غيرهم.
+
+103
+00:12:36,990 --> 00:12:41,490
+تقدر في الدارة براحتك عشوائيا، حط إيدك على أي واحد
+
+104
+00:12:41,490 --> 00:12:45,670
+من التسعة و تبتيه انه همومورفزم. تمام؟ نتبته بكل
+
+105
+00:12:45,670 --> 00:12:50,950
+سهولة.طب بدنا نيجي نطبق سؤال 24 اللي هو سؤال
+
+106
+00:12:50,950 --> 00:12:58,030
+الوزير سؤال 24 جالي ما هي الاحتمالات الممكنة لل
+
+107
+00:12:58,030 --> 00:13:02,550
+Phi of 1 و 0؟
+
+108
+00:13:02,550 --> 00:13:10,110
+موجودة و بيبي Zero من الاحتمالات الممكنة هلا بقول
+
+109
+00:13:10,110 --> 00:13:19,700
+ممكن تكون Zero و Zero آخر واحدصح؟ وممكن يتكون واحد
+
+110
+00:13:19,700 --> 00:13:29,500
+وواحد صح؟ وممكن يتكون واحد وزيرو اللي هو identity
+
+111
+00:13:29,500 --> 00:13:35,460
+وممكن يتكون zero واحد، في غير هيكل؟ لأ، يبقى
+
+112
+00:13:35,460 --> 00:13:41,260
+ماعنديش الا اربعة homomorphism لأ خامسة لأ هذا ال
+
+113
+00:13:41,260 --> 00:13:46,820
+zero homomorphism هذا اللي هوالوين هذا هو ال
+
+114
+00:13:46,820 --> 00:13:51,240
+identity homomorphism واتنين هذول هي الأربعة لا
+
+115
+00:13:51,240 --> 00:13:55,520
+أيوجد غيرها. رغم ان هو المتبادل من الذول بيقول
+
+116
+00:13:55,520 --> 00:13:58,440
+الزد فيها مالة نقية من العناصر ومالة نهاية من
+
+117
+00:13:58,440 --> 00:14:02,940
+العناصر والزد ذلك صمع زد فيها مريض ممكن يكون مالة
+
+118
+00:14:02,940 --> 00:14:06,960
+نهاية ولا مالة نهاية ولا حاجة التبديلات الممكنة
+
+119
+00:14:06,960 --> 00:14:12,680
+للأربعة عناصر الموجودة فقط لا ريحةيبقى هذا اربعة و
+
+120
+00:14:12,680 --> 00:14:16,880
+عشرين اللي كان مطلوب و زيادة عليه سؤال خمسة و
+
+121
+00:14:16,880 --> 00:14:20,720
+عشرين خمسة و عشرين و بعدين كل سؤال اتنين و تلاتين
+
+122
+00:14:20,720 --> 00:14:27,700
+مش هاد اللي هو القسمة على الاحداشر يبقى بيجي لسؤال
+
+123
+00:14:27,700 --> 00:14:35,160
+اتنين و تلاتين بيقول ال N positive integer و اثبت
+
+124
+00:14:35,160 --> 00:14:46,890
+ال proof ان ال N is divisibleby A11 if and only if
+
+125
+00:14:46,890 --> 00:14:55,370
+if and only if الـ A9 ناقص الـ A1 زائد الـ A2 ناقص
+
+126
+00:14:55,370 --> 00:15:04,710
+زائد ناقص واحد to the power K للـ AK is divisible
+
+127
+00:15:04,710 --> 00:15:10,970
+by 11 تمام؟
+
+128
+00:15:11,810 --> 00:15:16,850
+طيب، احنا أخدنا سؤال تفعى الـDivision من بقى تسعة،
+
+129
+00:15:16,850 --> 00:15:22,830
+مظبط؟ طيب، احنا هذا مش هنحله، هنعطيك المفتاح ونروح
+
+130
+00:15:22,830 --> 00:15:26,630
+لسؤال أربعة وثلاثين اللي يجيب سؤاله يقول تسعة
+
+131
+00:15:26,630 --> 00:15:30,210
+وسؤاله يقول إحتاشر اتنين بسؤال الواحد، يقول
+
+132
+00:15:30,210 --> 00:15:36,250
+خلاصنا، وبنمرنك كيفية عملية الحسابات من سؤال أربعة
+
+133
+00:15:36,250 --> 00:15:40,940
+دنيا، خلّينا مع هذا.طيب هذا لما أخدنا ايه المثال
+
+134
+00:15:40,940 --> 00:15:45,040
+السابق دي باسم البرتصال كان كل العلاصر هذه موجبة
+
+135
+00:15:45,040 --> 00:15:50,540
+صح؟ من أين أتت هذه السالبة هذا اللي بدنا نجاوب
+
+136
+00:15:50,540 --> 00:15:55,800
+عليه؟ نقوله بسيطة، مشان نثبت هذا الكلام بدنا نعرف
+
+137
+00:15:55,800 --> 00:16:04,080
+في من Z إلى Z11 بالنياد شرع ال homomorphism اللي
+
+138
+00:16:04,080 --> 00:16:10,970
+على الشكل التاليفاي اف اكس بده يساوي ال X موديولو
+
+139
+00:16:10,970 --> 00:16:15,390
+11 مش هذا ال natural homomorphism اللي عرفناه في
+
+140
+00:16:15,390 --> 00:16:19,050
+حالة التسعة ماجينا نقول فاي اف اكس بيساوي X
+
+141
+00:16:19,050 --> 00:16:24,630
+موديولو 9 هنا X موديولو main 11 أي integer ان
+
+142
+00:16:24,630 --> 00:16:31,130
+حاطناه على الصيغة ا ك عشر أقصى ك زاد ا كمنصة عشر
+
+143
+00:16:31,130 --> 00:16:36,270
+أقصى ك minus one زاد زاد ا one في عشرة زاد ا نود
+
+144
+00:16:36,600 --> 00:16:44,200
+تذكروا؟ اه مظبوط يفجأى اي ان عندى هنا بتعمله بنفس
+
+145
+00:16:44,200 --> 00:16:49,580
+الطريقة مع مراحظة ما يأتي فى زد عشر فى زد احداش يا
+
+146
+00:16:49,580 --> 00:16:56,880
+بناة الاحداش قداش تساوي ازيرة يعني معنى هذا الكلام
+
+147
+00:16:56,880 --> 00:17:02,440
+ان العشرة تساوي قداش يفجأى الان اللى حطناها بده
+
+148
+00:17:02,440 --> 00:17:06,740
+يشيل كل عشرة ويحط مكانهاسالب واحد بيصير سالب واحد
+
+149
+00:17:06,740 --> 00:17:10,180
+قصة واحد بسالب واحد سالب واحد تربيه بالموجب سالب
+
+150
+00:17:10,180 --> 00:17:13,980
+واحد تكييف السالب قصة اربعة موجب قصة خمسة سالب من
+
+151
+00:17:13,980 --> 00:17:18,940
+هنا سيظهر هذا سالب موجب موجب سالب الى اتنين عرفنا
+
+152
+00:17:18,940 --> 00:17:25,440
+من وين هذه بدأ تطلع من هذه طبعا احنا قلنا سابقا ان
+
+153
+00:17:25,440 --> 00:17:34,680
+ال N تساوي AK عشر عوز K زي AK minus ال oneعشرة أوس
+
+154
+00:17:34,680 --> 00:17:40,600
+كي ماينوس ال one زائد a one في عشرة زائد a نص
+
+155
+00:17:40,600 --> 00:17:46,600
+تذكرون؟ طيب ممتاز لنا، بدي أشيل كل عشرة هذه و أحط
+
+156
+00:17:46,600 --> 00:17:51,440
+مكانها سالب واحد، بصي لنا سالب موجب، سالب موجب،
+
+157
+00:17:51,440 --> 00:17:52,900
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+158
+00:17:52,900 --> 00:17:55,280
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+159
+00:17:55,280 --> 00:17:56,340
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+160
+00:17:56,340 --> 00:17:57,300
+سالب، سالب، سالب، سالب، سالب، سالب، سالب، سالب،
+
+161
+00:17:57,300 --> 00:18:01,080
+سالب، سالب، سالب،
+
+162
+00:18:02,410 --> 00:18:06,990
+مع السؤال اللي خدناه في المحاضرة اتنين بسؤال واحد
+
+163
+00:18:06,990 --> 00:18:12,450
+و هو سؤال اربعة و تلاتين يعني بدك تسوي التفتيك
+
+164
+00:18:12,450 --> 00:18:17,570
+اللي هنا بنات مثل المثال حرفيا بس بده يشيل كل عشر
+
+165
+00:18:17,570 --> 00:18:23,490
+و يحط مكانها سالب واحد وبالتالي عرف طريقة القسم
+
+166
+00:18:23,490 --> 00:18:28,830
+على مين على الاحداشر سؤال اربعة و تلاتين بيقول ما
+
+167
+00:18:28,830 --> 00:18:35,330
+يقتينسؤال اربعة و تلاتين قولي show them the number
+
+168
+00:18:35,330 --> 00:18:43,490
+ال number ان اللي هو بده يساوي بده يساوي تسعة
+
+169
+00:18:43,490 --> 00:18:52,570
+تمانية تسعة سبعة تمانية تسعة سبعة ستة خمسة اربعة
+
+170
+00:18:52,570 --> 00:19:00,830
+ستة خمسة اربعة خمسة اتنين سبعة خمسة اتنين سبعةو
+
+171
+00:19:00,830 --> 00:19:17,510
+609 609 و 805 805 is divisible by 99 يبقى هذا is
+
+172
+00:19:17,510 --> 00:19:28,450
+divisible by 99 خلّيني أبدا أشوف بيكسب على ال 11
+
+173
+00:19:28,450 --> 00:19:34,300
+ولا لأ؟إذا قسم على الـ11 وقسم على الـ9، يعني أنا
+
+174
+00:19:34,300 --> 00:19:39,520
+بقسم على الـ99، صح ولا لا؟ يبقى قصتنا بسيطة، إذا
+
+175
+00:19:39,520 --> 00:19:43,820
+أثبت أن هذا الرقم اليوم دي اللي ما شاء الله عليه،
+
+176
+00:19:43,820 --> 00:19:48,100
+بقى ست عشر رقم ولا جدش، واحد، اتنين، تلاتة، اربع،
+
+177
+00:19:48,100 --> 00:19:53,800
+خمس، خمساشر، ست عشر رقم، مليارات، هه، هه، وكيف أنت
+
+178
+00:19:53,800 --> 00:19:56,620
+تقسمها؟ إذا حُط على ال calculator وضع اقسم عادي،
+
+179
+00:19:56,620 --> 00:20:02,110
+يعني قصة طويلة.لأ بدنا نروح يا بناتي نعرف function
+
+180
+00:20:02,110 --> 00:20:13,810
+دي فاي فاي من زد إلى زد احداشر باي فاي of X يساوي
+
+181
+00:20:13,810 --> 00:20:20,110
+X modulo 11 اللي هو 100 اللي عندنا هنا تمام؟ الحين
+
+182
+00:20:20,110 --> 00:20:25,550
+مش هكتب المقام ده هكتب بداله in يبقى بروح بقوله
+
+183
+00:20:25,550 --> 00:20:37,790
+هنا ال in isdivisible by 11 if and only if ال N
+
+184
+00:20:37,790 --> 00:20:45,390
+تقسم ال 11 إذا كانت ال N تسوى 11 برقم if and only
+
+185
+00:20:45,390 --> 00:20:57,820
+if ال N تساوي 11 M و ال M هذا رقم موجود في ذلكيبقى
+
+186
+00:20:57,820 --> 00:21:04,060
+هذا الكلام صحيح if and only if الـ Phi of N بدي
+
+187
+00:21:04,060 --> 00:21:15,100
+ساوي ال Phi of 11M ال Phi of 11M طبقا للتعريف
+
+188
+00:21:15,100 --> 00:21:27,930
+يساوي 11M modulo M يعني قداشر داشر Mموديول 11 يعني
+
+189
+00:21:27,930 --> 00:21:34,590
+موديول 11 صحيح موديول 11 يبقى ناتج جدار يساوي zero
+
+190
+00:21:34,590 --> 00:21:40,370
+إذا وصلنا هنا بنات ال five of n بدها ساوي zero if
+
+191
+00:21:40,370 --> 00:21:45,390
+and only if هاي ال elements اللي علنا يبقى بدها
+
+192
+00:21:45,390 --> 00:21:50,370
+ابدا بال a node من الخلف يبقى بداجي يقول if and
+
+193
+00:21:50,370 --> 00:21:58,080
+only if اللي همين خمسة خمسةسالف Zero زائد تمانية
+
+194
+00:21:58,080 --> 00:22:06,060
+سالف تسعة زائد Zero ناقص ستة زائد سبعة ناقص اتنين
+
+195
+00:22:06,060 --> 00:22:16,220
+زائد خمسة زائد خمسة سبعة اتنين خمسة ناقص اربعة
+
+196
+00:22:16,220 --> 00:22:25,820
+زائد خمسة ناقص ستة زائد سبعةنقص تسعة زائد تمانية
+
+197
+00:22:25,820 --> 00:22:35,740
+ناقص تسعة كدهش هدول مجموعة يبقى
+
+198
+00:22:35,740 --> 00:22:40,220
+هذا طيب ويقول يبقى سوى إذا كان هذا كله سوى كدهش؟
+
+199
+00:22:40,220 --> 00:22:43,900
+Zero هده بيسوي Zero ولا لا؟ I speak within a
+
+200
+00:22:43,900 --> 00:22:49,280
+uniform spectrum يبقى هذا الكلام كله بيبقى سوى
+
+201
+00:22:49,280 --> 00:22:58,750
+Zeroطيب الان ال zero او if and only if خلينا نشي
+
+202
+00:22:58,750 --> 00:23:09,950
+ترتيب اذا كان هذا الرقم is divisible by 11 طبعا؟
+
+203
+00:23:09,950 --> 00:23:16,330
+طيب هذا كلام if and only if مجموعهم كلهم zero is
+
+204
+00:23:16,330 --> 00:23:20,970
+divisible by 11
+
+205
+00:23:23,190 --> 00:23:30,530
+زيرو بنقسم بال 11 ولا لا؟ اه بيقسم بدون باقل يفجأه
+
+206
+00:23:30,530 --> 00:23:34,910
+يسأله الف زيرو is divisible by 11 يفجأه بناء عليه
+
+207
+00:23:34,910 --> 00:23:42,830
+رقم ان بصير يقسم بمن؟ بال 11 يفجأه هنا الان الرقم
+
+208
+00:23:42,830 --> 00:23:52,570
+الكبير هذا is divisible by 11بالمثل بدنا نروح
+
+209
+00:23:52,570 --> 00:23:58,450
+للتسعة بس التسعة مافيش فيها زائد وناقص كله بالزائد
+
+210
+00:23:58,450 --> 00:24:03,390
+طيب الان بقى بنفس الطريقة بدنا نعرف function من z
+
+211
+00:24:03,390 --> 00:24:11,530
+ل z تسعة يبقى بالداخل اقوله define a
+
+212
+00:24:11,530 --> 00:24:22,710
+function f من z الى z تسعة by اللي همينfive of x
+
+213
+00:24:22,710 --> 00:24:29,350
+يساوي ال X modulo تسعة ماتيش ابدأ كل الشغل اشتغال
+
+214
+00:24:29,350 --> 00:24:34,230
+فبدا ابدأ من هنا دول يبقى او بدا اقول ان ال N is
+
+215
+00:24:34,230 --> 00:24:38,810
+divisible و اخش على هدول دول اللي يبقى باجي بقوله
+
+216
+00:24:38,810 --> 00:24:49,960
+ال N is divisible by تسعة F عنده الفمجموعهم بدي
+
+217
+00:24:49,960 --> 00:24:56,260
+يقسم بواسطة 9 يبقى بدي اقول if and only if اللي هو
+
+218
+00:24:56,260 --> 00:25:12,160
+9 زائد 8 زائد 9 زائد 7 زائد 6 5 4 6 زائد 5 زائد 4
+
+219
+00:25:12,160 --> 00:25:21,070
+زائدخمسة اتنين سبعة خمسة زائد اتنين زائد سابعة هو
+
+220
+00:25:21,070 --> 00:25:26,590
+ستة صفر تسعة زائد ستة زائد صفر زائد تسعة زائد
+
+221
+00:25:26,590 --> 00:25:33,110
+تمانية زائد zero زائد خمسة يبقى هاي المجموع بتبعهم
+
+222
+00:25:33,110 --> 00:25:38,110
+بالضبط تماما زي ما قلنا هذا الكلام is divisible by
+
+223
+00:25:38,110 --> 00:25:41,370
+تسعة هذا الكلام is
+
+224
+00:25:43,710 --> 00:25:49,730
+divisible by 9 هذا الكلام يمكن ان تقوله اذا كتش
+
+225
+00:25:49,730 --> 00:25:57,390
+مجموعة هذه البنات تسعين يبقى التسعين is divisible
+
+226
+00:25:57,390 --> 00:26:05,470
+by 9 طب هذي تقسم بالتسعة ولا لا صح يبقى بتقسم
+
+227
+00:26:05,470 --> 00:26:10,810
+والنتج يسوى عشرة معناته ان ال N هذي is divisible
+
+228
+00:26:10,810 --> 00:26:22,620
+by 9يبقى so ال N is divisible by 9 هذه رقم اتنين
+
+229
+00:26:22,620 --> 00:26:33,180
+وهذه رقم واحد طيب اذا from واحد
+
+230
+00:26:33,180 --> 00:26:40,460
+and اتنين ال N is divisible
+
+231
+00:26:41,490 --> 00:26:51,390
+by both 11 and 9 تقسم بيلي اتنين يبقى تقسم بحاصل
+
+232
+00:26:51,390 --> 00:26:59,790
+ضاربينها هذا بده يعطينا ان ال in is divisible by
+
+233
+00:26:59,790 --> 00:27:06,690
+تسعة وتسعين وانتهينا من المسألة يبقى هذه المسألة
+
+234
+00:27:06,690 --> 00:27:11,080
+جبت القسم على تسعة وجبت القسم على احدانقسم على
+
+235
+00:27:11,080 --> 00:27:15,660
+تسعة مثال في المحاضرة المرة قبل الماضية والاحدى
+
+236
+00:27:15,660 --> 00:27:20,260
+عشرين في محاضرة اليوم السؤال اتنين و تلاتين
+
+237
+00:27:20,260 --> 00:27:29,760
+هيطبقناه على سؤال اربع و تلاتين بعد ذلك بنجي لسؤال
+
+238
+00:27:29,760 --> 00:27:37,180
+اتنين واربعين جالي كل ring homomorphism سؤال اتنين
+
+239
+00:27:37,180 --> 00:27:38,100
+واربعين
+
+240
+00:27:41,570 --> 00:27:49,130
+الرنج homomorphisms في من ال six rational number
+
+241
+00:27:49,130 --> 00:27:57,590
+للست rational number بتعرف مين هم ؟
+
+242
+00:27:57,590 --> 00:28:07,990
+مين ؟ يالا حد حلت فيك السؤال ؟ يعني
+
+243
+00:28:07,990 --> 00:28:12,020
+ال identity functionبس بدنا نثبت انها ال identity
+
+244
+00:28:12,020 --> 00:28:17,660
+function اه انا اظهر صحيح ان كلامي مظبوط هو ال
+
+245
+00:28:17,660 --> 00:28:23,500
+identity function ولا يوجد غيرها كيف كالتالي؟ خلوي
+
+246
+00:28:23,500 --> 00:28:31,380
+ولا كده solution milligrams
+
+247
+00:28:31,380 --> 00:28:37,820
+five of one بده يساوي ال one مظبوط؟ طيب الان لو
+
+248
+00:28:37,820 --> 00:28:46,570
+جيت اخدتالـ N موجودة في Z والـ Z صاحب 6 من 100 من
+
+249
+00:28:46,570 --> 00:28:55,650
+الـ Q يبقى الـ N موجودة في الـ Q ثم Phi of N بقدر
+
+250
+00:28:55,650 --> 00:29:02,070
+اكتبها Phi of واحد زائد واحد زائد واحد اكمرة بنات
+
+251
+00:29:02,070 --> 00:29:11,970
+اكمرة in Piطيب الفي أنا بقول انه homomorphism طبعا
+
+252
+00:29:11,970 --> 00:29:16,390
+وانا فرض انه في عبارة عن homomorphism يبقى هذا
+
+253
+00:29:16,390 --> 00:29:22,030
+الكلام بده يساوي في of one زائد في of one زائد
+
+254
+00:29:22,030 --> 00:29:31,150
+زائد في of one كمان قداش in times يبقى هذا معناه
+
+255
+00:29:31,150 --> 00:29:40,600
+ان الفي of inيساوي N في ال 5 of 1 فال 5 of 1 يبقى
+
+256
+00:29:40,600 --> 00:29:46,280
+داشر يبقى واحد يبقى هذا بده يعطينا انه 5 of N
+
+257
+00:29:46,280 --> 00:29:53,560
+يساوي ال N في واحد هذا بده يعطينا ال 5 of N بده
+
+258
+00:29:53,560 --> 00:30:02,300
+ساوي ال N بده ساوي ال N يبقى صارت هذه ال identity
+
+259
+00:30:02,300 --> 00:30:09,600
+mapو هذه كمان هي ال identity map بس هدول على مين؟
+
+260
+00:30:09,600 --> 00:30:16,140
+على الأعداد الصحيحة بدنا نشوف الأعداد rational
+
+261
+00:30:16,140 --> 00:30:22,340
+اللي بتكون على شكل قصور اعتيادية طبعا احنا عندنا
+
+262
+00:30:22,340 --> 00:30:27,300
+set of rational numbers AQ كل الأعداد اللي على
+
+263
+00:30:27,300 --> 00:30:34,010
+صيغة M على N بحيث ال M و ال N موجودة في ال Zو ال N
+
+264
+00:30:34,010 --> 00:30:46,670
+لا تساوي زي ما يبقى
+
+265
+00:30:46,670 --> 00:30:51,090
+أثبتنا ان ال homomorphisms على الأعداد الصحية هي
+
+266
+00:30:51,090 --> 00:30:55,690
+identity function نيجي على القصور اللي ماهياش
+
+267
+00:30:55,690 --> 00:31:05,330
+أعداد صحية يبقى أنا بتاخد Phi of M على Mأليست Phi
+
+268
+00:31:05,330 --> 00:31:17,150
+of M في N أس ناقص واحد صح ؟ طيب أليست هذه Phi of M
+
+269
+00:31:17,150 --> 00:31:28,210
+في Phi of N أس ناقص واحد صحيح طيب نرجع لل groups
+
+270
+00:31:28,210 --> 00:31:36,150
+لو رجعنا لل groups هذه Phi of Mفي Phi of N أُس
+
+271
+00:31:36,150 --> 00:31:44,270
+هالي واحد طب ال Phi of M مش هي ال M من العلاقة
+
+272
+00:31:44,270 --> 00:31:50,170
+اللي عندنا هذه لإنه integers وهذه اللي هو main
+
+273
+00:31:50,170 --> 00:31:57,270
+وهذه Phi of N اللي هو ال N أُس ناقص واحد يبقى صارة
+
+274
+00:31:57,270 --> 00:32:05,880
+ال M على Nيبقى Phi of M على N هي M على N يبقى هنا
+
+275
+00:32:05,880 --> 00:32:15,720
+Phi of Q بدها تساوي الـ Q لكل Q اللي موجودة في
+
+276
+00:32:15,720 --> 00:32:21,600
+كبتلة Q مين هي ال function هذه ال identity
+
+277
+00:32:21,600 --> 00:32:27,910
+function كما زعمت زميلتكم قبل قليليبقى هذه الـ
+
+278
+00:32:27,910 --> 00:32:39,450
+Identity Map أو الـ Identity Homomorphism طبعا؟
+
+279
+00:32:39,450 --> 00:32:47,670
+إذا قبل قليل من ZN إلى ZN مالجيناش أي زومورفزم إلا
+
+280
+00:32:47,670 --> 00:32:53,780
+الـ Identity Mapوهنا من ال EQ للي EQ مالاجيناش إلا
+
+281
+00:32:53,780 --> 00:33:00,200
+ال identity homomorphism هذا سؤال اتنين واربعين
+
+282
+00:33:00,200 --> 00:33:04,620
+أظن كان معانا سبعة واربعين؟ هذا محلول عندك في
+
+283
+00:33:04,620 --> 00:33:11,180
+الكتاب تفصيليا يبقى خلالك روحي راجعي وكتبيه الآن
+
+284
+00:33:11,180 --> 00:33:15,620
+أهم سؤال عندي على جد اللواجت ضايل سؤال ستة وستين
+
+285
+00:33:15,620 --> 00:33:24,420
+اللي هو خمسة مطالبتمام وبيشمل الفكرة تبعت سؤال 14
+
+286
+00:33:24,420 --> 00:33:29,900
+اللي تركناه وقلنا لك جايب إذا بدي أروح لسؤال 66
+
+287
+00:33:29,900 --> 00:33:33,160
+سؤال
+
+288
+00:33:33,160 --> 00:33:42,680
+66 بيقول ليش احنا ring اعطيه كل المصرفات اللي على
+
+289
+00:33:42,680 --> 00:33:52,220
+الشكل a,b,b,aبحيث ان ال A و ال B موجودات في الستة
+
+290
+00:33:52,220 --> 00:34:03,000
+انتجات وعندنا Phi معرفة من ال A B D A تساوي ال A
+
+291
+00:34:03,000 --> 00:34:12,140
+ناقص ال B طلب المطلوب الأول نمرأ A show Phi is
+
+292
+00:34:12,140 --> 00:34:16,360
+homomorphism والله يشوف لأ homomorphism
+
+293
+00:34:20,790 --> 00:34:28,730
+خلّي بالك هنا يبقى بدي أخد الحالة الأولى وهي نصف
+
+294
+00:34:28,730 --> 00:34:33,570
+الأول من ال homomorphism تبع الجمع يبقى بدي أخد
+
+295
+00:34:33,570 --> 00:34:42,970
+Phi of مجموع مصرفتين موجودتين في R والتكن A B B A
+
+296
+00:34:42,970 --> 00:34:54,130
+زائد C D D C و7 يعرف جديشجدفة يقول جمع المصفوفات
+
+297
+00:34:54,130 --> 00:35:00,430
+حسب ما تعلمته في الجبر الخاطى كل عنصر لعنى غيره
+
+298
+00:35:00,430 --> 00:35:09,590
+تطلع المصفوفة التالية A زائد ال C بي زائد ال D بي
+
+299
+00:35:09,590 --> 00:35:18,690
+زائد ال D بي زائد ال D ال A زائد ال C جسرت مصفوفة
+
+300
+00:35:18,690 --> 00:35:25,080
+واحدةحسب ال definition اللى عندنا بده يساوي ال A
+
+301
+00:35:25,080 --> 00:35:32,360
+ناقص ال B يفجأ هذا بده يساوي ال A زي ال C ناقص ال
+
+302
+00:35:32,360 --> 00:35:39,840
+B زي ال D اللى بقدر اكتبها على الشكل التالف ال A
+
+303
+00:35:39,840 --> 00:35:49,940
+ناقص ال B زي ال C ناقص ال D حسب ال definitionفاي
+
+304
+00:35:49,940 --> 00:35:57,680
+of المصوفة هذه يبقى هذا فاي of المصوفة a b b a
+
+305
+00:35:57,680 --> 00:36:06,540
+زائد فاي of المصوفة الثانية فاي of ال b .. ال ..
+
+306
+00:36:06,540 --> 00:36:24,910
+ال c b ال c b ال c d c dDC and يبقى بالنسبة للجمعة
+
+307
+00:36:24,910 --> 00:36:30,370
+مباشرة لا في لف ولا في دوران ولا في صعوبة بتاخد
+
+308
+00:36:30,370 --> 00:36:40,290
+Phi of حاصل الضرب A B B A في مين في C D D C ويسوي
+
+309
+00:36:40,290 --> 00:36:47,540
+Phi ofضرب المصفات الصف الأول في العمود الأول لو
+
+310
+00:36:47,540 --> 00:36:57,120
+نجمع بيعطينا العمصر الأول يبقى AC زائد BD يبقى AC
+
+311
+00:36:57,120 --> 00:37:04,300
+زائد BD هذا العمصر الأول في العمود الأول الصف
+
+312
+00:37:04,300 --> 00:37:09,230
+الأول في العمود التاني بيعطينا العمصر الثانييبقى
+
+313
+00:37:09,230 --> 00:37:18,390
+AD زائد BC يبقى AD زائد BC الصف الثاني في العمود
+
+314
+00:37:18,390 --> 00:37:28,210
+الأول بيعطينا AD زائد BC والعنصر الأخير AC زائد BD
+
+315
+00:37:28,210 --> 00:37:35,310
+طيب صارت كلها مصفوفة واحدة مش مصفوفتينحسب التعريف
+
+316
+00:37:35,310 --> 00:37:39,270
+اللى عندنا يبقى ال element اللى فى الصفر الاول
+
+317
+00:37:39,270 --> 00:37:44,490
+ناقص ال element اللى فى الصفر الثانى يبقى هذه بده
+
+318
+00:37:44,490 --> 00:37:53,930
+يعطينا ميمو ال AC زي دي ال BD ناقص ال AD ناقص ال
+
+319
+00:37:53,930 --> 00:38:01,850
+BC اعتبريلي هذه المعادلة رقم واحد بدي اجي اخد Phi
+
+320
+00:38:02,920 --> 00:38:12,400
+of ال A P B A في Phi of C D D C by yourself هذه يا
+
+321
+00:38:12,400 --> 00:38:20,340
+بناد اللي همين ال A ناقص ال B و هذه ال C ناقص ال D
+
+322
+00:38:20,340 --> 00:38:30,160
+بدي أضرب القوشين في بعض يبقى هذه ب A C A C ناقص
+
+323
+00:38:30,160 --> 00:38:44,210
+فناقص بزائدBD ناقص B ناقص ال A D ناقص ال B C B C
+
+324
+00:38:44,210 --> 00:38:53,270
+طلع يشوف ايه هذه هيها ها هيها بالحرف الواحد يبقى
+
+325
+00:38:53,270 --> 00:39:03,210
+هذه اتنين يبقى بروح بقوله هنا from واحد ان اتنينWe
+
+326
+00:39:03,210 --> 00:39:10,370
+have ان الـ Phi of ABDA
+
+327
+00:39:10,370 --> 00:39:25,750
+مضروبة في CDDC بتشاوي Phi of ABDA في Phi of CDDC
+
+328
+00:39:25,750 --> 00:39:29,450
+وبالتالي Phi is homomorphism
+
+329
+00:39:45,400 --> 00:39:55,480
+المصمم الثاني خلصنا ايه قال بيه بده find الكرن
+
+330
+00:39:55,480 --> 00:40:05,520
+الالفاية بقوله الكرن الالفاية هو كل المصفوفات a,
+
+331
+00:40:05,860 --> 00:40:11,120
+d, b, a, f,
+
+332
+00:40:14,230 --> 00:40:20,890
+بحيث ان ال file of a, b, b, a بده يساوي zero
+
+333
+00:40:20,890 --> 00:40:28,290
+مظبوط؟ مش هيك التعريف؟ طيب، هذا الكلام معناه مين؟
+
+334
+00:40:28,290 --> 00:40:36,350
+كل المصفات a, b, b, a صدش ده صورة هذا العنصر هو a
+
+335
+00:40:36,350 --> 00:40:43,940
+ناقص ال b يبقى ال a ناقص ال b بده يساوي zeroيبقى
+
+336
+00:40:43,940 --> 00:40:51,700
+هذا الكلام كل المصروفات a,b,b,a such ذات ال a
+
+337
+00:40:51,700 --> 00:40:57,520
+تساوي ال b إذا انا هشيل كل b و أحط مكانها a أو
+
+338
+00:40:57,520 --> 00:41:04,440
+أشيل كل a و أحط مكانها b يبقى هذا الكلام بده يساوي
+
+339
+00:41:04,440 --> 00:41:11,820
+كل المصروفات اللي ع الشكل a,a,a,a بحيث ال a موجود
+
+340
+00:41:11,820 --> 00:41:18,560
+وينموجود فيه زر يبقى الكيرن التابع هذه ال function
+
+341
+00:41:18,560 --> 00:41:24,400
+كل المصفوفات اللي نظامها اتنين في اتنين واللي جميع
+
+342
+00:41:24,400 --> 00:41:30,220
+أنصارها متساوية قال لي بعد ذلك المطلوب التالت
+
+343
+00:41:30,220 --> 00:41:41,920
+نمرسي قال لي شو؟ لأ ان ال R Modular Kern لل Phi
+
+344
+00:41:42,290 --> 00:41:50,890
+Isomorphic لمين؟ Isomorphic to Z Solution
+
+345
+00:41:50,890 --> 00:41:59,610
+هذه
+
+346
+00:41:59,610 --> 00:42:06,600
+مرت علينا في نظرية من نظريات خلال هذا الشهر داإيش
+
+347
+00:42:06,600 --> 00:42:10,640
+اسمها؟ الـ first isomorphism ممتاز جدا، يبقى أنا
+
+348
+00:42:10,640 --> 00:42:16,380
+بدأ أروح على ال first isomorphism theorem ونقارنها
+
+349
+00:42:16,380 --> 00:42:20,980
+مع مين؟ مع المطلوب، يمكن تصبط ويمكن ما تصبطش الله
+
+350
+00:42:20,980 --> 00:42:27,600
+أعلم، طب الله بقول هنا from أو قبل هيك، we know
+
+351
+00:42:27,600 --> 00:42:28,240
+that
+
+352
+00:42:31,630 --> 00:42:40,230
+إن الكيرن الـ alpha is an ideal of R.مظبوط يا
+
+353
+00:42:40,230 --> 00:42:46,150
+عزيزي؟ الكيرن الـ ideal. أثبتنا نظرية كذلك خلال
+
+354
+00:42:46,150 --> 00:42:56,010
+هذا الشرطة.طيب بروح بقول هنا by the isomorphism
+
+355
+00:42:56,010 --> 00:43:05,590
+theorem. We haveحدة بيذكراها في Ego ان R موديول
+
+356
+00:43:05,590 --> 00:43:14,010
+الكرن لـ Phi ايزو مورفك لميه؟ لا Phi of R Phi of R
+
+357
+00:43:14,010 --> 00:43:22,210
+طب هو ايش المطلوب؟ اثبت ايزو مورفك لـ Z بنقول إذا
+
+358
+00:43:22,210 --> 00:43:29,710
+قدرنا نثبت ان Phi of R ايزو مورفك لـ Z بتم المطلوب
+
+359
+00:43:30,380 --> 00:43:35,980
+والأسهل من ذلك انه نثبت ان ال five of R هي Z
+
+360
+00:43:35,980 --> 00:43:41,680
+itself إذا قدرنا نثبت هذا الكلام يقول خلصنا تمام
+
+361
+00:43:41,680 --> 00:43:50,400
+يبقى فاجب أقوله F we show them إذا قدرنا نثبت ان
+
+362
+00:43:50,400 --> 00:44:01,930
+ال five of R تساوي Z يبقى then wehave the result
+
+363
+00:44:01,930 --> 00:44:08,730
+يكون خلصنا، حصلنا على النتيجة لذلك بدي أحاول أثبت
+
+364
+00:44:08,730 --> 00:44:14,090
+أنه كل واحدة فيهم subset من التالية يبقى بروح
+
+365
+00:44:14,090 --> 00:44:23,370
+بقوله little x موجودة في الـPhi of R تمام؟
+
+366
+00:44:23,370 --> 00:44:38,030
+then ال Xتساوي فاي of مصروف من R will تكون A1 B1
+
+367
+00:44:38,030 --> 00:44:45,650
+B1 A1 فاي
+
+368
+00:44:45,650 --> 00:44:51,210
+of هذه X موجودة في فاي of عريب X تساوي فاي of
+
+369
+00:44:51,210 --> 00:44:57,640
+element من R من ما يكون يكونطيب هذا مشوعي عبارة عن
+
+370
+00:44:57,640 --> 00:45:04,080
+a1 ناقص b1 طب a1 و b1 وين موجوداتها دول؟ في z
+
+371
+00:45:04,080 --> 00:45:08,860
+الفرق بينها موجود في z لأن هذول الفرق بين any two
+
+372
+00:45:08,860 --> 00:45:16,440
+integers is an integer يبقى هذا موجود في z يبقى
+
+373
+00:45:16,440 --> 00:45:24,040
+sir phi of a subset من مين؟ subset من zنعمل
+
+374
+00:45:24,040 --> 00:45:32,500
+العملية العكسية on the other hand let
+
+375
+00:45:32,500 --> 00:45:40,320
+ال X موجودة في Z إذا قدرنا نثبت إن ال X موجودة في
+
+376
+00:45:40,320 --> 00:45:46,240
+Phi R، يكون خلاص تم المطلوب تمام؟ يبقى افترضنا إن
+
+377
+00:45:46,240 --> 00:45:56,000
+X موجودة في Z then ال X تساويممكن احطها فرق بين
+
+378
+00:45:56,000 --> 00:46:02,460
+any two انتجارات بدون مشاكل حتى لو كانت zero ممكن
+
+379
+00:46:02,460 --> 00:46:06,600
+احطها zero ناقص zero ممكن احطها خمسة ناقص خمسة مية
+
+380
+00:46:06,600 --> 00:46:11,980
+ناقص هادى جدا يبقى ال element اللى أخدته فاقدر
+
+381
+00:46:11,980 --> 00:46:18,500
+احطه كفرق بين two انتجارات يبقى then ال X بده يقول
+
+382
+00:46:18,500 --> 00:46:27,490
+ايه ناقص ال B مثلاقبل A نقص ال V مش هي عبارة عن
+
+383
+00:46:27,490 --> 00:46:40,950
+Phi of A,B,B,A وهذه موجودة في Phi of A صح؟
+
+384
+00:46:40,950 --> 00:46:47,930
+فهذه موجودة في Phi of A يبقى ال element اللي خدته
+
+385
+00:46:47,930 --> 00:46:56,250
+في Z لجته موجود وين؟ في Phi of Aيبقى هنا سا اللي
+
+386
+00:46:56,250 --> 00:47:06,670
+هو ال z subject من five of a سميلي الأولى رقم واحد
+
+387
+00:47:06,670 --> 00:47:14,450
+وسميلي هذه رقم اتنين فبنروح نقوله from واحد and
+
+388
+00:47:14,450 --> 00:47:25,030
+اتنين we have ان ال five of aتساوي الـ Z itself
+
+389
+00:47:25,030 --> 00:47:28,350
+طيب
+
+390
+00:47:28,350 --> 00:47:45,050
+ليش وصلنا؟
+
+391
+00:47:45,050 --> 00:47:48,350
+يبقى
+
+392
+00:47:48,350 --> 00:47:54,190
+صاروا اتنين دول متساوياتين ساعةالـR موديول الكيرني
+
+393
+00:47:54,190 --> 00:48:00,350
+للـPhi أيزو مورفك لـPhi of R اللي بتساوي مينا منها
+
+394
+00:48:00,350 --> 00:48:08,030
+Z إذا معنى هذا الكلام أنه R موديول الكيرني للـPhi
+
+395
+00:48:08,030 --> 00:48:15,950
+أيزو مورفك لمين؟ لـZ بسأله
+
+396
+00:48:15,950 --> 00:48:20,510
+كمان سؤال، الحين كم سؤال سؤال؟ تلاتة سؤال الرابع
+
+397
+00:48:21,250 --> 00:48:30,430
+المرأة دي بقول هل الكيرن ال ال5 is a prime ideal
+
+398
+00:48:30,430 --> 00:48:34,490
+ولا لا؟
+
+399
+00:48:34,490 --> 00:48:43,690
+سمع، بنفع، طيب، وده بتبدأ بطريقتنا، طريقتنا
+
+400
+00:48:43,690 --> 00:48:48,210
+الأخرى، يا إما بوسطة ال definition، يا إما
+
+401
+00:48:48,210 --> 00:48:54,630
+بالنظريةبتاعة الار موديولو موديولو مين؟ موديولو
+
+402
+00:48:54,630 --> 00:49:00,950
+الكيرنل تبقى integral domain إذا كان الكيرنل ال
+
+403
+00:49:00,950 --> 00:49:07,250
+prime صح ولا لأ؟ اه يعني إيش ممكن أعمل؟ يعني ممكن
+
+404
+00:49:07,250 --> 00:49:14,530
+أخد mass of تين موجودات في الأرض بحيث حصل ضربهم
+
+405
+00:49:14,530 --> 00:49:18,950
+يكون في الكيرنلو أثبت يا الأولى في ال kernel يا
+
+406
+00:49:18,950 --> 00:49:23,090
+التانية في ال kernel إيه الحدث ذلك؟ بقوله يبقى هذا
+
+407
+00:49:23,090 --> 00:49:28,330
+prime ideal هذا الطريقة الأولى طويلة شوية مية
+
+408
+00:49:28,330 --> 00:49:32,050
+المية بس طويلة شوية اللي أقصر منها احنا قولنا
+
+409
+00:49:32,050 --> 00:49:37,630
+isomorphic لمين؟ لزد لما نقول في عندي ring
+
+410
+00:49:37,630 --> 00:49:41,370
+isomorphic ل ring التانية يبقى ال ring الأولى
+
+411
+00:49:41,370 --> 00:49:46,560
+والتانية كلهم لهم نفس الخواصة الرياضيةطب الـ z is
+
+412
+00:49:46,560 --> 00:49:50,740
+an integral domain؟ انتجرال دومينة خدناها قبل ذلك
+
+413
+00:49:50,740 --> 00:49:59,580
+يبقى بالي بقوله since بما ان ال z is an integral
+
+414
+00:49:59,580 --> 00:50:12,600
+domain we have ان ال R modulo الكرمي لل 5 is an
+
+415
+00:50:12,600 --> 00:50:24,690
+integraldomain طيب هذا بده يعطيني by a previous
+
+416
+00:50:24,690 --> 00:50:34,890
+theorem by a previous theorem by
+
+417
+00:50:34,890 --> 00:50:39,550
+a previous theorem هذه integral domain
+
+418
+00:50:43,640 --> 00:50:51,740
+الـ prime ideal و هو المطلوب خلصنا من دين جيل
+
+419
+00:50:51,740 --> 00:51:00,220
+الريب بيسأل هل هذا maximal ولا لا؟ يبقى أزة اللي
+
+420
+00:51:00,220 --> 00:51:07,940
+هو ال kern اللوفاية maximum ideal ولا لا؟
+
+421
+00:51:11,030 --> 00:51:16,870
+بس الاسئلة التالية هل ال z فيه؟ يبقى لا يمكن ال R
+
+422
+00:51:16,870 --> 00:51:21,190
+موديل الكون ان انا اكون فيه يبقى لا يمكن الكون ان
+
+423
+00:51:21,190 --> 00:51:27,490
+انا اكون ماكسيما هذي احد الطرق تمام؟ يبقى value
+
+424
+00:51:27,490 --> 00:51:42,040
+بيقوله since بيبقى ان ال z ال z عندى is notA field
+
+425
+00:51:42,040 --> 00:51:47,580
+ليش؟ لأنه مش كل أنصار له معكوث. مش هو ال unity.
+
+426
+00:51:47,720 --> 00:51:52,340
+اتنين والتلاتة والاربعة ولا واحد له معكوث في ذاته.
+
+427
+00:51:52,740 --> 00:52:00,300
+That is not a field. We have in our modular kernel
+
+428
+00:52:00,300 --> 00:52:08,910
+الفائض is not a field.يبقى هذا يقدر يعطيك الكيرن
+
+429
+00:52:08,910 --> 00:52:18,730
+اللي الفاي is not maximal طيب
+
+430
+00:52:18,730 --> 00:52:25,970
+أنا ماجدتش في بالي النظرية لكن تعريف الفيل ان اي
+
+431
+00:52:25,970 --> 00:52:32,910
+عنصر له معكوس طب لو كده اثبت او ااخد و لو عنصر
+
+432
+00:52:32,910 --> 00:52:37,130
+واحد مالاقيش عنصر غير صفري بسمايكونش لو ماكوش
+
+433
+00:52:37,130 --> 00:52:39,750
+بيبقى اللي يصير فيه دول وبالتالي بيبقى اللي يصير
+
+434
+00:52:39,750 --> 00:52:46,070
+هذا maximal ID مظهر؟ طيب تعالى نشوف بدنا طريقة
+
+435
+00:52:46,070 --> 00:52:56,030
+ثانية للورهام يبقى بداخل let اللي هو main let مثلا
+
+436
+00:52:56,030 --> 00:53:04,280
+خمسة اتنين اتنين خمسة زائد الكرن لل fiveموجودة في
+
+437
+00:53:04,280 --> 00:53:11,120
+الار موديول الكيرني للفارق بدي
+
+438
+00:53:11,120 --> 00:53:19,660
+أبيل ان هذا عنصر غير صفري تمام؟ then هذا شو بده
+
+439
+00:53:19,660 --> 00:53:27,620
+يساوي؟ الخمسة اتنين اتنين خمسة زائد الكيرني للفارق
+
+440
+00:53:27,620 --> 00:53:35,120
+يساوي تلاتة Zero Zeroثلاث، اتنين، اتنين، اتنين
+
+441
+00:53:35,120 --> 00:53:42,660
+زائد الكيرن للـ Phi صحيح ؟ مجموع
+
+442
+00:53:42,660 --> 00:53:46,900
+المصفوفة هناك تتطلع هذه طب هذا موجود في الكيرن
+
+443
+00:53:46,900 --> 00:53:53,980
+المصفوفة هذه لأن الكيرن الـAAA موجود في الكيرن
+
+444
+00:53:53,980 --> 00:53:59,320
+يبقى ما يسهل عليها الطير يولد مع الكيرنيبقى بقول
+
+445
+00:53:59,320 --> 00:54:08,480
+هذا الكلام بدي يسوى 3003 زي الكرن الالفاية هل هذا
+
+446
+00:54:08,480 --> 00:54:16,980
+بيسوى الكرن الالفاية؟ لا يسوى الكرن الالفاية يبقى
+
+447
+00:54:16,980 --> 00:54:24,520
+هذا اضمان a zero element يبقى هنا ساعة اللي هو من
+
+448
+00:54:24,520 --> 00:54:27,480
+3003
+
+449
+00:54:27,930 --> 00:54:38,070
+زائد الكائن اللى الفاية is a non zero n بدى افترض
+
+450
+00:54:38,070 --> 00:54:46,190
+انه يلو معكوس طبعا طيب لما يلو معكوس بدى اشوف هل
+
+451
+00:54:46,190 --> 00:54:52,670
+بوصل الى تناقض والله بصير كلامي صحيح انا فضالي
+
+452
+00:54:52,670 --> 00:54:57,030
+بقولهم as you want that
+
+453
+00:54:58,690 --> 00:55:09,050
+إنه تلاتة Zero Zero تلاتة زادة كيرن للفاي مضروف A
+
+454
+00:55:09,050 --> 00:55:20,850
+B B A زادة كيرن للفاي كل هذا مضروف هذا بده يساوي
+
+455
+00:55:20,850 --> 00:55:26,270
+ال unity من ال unity واحد Zero Zero واحد اللي هو
+
+456
+00:55:26,270 --> 00:55:37,550
+موجود في A1001 زائد الكيرن للـ 5 يبقى
+
+457
+00:55:37,550 --> 00:55:49,370
+هذا معناته يا بنات ان التلاتة 003 في ال A B B A
+
+458
+00:55:49,370 --> 00:56:01,420
+سبب واحد 001 مظبوط؟ عشان اكترطيب هذا معناه هو
+
+459
+00:56:01,420 --> 00:56:06,920
+المصروف التالي الصف الأول في العمود الأول تلاتة A
+
+460
+00:56:06,920 --> 00:56:13,640
+و هنا تلاتة B و هنا تلاتة B و هنا تلاتة A بدها
+
+461
+00:56:13,640 --> 00:56:20,100
+تساوي واحد Zero واحد طيب هذا ايش معناه ان تلاتة A
+
+462
+00:56:20,100 --> 00:56:27,320
+بدها تساوي واحديعني ايه تسوى كده؟ هل التوتس موجود
+
+463
+00:56:27,320 --> 00:56:33,740
+في Z؟ يبقى هذا does not belong to Z يبقى فرض اللي
+
+464
+00:56:33,740 --> 00:56:38,660
+فرضته هذا غلط ولا صح؟ غلط يعني معناه أن العنصر هذا
+
+465
+00:56:38,660 --> 00:56:44,760
+مالوش معكوس عنصر غير صفري مالوش معكوس يبقى لا يمكن
+
+466
+00:56:44,760 --> 00:56:49,840
+أن يكون هذا فيل لإن الفيل كل عنصر غير صفري لهو
+
+467
+00:56:49,840 --> 00:56:59,630
+معكوسطيب كويس مش موجود في 6 الخمسة اتنين اتنين
+
+468
+00:56:59,630 --> 00:57:06,650
+خمسة زائد الكيرن اللي ال five has no
+
+469
+00:57:06,650 --> 00:57:11,070
+multiplicative
+
+470
+00:57:11,070 --> 00:57:20,450
+inverse هذا بده يعطينا ان ال RModular Kernel لـ
+
+471
+00:57:20,450 --> 00:57:29,150
+Phi is not a field مدام ما هوش فين يبقى ال Kernel
+
+472
+00:57:29,150 --> 00:57:38,610
+لـ Phi is not maximal يبقى عندك طريقتين لإثبات
+
+473
+00:57:38,610 --> 00:57:44,110
+الـPrime وعندك طريقتين لإثبات نين لإثبات ال
+
+474
+00:57:44,110 --> 00:57:47,510
+maximum أعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9b383c585f084c1afb67f388e166f043b2b4161b
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/yvrW5DYfxvc_raw.srt
@@ -0,0 +1,1632 @@
+1
+00:00:20,670 --> 00:00:26,050
+بسم الله الرحمن الرحيم عوضنا على بدأ احنا بدأنا في
+
+2
+00:00:26,050 --> 00:00:30,790
+ring homomorphism المرة الماضية و كتبنا نص نظرية
+
+3
+00:00:30,790 --> 00:00:35,710
+طبعا الكتاب مابرهنشيشي و قال زي تبعت ال group و
+
+4
+00:00:35,710 --> 00:00:39,670
+احنا مش هنقول زي مجلة لأ بدنا نروح نبرهن هذه
+
+5
+00:00:39,670 --> 00:00:45,590
+النظرية ثمان نقاط هذه النظرية النقطة الأولى بقول
+
+6
+00:00:45,590 --> 00:00:51,620
+لو كان ال in is a positive integerوالـ R موجود في
+
+7
+00:00:51,620 --> 00:00:58,420
+R بدنا نثبت انه الـ Phi in R بيسوي N في Phi of R
+
+8
+00:00:58,420 --> 00:01:03,740
+وكذلك نثبت انه Phi of R to the power N بيسوي Phi
+
+9
+00:01:03,740 --> 00:01:08,400
+of R كلها to the power N يعني بقى ال proof التاني
+
+10
+00:01:08,400 --> 00:01:14,700
+بدي أبدأ بالنقطة الأولى Phi of الـ N في R هذه بقدر
+
+11
+00:01:14,700 --> 00:01:19,810
+أكتبها للشكل تاني Phi ofالان يا بنات واحد وارتوبها
+
+12
+00:01:19,810 --> 00:01:24,510
+واحد زائد واحد زائد واحد الى اخرى يبقى واحد زائد
+
+13
+00:01:24,510 --> 00:01:31,010
+واحد زائد زائد واحد كل هذا في R اللي برا اللي
+
+14
+00:01:31,010 --> 00:01:37,490
+عندنا هنا تمام هذا الكلام يساوي من حسب قانون
+
+15
+00:01:37,490 --> 00:01:42,690
+التوزيع ال distributive law هذه بيصير واحد في R
+
+16
+00:01:42,690 --> 00:01:51,240
+اللي هي ب R تماموالثانية بـR والثالثة بـR والاخر
+
+17
+00:01:51,240 --> 00:01:57,020
+واحدة اللي هي بـA. طبعا عددهم هذول كده؟ كم واحد؟
+
+18
+00:01:57,020 --> 00:02:04,440
+يبقى N Phi. يبقى N من المرات. هذول عددهم كذلك N من
+
+19
+00:02:04,440 --> 00:02:08,880
+المرات. الآن في راسي النظرية قال لي Phi is a
+
+20
+00:02:08,880 --> 00:02:15,680
+homomorphism. إذاً هذا الكلام بيساوي Phi of R.زائد
+
+21
+00:02:15,680 --> 00:02:24,640
+Phi of R زائد زائد Phi of R هذول كذلك M times M من
+
+22
+00:02:24,640 --> 00:02:32,760
+المرات يبقى كلهم زي بعض يبقى M في عددهم يبقى M في
+
+23
+00:02:32,760 --> 00:02:37,180
+Phi of R أظن و هو المطلوب انتهينا من النقطة
+
+24
+00:02:37,180 --> 00:02:43,920
+الأولى. الآن بتاجي للنقطة ثانية Phi of R to the
+
+25
+00:02:43,920 --> 00:02:54,240
+power Mبتساوي Phi of R في R في R كذلك عددهم M Phi
+
+26
+00:02:54,240 --> 00:02:59,940
+homomorphism إذا هتدخل على كل واحدة منهم Phi of R
+
+27
+00:02:59,940 --> 00:03:07,900
+في Phi of R في Phi of R عددهم كم؟ M من المرات
+
+28
+00:03:07,900 --> 00:03:15,800
+ومكرر يبقى Phi of R كله to the power Mوهو المطلوب
+
+29
+00:03:15,800 --> 00:03:25,720
+النقطة الثانية بيقول لي Phi of A Phi of A اللي هو
+
+30
+00:03:25,720 --> 00:03:35,100
+كل العناصر Phi of A such that وبحيث ان ال A موجود
+
+31
+00:03:35,100 --> 00:03:46,230
+في ال A is a subring of Sيبقى هذا is a subring of
+
+32
+00:03:46,230 --> 00:03:52,850
+S طبعا احنا معانا من رأس النظرية Phi من R إلى S is
+
+33
+00:03:52,850 --> 00:03:58,110
+homomorphism و ال A عبارة عن subring و ال B عبارة
+
+34
+00:03:58,110 --> 00:04:03,150
+عن ideal هي كنص النظرية اللي مكتوب معاكم من المرة
+
+35
+00:04:03,150 --> 00:04:10,320
+الماضية الآن بدنا نثبت هذا عبارة عن subringبنقوله
+
+36
+00:04:10,320 --> 00:04:15,540
+بسيطة خالص يبقى النقطة الأولى من إثبات ال subring
+
+37
+00:04:15,540 --> 00:04:24,260
+بقوله Phi of A is non-empty non-empty ليش؟ because
+
+38
+00:04:24,260 --> 00:04:33,920
+ال A is non-empty is non-empty اللي هي subring طيب
+
+39
+00:04:33,920 --> 00:04:43,590
+نقطة ثانية بدي أخد عنصرينوليكن X وY موجود في Phi
+
+40
+00:04:43,590 --> 00:04:53,590
+of A يبقى ممكن يكون شكلهم هذا يقدر يعطينا ان X
+
+41
+00:04:53,590 --> 00:05:09,960
+تساوي Phi of A وY تساوي Phi of B هذا الكلام forSum
+
+42
+00:05:09,960 --> 00:05:18,420
+a وb اللى موجودة فى subring a كويس، بتشوف الفرق فى
+
+43
+00:05:18,420 --> 00:05:26,260
+ما بينهما يبجى ال X ناقص ال Y لسبب Phi of a ناقص
+
+44
+00:05:26,260 --> 00:05:33,120
+Phi of b هذا بده يعطينا الان Phi homomorphism إذا
+
+45
+00:05:33,120 --> 00:05:42,310
+ال X ناقص ال Yيساوي Phi of A ناقص B، ليش؟ لأن Phi
+
+46
+00:05:42,310 --> 00:05:49,670
+is a homomorphism طيب، هذا الكلام إيش بيعطينا؟
+
+47
+00:05:49,670 --> 00:05:56,230
+بيعطينا إن ال X ناقص ال Y موجودة هذا ال A ناقص ال
+
+48
+00:05:56,230 --> 00:06:02,750
+B وين موجود؟ في ال sub ring A، تمام؟ في ال sub
+
+49
+00:06:02,750 --> 00:06:08,800
+ring Aيبقى معنا هذا الكلام موجود في Phi of A
+
+50
+00:06:08,800 --> 00:06:12,880
+أثبتنا ال condition التالي من ال sub ring ال
+
+51
+00:06:12,880 --> 00:06:18,720
+condition التالي بدي أخد عنصرين من ال sub ring بدي
+
+52
+00:06:18,720 --> 00:06:23,580
+أثبت أن حاصل ضربهما موجود داخل ال sub ring اللي
+
+53
+00:06:23,580 --> 00:06:35,500
+عندنا يبقى let X وY موجودة في Phi of Aالـ X بده
+
+54
+00:06:35,500 --> 00:06:46,620
+تساوي في of A و ال Y بده يساوي في of B for some A
+
+55
+00:06:46,620 --> 00:06:54,920
+و B اللي موجودة في ال sub ring A بده أخد حاصل
+
+56
+00:06:54,920 --> 00:07:03,520
+الضرب X في Y يبقى هذا الكلام بده يساوي في of Aفي
+
+57
+00:07:03,520 --> 00:07:10,320
+Phi of B Phi homomorphism إذا هذا الكلام بتسوي Phi
+
+58
+00:07:10,320 --> 00:07:20,360
+of AB هذه موجودة في Phi of A ولا لا؟ ليش؟ لإن ال A
+
+59
+00:07:20,360 --> 00:07:26,860
+في B موجودة في ال sub ring A يبقى هنا موجودة في
+
+60
+00:07:26,860 --> 00:07:40,530
+Phi A يبقى ضص وهكذا ال Phiof A is a subring of S
+
+61
+00:07:40,530 --> 00:07:48,210
+هذا النقطة الثانية النقطة التالتة النقطة
+
+62
+00:07:48,210 --> 00:07:53,050
+التالتة بتقولي لو كان ال A ideal يبقى بطلة ال A
+
+63
+00:07:53,050 --> 00:07:59,670
+صير subring بدنا نفترضها انها ايdeal يبقى ال A
+
+64
+00:07:59,670 --> 00:08:08,560
+idealتمام؟ هذه المعطيات الأولى في المثل Ideal of A
+
+65
+00:08:08,560 --> 00:08:17,800
+وفي نفس الوقت الـ Phi is unto والـ Phi is unto ال
+
+66
+00:08:17,800 --> 00:08:24,440
+Phi is unto يبقى Phi of A is an ideal يبقى هذا
+
+67
+00:08:24,440 --> 00:08:33,880
+يريحنا أن Phi of A is anideal of اسم هذا اللي بنا
+
+68
+00:08:33,880 --> 00:08:43,760
+نثبه ال proof فالي باركوا يعنى ان ال a في رأس
+
+69
+00:08:43,760 --> 00:08:48,460
+النظرية يقول لصبرينج هنا افترض هي ايش؟ ideal لو
+
+70
+00:08:48,460 --> 00:08:53,820
+كانت ideal و Phi كانت onto يعني غطت جميع عناصر اسم
+
+71
+00:08:53,820 --> 00:08:59,730
+بلاستثناءأو الـ Range ساوى الـ Codomain اللي هو S
+
+72
+00:08:59,730 --> 00:09:04,130
+يبقى الـ Phi of A بداية تفتح انه عبارة عن ايش؟ ID
+
+73
+00:09:04,130 --> 00:09:11,770
+طب السؤال هو هل ال Phi of A Sub-Range؟
+
+74
+00:09:11,770 --> 00:09:19,130
+نعم، نقطة ثانية، ايه باجي بقولك from part
+
+75
+00:09:19,130 --> 00:09:31,810
+two ال Phi of Ais a subring of الـ S يبقى لنا بس
+
+76
+00:09:31,810 --> 00:09:37,350
+أخر شرط من شروط ال ID يبقى ال file non-empty و
+
+77
+00:09:37,350 --> 00:09:42,310
+الفرق بين أي عصر موجود فيهالما كان الصبرينج باقينا
+
+78
+00:09:42,310 --> 00:09:47,910
+ناخد عنصرين من نفس الست لكن هنا لأ بدي أخد عنصر من
+
+79
+00:09:47,910 --> 00:09:53,250
+الست و عنصر من ال ring الأصلية بدي أحصل ضربهم يكون
+
+80
+00:09:53,250 --> 00:10:02,670
+موجود في في او اي ان حدث ذلك بقول في او اي is an
+
+81
+00:10:02,670 --> 00:10:05,410
+ideal of S لذلك
+
+82
+00:10:13,750 --> 00:10:22,250
+الـ X موجودة في الـ Phi of A يبقى أخد Element
+
+83
+00:10:22,250 --> 00:10:26,270
+موجود في الـ6 اللي عندنا و Element موجود في
+
+84
+00:10:26,270 --> 00:10:31,530
+الـRing الأصلية يبقى
+
+85
+00:10:31,530 --> 00:10:41,840
+ذنبالـ R موجودة في الـ R and ال X بده يساوي Phi of
+
+86
+00:10:41,840 --> 00:10:54,380
+A for some A اللي موجودة في A then بده
+
+87
+00:10:54,380 --> 00:11:03,080
+أخد ال همين بده أثبت أن ال R في X هذه موجودة وين؟
+
+88
+00:11:03,240 --> 00:11:09,540
+موجودة في الـPhi of A طب استنوا شوية انا ماخد R
+
+89
+00:11:09,540 --> 00:11:14,520
+لكن لا لا لا استنى بدنا ناخد بدنا نطبق هذا
+
+90
+00:11:14,520 --> 00:11:20,120
+فالsubring من مين من ال S يبقى هذا يا بنات مش
+
+91
+00:11:20,120 --> 00:11:30,600
+صحيحة هذي بدى اخد مثلا T موجودة في S لأن Phi of A
+
+92
+00:11:30,600 --> 00:11:35,290
+element في Sوانا بدي أثبت ان الـ Phi of A capital
+
+93
+00:11:35,290 --> 00:11:42,490
+هو ideal في من؟ في ال S لأن Phi A موجودة في S طيب
+
+94
+00:11:42,490 --> 00:11:48,290
+كويس الان T موجودة في S و ال Phi is .. انتوا يبقى
+
+95
+00:11:48,290 --> 00:11:55,470
+إيه له أصل في ال ring R ولا لا؟ يبقى هنا بدي أجي
+
+96
+00:11:55,470 --> 00:12:05,970
+أقول له since بما أن since ال Phiis onto and ات
+
+97
+00:12:05,970 --> 00:12:14,150
+موجود في الاسم there exist r موجود في الار such
+
+98
+00:12:14,150 --> 00:12:23,930
+that بحيث ان ات تساوي five of r نظرا
+
+99
+00:12:23,930 --> 00:12:29,290
+لان five is onto يبقى اي element اخده من ال code
+
+100
+00:12:29,290 --> 00:12:35,140
+mainهنجيله أصل في ال domain اللي هو R T تساوي Phi
+
+101
+00:12:35,140 --> 00:12:43,860
+of R طيب أنا بدي أثبت الآن أنه A T في ال X موجودة
+
+102
+00:12:43,860 --> 00:12:50,460
+وين في ال Phi of A صح ولا لأ مش هنفدل يعني بدي
+
+103
+00:12:50,460 --> 00:12:56,460
+أثبت Phi of A is an ideal إذا بدي أخد الآن T في X
+
+104
+00:12:56,460 --> 00:13:05,420
+يساوي ال T عندي بمين؟فاي of R وال X عندي في of A
+
+105
+00:13:05,420 --> 00:13:14,840
+فيهومومورفزم يبقى هذا الكلام في of R في A طيب
+
+106
+00:13:14,840 --> 00:13:23,020
+السؤال هو هل هذا ال element موجود في A؟ اه ليش انه
+
+107
+00:13:23,020 --> 00:13:29,990
+فرضين A ايديل وهذا element موجود في ال idealيبقى
+
+108
+00:13:29,990 --> 00:13:34,650
+هذا element موجود في ال ring A يبقى حاصل ضربهما
+
+109
+00:13:34,650 --> 00:13:43,770
+يكون موجود يبقى هذا موجود في Phi of A ليش؟ because
+
+110
+00:13:43,770 --> 00:13:55,290
+ال A موجود في ال A and ال A is an ideal يبقاش اللي
+
+111
+00:13:55,290 --> 00:14:05,160
+حصل هنا ال T في Xموجودة في Phi of A في Phi of A
+
+112
+00:14:05,160 --> 00:14:14,320
+بنفس الطريقة Similarly بنفس الطريقة ال XT موجودة
+
+113
+00:14:14,320 --> 00:14:21,700
+في Phi of A إذا انتحققت شروط ال ideal صحيح يبقى
+
+114
+00:14:21,700 --> 00:14:35,780
+بقوله Therefore ولهذا Phi of Ais an ideal of S هذا
+
+115
+00:14:35,780 --> 00:14:41,380
+النقطة التالتة النقطة الرابعة النقطة الرابعة دي
+
+116
+00:14:41,380 --> 00:14:50,440
+يقولي Phi inverse of B بينا نثبت ان Phi inverse of
+
+117
+00:14:50,440 --> 00:14:56,300
+B اللي هو عبارة عن كل العناصر I الموجودة في ال
+
+118
+00:14:56,300 --> 00:15:06,330
+ring Rبحكي ان فاي of R موجودة في بيه ايش بنا نسبته
+
+119
+00:15:06,330 --> 00:15:14,410
+هذا اثبت هذه فاي inverse is an ideal is an ideal
+
+120
+00:15:14,410 --> 00:15:20,430
+of R خلينا
+
+121
+00:15:20,430 --> 00:15:30,430
+نلقي هنا احنا بنا كالنا فاي منالار الى اس هذا
+
+122
+00:15:30,430 --> 00:15:35,910
+معروف homomorphism مظبوط طب الفاي انفرست بدى يكون
+
+123
+00:15:35,910 --> 00:15:40,490
+من و لا و لا من اس لأ ار من اس لأ ار يبقى لو كان
+
+124
+00:15:40,490 --> 00:15:45,070
+هذا one to one and one to two يبقى في انفرست exist
+
+125
+00:15:45,070 --> 00:15:51,990
+وبدى يكون من الاس لغاية ار ممتاز جدا طيب هو قاللي
+
+126
+00:15:51,990 --> 00:15:59,440
+اصلا ال بي ايديل في مين؟فى S طلع نص النظرية من
+
+127
+00:15:59,440 --> 00:16:06,480
+البداية جالى A subring من R و ال B ideal من S و
+
+128
+00:16:06,480 --> 00:16:15,400
+عندنا هنا ال B ideal of S جالى اثبت انه Phi
+
+129
+00:16:15,400 --> 00:16:20,880
+inverse يبقى B موجود وان فى S يبقى Phi inverse لما
+
+130
+00:16:20,880 --> 00:16:26,500
+اتأثر على ال ideal بترجع لمين؟ ترجع ال Aيبقى بدنا
+
+131
+00:16:26,500 --> 00:16:32,460
+نثبت انه Phi inverse لما يأثر على P بيعطيني عناصر
+
+132
+00:16:32,460 --> 00:16:38,980
+من ال ring R من هم اللي هم صورهم موجودة في ال
+
+133
+00:16:38,980 --> 00:16:43,340
+ideal P ايش بدنا نثبت ال Phi inverse of P؟ بدنا
+
+134
+00:16:43,340 --> 00:16:49,340
+نثبت انه ideal يعني بدنا نثبت الشروب التلاتة اللي
+
+135
+00:16:49,340 --> 00:16:54,620
+أثبتناهم هنا واحد اتنين تلاتةهنا اثبتنا ان فاي of
+
+136
+00:16:54,620 --> 00:17:01,960
+a sub ring و بعد هيك حولنا لمين لل ideal طيب الآن
+
+137
+00:17:01,960 --> 00:17:07,560
+بتدجل الشرط الأول من شروط ال ideal بقول لهم فاي
+
+138
+00:17:07,560 --> 00:17:15,080
+inverse of b is non empty معقول؟ ايش السبب؟
+
+139
+00:17:15,080 --> 00:17:19,480
+because ال b is non empty
+
+140
+00:17:22,200 --> 00:17:28,660
+لأن الـ B عبارة عن Ideal والـ Ideal non-empty طيب،
+
+141
+00:17:28,660 --> 00:17:33,060
+النقطة الثانية، بدنا ناخد عنصرين في الـ Phi
+
+142
+00:17:33,060 --> 00:17:39,720
+inverse of B يبقى بالذات يقولّه افترض الـ X والـ Y
+
+143
+00:17:39,720 --> 00:17:45,540
+موجودة في الـ Phi inverse of B بدي أثبت أن الفرق
+
+144
+00:17:45,540 --> 00:17:50,480
+فيما بينهما موجود وين في الـ Phi inverse of B، إن
+
+145
+00:17:50,480 --> 00:17:54,520
+حدث ذلكبكون انتهيت من الشرط التالي و بيبقى عليه
+
+146
+00:17:54,520 --> 00:18:00,940
+مايعني الشرط التالي كون هذول موجودات هنا معناه هذا
+
+147
+00:18:00,940 --> 00:18:10,320
+الكلام ان X بيساوي في انفرس of عنصر من عناصر ال ID
+
+148
+00:18:10,320 --> 00:18:17,580
+ال B صحيح ولا لأ X موجودة هنا ايش ممكن يكون شكلها
+
+149
+00:18:17,580 --> 00:18:26,230
+يبقى X بيساوي في انفرس of P1والـ y بيكون فاي انفرس
+
+150
+00:18:26,230 --> 00:18:38,690
+of b2 for some b1 وb2 اللي موجودة في b طيب الجميل
+
+151
+00:18:38,690 --> 00:18:44,830
+هذا بيعطي لبنات مين؟ لو أثرت على الطرفين بفاي
+
+152
+00:18:44,830 --> 00:18:56,820
+بيصير فاي of x بيكون بيساوي ال b1and Phi of Y بده
+
+153
+00:18:56,820 --> 00:19:05,860
+يساوي P2 فبكيس الان لو جيت جمعت الاتنين هدول مع
+
+154
+00:19:05,860 --> 00:19:11,740
+بعض والله احنا بدنا اطرح لا اطرح ولا يهمك يبقى هذا
+
+155
+00:19:11,740 --> 00:19:19,930
+الكلام بده يعطينا Phi of X ناقص Phi of Yيساوي B1
+
+156
+00:19:19,930 --> 00:19:26,190
+ناقص B2 لكن في عبارة عن ايه يا عزيزي همومورفزم
+
+157
+00:19:26,190 --> 00:19:33,890
+نظرا لان همومورفزم هذا بده يعطينا ان في X ناقص ال
+
+158
+00:19:33,890 --> 00:19:42,930
+Y بده يساوي B1 ناقص ال B2 بده يؤثر بفي انفرس على
+
+159
+00:19:42,930 --> 00:19:49,910
+الطرفينلو أثرنا بفاي انفرس على الطرفين هذا بيعطينا
+
+160
+00:19:49,910 --> 00:19:59,050
+ان X ناقص ال Y بيساوي فاي انفرس of B1 ناقص ال B2
+
+161
+00:19:59,050 --> 00:20:05,650
+هذا B1 ناقص B2 موجود وين؟ في capital B اللي هو
+
+162
+00:20:05,650 --> 00:20:11,210
+ideal تمام؟ من شروط ال ideal لو أخدت عنصرين فيه
+
+163
+00:20:11,210 --> 00:20:15,660
+وطرحتم من بعض يكون موجود وين؟و نفس الواضح إذا هذا
+
+164
+00:20:15,660 --> 00:20:23,940
+موجود one في ال ideal P يبقى هذا بده يعطينا إن ال
+
+165
+00:20:23,940 --> 00:20:31,420
+X ناقص ال Y موجود في Phi inverse of P يبقى انتهينا
+
+166
+00:20:31,420 --> 00:20:35,940
+من ال condition الثاني بدنا نروح لل condition
+
+167
+00:20:35,940 --> 00:20:37,560
+التالت
+
+168
+00:20:45,070 --> 00:20:49,350
+يبقى ال condition التالت والأخير مشان أثبت انه هذا
+
+169
+00:20:49,350 --> 00:20:56,850
+I دي فاي انفرست بيه هذا موجود في ال S ولا في ال R؟
+
+170
+00:20:56,850 --> 00:21:02,010
+في ال R طبعا يبقى في انفرست بيه عندما يؤثر عليه
+
+171
+00:21:02,010 --> 00:21:08,250
+بيوديه لوين؟ لل R يبقى بيروح أخر element موجود هنا
+
+172
+00:21:08,250 --> 00:21:14,790
+و element موجود وين؟ في ال R طبعايبقى بالضبط اقول
+
+173
+00:21:14,790 --> 00:21:25,830
+هنا let ال X موجود في ال Phi inverse of B and ال R
+
+174
+00:21:25,830 --> 00:21:36,010
+موجودة في ال R يبقى ال R أخدتها موجودة في ال R هو
+
+175
+00:21:36,010 --> 00:21:43,830
+Phi inverse ال element اللي فيهاالـ domain تبعها
+
+176
+00:21:43,830 --> 00:21:51,450
+مين هو؟ S واللي بدي أثبت انه Phi inverse of B صح؟
+
+177
+00:21:51,450 --> 00:21:56,290
+بدي أثبت Phi inverse of B عبارة عن ideal يبقى بدي
+
+178
+00:21:56,290 --> 00:22:03,530
+أخد element من مين؟ من Phi inverse of B و بدي أخد
+
+179
+00:22:03,530 --> 00:22:09,290
+element من ال ring اللي هو موجود فيها من ال ring
+
+180
+00:22:09,290 --> 00:22:18,170
+اللي موجود فيها؟ R ولا S؟سكت الشعب وصرت اقتراحات
+
+181
+00:22:18,170 --> 00:22:23,370
+بديش اقتراحات بدنا كلام مليان سؤال مرة تانية صح
+
+182
+00:22:23,370 --> 00:22:28,410
+بقى معايا كويسة احنا الان بدنا نثبت ان فاي انفرس
+
+183
+00:22:28,410 --> 00:22:36,770
+عبارة عن مين؟ شوف فاي انفرس ايديل of A ندخل عنصر
+
+184
+00:22:36,770 --> 00:22:43,400
+من R وعنصر من فاي انفرس of B هي خدناعنصر من Phi
+
+185
+00:22:43,400 --> 00:22:53,260
+inverse of B هو عنصر موجود في R بدأ جهازي اخد Phi
+
+186
+00:22:53,260 --> 00:23:04,200
+of X A لو جهت هنا اخد Phi of X A خديلي هذا يعني ان
+
+187
+00:23:04,200 --> 00:23:13,910
+X بده يساوي Phi inverse of Bالـ R موجودة في R هذا
+
+188
+00:23:13,910 --> 00:23:23,190
+يعني ان الـ Phi of X بده يساوي B and الـ R موجودة
+
+189
+00:23:23,190 --> 00:23:33,150
+فيها صحيح؟ صحيح الان بده ياخد Phi of X في R Phi
+
+190
+00:23:33,150 --> 00:23:41,420
+of X في R هذا الكلام بده يساوي Phi of Xفي Phi of A
+
+191
+00:23:41,420 --> 00:23:49,820
+هذا الكلام يساوي Phi of X بقدرش بيه بيه و هذا Phi
+
+192
+00:23:49,820 --> 00:23:57,700
+of A طب بيه وين موجود بيه
+
+193
+00:23:57,700 --> 00:24:02,980
+بيه هذا لحاله وين موجود بيه بيه يعني هذا belongs
+
+194
+00:24:02,980 --> 00:24:05,280
+to بيه هذا وين موجود
+
+195
+00:24:27,220 --> 00:24:33,800
+يبقى هذا موجود في بي لأن بي عبارة عن ideal يبقى
+
+196
+00:24:33,800 --> 00:24:42,010
+معنى هذا الكلام ان ال XR موجودفي Phi inverse of P
+
+197
+00:24:42,010 --> 00:24:48,690
+مظبوط يبقى أخدت element من ال ring و element من
+
+198
+00:24:48,690 --> 00:24:53,270
+Phi inverse of P وجدت حصل ضربه ما موجود في Phi
+
+199
+00:24:53,270 --> 00:25:03,010
+inverse of P بقوله هنا similarly ال Rx موجود في
+
+200
+00:25:03,010 --> 00:25:09,210
+Phi inverse of Pإذا اتحققت الشروط التالتة يا بنات
+
+201
+00:25:09,210 --> 00:25:15,710
+هذا من هنا هو الشرط التالف اتحققت الشروط التالتة
+
+202
+00:25:15,710 --> 00:25:23,170
+ده يبقى بروح بقول الله اص و هكذا five inverse of B
+
+203
+00:25:23,170 --> 00:25:33,370
+is an ideal of A هذا نقطة رقم كم؟ اربعة نقطة رقم
+
+204
+00:25:33,370 --> 00:25:39,950
+خمسةالنقطة رقم خمسة من هذه النظرية بتقول لي ان لو
+
+205
+00:25:39,950 --> 00:25:45,550
+كانت ال R is commutative يبقى صورتها في S is
+
+206
+00:25:45,550 --> 00:25:53,730
+commutative يبقى هنا ال R is commutative
+
+207
+00:25:53,730 --> 00:26:01,330
+implies ان ال Phi of R is commutative
+
+208
+00:26:04,580 --> 00:26:09,260
+هي اللي بدنا نثب طيب
+
+209
+00:26:09,260 --> 00:26:17,360
+ال R is commutative شو معناها يبقى ن approve ال R
+
+210
+00:26:17,360 --> 00:26:29,140
+is commutative هذا يتطلب ايه يتطلب ان ال X في Y
+
+211
+00:26:29,560 --> 00:26:36,060
+بتساوي ال Y في X لكل ال X و Y اللي موجودة في R
+
+212
+00:26:36,060 --> 00:26:44,660
+بلاستيكنات تمام شو رايك أثر على الطرفين بفاي يبقى
+
+213
+00:26:44,660 --> 00:26:55,600
+هذا يعني ان فاي X Y بيساوي فاي و Y في X فمن راسي
+
+214
+00:26:55,600 --> 00:27:00,350
+المسألة فوق في عبارة عنHomomorphism مدام
+
+215
+00:27:00,350 --> 00:27:08,070
+Homomorphism يبقى Phi of X في Phi of Y بده سوى Phi
+
+216
+00:27:08,070 --> 00:27:17,790
+of Y في Phi of X يبقى هذا ايش معناه ان Phi of R is
+
+217
+00:27:17,790 --> 00:27:25,990
+commutative يبقى هذا معناته ان Phi of R is
+
+218
+00:27:29,440 --> 00:27:35,260
+Commutative انت هنا من النقطة الخامسة بالضرورة
+
+219
+00:27:35,260 --> 00:27:53,440
+الوحدة النقطة السادسة طيب
+
+220
+00:27:53,440 --> 00:28:00,100
+النقطة السادسةالنقطة السادسة بتقول ما يتيح لو كانت
+
+221
+00:28:00,100 --> 00:28:05,860
+ال R has a unity الواحد موجود في ال R اللي هو ال
+
+222
+00:28:05,860 --> 00:28:12,940
+unity و ال S مابتسويش ال zero وزيادة على ذلك ال
+
+223
+00:28:12,940 --> 00:28:20,340
+five is unto ان حدث ذلك و ال five is one هذا بده
+
+224
+00:28:20,340 --> 00:28:34,280
+يعطينا ان ال five of oneis the unity of this.يبقى
+
+225
+00:28:34,280 --> 00:28:42,660
+هذا هو ال unity of this.طيب،
+
+226
+00:28:42,660 --> 00:28:50,120
+يعطينا ثلاث معقيات ومطلوب مين؟ مطلوب واحد، بس يبقى
+
+227
+00:28:50,120 --> 00:28:55,920
+يعطيني الـR هيظهر على ال ring with unity.عندنا الـ
+
+228
+00:28:55,920 --> 00:29:05,720
+S لا تساوي Zero يعني الـ S لا تساوي Zero as a set
+
+229
+00:29:05,720 --> 00:29:10,420
+ما تساويش الست اللي هي Zero ومعطينا المعطيات
+
+230
+00:29:10,420 --> 00:29:16,040
+التالتة انه Phi is onto نظرة لهذه المعطيات التي
+
+231
+00:29:16,040 --> 00:29:20,760
+تلت ريشه ان Phi of one هو ال unity تبع من؟ تبع
+
+232
+00:29:20,760 --> 00:29:27,010
+ring S نقوله بسيطة إذا جدرنانثبت انه five of one
+
+233
+00:29:27,010 --> 00:29:32,610
+ضرب أي element من S من اليمين ومن الشمال بيقين ال
+
+234
+00:29:32,610 --> 00:29:36,350
+element اللي فيه S بيصير five of one هو ال unity.
+
+235
+00:29:39,550 --> 00:29:49,330
+صح؟ طيب، الآن بدكي أقوله only the small s موجودة
+
+236
+00:29:49,330 --> 00:29:57,520
+في capital S. تمام؟طيب الفي قال لي إيش؟ قال لي on
+
+237
+00:29:57,520 --> 00:30:05,860
+to إيش يعني on to؟ يعني كل عنصر في S له أصل وين؟
+
+238
+00:30:05,860 --> 00:30:16,500
+في R صح ولا لأ يبقى then there exist R موجود في R
+
+239
+00:30:16,500 --> 00:30:25,030
+such that وبحيث أن ال S هذهالـ S Small اللي عندها
+
+240
+00:30:25,030 --> 00:30:34,770
+بدها ساوي Phi of R طيب خلينا نيجي ناخد الآن Phi of
+
+241
+00:30:34,770 --> 00:30:45,030
+1 مضروبة في S Phi of 1 عنصر وين؟ في S؟ إذا بدي
+
+242
+00:30:45,030 --> 00:30:51,050
+أضربه في مين؟ في عنصر تاني من Sهذا الكلام يساوي
+
+243
+00:30:51,050 --> 00:30:59,310
+فاي of one فيه ال S سوينها صارت ان فاي of ار يبقى
+
+244
+00:30:59,310 --> 00:31:07,390
+فاي of ار يبقى في همومورفيزم يبقى في of واحد مضروف
+
+245
+00:31:07,390 --> 00:31:14,610
+من في الار ال unity من ار لما اضربه في عنصر من
+
+246
+00:31:14,610 --> 00:31:20,400
+عناصر ار بيعطيني نفسي العنصريبقى هذا بيعطيني Phi
+
+247
+00:31:20,400 --> 00:31:26,960
+of R Phi of R هي مين؟ هي S يبقى لما ضرب Phi of 1
+
+248
+00:31:26,960 --> 00:31:31,340
+في S طلع الـ S تشوف الشجرة التانية أو الاتجاه
+
+249
+00:31:31,340 --> 00:31:41,780
+الآخر لو أخدت S S small مضروبة في مين؟ في Phi Phi
+
+250
+00:31:41,780 --> 00:31:50,610
+of 1 أشوف إيش تساويالـ S هي Phi of 1 of R مضروبة
+
+251
+00:31:50,610 --> 00:31:57,310
+في Phi of 1 الـ Phi عبارة عن همومورفيزم إذاً هذه
+
+252
+00:31:57,310 --> 00:32:03,190
+Phi of R مضروبة في 1 الـ R والـ 1 elements من
+
+253
+00:32:03,190 --> 00:32:10,230
+عناصر ال ring إذاً هذا يعتبر Phi of R لأن ال unity
+
+254
+00:32:10,230 --> 00:32:15,050
+تبع ال ring اللي هو واحد طيب Phi of R هو عبارة عن
+
+255
+00:32:15,050 --> 00:32:21,350
+مين؟عن ال S من هذا الكلام ايش ما اقدر استنتج انه
+
+256
+00:32:21,350 --> 00:32:26,510
+five one of S يساوي S of five one يساوي ال S ايش
+
+257
+00:32:26,510 --> 00:32:32,350
+معنى هذا الكلام انه five of one هو ال unity تبع ال
+
+258
+00:32:32,350 --> 00:32:42,390
+S هذا بده يعطينا انه five of one is the unity of S
+
+259
+00:32:42,390 --> 00:32:45,350
+تمام
+
+260
+00:32:45,800 --> 00:32:50,960
+هذا النقطة قدش السادسة النقطة السابعة النقطة
+
+261
+00:32:50,960 --> 00:32:56,720
+السابعة بتقول لي فاي is an isomorphism فاي is
+
+262
+00:32:56,720 --> 00:33:06,440
+isomorphism if and only if الفاي is on two and
+
+263
+00:33:06,440 --> 00:33:12,960
+الكرنل للفاي هو
+
+264
+00:33:12,960 --> 00:33:21,710
+الستالمكوّنة فقط من العمصر A صفري تمام؟ مافيش غيره
+
+265
+00:33:21,710 --> 00:33:26,390
+طيب if and don't if معناه القرهان بده يسير وين؟ في
+
+266
+00:33:26,390 --> 00:33:35,070
+التجاهين يبقى بالدرجة أقوله لـPro Assume افترض
+
+267
+00:33:35,070 --> 00:33:44,930
+that الـPhi is an isomorphism إيش يعني؟يعني الـ
+
+268
+00:33:44,930 --> 00:33:50,570
+Phi homomorphism Phi is one to one Phi is one ..
+
+269
+00:33:50,570 --> 00:33:57,850
+مظبوط؟ هذا معناه يبقى هذا معناه ان Phi is
+
+270
+00:33:57,850 --> 00:34:10,350
+homomorphism and one to one and .. and on تمام؟
+
+271
+00:34:10,350 --> 00:34:15,110
+طيب إذا أثبتنا له هذا المطلوب ولا لا؟طيب بس مثل
+
+272
+00:34:15,110 --> 00:34:20,370
+طول نثبتله مين؟ ان الكيرن لـ Phi يساوي الست التي
+
+273
+00:34:20,370 --> 00:34:28,010
+لا تحتوي الا على الصفر طيب سؤال اذا اثبتت ان هذه
+
+274
+00:34:28,010 --> 00:34:33,310
+subset من هذه و هذه subset من هذه مش بتم المطلوب
+
+275
+00:34:33,310 --> 00:34:42,190
+طب السؤال هو هل ال zero subset من الكيرن لـ Phi؟
+
+276
+00:34:43,280 --> 00:34:52,860
+صحيح لإن فاي اف زيرو موجود في ال kernel يبقى هذا
+
+277
+00:34:52,860 --> 00:34:57,660
+صحيح لإن فاي اف زيرو موجود في ال kernel يبقى هذا
+
+278
+00:34:57,660 --> 00:34:58,160
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+279
+00:34:58,160 --> 00:34:59,360
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+280
+00:34:59,360 --> 00:35:00,460
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+281
+00:35:00,460 --> 00:35:03,260
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+282
+00:35:03,260 --> 00:35:06,560
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+283
+00:35:06,560 --> 00:35:10,140
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقى هذا
+
+284
+00:35:10,140 --> 00:35:13,820
+صحيح لإن فاي أف زيرو موجود في ال kernel يبقىبدو
+
+285
+00:35:13,820 --> 00:35:19,060
+يساوي Zero يبقى هذا بدي اعتبره النقطة رقم واحد
+
+286
+00:35:19,060 --> 00:35:25,480
+بدالي للنقطة رقم اتنين بدي اقول افترض ان X موجود
+
+287
+00:35:25,480 --> 00:35:32,200
+في كيرنل الفاية اذا كدرت اثبت ان X موجود هنا بيكون
+
+288
+00:35:32,200 --> 00:35:37,200
+تم المطلوب يكون خلصنا من هالشغل هذا يبقى then
+
+289
+00:35:37,200 --> 00:35:49,770
+الفاية of X بدو يساوي Zeroفى I
+
+290
+00:35:49,770 --> 00:35:53,530
+of X بده يساوي Zero لإنها موجودة في ال kernel من
+
+291
+00:35:53,530 --> 00:35:57,250
+تعريف ال kernel كل العناصر اللي موجودة في ال ring
+
+292
+00:35:57,250 --> 00:36:01,770
+اللي صاروا تم Zero مظبوط؟ إذا أنا استخدمت تخالب
+
+293
+00:36:01,770 --> 00:36:08,390
+على كأنة يبقى .. يبقى أنا استخدمت التعريف تبع ال
+
+294
+00:36:08,390 --> 00:36:14,790
+kernelكيرن للـ Phi كل العناصر اللي في R بحيث Phi
+
+295
+00:36:14,790 --> 00:36:19,410
+of R بده سوى Zero يبقى أنا أخد X موجودة في الكيرن
+
+296
+00:36:19,410 --> 00:36:23,310
+اللي هيبقى صورة هذا ال X بده تسوى مين؟ بده تسوى
+
+297
+00:36:23,310 --> 00:36:32,150
+Zero طيب أليس هذا هو Phi of Zero؟ صح؟ طيب يبقى
+
+298
+00:36:32,150 --> 00:36:38,360
+الصورة عند مين؟ صورتين متساويتين Phi of Xبدي يساوي
+
+299
+00:36:38,360 --> 00:36:44,840
+فاي of زيرو والفاي هذه مالها one to one يبقى إذا
+
+300
+00:36:44,840 --> 00:36:49,420
+كانت ال function one to one وخات صوتين متساويتين
+
+301
+00:36:49,420 --> 00:36:56,100
+بدي يكون الأصل متساوي يبقى هذا معناه إن ال X بدي
+
+302
+00:36:56,100 --> 00:37:05,120
+يساوي اللي هو ال zero because فاي is one to one
+
+303
+00:37:05,730 --> 00:37:12,910
+مدام ال X بدها تساوي Zero معناته ان ال X موجودة في
+
+304
+00:37:12,910 --> 00:37:18,490
+الست التي لا يوجد فيها الا العنصر الصفري طب ماش
+
+305
+00:37:18,490 --> 00:37:25,410
+اللي عاملتها؟ أخدت X موجودة في ال kernel لجأت ال X
+
+306
+00:37:25,410 --> 00:37:31,410
+موجودة وين؟ في ال Zero يبقى بلاءً عليه So ال
+
+307
+00:37:31,410 --> 00:37:37,730
+kernel لل Phi صار ست من مين؟من الست اللي عندها هذه
+
+308
+00:37:37,730 --> 00:37:43,790
+و هذه العلاقة رقم اتنين اذا بروح اقوله if from
+
+309
+00:37:43,790 --> 00:37:56,490
+واحد and اتنين we have ان ال kernel لل file بده
+
+310
+00:37:56,490 --> 00:38:02,530
+يساوي فقط الست المكونة من element واحد وهذا ال
+
+311
+00:38:02,530 --> 00:38:08,610
+element هو العمصر الصفريخلصنا النقطة هذه؟ خلاص؟
+
+312
+00:38:08,610 --> 00:38:10,810
+خلصنا نصها.
+
+313
+00:38:13,210 --> 00:38:20,890
+ليش؟ بسبب وجود ال F and only F. يبقى بسبب وجود ال
+
+314
+00:38:20,890 --> 00:38:26,770
+F and only F يبقى بدنا نروح نمشي الاتجاه الثاني.
+
+315
+00:38:31,690 --> 00:38:34,630
+يبقى بدنا نروح أقولك Converse.
+
+316
+00:38:39,350 --> 00:38:44,110
+هي اللي عندها فاي is an isomorphism عشان لو لفت
+
+317
+00:38:44,110 --> 00:38:49,810
+فاي is onto يبقى انا بده افترض ان فاي is onto و ال
+
+318
+00:38:49,810 --> 00:38:54,350
+kern اللي بده يساوي zero و بده اثبت ان فاي هذي
+
+319
+00:38:54,350 --> 00:38:59,970
+عبارة عن isomorphism يبقى بده اجي و اقوله assume
+
+320
+00:38:59,970 --> 00:39:15,440
+that فاي من R الى S isانتوا ترى دول ماطلوة وال
+
+321
+00:39:15,440 --> 00:39:25,000
+كيرنل يساوي زيرو and الكيرنل للفاي بده يساوي ست
+
+322
+00:39:25,000 --> 00:39:33,260
+زيرو want to show that
+
+323
+00:39:33,260 --> 00:39:42,720
+فاي is aIsomorphism مش هلا اثبت انه Phi
+
+324
+00:39:42,720 --> 00:39:48,000
+Isomorphism بالذات بالتلت شغلات انه homomorphism و
+
+325
+00:39:48,000 --> 00:39:53,860
+one to one و أنتوا طب احنا فرضين انه أنتوا و مرسى
+
+326
+00:39:53,860 --> 00:40:01,420
+المثل Isomorphism ضال إيه؟ one to one مظبوط؟ يبقى
+
+327
+00:40:01,420 --> 00:40:14,010
+بعدى بقول since Phiمن R إلى S من R إلى S is
+
+328
+00:40:14,010 --> 00:40:25,610
+homomorphic and الـ Phi is Onto أحنا فرضينه Assume
+
+329
+00:40:25,610 --> 00:40:31,230
+that هي Onto ومن رأس المثلة فرضين أنه homomorphic
+
+330
+00:40:31,230 --> 00:40:36,640
+إيش ضلالينا؟بس اثبت انه one to one اذا قدرت اثبت
+
+331
+00:40:36,640 --> 00:40:41,400
+انه one to one بكون خلصنا بصير الفاى عبارة عن ايه؟
+
+332
+00:40:41,400 --> 00:40:48,000
+isomorphism يبقى بعدي بقوله هنا احكاية ال one to
+
+333
+00:40:48,000 --> 00:40:56,900
+one بدنا نستفيد من الشغل ان الكيرن يساوي zero يبقى
+
+334
+00:40:56,900 --> 00:41:05,660
+بعدي بقوله let x و yموجودة في الكيرن للـ Phi.
+
+335
+00:41:09,360 --> 00:41:18,280
+Then الـ Phi of X بده يساوي Zero and ال Phi of Y
+
+336
+00:41:18,280 --> 00:41:19,640
+بده يساوي Zero.
+
+337
+00:41:22,740 --> 00:41:29,680
+صحيح؟ يبقى هذا إيش بيعطينا يا بنات؟ إن ال Phi of X
+
+338
+00:41:29,680 --> 00:41:36,560
+بده يساوي ال Phi of Y.صحيح ولا لا؟ لكل ال X وال Y
+
+339
+00:41:36,560 --> 00:41:40,980
+اللي موجودة وين؟ اللي موجودة في ال kernel تمام؟
+
+340
+00:41:40,980 --> 00:41:49,060
+يبقى أخد صورتين متساويتين إذا قررت أثبت أنه الأصل
+
+341
+00:41:49,060 --> 00:41:53,420
+تبعهم متساوي بصير وانت وانا بكون خلصها من هالشغل
+
+342
+00:41:53,420 --> 00:42:00,280
+مظبوط؟ طيب احنا عندنا Phi of X يسوى Phi of Y يبقى
+
+343
+00:42:00,280 --> 00:42:07,260
+Phi of Xنقص Phi of Y بدي سوى مان Zero Phi
+
+344
+00:42:07,260 --> 00:42:14,540
+homomorphism يبقى هذا بدي اعطيلك ان Phi of X نقص
+
+345
+00:42:14,540 --> 00:42:22,040
+ال Y بدي سوى Zero طيب هذا معناه ان ال X نقص ال Y
+
+346
+00:42:22,040 --> 00:42:32,240
+موجودة في كيرن لفاي صح؟ طب قدش كيرن لفاي؟هو Zero
+
+347
+00:42:32,240 --> 00:42:37,440
+صحيح ولا لا؟ احنا فرضينه هى يبقى هذا كده بده
+
+348
+00:42:37,440 --> 00:42:44,000
+يساوي؟ Zero هذا معناته ان ال X ناقص ال Y بده يساوي
+
+349
+00:42:44,000 --> 00:42:50,920
+Zero هذا معناته ان ال X بده يساوي 100 ال Y يبقى So
+
+350
+00:42:50,920 --> 00:42:59,600
+ال Phi is one to one Thus وهكذا ال Phi is
+
+351
+00:43:01,640 --> 00:43:07,380
+isomorphism ضالة النقطة الأخيرة النقطة الأخيرة
+
+352
+00:43:07,380 --> 00:43:15,260
+بتقول ما ياتي لو كانت الفاي isomorphism then الفاي
+
+353
+00:43:15,260 --> 00:43:23,760
+انفرست is isomorphism if الفاي is isomorphism
+
+354
+00:43:23,760 --> 00:43:30,120
+then الفاي انفرست is isomorphism
+
+355
+00:43:31,020 --> 00:43:34,760
+طبعا هو كتبلك on two تنتين on two ما هو ال
+
+356
+00:43:34,760 --> 00:43:40,220
+isomorphism تعني one to one and on two يبقى كتبها
+
+357
+00:43:40,220 --> 00:43:45,740
+و الله ما كتبهاش سيان تفرجش عندنا ليش؟ لأن ال
+
+358
+00:43:45,740 --> 00:43:52,600
+isomorphism في حد ذاته هو homomorphism وهو one to
+
+359
+00:43:52,600 --> 00:43:59,510
+one and on two في نفس الوقت طيبيبقى انا بدي افترض
+
+360
+00:43:59,510 --> 00:44:07,690
+ان الـ Phi هذا ايزو مورفيزيوم ال approved assume
+
+361
+00:44:07,690 --> 00:44:20,390
+that ان ال Phi is an isomorphism طيب
+
+362
+00:44:20,390 --> 00:44:26,320
+يعني ال Phi is one to one and unto صح؟يبقى هذا بده
+
+363
+00:44:26,320 --> 00:44:34,540
+يعطينا فاي is one to one and unto نرجع لمبادئ
+
+364
+00:44:34,540 --> 00:44:39,560
+الرياضية principle of mathematics تمام؟ بجرر نقول
+
+365
+00:44:39,560 --> 00:44:44,420
+والله ده ال function one to one and unto يبقى ال
+
+366
+00:44:44,420 --> 00:44:49,180
+inverse exist وفي نفس الوقت one to one and unto
+
+367
+00:44:49,180 --> 00:44:54,790
+وفي كل كلاص بيه في أول sectionقلنا ال existence
+
+368
+00:44:54,790 --> 00:45:00,150
+للمعكوس ان تكون الدالة one to one صح ولا لأ؟ هذا
+
+369
+00:45:00,150 --> 00:45:05,330
+شرط وجوده المعكوس مدام ال Phi one to one and unto
+
+370
+00:45:05,330 --> 00:45:13,590
+هذا بده يقينا ان ال Phi inverse exist and ال Phi
+
+371
+00:45:13,590 --> 00:45:22,010
+inverse is one to one and unto ايش ضايل علينا؟نثبت
+
+372
+00:45:22,010 --> 00:45:32,930
+ان هو homomorphism يبقى it remains that ضايل علينا
+
+373
+00:45:32,930 --> 00:45:42,030
+نثبت ان الـ Phi inverse is a homomorphism why؟
+
+374
+00:45:42,030 --> 00:45:46,110
+يبقى بده روح اخد Phi inverse بده يكون من وين لوين
+
+375
+00:45:46,110 --> 00:45:57,310
+من S لRمن S إلى R يعني من R إلى S يبقى Phi inverse
+
+376
+00:45:57,310 --> 00:46:06,530
+من S إلى R يبقى بدالي أقول له let له S واحد و S
+
+377
+00:46:06,530 --> 00:46:14,290
+اتنين موجودة في S طيب هنا عندنا ال Phi one to one
+
+378
+00:46:14,290 --> 00:46:20,630
+and onto يبقى ال S واحد و ال S اتنين أصلا وين في R
+
+379
+00:46:21,350 --> 00:46:30,810
+يبقى then ال S واحد بده يساوي اللي هو Phi of R
+
+380
+00:46:30,810 --> 00:46:40,670
+واحد and S اتنين بده يساوي Phi of R اتنين كويس
+
+381
+00:46:40,670 --> 00:46:48,470
+اذا لو جيت اخدت S واحد زائد S اتنين يبقى بده يساوي
+
+382
+00:46:48,470 --> 00:46:57,040
+Phi of R واحدزائد Phi of R2 هذا هو مورفزيوم يبقى
+
+383
+00:46:57,040 --> 00:47:05,220
+Phi of R1 زائد R2 احنا بدنا ال Phi inverse يبقى
+
+384
+00:47:05,220 --> 00:47:11,140
+بروح بقوله ال Phi inverse لما يأثر على مجموعة ال
+
+385
+00:47:11,140 --> 00:47:17,460
+two elements اللي موجودات في S بده يساوي ال Phi
+
+386
+00:47:17,460 --> 00:47:24,880
+inverse لل Phi of R1زائد R2 الـ function و معكوسها
+
+387
+00:47:24,880 --> 00:47:30,800
+تلغي بعضها لما كل عنصر هذا في domainها يبقى ال R1
+
+388
+00:47:30,800 --> 00:47:36,320
+زائد R2 طب ال R1 يا بنات من هنا مين هو؟ Phi
+
+389
+00:47:36,320 --> 00:47:45,840
+inverse of S1 يبقى هذا Phi inverse of S1 زائد Phi
+
+390
+00:47:45,840 --> 00:47:52,820
+inverse of S2يبقى هاي أثبتنا ال condition الأول من
+
+391
+00:47:52,820 --> 00:47:57,340
+ال two conditions تبعات ال homomorphism بدنا ال
+
+392
+00:47:57,340 --> 00:48:04,660
+condition التاني يبقى and بدي أخد من؟ بدي أخد
+
+393
+00:48:04,660 --> 00:48:15,680
+element من S ولكن S مثلا YS او بدي أخد ال phi of
+
+394
+00:48:15,680 --> 00:48:17,020
+S1
+
+395
+00:48:23,030 --> 00:48:30,450
+5 of S1 ال condition التاني بدك تاخد element من ال
+
+396
+00:48:30,450 --> 00:48:35,870
+ring مش احنا بدنا نثبت ان ال homomorphism بدي اخد
+
+397
+00:48:35,870 --> 00:48:40,890
+اتنين من ال ring و اخد حاصل دور بيهم هقوله كويس
+
+398
+00:48:40,890 --> 00:48:48,440
+يعني بدي اخد اما انا اتنين بدي اخد S1 S2يبقى هذا
+
+399
+00:48:48,440 --> 00:48:55,740
+بدل يساوي Phi of R1 في Phi of R2 ال Phi
+
+400
+00:48:55,740 --> 00:49:02,340
+همومورفيزيوم يبقى Phi of R1 R2 فبدي أثر على
+
+401
+00:49:02,340 --> 00:49:08,140
+الطرفين ب Phi inverse يبقى بيصير Phi inverse of S1
+
+402
+00:49:08,140 --> 00:49:17,630
+S2 بدل يساوي Phi inverse ل Phi of R1 R2هذا الكلاب
+
+403
+00:49:17,630 --> 00:49:29,190
+بده يساوي R1 R2 مين ال R1؟ Phi inverse of S1 يبقى
+
+404
+00:49:29,190 --> 00:49:36,790
+يساوي Phi inverse of S1 ب Phi inverse of S2 plus
+
+405
+00:49:36,790 --> 00:49:44,230
+وهكذا ال Phi inverse is a homomorphism وهذا بده
+
+406
+00:49:44,230 --> 00:49:45,150
+يخلينا
+
+407
+00:49:50,900 --> 00:49:57,980
+عن إيه خلصنا النظرية فقط هذه لا غير ومرة جاية
+
+408
+00:49:57,980 --> 00:50:00,320
+بنكمل اعطاك العالم
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/zUtNMJNFbCQ.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/zUtNMJNFbCQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e5ea6bb68358489f4f5acb344d90f849bc37c34b
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/zUtNMJNFbCQ.srt
@@ -0,0 +1,1523 @@
+
+1
+00:00:20,820 --> 00:00:25,980
+بسم الله الرحمن الرحيم، نكمل النظرية التي انتهينا 
+
+2
+00:00:25,980 --> 00:00:30,040
+منها في المرة الماضية، انتهينا من الشطر الأول،
+
+3
+00:00:30,040 --> 00:00:34,640
+بقي الشطر الثاني، فكان باختصار أن النظرية
+
+4
+00:00:34,640 --> 00:00:44,480
+البردية، الـ R modulo A is a ring if and only if
+
+5
+00:00:44,480 --> 00:00:56,720
+الـ A is an ID، تمام؟ افترضنا أن الـ A is
+
+6
+00:00:56,720 --> 00:01:02,320
+an ideal، و أثبتنا أن الـ ring تحت العمليتين
+
+7
+00:01:02,320 --> 00:01:11,040
+اللي هو الـ A + الـ A + الـ B + الـ A، كـ two
+
+8
+00:01:11,040 --> 00:01:18,160
+elements، يساوي A + الـ B + الـ A، و عملية
+
+9
+00:01:18,160 --> 00:01:25,500
+الضرب، A + الـ A × الـ B + الـ A = AB +
+
+10
+00:01:25,500 --> 00:01:29,680
+الـ A، هي الـ two operations اللي كانت على الـ factor
+
+11
+00:01:29,680 --> 00:01:35,440
+ring، اللي هو الـ R modulo A، تمام؟ المرة اللي فاتت
+
+12
+00:01:35,440 --> 00:01:41,120
+افترضنا أنه A عبارة عن ideal، و أثبتنا أن الـ R
+
+13
+00:01:41,120 --> 00:01:46,060
+modulo A is a ring. الآن بدنا نمشي في الاتجاه
+
+14
+00:01:46,060 --> 00:01:53,370
+المعكس.  الجبوح بقوله، بنتكمل conversely، بعد الشيء اللي
+
+15
+00:01:53,370 --> 00:01:58,330
+كتبناه المرة اللي فاتت، بقوله conversely, assume
+
+16
+00:01:58,330 --> 00:02:01,390
+that
+
+17
+00:02:01,390 --> 00:02:09,290
+افترض أن الـ R modulo A is a ring، شو اللي بدنا
+
+18
+00:02:09,290 --> 00:02:15,990
+نعمله؟  to show that
+
+19
+00:02:17,730 --> 00:02:24,690
+أن الـ A is an ID. يبقى هذا اللي بنثبته.  سأحاول نثبت
+
+20
+00:02:24,690 --> 00:02:30,510
+أنه A is an ID. طبعاً تعلمنا في مبادئ الرياضيات أن
+
+21
+00:02:30,510 --> 00:02:36,430
+هناك أكثر من طريقة للبرهان،  في منها حاجة اسمه الـ Direct
+
+22
+00:02:36,430 --> 00:02:41,510
+Proof، حيث الـ Proof بواسط Contradiction أو
+
+23
+00:02:41,510 --> 00:02:45,790
+Contrapositive. سأحاول نثبت هذا الكلام بواسط
+
+24
+00:02:45,790 --> 00:02:51,780
+Contradiction. Okay، احنا بنقول بدنا نحاول نثبت، نبين
+
+25
+00:02:51,780 --> 00:02:59,160
+أن الـ A is an ideal of الـ ring اللي عندنا، هذا of A.
+
+26
+00:02:59,160 --> 00:03:04,220
+ده بقوله suppose not، افترض أن هذا الكلام مش صحيح،
+
+27
+00:03:04,220 --> 00:03:16,250
+يبقى suppose not يعني افترض أن هذا ليس ideal. يبقى
+
+28
+00:03:16,250 --> 00:03:23,770
+بمعنى بقوله، لو كان الـ A موجود في A، و الـ R موجود
+
+29
+00:03:23,770 --> 00:03:30,110
+في R، then AR، ما أقدر أقول موجود في A؟ ليس
+
+30
+00:03:30,110 --> 00:03:39,910
+بالضرورة، يبقى ليس موجود في A، or  AR، A ليس
+
+31
+00:03:39,910 --> 00:03:46,890
+موجود فيه، هذا هو. طيب، لو أخدت الحالة الأولى، if
+
+32
+00:03:46,890 --> 00:03:56,670
+الـ AR ليس موجود في A، then AR + A، هل
+
+33
+00:03:56,670 --> 00:04:00,650
+تساوي A؟
+
+34
+00:04:00,650 --> 00:04:08,370
+ليس موجود في A، if AR ليس موجود في A، then AR
+
+35
+00:04:08,370 --> 00:04:13,820
++ A، هل تساوي A؟ لا، لا، لا، لا، وسمّي لي
+
+36
+00:04:13,820 --> 00:04:20,080
+هذه العلاقة (أيه)؟ وسمّي لي هذه العلاقة رقم واحد، و بدنا
+
+37
+00:04:20,080 --> 00:04:26,120
+نروح نجيب علاقة ثانية و نشوف ايش بده يحصل عندنا.
+
+38
+00:04:26,120 --> 00:04:37,020
+الآن، لو جيت بـ A + A، واحنا قايلين الـ A
+
+39
+00:04:37,020 --> 00:04:43,460
+موجودة وين؟ الـ A. طيب، إن كان هذا موجود في الـ A، يبقى
+
+40
+00:04:43,460 --> 00:04:50,620
+هذا بده يعطينا الـ A itself، والسبب فيه، أو بده يساوي
+
+41
+00:04:50,620 --> 00:04:55,440
+اللي هو الـ zero + A، و اللي هو بده يساوي الـ A
+
+42
+00:04:55,440 --> 00:05:04,080
+itself. ليش؟ لأنه في بداية المثال قال A is a sub
+
+43
+00:05:04,080 --> 00:05:11,400
+ring، مظبوط؟ يبقى A subring، يبقى هذا الكلام موجود
+
+44
+00:05:11,400 --> 00:05:19,880
+هنا. طيب، بتروح آخذ element من من الـ factoring R
+
+45
+00:05:19,880 --> 00:05:24,960
+modulo A، مع الـ element هذا، و أشوف وين بده يوصلني.
+
+46
+00:05:24,960 --> 00:05:36,080
+طيب، then، لو أخدت الـ A + A، وضربته في R +
+
+47
+00:05:36,080 --> 00:05:45,040
+A، هذا الكلام بده يساوي قدّاش؟ AR + A، طبقاً
+
+48
+00:05:45,040 --> 00:05:51,300
+لعملية الضرب المعرفة علينا على الـ factoring R
+
+49
+00:05:51,300 --> 00:06:00,100
+modulo A، و A + A هي zero + A، يبقى
+
+50
+00:06:00,100 --> 00:06:07,960
+كمان zero + A × R + A، بده يساوي
+
+51
+00:06:07,960 --> 00:06:15,720
+zero + A، تمام؟ هذا العضو هو هذا العضو. حصل
+
+52
+00:06:15,720 --> 00:06:21,700
+الضرب، و حصل الضرب. إذا من الاثنين هدول
+
+53
+00:06:21,700 --> 00:06:27,320
+بقدر أقوله AR + A بده يساوي A itself،
+
+54
+00:06:27,320 --> 00:06:35,670
+مظبوط؟ طب ايش رأيك هذا و هذا؟ contradiction، يبقى
+
+55
+00:06:35,670 --> 00:06:40,570
+this is a contradiction.
+
+56
+00:06:40,570 --> 00:06:44,490
+طيب،
+
+57
+00:06:44,490 --> 00:06:50,290
+ايش جاب التناقض هذا؟ أنه فرضت أن الـ A ليس ideal،
+
+58
+00:06:50,290 --> 00:06:57,290
+يبقى ليس ideal هو خطأ، والحقيقة أنه ideal، يبقى
+
+59
+00:06:57,290 --> 00:07:09,040
+بقوله thus، وهكذا، اللي هو الـ A is an ideal of ring
+
+60
+00:07:09,040 --> 00:07:14,780
+R، إذاً
+
+61
+00:07:14,780 --> 00:07:20,160
+بناءً على هذا، من الآن فصاعداً، الـ factor هو الـ ring R
+
+62
+00:07:20,160 --> 00:07:26,900
+modulo A، عناصرها كلها left cosets، اللي هو element
+
+63
+00:07:26,900 --> 00:07:35,660
+من R، و element من AR + A (كبتر A)، هو عنصر موجود
+
+64
+00:07:35,660 --> 00:07:41,680
+وين؟ في الـ factoring R modulo A. الآن بناخد بعض
+
+65
+00:07:41,680 --> 00:07:48,720
+الأمثلة على ذلك. أول مثال على هذا الموضوع، نُفجّر
+
+66
+00:07:48,720 --> 00:07:56,200
+examples، نملك
+
+67
+00:07:56,200 --> 00:08:08,180
+واحد، الـ Z modulo 4Z، عناصرها: الـ 0 +
+
+68
+00:08:08,180 --> 00:08:17,160
+4Z، و 1 + 4Z، و 2 + 4Z، و 3 + 4Z، بالشكل اللي عندنا هنا.
+
+69
+00:08:17,160 --> 00:08:24,000
+factor
+
+70
+00:08:30,050 --> 00:08:40,670
+Ring is a factor ring because، الأربعة
+
+71
+00:08:40,670 --> 00:08:52,750
+Z is an ideal of the ring Z. طب، نحن أقنعناكم بمثال
+
+72
+00:08:52,750 --> 00:09:02,970
+سابقاً أن nZ is an ideal of Z، عدد صحيح موجب، in
+
+73
+00:09:02,970 --> 00:09:11,450
+positive integer. يبقى 2Z, 3Z, 4Z, 5Z, 6Z، كلّه
+
+74
+00:09:11,450 --> 00:09:15,230
+عبارة عن ideal في الـ ring الأساسي، اللي هو main Z.
+
+75
+00:09:15,230 --> 00:09:20,530
+وبالتالي، مادام ideal، يبقى هذه عبارة عن factor ring
+
+76
+00:09:20,530 --> 00:09:28,260
+مكونة من، main، مكونة من أربعة عناصر. الآن، بناءً على
+
+77
+00:09:28,260 --> 00:09:33,020
+هذا التعريف، بدنا نعرف لك كيف، أو نوريك كيف بتجمع
+
+78
+00:09:33,020 --> 00:09:40,860
+هذه العناصر، أو بتضربها.  مثلاً، Note that، لاحظ لي
+
+79
+00:09:40,860 --> 00:09:48,720
+ما يأتي. الآن، لو بدي أجي أقول 2 + 4Z،
+
+80
+00:09:48,720 --> 00:09:54,940
+تمام؟ هذا عنصر، بدي أجمعه مع 3 + 4Z،
+
+81
+00:09:55,310 --> 00:09:59,970
+طبقاً للكلام اللي احنا قلناه هنا، 2 +
+
+82
+00:09:59,970 --> 00:10:07,450
+3 = 5 + 4Z، لكن الخمسة هذه بقدر
+
+83
+00:10:07,450 --> 00:10:13,350
+اكتبها 1 + 4 + 4Z، الأربعة
+
+84
+00:10:13,350 --> 00:10:17,690
+موجودة في الـ 4Z، ولا لا؟ لا، إذا بتعطيني 4
+
+85
+00:10:17,690 --> 00:10:26,040
+Z، it's the same، يبقى هذا 1 + 4Z. ولو بدي
+
+86
+00:10:26,040 --> 00:10:32,720
+أضرب، ضرب، يبقى 2 + 4Z مضروبة في 3
+
+87
+00:10:32,720 --> 00:10:38,900
++ 4Z، يبقى 2 × 3 = 6 +
+
+88
+00:10:38,900 --> 00:10:45,300
+4Z، الستة بقدر أقول اللي هي 2 + 4
+
+89
+00:10:45,300 --> 00:10:51,120
++ 4Z، يعني 2 + 4Z، لأن
+
+90
+00:10:51,120 --> 00:10:56,330
+الأربعة موجودة في 4Z. يبقى هذه عملية
+
+91
+00:10:56,330 --> 00:11:02,550
+الضرب اللي بتتم. طيب، حد فيكم يقدر يجيب لي ID
+
+92
+00:11:02,550 --> 00:11:07,850
+important element من الـ group، من الـ ring هذه؟ ID
+
+93
+00:11:07,850 --> 00:11:11,910
+important، يعني مربع الـ element بده يعطيني نفس الـ
+
+94
+00:11:11,910 --> 00:11:18,030
+element. 2 + 4Z، 2 + 4Z
+
+95
+00:11:18,030 --> 00:11:25,310
+is an ID important، يعني لو ربعته بيطلع نفسه؟ لا،
+
+96
+00:11:25,310 --> 00:11:31,990
+مش صحيح، بيطلع zero، يبقى هذا nilpotent element، هذا
+
+97
+00:11:31,990 --> 00:11:41,390
+nilpotent، ليش؟ لأنه 2 + 4Z، كل تربيع
+
+98
+00:11:41,390 --> 00:11:45,110
+يساوي 4 + 4Z، اللي هو بده يساوي 4Z،
+
+99
+00:11:45,110 --> 00:11:50,250
+اللي هو الـ zero element. يبقى الـ 4Z هو الـ zero
+
+100
+00:11:50,250 --> 00:11:55,440
+element في الـ ring اللي عندنا هذه. و 1 + 4Z،
+
+101
+00:11:55,440 --> 00:12:02,540
+و 0 + 4Z، 2 + 4Z is ID important، هدول
+
+102
+00:12:02,540 --> 00:12:11,420
+اثنين كمان ID important. طب و الـ 3 + 4Z؟
+
+103
+00:12:11,420 --> 00:12:17,560
++ 4Z؟ لا، بيطلع 1. طب لما نربعه، احنا قدّيش؟ 9
+
+104
+00:12:17,560 --> 00:12:20,500
++ 4Z،  1 + 4Z، 1 + 4Z، يبقى هذا
+
+105
+00:12:20,500 --> 00:12:26,520
+unit، صح؟ لأنه تسعة، شيل منها اربعة، وفضل واحد، اللي
+
+106
+00:12:26,520 --> 00:12:34,860
+هو الـ unity. يبقى هذا بذاته as a unit. يبقى أي
+
+107
+00:12:34,860 --> 00:12:39,240
+عناصر ايش important، و ايش not important، و ايش
+
+108
+00:12:39,240 --> 00:12:44,760
+units، و ما إلى ذلك. طيب، أروح لمين؟ للـ ring الثانية.
+
+109
+00:12:44,760 --> 00:12:55,890
+مثال اثنين. مثال اثنين، بيقول لي 2Z modulo 6Z،
+
+110
+00:12:55,890 --> 00:13:03,830
+modulo 6Z، اللي هي عناصرها، اللي هي بده الـ
+
+111
+00:13:03,830 --> 00:13:14,170
+set. بنعرف نجيب عناصرها؟ 0 + 6Z، و
+
+112
+00:13:14,170 --> 00:13:21,670
+الثاني 1 + 6Z، واحد مش موجود في 2Z،
+
+113
+00:13:21,670 --> 00:13:28,070
+يبقى بعد zero في 2Z، يبقى 2 + 6Z،
+
+114
+00:13:28,070 --> 00:13:35,870
+طيب و اللي بعده 4 + 6Z. خلاص، انتهينا. اللي
+
+115
+00:13:35,870 --> 00:13:40,790
+بعده 6 + 6Z، اللي هو 0 + 6Z، يبقى
+
+116
+00:13:40,790 --> 00:13:46,990
+هذه الـ rings ما فيها إلا ثلاثة عناصر. يعني
+
+117
+00:13:46,990 --> 00:13:53,230
+عندي ثلاثة left cosets، تمام؟ يبقى ثلاثة عناصر فقط
+
+118
+00:13:53,230 --> 00:14:03,010
+لا غير. خليني أسأل: طب ليش هذه 6Z ideal؟ زي الأربعة
+
+119
+00:14:03,010 --> 00:14:12,750
+Z ما كانت ideal؟ يبقى هذه هـ هـ، هذي factor ring، هذي factor
+
+120
+00:14:12,750 --> 00:14:31,160
+ring because الـ 6Z is an ideal in the ring 2
+
+121
+00:14:31,160 --> 00:14:37,760
+Z. يا ريت تشيك لي عليها، يعني في الطريق، تروحي تثبتي
+
+122
+00:14:37,760 --> 00:14:44,610
+أن الـ 6Z عبارة عن ideal تماماً في 2Z. طب، خليني
+
+123
+00:14:44,610 --> 00:14:52,410
+أسأل: ها، فيها unity هذه؟ يعني identity element، 4
+
+124
+00:14:52,410 --> 00:14:56,970
++ 6Z، مئة بالمئة هذا الكلام صحيح. يبقى الـ
+
+125
+00:14:56,970 --> 00:15:00,890
+unity، مش تقول لي ما فيش، واحد يقول ما فيش unity، لأن الـ
+
+126
+00:15:00,890 --> 00:15:08,970
+unity هنا هو 4 + 6Z.  not that، لاحظ لي
+
+127
+00:15:08,970 --> 00:15:20,700
+أن 4 + 6Z is the unity of 2
+
+128
+00:15:20,700 --> 00:15:30,000
+Z modulo 6Z. طب ايش رأيك؟ أنا أزعم أن هذا كمان
+
+129
+00:15:30,000 --> 00:15:38,560
+ايش أزعم؟ هذا ID important، صح؟ طب و هذا كمان ID
+
+130
+00:15:38,560 --> 00:15:45,710
+important؟ مظبوط؟ طب و هذا؟ يعني كيف بده يجي مثلاً؟
+
+131
+00:15:45,710 --> 00:15:50,990
+4 + 6Z،  لو ضربت هذا هذا، كده كده؟
+
+132
+00:15:50,990 --> 00:15:55,370
+كده كده؟ كده كده كده كده كده كده كده كده كده كده
+
+133
+00:15:55,370 --> 00:15:56,350
+كده كده كده كده كده كده كده كده كده كده كده كده
+
+134
+00:15:56,350 --> 00:15:56,410
+كده كده كده كده كده كده كده كده كده كده كده كده
+
+135
+00:15:56,410 --> 00:16:03,730
+كده كده كده كده كده كده كده كده كده
+
+136
+00:16:03,730 --> 00:16:10,550
+كده
+
+137
+00:16:10,550 --> 00:16:18,120
+كده، اللي هو الـ unity، حتى أقول هذا is a unit. طيب، لو
+
+138
+00:16:18,120 --> 00:16:26,060
+ربعته، بيطلع قدّاش هذا، صح؟ لو كعّبته بيطلع نفسه،
+
+139
+00:16:26,060 --> 00:16:31,340
+و هكذا. يبقى هذا مكفول. لحد هنا عرفنا هذا الـ unity، و
+
+140
+00:16:31,340 --> 00:16:39,260
+الله يعطينا العافية. طب نروح لمثال ثلاثة. مثال ثلاثة،
+
+141
+00:16:46,340 --> 00:16:59,280
+ثلاثة: لتكن الـ R = M₂(Z)، ولتكن كل العناصر على
+
+142
+00:16:59,280 --> 00:17:07,240
+شكل المصفوفات، a b c d، بحيث الـ a و الـ b و الـ c و الـ
+
+143
+00:17:07,240 --> 00:17:17,120
+d كلها أعداد صحيحة، يبقى موجودة في Z، وخذي لي الـ I، كل
+
+144
+00:17:17,120 --> 00:17:26,120
+المصفوفات اللي على الشكل 2a 2b 2c 2d،
+
+145
+00:17:26,120 --> 00:17:33,840
+وبحيث أن الـ a و الـ b و الـ c و الـ d كلها أعداد
+
+146
+00:17:33,840 --> 00:17:39,420
+صحيحة، كذلك موجودة في Z. then
+
+147
+00:17:45,280 --> 00:17:57,040
+then الـ I is an ideal of اللي هو الـ M₂(Z)،
+
+148
+00:17:57,040 --> 00:18:03,000
+because، مقتنعين.
+
+149
+00:18:03,000 --> 00:18:10,800
+طيب نرجع ثاني، الـ ring اللي عندنا دي M₂(Z). بقى هي
+
+150
+00:18:10,800 --> 00:18:17,790
+مجموعة المصفوفات اللي نظامها 2 × 2، وبحيث الـ a والـ b
+
+151
+00:18:17,790 --> 00:18:22,710
+والـ c والـ d كلهم أعداد صحيحة، موجودة في Z، يعني
+
+152
+00:18:22,710 --> 00:18:28,470
+ممكن 0، وممكن 1، وممكن 2، و -2، 3، و -13،
+
+153
+00:18:28,470 --> 00:18:36,770
+يعني أرقام موجبة وسالبة وصفر. كلها. روحت أخدت الـ 2I، كل
+
+154
+00:18:36,770 --> 00:18:42,120
+العناصر اللي هي أعداد زوجية. يبقى الـ a و الـ b و الـ c
+
+155
+00:18:42,120 --> 00:18:46,660
+لو كانت فردية وضربتها في اثنين بيصير أعداد زوجية.
+
+156
+00:18:46,660 --> 00:18:51,480
+يبقى صارت بالشكل هذا، و a و b و c، سواء كان a و b و
+
+157
+00:18:51,480 --> 00:18:55,480
+c فردي والله زوجي، ما بتفرقش هنا، لكن روح ضربتها في
+
+158
+00:18:55,480 --> 00:18:58,040
+اثنين، ولما ضربت في اثنين، الفردي بيصير زوجي، و
+
+159
+00:18:58,040 --> 00:19:04,120
+الزوجي بيبقى زوجي كما هو. طيب، نحن نزعم أن الـ I is
+
+160
+00:19:04,120 --> 00:19:09,780
+an ideal، اللي يبقى بنروح نطبق الشروط الثلاثة على الـ
+
+161
+00:19:09,780 --> 00:19:15,300
+subset اللي أخذناه، علشان تكون ideal. إذا النقطة الأولى،
+
+162
+00:19:15,300 --> 00:19:22,840
+بروْح بقوله I is not empty، because
+
+163
+00:19:22,840 --> 00:19:29,740
+أو since، الـ zero، الـ zero، الـ zero، الـ zero موجودة في
+
+164
+00:19:29,740 --> 00:19:37,660
+I، أكيد؟ طب، هنا I أعداد زوجية، يبقى بقدر أكتب هذا
+
+165
+00:19:37,660 --> 00:19:43,820
+الكلام: 2 × 0، 2 × 0، 2 × 0،
+
+166
+00:19:43,820 --> 00:19:50,480
+2 × 0، يبقى موجودة في I ولا لا؟ يبقى موجودة
+
+167
+00:19:50,480 --> 00:19:57,780
+في I. يبقى صارت كلها على شكل أعداد زوجية. إذا الـ I
+
+168
+00:19:57,780 --> 00:20:
+
+223
+00:27:07,970 --> 00:27:16,770
+تبعناه صحيح، طيب
+
+224
+00:27:16,770 --> 00:27:30,350
+this is true because هتقولي
+
+225
+00:27:30,350 --> 00:27:35,810
+أي مصفوفة؟ أها يالا
+
+226
+00:27:35,810 --> 00:27:42,270
+اعطيني مصفوفة من عندك، أكبر الأرقام شوية مش مشكلة
+
+227
+00:27:42,270 --> 00:27:45,510
+جدمك موديكي تظهر عشان لا تواصليه و تسافر ماعنديكي
+
+228
+00:27:45,510 --> 00:27:51,890
+مشكلة، أقولي: أيوة، اتنين، أربعة، تلاتة، وثمانية، تلاتة، و
+
+229
+00:27:51,890 --> 00:27:56,750
+كده؟ تمانية، تلاتة، مش رايكِ أنا أحط ده، خطر أحط سالب
+
+230
+00:27:56,750 --> 00:28:01,510
+مع موجب، مع فردي، مع زوجي، حتى نحط كل الاحتمالات الواردة
+
+231
+00:28:01,510 --> 00:28:07,050
+نقول هذه ناقص خمسة، بيمشي الحال، طيب، ونقول هذه اللي
+
+232
+00:28:07,050 --> 00:28:14,810
+حقتها زوجي، بدي أحطها فردي وليكن أحد عشر مثلا، وهذه
+
+233
+00:28:14,810 --> 00:28:20,270
+بدي أكبرها شوية، فالتي زوجي بدي أقول عليها أربعة
+
+234
+00:28:20,270 --> 00:28:27,810
+كويس؟ يبقى هذه مصفوفة زائد الـ I، بدي أشوف هل بقدر
+
+235
+00:28:27,810 --> 00:28:33,610
+أكتبها على الصيغة اللي عندها هذه ولا لأ، والله إذا
+
+236
+00:28:33,610 --> 00:28:38,550
+قدرت أكتب وأبصير كلامنا صحيح مائة بالمائة، طيب هذا
+
+237
+00:28:38,550 --> 00:28:44,350
+الكلام يساوي، بدي أكتب هذه على صيغة مجموعة مصفوفات
+
+238
+00:28:44,350 --> 00:28:51,650
+تين، طيب لو جات، فقلت هنا zero، و هذه، وهذه زائد لو
+
+239
+00:28:51,650 --> 00:28:58,200
+حطيت zero بتظل الأربعة زي ما هي، صح؟ طيب هذه 11 فردي
+
+240
+00:28:58,200 --> 00:29:03,860
+بتخليها زوجي، وكمان  مقعد، يبقى بقى الدرجون واحد
+
+241
+00:29:03,860 --> 00:29:14,100
+وعشرة، يبقى هذه واحد، وهذه هنا عشرة، تمام؟ طيب نجي
+
+242
+00:29:14,100 --> 00:29:20,240
+لمين؟ للتلاتة، تلاتة فردي كمان، يبقى بقى الدرجون هنا
+
+243
+00:29:20,240 --> 00:29:26,610
+واحد وهنا اتنين، هذه مجموعهم تلاتة، ناقص خمسة، واحد
+
+244
+00:29:26,610 --> 00:29:34,790
+وسالب ستة، واحد وسالب ستة زائد الـ I، مصبوط، هكذا السؤال
+
+245
+00:29:34,790 --> 00:29:39,470
+هو هذا العنصر موجود في الـ I ولا لا؟ لأن كل
+
+246
+00:29:39,470 --> 00:29:45,870
+العناصر التابعة لهذه المصفوفة أعداد زوجية، إذا هذه
+
+247
+00:29:45,870 --> 00:29:51,270
+موجودة، يبنى، لمجموعة مع الـ I بتعطيني الـ I itself، يبقى
+
+248
+00:29:51,270 --> 00:29:58,640
+هذا الكلام يساوي zero، واحد، واحد زائد الـ I، يبقى
+
+249
+00:29:58,640 --> 00:30:03,600
+طالع كلامنا هذا صح ولا لا يا بنات؟ مظبوط؟ طيب
+
+250
+00:30:03,600 --> 00:30:08,240
+السؤال الجميل جدا اللي لسه بدنا نطرحه، ما
+
+251
+00:30:08,240 --> 00:30:17,760
+طرحناهوش، كم عنصر في هذه الحلقة؟ أيه؟
+
+252
+00:30:17,760 --> 00:30:22,520
+يعني ما نهايتها؟
+
+253
+00:30:26,010 --> 00:30:35,310
+يعني كده بتقدري؟ خمسة، ستة مثلا؟ سبعين؟ ستة عشر؟
+
+254
+00:30:35,310 --> 00:30:47,730
+عشرين؟ مية؟ ستة عشر عنصر فقط، فالناس اللي هو السبب
+
+255
+00:30:47,730 --> 00:30:58,050
+and the order of the M two of Z Modulo I يساوي 16
+
+256
+00:30:58,050 --> 00:31:02,570
+because بدنا
+
+257
+00:31:02,570 --> 00:31:08,030
+نروح نشوف كم عنصر على الشكل هذا بيكون عندنا 16
+
+258
+00:31:08,030 --> 00:31:11,670
+عنصر
+
+259
+00:31:11,670 --> 00:31:17,470
+بدنا نعرف بس مجرد نتعرف عليهم كلهم واحد، كلهم واحد
+
+260
+00:31:17,470 --> 00:31:23,270
+كلهم صفر، أحد أصفار، كله بواحد، عنصرين صفريين، والباقي
+
+261
+00:31:23,270 --> 00:31:27,250
+بواحد واحد، تلات عناصر أصفار، واحد بيكون، خلص نجدها
+
+262
+00:31:27,250 --> 00:31:32,870
+الستة عشر، تعرف تكتبها ولا تكتبها؟ يعني بلاش تكتبها؟
+
+263
+00:31:32,870 --> 00:31:40,090
+بلاش؟ طيب بتروحي بس بدي أعطيكي كيف يبقى بتقولي
+
+264
+00:31:40,090 --> 00:31:48,190
+zero، واحد، واحد، واحد، تمام، بعد هيك بحط الـ zero هنا
+
+265
+00:31:48,190 --> 00:31:51,910
+بعدين بحط الـ zero هنا، والباقي كله بواحد، يعني
+
+266
+00:31:51,910 --> 00:31:56,130
+بحط عنصر صفر، والباقي كله واحد، هذا بتطلع لي كده؟
+
+267
+00:31:56,130 --> 00:32:03,550
+بتطلع لي أربعة عناصر، بعد هيك حط لي zero، zero، واحد
+
+268
+00:32:03,550 --> 00:32:12,210
+واحد، هذا بتطلع لي كده؟ ستة عناصر، ستة؟ اه، ستة، كيف؟
+
+269
+00:32:12,210 --> 00:32:18,980
+هذا نزلته تحت وطلعت هذا فوق، خلت العمود الأول صفر
+
+270
+00:32:18,980 --> 00:32:22,540
+واحد، واحد، خلت العمود الثاني صفر، والأول واحد
+
+271
+00:32:22,540 --> 00:32:27,880
+واحد، خلت القطر الرئيسي أصفار، والباقي واحد واحد،
+
+272
+00:32:27,880 --> 00:32:31,060
+ خلت القطر الرئيسي واحد واحد، والباقي أصفار، يبقى
+
+273
+00:32:31,060 --> 00:32:35,720
+قبل الستة، تعالى صاروا أربعة، عشرة، يبقى هذا واحد
+
+274
+00:32:35,720 --> 00:32:41,520
+من ستة، هذا واحد من أربعة، فإخسار كم ده؟ إخسار
+
+275
+00:32:41,520 --> 00:32:42,120
+عشرة
+
+276
+00:32:52,570 --> 00:32:55,170
+عشرة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة
+
+277
+00:32:55,170 --> 00:32:56,050
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة
+
+278
+00:32:56,050 --> 00:32:58,090
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة
+
+279
+00:32:58,090 --> 00:32:58,510
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة
+
+280
+00:32:58,510 --> 00:33:03,310
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة
+
+281
+00:33:03,310 --> 00:33:05,770
+أ
+
+282
+00:33:12,460 --> 00:33:16,660
+كام؟ ما تطلعش على شكل الـ I، على شكل الـ I؟ أه مهما تكون
+
+283
+00:33:16,660 --> 00:33:24,340
+الـ I اللي هو الـ Identity، أه ليش؟ إحنا جبناها أصلا هذه
+
+284
+00:33:24,340 --> 00:33:29,820
+من هذه، يعني قدرنا نوصل هذه إلى الشكل اللي...
+
+285
+00:33:29,820 --> 00:33:34,800
+السبب في ذلك أن هذه موجودة في الـ I، لأ، طلعنا على شكلها
+
+286
+00:33:34,800 --> 00:33:38,780
+وبالتالي حصلنا على هذه، ولو ما طلعناش على شكلها
+
+287
+00:33:38,780 --> 00:33:44,440
+ما قدرناش نجيب هذه، صحيح ولا لأ؟ يبقى الشكل ضروري جدا
+
+288
+00:33:44,440 --> 00:33:50,480
+يبقى هنا كل واحدة من الستة عشر دول بصير زائد الـ I، يعني
+
+289
+00:33:50,480 --> 00:33:55,580
+بيقولوا لي هذه زائد الـ I هي 4 عناصر، هذه زائد الـ I هي 6
+
+290
+00:33:55,580 --> 00:34:03,000
+عناصر، هذه زائد الـ I هي 4 عناصر، هذه زائد الـ I هي 16 عنصر
+
+291
+00:34:03,000 --> 00:34:08,960
+يعني كل عنصر مصفوفة من الستة عشر زائد الـ I، أنا بس مجرد
+
+292
+00:34:08,960 --> 00:34:15,300
+أوريه كمان، أوريكم العناصر بالنسبة لمثال رقم 4
+
+293
+00:34:15,300 --> 00:34:26,120
+مثال رقم 4 يقول: consider the factor ring, factor
+
+294
+00:34:26,120 --> 00:34:32,260
+ring
+
+295
+00:34:32,260 --> 00:34:36,940
+of Gaussian
+
+296
+00:34:41,160 --> 00:34:50,240
+integers، أعداد الأعداد الصحيحة اللي هي Z، of I modulo الـ
+
+297
+00:34:50,240 --> 00:34:55,800
+principal ideal generated by 2 minus الـ I، اللي
+
+298
+00:34:55,800 --> 00:35:04,590
+هو بده يساوي كل العناصر A زائد B في I زائد الـ
+
+299
+00:35:04,590 --> 00:35:11,590
+principal ideals generated by 2 minus I، بحيث أن الـ
+
+300
+00:35:11,590 --> 00:35:22,390
+A والـ B موجودة في Z، الـ A والـ B موجودة في Z
+
+301
+00:35:22,390 --> 00:35:26,250
+بنحاول
+
+302
+00:35:26,250 --> 00:35:32,560
+ناخد بعض المعلومات المهمة في هذا الموضوع، وهي
+
+303
+00:35:32,560 --> 00:35:39,980
+معلومات على غير العادة، كيف كنت تاني؟ إحنا بنقول
+
+304
+00:35:39,980 --> 00:35:44,180
+الآن أعطاني هذا ideal وأجري هذه الـ factor ring
+
+305
+00:35:44,180 --> 00:35:49,000
+تبع جاوسيا، كيف الشغل فيها مش عارفين، لكن أنتِ تعرفي
+
+306
+00:35:49,000 --> 00:35:51,520
+على كيفية العمل داخل هذه الحلقة
+
+307
+00:35:55,360 --> 00:35:59,860
+هذه الحلقة لم تتواجد في الطبعات الأولى لهذا
+
+308
+00:35:59,860 --> 00:36:02,440
+الكتاب، لا في الأولى ولا في الثانية، ولا حتى في
+
+309
+00:36:02,440 --> 00:36:06,580
+السادسة، ظهر هذا المثال في الطبعة السابعة، وما كانش
+
+310
+00:36:06,580 --> 00:36:11,020
+موجود في الطبعات اللي قبلها، طب نشوف كيف يكون الشغل
+
+311
+00:36:11,020 --> 00:36:16,700
+في هذا، في هذا، في هذه الحلقة، خلي بالكِ فيها الآن
+
+312
+00:36:16,700 --> 00:36:23,490
+أنا بدي أسأل: هل الاثنين ناقص الـ I موجودة في الـ
+
+313
+00:36:23,490 --> 00:36:28,030
+principal ideal generated by 2 minus الـ I
+
+314
+00:36:28,030 --> 00:36:36,130
+موجودة، ممتاز جدا، يبقى معناه هذا الكلام أن اثنين
+
+315
+00:36:36,130 --> 00:36:42,210
+موجودة في هذا العنصر، هذا معناه أن الـ 2
+
+316
+00:36:42,210 --> 00:36:49,170
+ناقص الـ I زي الـ principal ideal generated by 2
+
+317
+00:36:49,170 --> 00:36:54,870
+minus الـ I بتساوي زائد الـ 0، reference بالـ Identity الـ
+
+318
+00:36:54,870 --> 00:37:00,050
+generated by 2 minus الـ I، فلو جماعة بصير معاه و
+
+319
+00:37:00,050 --> 00:37:06,630
+بضلش عندي اللي هذا، يعني معنى هذا الكلام أن الـ 2
+
+320
+00:37:06,630 --> 00:37:12,850
+ناقص الـ I بتساوي 0، لأن الـ left coset بتساوي left
+
+321
+00:37:12,850 --> 00:37:19,730
+coset، يبقى 2 ناقص الـ I بدها تساوي 0 داخل الحلقة اللي
+
+322
+00:37:19,730 --> 00:37:27,670
+عندنا هذه، طيب هذا معناته أن الـ I بدها تساوي 2
+
+323
+00:37:27,670 --> 00:37:30,750
+إيش؟
+
+324
+00:37:30,750 --> 00:37:35,310
+I بده يساوي 2، مالكِ أنتِ؟ إيش اللي جرى لكِ؟ ولا
+
+325
+00:37:35,310 --> 00:37:38,570
+جرى ولا حاجة، إحنا مش هيرمشنا، بس إحنا بنشتغل
+
+326
+00:37:38,570 --> 00:37:43,230
+جبر، ما نشتغلش real numbers، لو بنتكلم في الأعداد
+
+327
+00:37:43,230 --> 00:37:48,560
+الحقيقية، وأنتِ مجنونة، عدد تخيلي بيساوي عدد حقيقي!
+
+328
+00:37:48,560 --> 00:37:53,320
+كل عدد حقيقي عبارة عن عدد تخيلي، إذا صار عندنا
+
+329
+00:37:53,320 --> 00:38:01,640
+اثنين زي اثنين بدها تساوي I،  الأدهى والأمر من ذلك
+
+330
+00:38:01,640 --> 00:38:07,080
+مش هيدي في بالكِ، لو ربعنا طرف الشمال كده بيكون؟ سنة
+
+331
+00:38:07,080 --> 00:38:12,320
+واحدة، وده كده ستة؟ أربعة، يعني إيش؟ يعني خمسة كده
+
+332
+00:38:12,320 --> 00:38:15,140
+تساوي؟ ستة
+
+333
+00:38:17,870 --> 00:38:23,950
+على كل حال، خطأ، بدنا نغير عاجلنا، إحنا ما بنشتغلش في
+
+334
+00:38:23,950 --> 00:38:29,410
+real numbers، بنشتغل في complex، مظبوط ولا لا؟ اثنين
+
+335
+00:38:29,410 --> 00:38:33,770
+بنشتغل complex، جبر اثنين مع بعض، مش أعداد
+
+336
+00:38:33,770 --> 00:38:37,730
+حقيقية، بلغة الأعداد الحقيقية ده كلام مش صحيح، لو
+
+337
+00:38:37,730 --> 00:38:41,090
+جاء يقولوا لواحد: خمسة يساوي صفر، يقولوا: أنتِ إجننتِ؟
+
+338
+00:38:41,090 --> 00:38:45,390
+خمسة يساوي صفر، يقولوا: لأ، ما إجننتِ، يعني كمال
+
+339
+00:38:45,390 --> 00:38:51,420
+العقل، والحمد لله، طيب هذه الشهادة، أنتِ عجلكِ بدكِ تطوعي
+
+340
+00:38:51,420 --> 00:38:55,180
+لرنقل جديد، أنتِ بتشتغلي الـ real numbers لها عناصر و
+
+341
+00:38:55,180 --> 00:38:59,820
+الـ complex لها عناصر، اثنين، الـ complex أنتِ بتشتغلي
+
+342
+00:38:59,820 --> 00:39:05,880
+عليها جبر، بقول له: اه، طيب، مرة ثانية، هو العنصر هذا
+
+343
+00:39:05,880 --> 00:39:10,710
+موجود هنا، أنا بقول له: صحيح، بقول له: ماشي، موافقين، طيب
+
+344
+00:39:10,710 --> 00:39:15,530
+يبقى هذا زائد الـ principal ideal هو zero زائد الـ
+
+345
+00:39:15,530 --> 00:39:19,410
+principal ideal هو الـ principal ideal itself، صار
+
+346
+00:39:19,410 --> 00:39:23,150
+left coset، left coset، يبقى هذا العنصر يساوي
+
+347
+00:39:23,150 --> 00:39:27,570
+zero، يبقى الـ I تساوي 2 داخل هذه الحلقة، طيب أنا
+
+348
+00:39:27,570 --> 00:39:34,230
+وراها بصير كلامنا غلط، مش صحيح، تمام، طيب كويس، ردعي
+
+349
+00:39:34,230 --> 00:39:38,370
+بصير I تربيع معروف عندنا بـ سالب واحد في الـ complex
+
+350
+00:39:38,820 --> 00:39:43,700
+يبقى سالب واحد يساوي أربعة، يبقى الخمسة بدها تساوي
+
+351
+00:39:43,700 --> 00:39:51,280
+zero، خمسة تساوي zero، very important، لها ما بعدها
+
+352
+00:39:51,280 --> 00:39:57,220
+طيب إحنا ادعينا أن العنصر تبع الحلقة اللي
+
+353
+00:39:57,220 --> 00:40:03,040
+عندنا هذا هو A زائد B i، كـ complex زائد الـ
+
+354
+00:40:03,040 --> 00:40:08,020
+principal ideal generated by 2 minus الـ i، تمام
+
+355
+00:40:08,470 --> 00:40:14,810
+قبل ما نبدأ نكمل، بدنا نروح نثبت لكم أن أي عنصر في
+
+356
+00:40:14,810 --> 00:40:19,730
+هذه الحلقة، بقدر أكتبه على دلالة ثابت زائد الـ
+
+357
+00:40:19,730 --> 00:40:24,030
+principal ideal generated by 2 minus الـ a
+
+358
+00:40:24,030 --> 00:40:29,090
+تمام؟ نبين لكم كيف الشغل هذا، طبعا بيطلعوا في بعض، و
+
+359
+00:40:29,090 --> 00:40:33,370
+لا يقصروا شيء، دعوة سكت
+
+360
+00:40:33,370 --> 00:40:37,350
+هل
+
+361
+00:40:37,350 --> 00:40:47,830
+يبقوا علامة؟ Not bad. ظهر فيني ما يأتي. الآن
+
+362
+00:40:47,830 --> 00:40:53,910
+لو جيت تقول: تلاتة زائد أربعة I، زائد الـ principal ID
+
+363
+00:40:53,910 --> 00:41:00,810
+generated by 2 minus الـ I. مش هذا عنصر موجود
+
+364
+00:41:00,810 --> 00:41:07,170
+هنا على الشكل هذا؟ هي اللي ما فيش اعتراف. طيب إحنا
+
+365
+00:41:07,170 --> 00:41:13,810
+طلعنا قبل قليل أن الـ I جداش 2، أما من هذا
+
+366
+00:41:13,810 --> 00:41:19,770
+الكلام: تلاتة زائد أربعة، اثنين زائد الـ principal I
+
+367
+00:41:19,770 --> 00:41:26,290
+D generated by 2 minus 2، 4، 8
+
+368
+00:41:26,290 --> 00:41:31,650
+8، 8، و 11، 11، من جهة هذا الكلام
+
+369
+00:41:31,650 --> 00:41:32,790
+11
+
+370
+00:41:49,350 --> 00:41:53,230
+ممتاز، يبقى صح،  الـ principal ideal generated by 0
+
+371
+00:41:53,230 --> 00:41:58,250
+اللي هو 0 itself، كيف عوضت عن الـ I بـ 2، وهذه؟
+
+372
+00:41:58,250 --> 00:42:07,470
+اللي لو حولتها بصير هذا هو العنصر الصفري، لأ، مش
+
+373
+00:42:07,470 --> 00:42:10,850
+عوضت فيها، الـ I اللي برا، كيف عوضت عندها 2 وهي
+
+374
+00:42:10,850 --> 00:42:14,490
+مش تابعة للـ principal I، كيف؟ إحنا بنشتغل داخل الـ
+
+375
+00:42:14,490 --> 00:42:19,210
+ring، داخل الـ ring الـ I بـ 2 صار عادي، وأنِي أخدت
+
+376
+00:42:19,210 --> 00:42:23,590
+العنصر من داخل الـ ring، إذا بدي أشيل الـ I وأكتب
+
+377
+00:42:23,590 --> 00:42:28,190
+بدلها 2، ما أحدش، كله كلام عندي صح ولا لا؟ يبقى
+
+378
+00:42:28,190 --> 00:42:34,250
+أحطها بـ 2، صار 11 زائد 2 إيه؟ يبقى صار كل
+
+379
+00:42:34,250 --> 00:42:40,050
+عنصر في الحلقة اللي أنا بقدر أكتبه على شكل
+
+380
+00:42:40,050 --> 00:42:46,570
+ثابت زائد الـ principal إيه دي، يبقى صار every
+
+381
+00:42:47,580 --> 00:42:57,360
+element in اللي هو من Z of I module الـ principal
+
+382
+00:42:57,360 --> 00:43:07,480
+ID generated by A is written as الـ A زي الـ
+
+383
+00:43:07,480 --> 00:43:14,140
+principal ID generated by 2 نقص الـ I، الـ A هو
+
+384
+00:43:14,140 --> 00:43:23,660
+عبارة عن عدد صحيح، والـ A is integer، طيب
+
+385
+00:43:23,660 --> 00:43:32,800
+كويس، بلاقيه ساعة لحد عشر، زي الـ principal ideal
+
+386
+00:43:32,800 --> 00:43:39,620
+generated by 2 minus الـ A، بتساوي يا بنات، واحد
+
+387
+00:43:39,620 --> 00:43:47,810
+زائد 2 في 5 زائد الـ Principal Ideal Generated
+
+388
+00:43:47,810 --> 00:43:53,770
+By 2 Minus الـI. الخمسة في قداش؟ zero في 2
+
+389
+00:43:5
+
+445
+00:49:33,360 --> 00:49:44,990
+اتنين-I بده يساوي 2-I يعني صار الواحد زي ال
+
+446
+00:49:44,990 --> 00:49:53,910
+principle ideal generated بده يساوي 2-I هذا الكلام
+
+447
+00:49:53,910 --> 00:50:00,410
+صحيح معناته أن الواحد موجود في الـ principle ideal
+
+448
+00:50:00,410 --> 00:50:09,730
+generated by 2-I طيب مدام واحد، طب هذا عناصره
+
+449
+00:50:09,730 --> 00:50:16,570
+element من الـ ring الأصلية مضروب في element من هنا، صح؟
+
+450
+00:50:16,570 --> 00:50:23,890
+ولا لا؟ يبقى هذا معناه إيش؟ معناته أن الواحد هذا
+
+451
+00:50:23,890 --> 00:50:30,120
+بده يساوي element من الـ ring الأصلية مع الاثنين
+
+452
+00:50:30,120 --> 00:50:38,840
+ناقص I في مين؟ في الـ A زائد  bi R سجة
+
+453
+00:50:38,840 --> 00:50:46,220
+الشعور، الواحد موجود هنا، صح؟ هذه من عناصرها الـ
+
+454
+00:50:46,220 --> 00:50:51,800
+principle، هذه بدي أجيب element من R وأضربه في
+
+455
+00:50:51,800 --> 00:50:57,320
+مين؟ في اللي هو الـ element اللي عندنا هذا، صح ولا
+
+456
+00:50:57,320 --> 00:51:04,040
+لا؟ ماذا تعريف الـ principle ideal generated by A؟
+
+457
+00:51:04,040 --> 00:51:08,820
+مش AR صحيح، يعني الـ R موجود في R، يعني جبنا element
+
+458
+00:51:08,820 --> 00:51:13,440
+من R وجبنا element من A وضربناهم في بعض، أنا عندي
+
+459
+00:51:13,440 --> 00:51:18,600
+الواحد موجود في الـ ring اللي عندنا هذه، صح ولا لأ؟
+
+460
+00:51:18,600 --> 00:51:22,940
+مدام الواحد موجود في اللي جوا الـ ideal، الواحد
+
+461
+00:51:22,940 --> 00:51:28,280
+موجود في الـ ideal، يبقى الواحد ده، حيث يحصل ضرب
+
+462
+00:51:28,280 --> 00:51:35,060
+element من هنا في element من الـ ring، صح ولا لا؟
+
+463
+00:51:35,060 --> 00:51:43,600
+مصبوط؟ يبقى بالبناء عليه بتساوي، وهادِها for some
+
+464
+00:51:43,600 --> 00:51:53,470
+الـ a زائد bi اللي موجودة في Z[i]، تمام؟ بدنا نضرب
+
+465
+00:51:53,470 --> 00:52:03,150
+هدول في بعض، يبقى هذا الكلام بيساوي 2A زائد B زائد
+
+466
+00:52:03,150 --> 00:52:15,010
+زائد، هذه بيصير عندي اللي في I، يبقى هذه 2B، اثنين B
+
+467
+00:52:15,010 --> 00:52:23,080
+وناقص الـ A، كل هذا الكلام في الـ I بيساوي واحد، هذا
+
+468
+00:52:23,080 --> 00:52:29,140
+سيقودنا إلى معادلتين، المعادلة الأولى 2A زائد B
+
+469
+00:52:29,140 --> 00:52:35,280
+يساوي واحد، والتانية 2B ناقص الـ A بده يساوي صفر
+
+470
+00:52:35,280 --> 00:52:39,260
+لأن الـ real بده يساوي الـ real، والـ complex بده
+
+471
+00:52:39,260 --> 00:52:43,200
+يساوي الـ complex، ما عنديش جزء بـ صفر، طيب نحل
+
+472
+00:52:43,200 --> 00:52:49,240
+المعادلة هذه، هذا بده يعطينا 2A زائد B يساوي واحد
+
+473
+00:52:49,240 --> 00:52:55,120
+وهذه بتضربها في اثنين، يبقى أربعة B ناقص اثنين A
+
+474
+00:52:55,120 --> 00:53:00,580
+يساوي صفر، أجمع هذه وهذه، بيروحوا مع بعض، بظل عندنا
+
+475
+00:53:00,580 --> 00:53:08,940
+مين؟ خمسة B، خمسة B، اللي هو B تساوي
+
+476
+00:53:08,940 --> 00:53:17,200
+الواحد، يبقى الـ B تساوي واحد على خمسة؟ واحد على خمسة؟
+
+477
+00:53:17,200 --> 00:53:22,350
+طب اللي هو الـ B، وأين موجودة هدول؟ to Z، يبقى هذا
+
+478
+00:53:22,350 --> 00:53:28,370
+does not belong to Z، يبقى الـ order يساوي واحد، كلام
+
+479
+00:53:28,370 --> 00:53:35,670
+غلط، مش صحيح، أنه قادني إلى نتيجة خاطئة، يبقى ساعة الـ
+
+480
+00:53:35,670 --> 00:53:41,010
+order لواحد زي الـ principle ideal generated لا
+
+481
+00:53:41,010 --> 00:53:47,550
+يمكن أن يساوي الواحد، هذا معناته أن الـ order للواحد
+
+482
+00:53:47,550 --> 00:53:54,370
+زي 2 ناقص I بده يساوي خمسة، وعدد العناصر هنا
+
+483
+00:53:54,370 --> 00:53:58,250
+كتبناهم، طلع خمسة، إذا لا يمكن لهذا اللي يكون
+
+484
+00:53:58,250 --> 00:54:07,730
+generator، ومافيش غيرهم، يبقى هنا therefore، ولهذا
+
+485
+00:54:07,730 --> 00:54:16,300
+اللي هو الـ... هذه مش واحد يا بنات، هذه واحد، هنا نوعا
+
+486
+00:54:16,300 --> 00:54:22,060
+يبقى therefore الواحد زي الـ principle ideal
+
+487
+00:54:22,060 --> 00:54:33,740
+generated by 2 ناقص الـ I is a generator، يبقى
+
+488
+00:54:33,740 --> 00:54:41,700
+هدفه يعطينا أن الـ order لمين؟ لـ Z[i] مدير الـ
+
+489
+00:54:41,700 --> 00:54:48,290
+principle ideal generated، باعي هذا بيساوي خمسة عناصر
+
+490
+00:54:48,290 --> 00:54:56,390
+تبع زعمنا قبل قليل، يبقى هذه خمسة عناصر فقط، زاغية
+
diff --git a/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/zUtNMJNFbCQ_raw.srt b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/zUtNMJNFbCQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..25dd3a892fee33861f182097dfdf3129806c2bb5
--- /dev/null
+++ b/PL9fwy3NUQKwbZEM9ek26xaPIiL_5tuWy3/zUtNMJNFbCQ_raw.srt
@@ -0,0 +1,1980 @@
+1
+00:00:20,820 --> 00:00:25,980
+بسم الله الرحمن الرحيم نكمل النظرية اللي انتهينا
+
+2
+00:00:25,980 --> 00:00:30,040
+منها في المرة الماضية، انتهينا في الشطرة الأول،
+
+3
+00:00:30,040 --> 00:00:34,640
+بقى الشطرة الثانية، فكان باختصار أنها النظرية
+
+4
+00:00:34,640 --> 00:00:44,480
+البردية الـR modulo A is a ring if and only if
+
+5
+00:00:44,480 --> 00:00:56,720
+الـA is an ID، تمام؟افترضنا ان الـ A is
+
+6
+00:00:56,720 --> 00:01:02,320
+an ideal و اثبتنا هذه ان ال ring تحت العمليتين
+
+7
+00:01:02,320 --> 00:01:11,040
+اللي هو ال A زائد ال A زائد ال B زائد ال A ك two
+
+8
+00:01:11,040 --> 00:01:18,160
+elements يساوي A زائد ال B زائد ال A andعملية
+
+9
+00:01:18,160 --> 00:01:25,500
+الضرب A زائد الـA في الـB زائد الـA يسوي AB زائد
+
+10
+00:01:25,500 --> 00:01:29,680
+الـA هي الـtwo operations اللي كانت على ال factor
+
+11
+00:01:29,680 --> 00:01:35,440
+ring اللي هو الـR modulo A تمام؟ المرة اللي فاتت
+
+12
+00:01:35,440 --> 00:01:41,120
+افترضنا انه A عبارة عن ideal و أثبتنا ان الـR
+
+13
+00:01:41,120 --> 00:01:46,060
+modulo A is A ring الآن بدنا نمشي في الاتجاه
+
+14
+00:01:46,060 --> 00:01:53,370
+المعكسالجبوح بقوله بنتكمل conversely بعد الشي اللي
+
+15
+00:01:53,370 --> 00:01:58,330
+كتبتيه المرة اللي فاتت بقوله conversely assume
+
+16
+00:01:58,330 --> 00:02:01,390
+that
+
+17
+00:02:01,390 --> 00:02:09,290
+افترضي ان ال R modulo A is a ring شو اللي بدنا
+
+18
+00:02:09,290 --> 00:02:15,990
+نعمله one two sure that
+
+19
+00:02:17,730 --> 00:02:24,690
+إن الـ A is an ID يبقى هذا اللي بنثبته هحاول نثبت
+
+20
+00:02:24,690 --> 00:02:30,510
+أنه A is ID طبعا اتعلمنا في مبادئ الرياضيات أن
+
+21
+00:02:30,510 --> 00:02:36,430
+هناك أكثر من طريقة للبرهان في أنحاج اسمه ال Direct
+
+22
+00:02:36,430 --> 00:02:41,510
+Probe في حيث ال Probe بواسط Contradiction أو
+
+23
+00:02:41,510 --> 00:02:45,790
+Contrapositive هحاول نثبت هذا الكلام بواسط
+
+24
+00:02:45,790 --> 00:02:51,780
+ContradictionOkay احنا بنقول بدنا نحاول نثبت نبين
+
+25
+00:02:51,780 --> 00:02:59,160
+ان ال A is an ideal of ال ring اللي عندنا هذي of A
+
+26
+00:02:59,160 --> 00:03:04,220
+ده يقوله suppose not افترض ان هذا كلام مش صحيح
+
+27
+00:03:04,220 --> 00:03:16,250
+يبقى suppose not يعني افترض ان هذا مش idealيبقى
+
+28
+00:03:16,250 --> 00:03:23,770
+بالي بقوله لو كان ال A موجود في A and ال R موجود
+
+29
+00:03:23,770 --> 00:03:30,110
+في R then ال A R ماقدر أقول موجود في A؟ ليس
+
+30
+00:03:30,110 --> 00:03:39,910
+بالضرورة، يبقى مش موجود في A or ال A or ال R، A مش
+
+31
+00:03:39,910 --> 00:03:46,890
+موجود فيه، هذا هوطيب، لو أخدت الحالة الأولى، if
+
+32
+00:03:46,890 --> 00:03:56,670
+الـAR مش موجود في A، then الـAR زائد الـA، هل
+
+33
+00:03:56,670 --> 00:04:00,650
+تساوي الـA؟
+
+34
+00:04:00,650 --> 00:04:08,370
+مش موجود في A، if الـAR مش موجود في A، then الـAR
+
+35
+00:04:08,370 --> 00:04:13,820
+زائد الـA، هل تساوي الـA؟ لأ، لأ، لأ، لأ،وسميلي
+
+36
+00:04:13,820 --> 00:04:20,080
+هذه العلاقة ايه؟ وسميلي هذه العلاقة رقم واحد وبدنا
+
+37
+00:04:20,080 --> 00:04:26,120
+نروح نجيب علاقة ثانية ونشوف ايش بده يحصل عندنا
+
+38
+00:04:26,120 --> 00:04:37,020
+الان لو جيت بط ال a زائد ال a واحنا قايلين ال a
+
+39
+00:04:37,020 --> 00:04:43,460
+موجودة وين؟ ال aطيب إن كان هذا موجود في ال a يبقى
+
+40
+00:04:43,460 --> 00:04:50,620
+هذا بدي يعطينا ال a itself والسبب فيه أو بدي ساوي
+
+41
+00:04:50,620 --> 00:04:55,440
+اللي هو ال zero زائد ال a و اللي هو بدي ساوي ال a
+
+42
+00:04:55,440 --> 00:05:04,080
+itself ليش؟ لأنه في بداية المثلة قال ال a is a sub
+
+43
+00:05:04,080 --> 00:05:11,400
+ring مظبوطيبقى ال a subring يبقى هذا الكلام موجود
+
+44
+00:05:11,400 --> 00:05:19,880
+هنا طيب بتروح أاخد element من من ال factoring R
+
+45
+00:05:19,880 --> 00:05:24,960
+modulo a مع ال element هذا و أشوف وين بدي يوصلني
+
+46
+00:05:24,960 --> 00:05:36,080
+طيب then لو أخدت ال a زائد ال a وضربته في R زائد
+
+47
+00:05:36,080 --> 00:05:45,040
+ال aهذا الكلام بده يساوي قداش A R زائد ال A طبقا
+
+48
+00:05:45,040 --> 00:05:51,300
+لعملية الضرب المعرفة عالمية على ال factoring R
+
+49
+00:05:51,300 --> 00:06:00,100
+modulo A and ال A زائد ال A هي Zero زائد ال A يبقى
+
+50
+00:06:00,100 --> 00:06:07,960
+كمان ال Zero زائد ال Aفي ال R زائد ال A بده يساوي
+
+51
+00:06:07,960 --> 00:06:15,720
+Zero زائد ال A تمام؟ هذا العمصر هو هذا العمصر حصل
+
+52
+00:06:15,720 --> 00:06:21,700
+الضرب يساوي و حصل الضرب يساوي إذا من الإتنين هدول
+
+53
+00:06:21,700 --> 00:06:27,320
+بقدر أقوله AR زائد ال A بده يساوي ال A itself
+
+54
+00:06:27,320 --> 00:06:35,670
+مظبوط؟ طب إيش رأيك هذا و هذا؟contradiction يبقى
+
+55
+00:06:35,670 --> 00:06:40,570
+this is contradiction
+
+56
+00:06:40,570 --> 00:06:44,490
+طب
+
+57
+00:06:44,490 --> 00:06:50,290
+ايش جاب التناقض هذا انه فرضت ان ال a ماهواش ideal
+
+58
+00:06:50,290 --> 00:06:57,290
+يبقى ماهواش ideal هو خطأ والحقيقة انه ideal يبقى
+
+59
+00:06:57,290 --> 00:07:09,040
+بقوله thus وهكذااللي هو الـ A is an ideal of ring
+
+60
+00:07:09,040 --> 00:07:14,780
+R إذا
+
+61
+00:07:14,780 --> 00:07:20,160
+بناء علي من الأن فصاعدا ال fact هو ال ring R
+
+62
+00:07:20,160 --> 00:07:26,900
+modulo A عناصرها كلهم left cosets اللي هو element
+
+63
+00:07:26,900 --> 00:07:35,660
+من R و element من AR زائد له كبتل A هو عنصر موجود
+
+64
+00:07:35,660 --> 00:07:41,680
+وين في ال factoring R modulo A الآن بناخد بعض
+
+65
+00:07:41,680 --> 00:07:48,720
+الأمثلة على ذلك أول مثال على هذا الموضوع نفجر
+
+66
+00:07:48,720 --> 00:07:56,200
+examples نملك
+
+67
+00:07:56,200 --> 00:08:08,180
+واحد الـ Zموديولو أربعة زد عناصرها ال E Zero زائد
+
+68
+00:08:08,180 --> 00:08:17,160
+أربعة زد و واحد زائد أربعة زد و إتنين زائد أربعة
+
+69
+00:08:17,160 --> 00:08:24,000
+زد و تلاتة زائد أربعة زد بالشكل اللي عندنا هنا
+
+70
+00:08:24,000 --> 00:08:28,460
+Factor
+
+71
+00:08:30,050 --> 00:08:40,670
+Ring is a factor ring because الأربعة
+
+72
+00:08:40,670 --> 00:08:52,750
+Z is an ideal of the ring Z طب نحن أقنعكم مثال
+
+73
+00:08:52,750 --> 00:09:02,970
+سابقا ان NZ is an ideal of Zعدد صحيح موجب in
+
+74
+00:09:02,970 --> 00:09:11,450
+positive integer يبقى 2 z 3 z 4 z 5 z 6 z كله
+
+75
+00:09:11,450 --> 00:09:15,230
+عبارة عن ideal في ال ring الأساسي اللي هو main z
+
+76
+00:09:15,230 --> 00:09:20,530
+وبالتالي مادام ideal يبقى هذه عبارة عن factor ring
+
+77
+00:09:20,530 --> 00:09:28,260
+مكونة من main مكونة من أربعة أنصار الآنبناء على
+
+78
+00:09:28,260 --> 00:09:33,020
+هذا التعريف بدنا نعرف لك كيف أو نوريك كيف بتجمع
+
+79
+00:09:33,020 --> 00:09:40,860
+هذه العناصر أوي بتضربيها مثلا Note that لاحظي لي
+
+80
+00:09:40,860 --> 00:09:48,720
+ما يأتي الان لو بدي أجي أقول اتنين زائد أربعة زيه
+
+81
+00:09:48,720 --> 00:09:54,940
+تمام؟ هذا عنصر بدي أجمع مع تلاتة زائد أربعة زيه
+
+82
+00:09:55,310 --> 00:09:59,970
+طبقًا للكلام اللي احنا جايلينه هنا اتنين زائد
+
+83
+00:09:59,970 --> 00:10:07,450
+تلاتة بخمسة زائد أربعة زد لكن الحمسة هذه بقدر
+
+84
+00:10:07,450 --> 00:10:13,350
+اكتبها واحد زائد أربعة زائد أربعة زد الأربعة
+
+85
+00:10:13,350 --> 00:10:17,690
+موجودة في الأربعة زد ولا لا لا إذا بتعطيني الأربعة
+
+86
+00:10:17,690 --> 00:10:26,040
+زد it's same يبقى هذا واحد زائد أربعة زد andلو بدى
+
+87
+00:10:26,040 --> 00:10:32,720
+اضرب ضرب يبقى اتنين زائد اربعة زد مضروبة في تلاتة
+
+88
+00:10:32,720 --> 00:10:38,900
+زائد اربعة زد يبقى اتنين في تلاتة في ستة زائد
+
+89
+00:10:38,900 --> 00:10:45,300
+اربعة زد الستة بقدر اقول اللى هى اتنين زائد اربعة
+
+90
+00:10:45,300 --> 00:10:51,120
+زائد اربعة زد يعني اتنين زائد مين اربعة زد لإن
+
+91
+00:10:51,120 --> 00:10:56,330
+الاربعة موجودة في مين الاربعة زديبقى هذه عملية
+
+92
+00:10:56,330 --> 00:11:02,550
+الضرب اللي بتتم طيب حد فيكم تقدر تجيبلي ID
+
+93
+00:11:02,550 --> 00:11:07,850
+important element من ال group من ال ring هذه ID
+
+94
+00:11:07,850 --> 00:11:11,910
+important يعني مربع ال element بدي يعطيني نفس ال
+
+95
+00:11:11,910 --> 00:11:18,030
+element اتنين زياد اربعة زياد اتنين زياد اربعة
+
+96
+00:11:18,030 --> 00:11:25,310
+زياد is an ID important يعني لو ربعته بيطلع نفسهلأ
+
+97
+00:11:25,310 --> 00:11:31,990
+مش صحيح بطلع Zero يبقى هذا نل potent element هذا
+
+98
+00:11:31,990 --> 00:11:41,390
+نل potent ليش؟ لأنه اتنين زاد اربعة زد كل ترفيع
+
+99
+00:11:41,390 --> 00:11:45,110
+يسوي اربعة زاد اربعة زد اللي هو بده يسوي اربعة زد
+
+100
+00:11:45,110 --> 00:11:50,250
+اللي هو ال zero element يبقى الاربعة زد هو ال zero
+
+101
+00:11:50,250 --> 00:11:55,440
+element في ال ring اللي عندنا هذهو 1 زي ده 4 زي ده
+
+102
+00:11:55,440 --> 00:12:02,540
+و 0 زي ده 4 زي ده اتنين اي دي importance هدول
+
+103
+00:12:02,540 --> 00:12:11,420
+اتنين كمان اي دي importance طب و التلاتة زي ده 4
+
+104
+00:12:11,420 --> 00:12:17,560
+زي ده لأ بتلع واحد طب لما ربنا احنا قداش بصيانة
+
+105
+00:12:17,560 --> 00:12:20,500
+واحد زي ده 4 زي ده واحد زي ده 4 زي ده يبقى هده
+
+106
+00:12:20,500 --> 00:12:26,520
+unit صح؟لأنه تسعة شيل منها أربعتين وفضل واحد اللي
+
+107
+00:12:26,520 --> 00:12:34,860
+هو ال unity يبقى هدفي حد ذاته as a unit يبقى أي
+
+108
+00:12:34,860 --> 00:12:39,240
+عناصر ايش important و ايش not important و ايش
+
+109
+00:12:39,240 --> 00:12:44,760
+units وما إلى ذلك طيب أروح لمين لل ring التانية
+
+110
+00:12:44,760 --> 00:12:55,890
+مثال اتنين مثال اتنينبيقول لي اتنين زي موديولو ستة
+
+111
+00:12:55,890 --> 00:13:03,830
+زي موديولو ستة زي اللي هي عناصرها اللي هي بدها الـ
+
+112
+00:13:03,830 --> 00:13:14,170
+cell بنت عارف اجيبلي عناصرها؟ Zero زيت ستة زي و
+
+113
+00:13:14,170 --> 00:13:21,670
+التاني واحد زيت ستة زيواحد مش موجود في اتنين زيت
+
+114
+00:13:21,670 --> 00:13:28,070
+يبقى بعد زيره في جين اتنين يبقى اتنين زيت ستة زيت
+
+115
+00:13:28,070 --> 00:13:35,870
+طيب و اللي بعده اربع زيت ستة زيت خلاص نهت اللي
+
+116
+00:13:35,870 --> 00:13:40,790
+بعده ستة زيت ستة زيت اللي هو Zero زيت ستة زيت يبقى
+
+117
+00:13:40,790 --> 00:13:46,990
+هذه ال rings مافيش فيها الا ثلاثةثلاث عناصر يعني
+
+118
+00:13:46,990 --> 00:13:53,230
+عندي ثلاثة left cosets تمام؟ يبقى ثلاثة عناصر فقط
+
+119
+00:13:53,230 --> 00:14:03,010
+لا غير خليني أسأل طب ليش هذه ستة Z ID؟ زي الأربعة
+
+120
+00:14:03,010 --> 00:14:12,750
+Z ماكانت ID يبقى هذه هه هذي factor ring هذي factor
+
+121
+00:14:12,750 --> 00:14:31,160
+ringbecause الست زد is an ideal in the ring اتنين
+
+122
+00:14:31,160 --> 00:14:37,760
+زد يا ريت تشيكيلي عليها يعني في الطريق تروحي تثبتي
+
+123
+00:14:37,760 --> 00:14:44,610
+ان الست زد عبارة عن ايديل تمين في اتنين زدطب خليني
+
+124
+00:14:44,610 --> 00:14:52,410
+أسأل ها فيها unity هذه يعني identity element أربعة
+
+125
+00:14:52,410 --> 00:14:56,970
+زائد ستة زيت مية المية هذه الكلام صحيح يبقى ال
+
+126
+00:14:56,970 --> 00:15:00,890
+unity مش تقولي مافيش واحد يقول مافيش unity لإن ال
+
+127
+00:15:00,890 --> 00:15:08,970
+unity هنا هو أربعة زائد ستة زيت not that لاحظي لي
+
+128
+00:15:08,970 --> 00:15:20,700
+أن الأربعة زائد ستة زيتis the unity of اتنين
+
+129
+00:15:20,700 --> 00:15:30,000
+زد مدينة ستة زد طب ايش رايك؟ انا ازعم ان هذا كمان
+
+130
+00:15:30,000 --> 00:15:38,560
+ايش ازعم؟ هذا ID important صح؟ طب و هذا كمان ID
+
+131
+00:15:38,560 --> 00:15:45,710
+important مظلوم؟ طب و هذا؟يعني كيف بده يجي مثلًا؟
+
+132
+00:15:45,710 --> 00:15:50,990
+أربعة زيادة ستة زيادة فلو ضربت هدف هدف كده كده؟
+
+133
+00:15:50,990 --> 00:15:55,370
+كده كده؟ كده كده كده كده كده كده كده كده كده كده
+
+134
+00:15:55,370 --> 00:15:56,350
+كده كده كده كده كده كده كده كده كده كده كده كده
+
+135
+00:15:56,350 --> 00:15:56,350
+كده كده كده كده كده كده كده كده كده كده كده كده
+
+136
+00:15:56,350 --> 00:15:56,410
+كده كده كده كده كده كده كده كده كده كده كده كده
+
+137
+00:15:56,410 --> 00:16:03,730
+كده كده كده كده كده كده كده كده كده
+
+138
+00:16:03,730 --> 00:16:10,550
+كده
+
+139
+00:16:10,550 --> 00:16:18,120
+كداللي هو الـ unity حتى أقول هذا is a unit طيب لو
+
+140
+00:16:18,120 --> 00:16:26,060
+ربعته بطلع قداش هذا صح؟ لو كانتوا تكعيب بطلع نفسه
+
+141
+00:16:26,060 --> 00:16:31,340
+و هكذا يبقى هذا مكفل لحد هنا عرفنا هذا ال unity و
+
+142
+00:16:31,340 --> 00:16:39,260
+الله يعطينا العافية طب نروح لمثال تلاتة مثال تلاتة
+
+143
+00:16:46,340 --> 00:16:59,280
+تلاتة لت ال R تساوي M2 of Z وليه كل العناصر على
+
+144
+00:16:59,280 --> 00:17:07,240
+شكل المصفوفات A B C D بحيث ال A و ال B و ال C و ال
+
+145
+00:17:07,240 --> 00:17:17,120
+D كلها أعداد صحيحة يبقى موجودة في Z وخديلي ال Iكل
+
+146
+00:17:17,120 --> 00:17:26,120
+المصفوفات اللي على الشكل 2A2B2C2D
+
+147
+00:17:26,120 --> 00:17:33,840
+وبحيث أن الـ A و ال B و ال C و ال D كلها أعداد
+
+148
+00:17:33,840 --> 00:17:39,420
+صحيحة كذلك موجودة في Z. then
+
+149
+00:17:45,280 --> 00:17:57,040
+then ال I is an ideal of اللي هو ال M2 of Z
+
+150
+00:17:57,040 --> 00:18:03,000
+because مقتنون
+
+151
+00:18:03,000 --> 00:18:10,800
+طيب نرجع تاني ال ring اللي عندنا دي M2ZD بقى هي
+
+152
+00:18:10,800 --> 00:18:17,790
+مجموعة المصحفاتاللي نضامها 2×2 وبحيث الـ A والـ B
+
+153
+00:18:17,790 --> 00:18:22,710
+والـ C والـ D كلهم أعداد صحيحة موجودة في Z يعني
+
+154
+00:18:22,710 --> 00:18:28,470
+ممكن 0 وممكن 1 وممكن 2 و- 2 ثلاثة و- ثلاثة عشر
+
+155
+00:18:28,470 --> 00:18:36,770
+يعني أرقام موجبة و سلم وصفر كلها روحت أخد لل 6I كل
+
+156
+00:18:36,770 --> 00:18:42,120
+العناصر اللي هي أعداد زوجيةيبقى ال A و ال B و ال C
+
+157
+00:18:42,120 --> 00:18:46,660
+لو كانت فردية و ضربتها في اتنين بيصير اعداد زوجية
+
+158
+00:18:46,660 --> 00:18:51,480
+يبقى صارت بالشكل هذا و A و B و C سواء كان A و B و
+
+159
+00:18:51,480 --> 00:18:55,480
+C فردي و الله زوجي مابتفرقش هنا لكن روح ضربتها في
+
+160
+00:18:55,480 --> 00:18:58,040
+اتنين و لما ضربوا في اتنين الفردي بيصير زوجي و
+
+161
+00:18:58,040 --> 00:19:04,120
+الزوجي بيبقى زوجي كما هو طيب نحن نزعم ان ال I is
+
+162
+00:19:04,120 --> 00:19:09,780
+an ID اللي يبقى بنروح نطبقالشروط التلاتة على ال
+
+163
+00:19:09,780 --> 00:19:15,300
+subset اللي أخدنا علشان تكون ID إذا النقطة الأولى
+
+164
+00:19:15,300 --> 00:19:22,840
+بروح بقوله I is not in because
+
+165
+00:19:22,840 --> 00:19:29,740
+أو since ال zero ال zero ال zero ال zero موجودة في
+
+166
+00:19:29,740 --> 00:19:37,660
+I أكيد؟ طب هنا I عداد زوجيةيبقى بقدر اكتب هذا
+
+167
+00:19:37,660 --> 00:19:43,820
+الكلام اتنين في زيرو اتنين في زيرو اتنين في زيرو
+
+168
+00:19:43,820 --> 00:19:50,480
+اتنين في زيرو يبقى موجودة في I ولا لا يبقى موجودة
+
+169
+00:19:50,480 --> 00:19:57,780
+في I يبقى صارت كلها على شكل أعداد زوجية إذا ال I
+
+170
+00:19:57,780 --> 00:20:05,520
+لن يمتي على الأقل فيها يجب فيها العنصر الصفريإنه 2
+
+171
+00:20:05,520 --> 00:20:15,680
+في 0 يبقى المصفوفة الصفرية موجودة في الـ I النقطة
+
+172
+00:20:15,680 --> 00:20:26,360
+الثانية أفترض أن A هو B موجودة في I ثم الـ A هذه
+
+173
+00:20:26,360 --> 00:20:31,200
+بدها تساوي 2A2B2C
+
+174
+00:20:31,570 --> 00:20:39,650
+أتنين D والـ B بدها تساوي اتنين X اتنين Y اتنين Z
+
+175
+00:20:39,650 --> 00:20:47,790
+اتنين W مثلاً بتاخد الفرق في ما بينهما الـ A ناقص
+
+176
+00:20:47,790 --> 00:20:54,670
+الـ B تفجر نطرح كل عنصر من ماضيره تفجر بتاخد اتنين
+
+177
+00:20:54,670 --> 00:21:01,600
+عامل مشترك بظل A ناقص Xبنطرح هذا العنصر من هذا
+
+178
+00:21:01,600 --> 00:21:07,820
+العنصر يبقى 2A-2X أخدنا التان عامل مشترك بضل ال A
+
+179
+00:21:07,820 --> 00:21:20,440
+-X الباقي بنفس الطريقة يبقى 2B-Y يبقى 2C-Z يبقى 2D
+
+180
+00:21:20,440 --> 00:21:29,070
+-W طيب عليك صح هذه على صورةاللي هو ال .. الست اللي
+
+181
+00:21:29,070 --> 00:21:33,830
+عندنا هذا الـ I إذا هذا ال element موجود وين؟
+
+182
+00:21:33,830 --> 00:21:41,810
+موجود في I وصلنا للنقطة الأخيرة بدي أخد element من
+
+183
+00:21:41,810 --> 00:21:47,510
+ال ring R الأصلية و element من ال I يبقى بداجي
+
+184
+00:21:47,510 --> 00:21:55,270
+أقوله little a بدأ تساوي a,b,c,dموجودة في الـ M2
+
+185
+00:21:55,270 --> 00:22:05,210
+of Z and الـ B يساوي 2X2Y2Z2W
+
+186
+00:22:05,210 --> 00:22:13,250
+موجودة في الـ I then بدأت اللي حصل ضربهما الـ A في
+
+187
+00:22:13,250 --> 00:22:21,190
+B يبقى الـ A, B, C, Dوهنا اتنين X اتنين Y اتنين Z
+
+188
+00:22:21,190 --> 00:22:26,290
+اتنين W بده يساعد مصروفة نظامها اتنين في اتنين
+
+189
+00:22:26,290 --> 00:22:30,230
+ومصروفة نظامها اتنين في اتنين اذا سينتج من ذلك
+
+190
+00:22:30,230 --> 00:22:35,850
+برضه مصروفة نظامها اتنين في اتنين بدنا نضرب الصف
+
+191
+00:22:35,850 --> 00:22:45,260
+الأول في العمود الأول ونجمع يبقى هذه اتنين A Xزائد
+
+192
+00:22:45,260 --> 00:22:54,580
+اتنين BZ اتنين BZ الصف الأول في العمود الثاني يبقى
+
+193
+00:22:54,580 --> 00:23:05,300
+اتنين AY زائد اتنين BW اتنين BW الصف الثاني في
+
+194
+00:23:05,300 --> 00:23:15,310
+العمود الأول اتنين CX زائد اتنين DZالصف ثاني في
+
+195
+00:23:15,310 --> 00:23:27,570
+العمودي الثاني يبقى اتنين cy زائد اتنين dw هذا
+
+196
+00:23:27,570 --> 00:23:33,570
+الكلام يساوي ممكن اكتبه على الشكل التليخات نتين
+
+197
+00:23:33,570 --> 00:23:41,840
+عامل مشترك ax زائد bz وهنا بنفس الطريقة اتنيناي
+
+198
+00:23:41,840 --> 00:23:51,960
+زائد بي دابليو وهنا اتنين في cx زائد dz وهنا كذلك
+
+199
+00:23:51,960 --> 00:24:01,120
+اتنين في الهو cy زائد dw عليه سادة على الشكل I
+
+200
+00:24:01,120 --> 00:24:06,610
+اللي هنا ان كل عصر فيهم مضروب في اتنينإذا هذا
+
+201
+00:24:06,610 --> 00:24:14,350
+موجود في I وبنفس الطريقة Similarly لو روح بدل ما
+
+202
+00:24:14,350 --> 00:24:20,090
+ضربت ال A في ال B ضربت ال B في A هلاقيها موجودة في
+
+203
+00:24:20,090 --> 00:24:32,870
+I يبقى هنا ضص وهكذا ال I is an ideal of M to
+
+204
+00:24:32,870 --> 00:24:41,690
+oppositeطيب احنا حتى الآن جبنا main جبنا و أثبتنا
+
+205
+00:24:41,690 --> 00:24:46,570
+ان ال I هو عبارة عن ideal في ال ring اللي عندنا
+
+206
+00:24:46,570 --> 00:24:54,090
+طبعا طيب بدنا نيجي لل factor ring factor ring اه
+
+207
+00:24:54,090 --> 00:25:00,130
+هي ال factor ring بدي اعرف ايه شكل العناصر فيها و
+
+208
+00:25:00,130 --> 00:25:08,280
+اكم عنصر موجود في هذه ال factor ringتمام يلجبجي
+
+209
+00:25:08,280 --> 00:25:21,000
+بيقوله the factor ring اللي هو مين؟ M2 of Z modulo
+
+210
+00:25:21,000 --> 00:25:35,070
+LI يساوي كل المصفوفات اللي على الشكل A وB وC وDهذا
+
+211
+00:25:35,070 --> 00:25:43,650
+element من هنا زائد I تمام؟
+
+212
+00:25:43,650 --> 00:25:54,070
+هذه أنا أزعم أنها تساوي من اللي هي تساوي R1 وR2
+
+213
+00:25:54,070 --> 00:26:05,870
+وR3 وR4 زائد ال I such that ال R Iموجودة في الـ
+
+214
+00:26:05,870 --> 00:26:14,070
+set 01 مرة
+
+215
+00:26:14,070 --> 00:26:20,410
+ثانية نفسر نفسر الكلام اللي احنا قاليله ال M2Z
+
+216
+00:26:20,410 --> 00:26:25,710
+modulo I أخذ element من ال ring هذي مين ما يكون
+
+217
+00:26:25,710 --> 00:26:32,500
+يكون سميته ABCD زغط I مية الميةبقوللي هذه تساوي
+
+218
+00:26:32,500 --> 00:26:37,740
+عمليا ا ر واحد ا ر اتنين ا ر ثلاثة ا ر اربعة زي اد
+
+219
+00:26:37,740 --> 00:26:44,920
+اعي مين الارات هدول بيقوللي ا ا يا اما صفر يا اما
+
+220
+00:26:44,920 --> 00:26:52,400
+واحد غير هيك يبعتلك الله بيقوللي يا سلام قاللي اه
+
+221
+00:26:52,400 --> 00:26:55,720
+هذا
+
+222
+00:26:55,720 --> 00:26:56,360
+السؤال
+
+223
+00:27:02,430 --> 00:27:07,970
+اللي احنا بنحاول أن نجيب عليه حتى يكون الكلام هذا
+
+224
+00:27:07,970 --> 00:27:16,770
+تبعناه صحيح طيب
+
+225
+00:27:16,770 --> 00:27:30,350
+this is a true because هتقولي
+
+226
+00:27:30,350 --> 00:27:35,810
+أي مصفوفةأها يالا
+
+227
+00:27:35,810 --> 00:27:42,270
+اعطيني مصوفة من عندك اكبر الأرقام شوية مش مشكلة
+
+228
+00:27:42,270 --> 00:27:45,510
+جدمك موديكي تظهر عشان لا تواصليه و تسافر ماعنديكي
+
+229
+00:27:45,510 --> 00:27:51,890
+مشكلة اقولي ايوة اتنين اربعة تلاتة وتمانية تلاتة و
+
+230
+00:27:51,890 --> 00:27:56,750
+كده؟ تمانية تلاتة مش رايكي انا احط ده خطر احط سالب
+
+231
+00:27:56,750 --> 00:28:01,510
+مع موجب مع فردي مع زوجيحتى نحط كل احتمالات الواردة
+
+232
+00:28:01,510 --> 00:28:07,050
+نقول هذه ناقص خمسة بيمشي الهان طيب و نقول هذه اللي
+
+233
+00:28:07,050 --> 00:28:14,810
+حقتها زوجي بدي أحطها فردي وليكن احد عشر مثلا و هذه
+
+234
+00:28:14,810 --> 00:28:20,270
+بدي أكبرها شوية فالتي زوجي بدي أقول عليها أربع
+
+235
+00:28:20,270 --> 00:28:27,810
+كويس؟ يبقى هاي مصوفة زائد I بدي أشوف هل بقدر
+
+236
+00:28:27,810 --> 00:28:33,610
+أكتبهاعلى الصيغة اللى عندها هادي ولا لأ و الله إذا
+
+237
+00:28:33,610 --> 00:28:38,550
+قدرت أكتب و أبصير كلامنا صحيح مائة بالمائة طيب هذا
+
+238
+00:28:38,550 --> 00:28:44,350
+الكلام يساوي بدي أكتب هادي على صيغة مجموعة مصحوف
+
+239
+00:28:44,350 --> 00:28:51,650
+تين طيب لو جات فقلت هنا zero و ايا و هادي زائد لو
+
+240
+00:28:51,650 --> 00:28:58,200
+حطيت zero بتظل الأربعة زي مهين صح؟طيب هذه 11 فردي
+
+241
+00:28:58,200 --> 00:29:03,860
+بتخليها الزوج وكمان مقعد يبقى بقى الدرجون واحد
+
+242
+00:29:03,860 --> 00:29:14,100
+وعشر يبقى هاي واحد وهادي هنا عشرة تمام؟ طيب نجي
+
+243
+00:29:14,100 --> 00:29:20,240
+لمن؟ للتلاتة، تلاتة فردي كمان يبقى بقى الدرجون هنا
+
+244
+00:29:20,240 --> 00:29:26,610
+واحد وهنا اتنين، هاي مجموعهم تلاتة، ناقص خمسةواحد
+
+245
+00:29:26,610 --> 00:29:34,790
+وسالب ستة واحد وسالب ستة زائد I مصبوط هكذا السؤال
+
+246
+00:29:34,790 --> 00:29:39,470
+هو هذا ال element موجود في I ولا لا؟ لأن كل
+
+247
+00:29:39,470 --> 00:29:45,870
+العماصر التبعات هذه المصوفة أعدادا زوجية إذا هذه
+
+248
+00:29:45,870 --> 00:29:51,270
+موجودة فيبني لمجموعة مع I بتعطيني I itself يبقى
+
+249
+00:29:51,270 --> 00:29:58,640
+هذا الكلام يساوي Zero واحد واحدزائد الـ I يبقى
+
+250
+00:29:58,640 --> 00:30:03,600
+طالع كلامنا هذا صح ولا لا يا بنات؟ مظبوط؟ طيب
+
+251
+00:30:03,600 --> 00:30:08,240
+السؤال الجميل جدا اللي لسه بدنا نطرحه، ما
+
+252
+00:30:08,240 --> 00:30:17,760
+طرحناهوش، كم عنصر في هذه ال ring؟ أيه؟
+
+253
+00:30:17,760 --> 00:30:22,520
+يعني ما لنهاية؟
+
+254
+00:30:26,010 --> 00:30:35,310
+يعني كده بتقدري؟ خمسة، ستة مثلًا؟ سبعين؟ ستة عشر؟
+
+255
+00:30:35,310 --> 00:30:47,730
+عشرين؟ مية؟ ستة عشر عنصر فقط. فالناس اللي هو السبب
+
+256
+00:30:47,730 --> 00:30:58,050
+and ال order ل ال M two of ZModulo I يساوي 16
+
+257
+00:30:58,050 --> 00:31:02,570
+because بدنا
+
+258
+00:31:02,570 --> 00:31:08,030
+نروح نشوف أكم عنصر على الشكل هذا بيكون عندنا 16
+
+259
+00:31:08,030 --> 00:31:11,670
+عنصر
+
+260
+00:31:11,670 --> 00:31:17,470
+بنا نعرف بس مجرد نتعرف عليهم كلهم واحد كلهم واحد
+
+261
+00:31:17,470 --> 00:31:23,270
+كلهم صفرأحد أصفره كله بواحد عصرين صفريين والباقي
+
+262
+00:31:23,270 --> 00:31:27,250
+بواحد واحد تلت عناصر أصفره واحد بيكون خلص نجدها
+
+263
+00:31:27,250 --> 00:31:32,870
+السبتاشر تعرف تكتبها ولا تكتبها؟ يعني بلاش تكتبها؟
+
+264
+00:31:32,870 --> 00:31:40,090
+بلاش؟ طيب بتروحي بس بدي أعطيكي كيف يبقى بتقولي
+
+265
+00:31:40,090 --> 00:31:48,190
+Zero واحد واحد واحد تمام بعد هيكبحط ال zero هنا
+
+266
+00:31:48,190 --> 00:31:51,910
+بعد حين بحط ال zero هنا و الباقي كله بواحد يعني
+
+267
+00:31:51,910 --> 00:31:56,130
+بحط أنصه صفر و الباقي كله واحد هذا بتطلعلي كده؟
+
+268
+00:31:56,130 --> 00:32:03,550
+بتطلعلي أربعة عناصر بعد هيك حطيلي zero zero واحد
+
+269
+00:32:03,550 --> 00:32:12,210
+واحد هذا بتطلعلي كده؟ ستة عناصر ستة؟ اه ستة كيف؟
+
+270
+00:32:12,210 --> 00:32:18,980
+هذا نزلتهم تحت وطلعت هذا فوقخلت العمود الأول أصفر
+
+271
+00:32:18,980 --> 00:32:22,540
+واحد واحد، خلت العمود التاني أصفر والأول واحد
+
+272
+00:32:22,540 --> 00:32:27,880
+واحد، خلت القطر الرئيسي أصفرا والباقي واحد واحد،
+
+273
+00:32:27,880 --> 00:32:31,060
+خلت القطر الرئيسي واحد واحد والباقي أصفرين، يبقى
+
+274
+00:32:31,060 --> 00:32:35,720
+قبل الستة تعالى صاروا أربعة عاشرة، يبقى هذا واحد
+
+275
+00:32:35,720 --> 00:32:41,520
+من ستة، هذا واحد من أربعة، فإخسار كم ده؟ إخسار
+
+276
+00:32:41,520 --> 00:32:42,120
+عاشر
+
+277
+00:32:52,570 --> 00:32:55,170
+عشرة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+278
+00:32:55,170 --> 00:32:55,170
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+279
+00:32:55,170 --> 00:32:55,170
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+280
+00:32:55,170 --> 00:32:55,170
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+281
+00:32:55,170 --> 00:32:56,050
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+282
+00:32:56,050 --> 00:32:58,090
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+283
+00:32:58,090 --> 00:32:58,510
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+284
+00:32:58,510 --> 00:32:58,510
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+285
+00:32:58,510 --> 00:33:03,310
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+286
+00:33:03,310 --> 00:33:05,770
+أ
+
+287
+00:33:12,460 --> 00:33:16,660
+كام؟ ماتطلعش ع شكل الـ I ع شكل الـ I؟ أه مهما تكون
+
+288
+00:33:16,660 --> 00:33:24,340
+الـ I اللي هو الـ ID أه ليش؟ احنا جبناها أصلا هادي
+
+289
+00:33:24,340 --> 00:33:29,820
+من هادي يعني قدرنا نوصل هادي إلى الشكل اللي ..
+
+290
+00:33:29,820 --> 00:33:34,800
+السبب في ذلك أن هادي موجود في I لأ طلعنا ع شكلها
+
+291
+00:33:34,800 --> 00:33:38,780
+وبالتالي حصلنا على هادي و لا لو ماتطلعناش ع شكلها
+
+292
+00:33:38,780 --> 00:33:44,440
+ماجدرناش نجيب هادي صحيح ولا لأ؟يبقى الصف ضروري جدا
+
+293
+00:33:44,440 --> 00:33:50,480
+يبقى هنا كل واحدة من الستاشة دول بصير زائد I يعني
+
+294
+00:33:50,480 --> 00:33:55,580
+بيقولولي هذه زائد I هي 4 عناصر هذه زائد I هي 6
+
+295
+00:33:55,580 --> 00:34:03,000
+عناصر هذه زائد I هي 4 عناصر هذه زائد I هي 16 عنصر
+
+296
+00:34:03,000 --> 00:34:08,960
+يعني كل عنصر مصفوفة من الستاشة زائد I أنا بس مجرد
+
+297
+00:34:08,960 --> 00:34:15,300
+أوريه كمانأوريكمين العناصر بالنسبة لمثال رقم 4
+
+298
+00:34:15,300 --> 00:34:26,120
+مثال رقم 4 يقول consider the factor ring factor
+
+299
+00:34:26,120 --> 00:34:32,260
+ring
+
+300
+00:34:32,260 --> 00:34:36,940
+of Gaussian
+
+301
+00:34:41,160 --> 00:34:50,240
+integers دوسر الانتجار اللي هي z of I modulo ال
+
+302
+00:34:50,240 --> 00:34:55,800
+principle ideal generated by اتنين minus ال I اللي
+
+303
+00:34:55,800 --> 00:35:04,590
+هو بده يساوي كل العناصر A زائد B في Iزائد ال
+
+304
+00:35:04,590 --> 00:35:11,590
+principle ideals generated by 2 minus I بحيث ان ال
+
+305
+00:35:11,590 --> 00:35:22,390
+A و ال B موجودة في Z ال A و ال B موجودة في Z
+
+306
+00:35:22,390 --> 00:35:26,250
+بنحاول
+
+307
+00:35:26,250 --> 00:35:32,560
+ناخد بعض المعلومات المهمة في هذا الموضوعوهي
+
+308
+00:35:32,560 --> 00:35:39,980
+معلومات على غير العادة كيف كنت تاني احنا بنقول
+
+309
+00:35:39,980 --> 00:35:44,180
+الان اعطاني هذا ideal و اجري هذه ال factor ring
+
+310
+00:35:44,180 --> 00:35:49,000
+تبع جاوسيا كيف الشغل فيها مش عارفين لكن انت أعرف
+
+311
+00:35:49,000 --> 00:35:51,520
+على كيفية العمل داخل هذه ال ring
+
+312
+00:35:55,360 --> 00:35:59,860
+هذه ال ring لم تتواجد في الطبعات الأولى لهذا
+
+313
+00:35:59,860 --> 00:36:02,440
+الكتاب لا في الأولى ولا في الثانية ولا حتى في
+
+314
+00:36:02,440 --> 00:36:06,580
+السادسة ظهر هذا المثال في الطبعة السابعة وماكانش
+
+315
+00:36:06,580 --> 00:36:11,020
+موجود في الطبعات اللي قبلها طب نشوف كيف يكون الشغل
+
+316
+00:36:11,020 --> 00:36:16,700
+في هذا في هذا في هذه ال ring خلي بالك فيها الأن
+
+317
+00:36:16,700 --> 00:36:23,490
+أنا بدي أتسأل هل الأتنينناقص ال I موجودة في ال
+
+318
+00:36:23,490 --> 00:36:28,030
+principle ideal generated by اتنين minus ال I
+
+319
+00:36:28,030 --> 00:36:36,130
+موجودة ممتاز جدا يبقى معناه هذا الكلام ان اتنين
+
+320
+00:36:36,130 --> 00:36:42,210
+موجودة في هذا ال element هذا معناه ان ال اتنين
+
+321
+00:36:42,210 --> 00:36:49,170
+ناقص ال I زي ال principle ideal generated by اتنين
+
+322
+00:36:49,170 --> 00:36:54,870
+minus ال Iبتساوي زائد لـ 0 reference بال ID الـ
+
+323
+00:36:54,870 --> 00:37:00,050
+generated by 2 minus ال I فلو جماعة بصير معاه و
+
+324
+00:37:00,050 --> 00:37:06,630
+بضلش عندي اللي هاد يعني معنى هذا الكلام ان ال 2
+
+325
+00:37:06,630 --> 00:37:12,850
+minus ال I بتساوي 0 لإن ال left coset بتساوي left
+
+326
+00:37:12,850 --> 00:37:19,730
+coset يبقى 2 ناقص ال I بدها 0 داخل ال ring اللي
+
+327
+00:37:19,730 --> 00:37:27,670
+عندنا هذاطيب هذا معناته ان ال I بدها تساوي اتنين
+
+328
+00:37:27,670 --> 00:37:30,750
+ايش؟
+
+329
+00:37:30,750 --> 00:37:35,310
+I بده يساوي اتنين مالك انت؟ ايش اللي جريلك؟ ولا
+
+330
+00:37:35,310 --> 00:37:38,570
+جرينا ولا حاجة، احنا مش هيرمشنا، بس احنا بنشتغل
+
+331
+00:37:38,570 --> 00:37:43,230
+جبه، ماشتغلش real number لو بنتكلم في الأعداد
+
+332
+00:37:43,230 --> 00:37:48,560
+الحقيقية وانت مجنون، عدد تخيلي بساوي عدد حقيقيلهو
+
+333
+00:37:48,560 --> 00:37:53,320
+كل عدد حقيقي عبارة عن عدد تخيله إذا صار عندنا
+
+334
+00:37:53,320 --> 00:38:01,640
+اتنين زي اتنين بدها تساوي I الأدهة والارمر من ذلك
+
+335
+00:38:01,640 --> 00:38:07,080
+مش هيدي في بالك لو ربعنا طرف الشمال كده بيكون؟ سنة
+
+336
+00:38:07,080 --> 00:38:12,320
+واحدة وده كده ستة؟ اربعة يعني ايش؟ يعني خمسة كده
+
+337
+00:38:12,320 --> 00:38:15,140
+تساوي؟ ستة
+
+338
+00:38:17,870 --> 00:38:23,950
+على كل واحد لخطأ بدنا نغيّر عاجلنا احنا بنشتغلش في
+
+339
+00:38:23,950 --> 00:38:29,410
+real number بنشتغل في complex مظبوط ولا لا؟ اتنين
+
+340
+00:38:29,410 --> 00:38:33,770
+بنشتغل complex على جبر اتنين مع بعض مش أعداد
+
+341
+00:38:33,770 --> 00:38:37,730
+حقيقية، بلغة الأعداد الحقيقية ده كلام مش صحيح لو
+
+342
+00:38:37,730 --> 00:38:41,090
+جاء يقولوا لواحد خمسة يساوي صفر، يقولوا انت انجنت؟
+
+343
+00:38:41,090 --> 00:38:45,390
+خمسة يساوي صفر، يقولوا لأ ما انجنت، يعني كمال
+
+344
+00:38:45,390 --> 00:38:51,420
+العقل، والحمد للهطب هاي الشهادة انت عجلك بدك تطوع
+
+345
+00:38:51,420 --> 00:38:55,180
+لرنقل جديد انت بتشتغل ال real number لها عناصر و
+
+346
+00:38:55,180 --> 00:38:59,820
+ال complex لها عناصر اتنين ال complex انت بتشتغل
+
+347
+00:38:59,820 --> 00:39:05,880
+عليها جبه بقوله اه طيب مرة تانية هو العنصر هذا
+
+348
+00:39:05,880 --> 00:39:10,710
+موجود هنا انا بقوله صحيح بقوله ماشي موافقينطيب
+
+349
+00:39:10,710 --> 00:39:15,530
+يبقى هذا زائد ال principle ideal هو zero زائد ال
+
+350
+00:39:15,530 --> 00:39:19,410
+principle ideal هو ال principle ideal itself صار
+
+351
+00:39:19,410 --> 00:39:23,150
+left coset left coset يبقى هذا ال element يساوي
+
+352
+00:39:23,150 --> 00:39:27,570
+zero يبقى ال I يساوي اتنين داخل هذه الليط طيب انا
+
+353
+00:39:27,570 --> 00:39:34,230
+ورا بصير كلامنا غلط مش صحيح تمام طيب كويس ردعي
+
+354
+00:39:34,230 --> 00:39:38,370
+بصير I تربية معروف عندنا بسالب واحد في ال complex
+
+355
+00:39:38,820 --> 00:39:43,700
+يبقى سالف واحد ساوي أربع يبقى الخمسة بدها ساوي
+
+356
+00:39:43,700 --> 00:39:51,280
+زيرو خمسة تساوي زيرو very important لها ما بعدها
+
+357
+00:39:51,280 --> 00:39:57,220
+طيب احنا ادعينا ان ال element تبع ال ring اللي
+
+358
+00:39:57,220 --> 00:40:03,040
+عندنا هذا هو a زائد bi ك complete زائد ال
+
+359
+00:40:03,040 --> 00:40:08,020
+principal ideal generated by اتنين minus ال i تمام
+
+360
+00:40:08,470 --> 00:40:14,810
+قبل ما نبدأ نكمل بدنا نروح نثبتلكوا انه اي عمصر في
+
+361
+00:40:14,810 --> 00:40:19,730
+هذه ال ring بقدر اكتبه على دلالة constant زائد ال
+
+362
+00:40:19,730 --> 00:40:24,030
+principle ideal generated by اتنين minus ال a
+
+363
+00:40:24,030 --> 00:40:29,090
+تمام؟ نبينكوا كيف الشغل هذا طبعا بيطلعوا في بعض و
+
+364
+00:40:29,090 --> 00:40:33,370
+لا يقصروا شيء دعوة سكت
+
+365
+00:40:33,370 --> 00:40:37,350
+هل
+
+366
+00:40:37,350 --> 00:40:47,830
+يبقوا علامة؟Not bad.ظهر فيني ما ياتي.الآن
+
+367
+00:40:47,830 --> 00:40:53,910
+لو جيت تقول تلاتة زائد أربعة I زائد ل principle ID
+
+368
+00:40:53,910 --> 00:41:00,810
+generated by اتنين minus ال I.مش هذا عمصر موجود
+
+369
+00:41:00,810 --> 00:41:07,170
+هنا على الشكل هذا؟ هي اللي مافيش اعتراف.طيب احنا
+
+370
+00:41:07,170 --> 00:41:13,810
+طلعنا قبل قليل ان ال I جداش اتنين اما من هذا
+
+371
+00:41:13,810 --> 00:41:19,770
+الكلام ثلاثة زائد اربعة اتنين زائد ال principle I
+
+372
+00:41:19,770 --> 00:41:26,290
+D generated by اتنين minus اتنين اربعة تمانية
+
+373
+00:41:26,290 --> 00:41:31,650
+تمانية تمانية و تلاتة احداش احداش من جه هذا الكلام
+
+374
+00:41:31,650 --> 00:41:32,790
+احداش
+
+375
+00:41:49,350 --> 00:41:53,230
+ممتاز يبقى صح الفرنسيب ال ideal generated by 0
+
+376
+00:41:53,230 --> 00:41:58,250
+اللي هو 0 itselfكيف عوضت عن ال I ب اتنين و هدى؟
+
+377
+00:41:58,250 --> 00:42:07,470
+اللي لو حولتها بصير هذا هو العنصر الصفرى لأ مش
+
+378
+00:42:07,470 --> 00:42:10,850
+عاوض فيها، ال I اللي برا كيف عوضت عندها اتنين و هي
+
+379
+00:42:10,850 --> 00:42:14,490
+مش متمنية لل principle I كيف؟ احنا بنشتغل داخل ال
+
+380
+00:42:14,490 --> 00:42:19,210
+ring، داخل ال ring ال I باتنين صار عاديواني أخدت
+
+381
+00:42:19,210 --> 00:42:23,590
+العمصر من داخل ال ring إذا بدي أشيل الآي و أكتب
+
+382
+00:42:23,590 --> 00:42:28,190
+بدله اتنين ماحدش كله كلام عندي صح ولا لا يبقى
+
+383
+00:42:28,190 --> 00:42:34,250
+حطلها باتنين صار احداشر زائد اتنين ايه يبقى صار كل
+
+384
+00:42:34,250 --> 00:42:40,050
+عمصر في ال ring اللي أنا بقدر أكتبه على شكل
+
+385
+00:42:40,050 --> 00:42:46,570
+constant زائد ل principle ايه دي يبقى صار every
+
+386
+00:42:47,580 --> 00:42:57,360
+Element in اللي هو من Z of I Module ال principle
+
+387
+00:42:57,360 --> 00:43:07,480
+ID generated by A is written as ال A زي ال
+
+388
+00:43:07,480 --> 00:43:14,140
+principle ID generated by اتنين نقص ال I ال A هو
+
+389
+00:43:14,140 --> 00:43:23,660
+عبارة عن انتجاروالـ A is integer طيب
+
+390
+00:43:23,660 --> 00:43:32,800
+كويس بلاقا عليه ساعة لحد عشر زي ال principle ideal
+
+391
+00:43:32,800 --> 00:43:39,620
+generated by اتنين minus ال A بتساوي يا بنات واحد
+
+392
+00:43:39,620 --> 00:43:47,810
+زائد اتنين في خمسةزائد لـPrincipal Ideal Generated
+
+393
+00:43:47,810 --> 00:43:53,770
+By 2 Minus الـI. الخمسة في قداش؟ Zero في اتنين
+
+394
+00:43:53,770 --> 00:43:59,910
+بزيرو زائد واحد بواحد. يبقى النتيجة صارت واحد زائد
+
+395
+00:43:59,910 --> 00:44:06,470
+لـPrincipal Ideal Generated By 2 Minus الـI. إيش
+
+396
+00:44:06,470 --> 00:44:11,330
+أربعة؟ Order إلها يساوي أربعة عليه مش ومافيك.
+
+397
+00:44:11,910 --> 00:44:16,610
+والله أنا مافيك، الحين أقولكي.طب بنين عليه ان
+
+398
+00:44:16,610 --> 00:44:22,370
+تفتزع منه أربع تقدر يجيبها بطلتي صاروا خمسة ويمكن
+
+399
+00:44:22,370 --> 00:44:27,310
+يبطلوا يصيروا ستة مادة ما تبطلوا طيب يبقى سعر ال
+
+400
+00:44:27,310 --> 00:44:32,370
+elements of
+
+401
+00:44:32,370 --> 00:44:42,370
+اللي هو ال .. الشي اسمها اللي هو Z of Rموديولة لـ
+
+402
+00:44:42,370 --> 00:44:47,650
+principle ideal generated by I بسبب ساعة من
+
+403
+00:44:47,650 --> 00:44:57,330
+عناصرها Zero زائد اتنين minus ال I واحد زائد اتنين
+
+404
+00:44:57,330 --> 00:45:04,850
+minus ال I و اتنين زائد لـ principle ideal
+
+405
+00:45:04,850 --> 00:45:11,740
+generated و كذلك التلاتةالأربعة زائد ال principle
+
+406
+00:45:11,740 --> 00:45:17,740
+ideal generated by اتنين minus ال I وأكا principle
+
+407
+00:45:17,740 --> 00:45:24,660
+ideal والأربعة زائد ال principle ideal generated
+
+408
+00:45:24,660 --> 00:45:32,080
+by اتنين minus ال I أنا أزعم هه زعمها مش كلامير
+
+409
+00:45:32,080 --> 00:45:36,550
+مية المية لغاية ما نثبته انه مية الميةإن عناصر
+
+410
+00:45:36,550 --> 00:45:39,530
+هدول بس العناصر اللي عملناها.
+
+411
+00:45:42,950 --> 00:45:49,410
+خُد الآن، بدي أثبت إنه ماعنديش إلا العناصر الخمسة
+
+412
+00:45:49,410 --> 00:45:55,250
+هدول فقط، لا غير، كويس؟ إحنا العملية اللي عندنا زي
+
+413
+00:45:55,250 --> 00:46:00,140
+ما انت شايفها كلها عملية جامعةيبقى لو بدى احسب ال
+
+414
+00:46:00,140 --> 00:46:05,180
+order لل element في حالة الجامعة بنضرب ال element
+
+415
+00:46:05,180 --> 00:46:12,220
+في الرقم اللى بنزعم انه ربما يكون هو ال order لو
+
+416
+00:46:12,220 --> 00:46:19,360
+جينا قولنا لك consider هديلي خمسة في الرقم اللى
+
+417
+00:46:19,360 --> 00:46:26,150
+طلع عندنا هذا عشواء اشتغلنا طلعاللي هو تلاتة زايد
+
+418
+00:46:26,150 --> 00:46:31,630
+أربعة I زايدها يساوي واحد زايدها تمام؟ لو جيت
+
+419
+00:46:31,630 --> 00:46:36,890
+قولتلك خديلي خمسة في واحد زايد ال principle ideal
+
+420
+00:46:36,890 --> 00:46:43,990
+generated by اتنين minus ال A يبقى هذا الكلام بده
+
+421
+00:46:43,990 --> 00:46:50,030
+يساوي خمسة في واحد خمسة زايد ال principle ideal
+
+422
+00:46:50,030 --> 00:46:57,490
+فالخمسة بيجي دي Zeroيبقى هذا الكلام بده يساوي Zero
+
+423
+00:46:57,490 --> 00:47:02,330
+زاد ال principle ideal generated by اللي هو ال
+
+424
+00:47:02,330 --> 00:47:09,510
+principle ideal generated by I فبناء عليه، قداش ال
+
+425
+00:47:09,510 --> 00:47:18,190
+order لهذا؟ خمسة وقد يكون أقل من خمسة صح ولا لأ؟
+
+426
+00:47:18,370 --> 00:47:22,650
+يبقى ال order لل element اللي احنا بيقول أقل عدد
+
+427
+00:47:22,650 --> 00:47:27,630
+صحيح بحطه أس لل element ليعطيني ال identity صح ولا
+
+428
+00:47:27,630 --> 00:47:33,490
+لأ؟ هيك أخدناه في ال groups صح؟ يبقى هنا أنا أخدته
+
+429
+00:47:33,490 --> 00:47:37,510
+أضرب اللي هو طلع مين طلع ال zero element يبقى ال
+
+430
+00:47:37,510 --> 00:47:42,210
+order يا خمسة يا شغلة تانية طب بدي أشوف مين الشغلة
+
+431
+00:47:42,210 --> 00:47:49,210
+التانية أليس هذا هو هذا؟ كدهش ال order لهذا؟وحد
+
+432
+00:47:49,210 --> 00:47:54,210
+وحد وحد يبقى ال order صار للواحد زائد التانية اما
+
+433
+00:47:54,210 --> 00:47:59,350
+واحد يا اما خمسة لأن هذا ال element يكافئ ال
+
+434
+00:47:59,350 --> 00:48:03,290
+element هذا تماما هذا ال order اللي يساوى واحد
+
+435
+00:48:03,290 --> 00:48:08,790
+يبقى ال order اما واحد واما خمسة يبقى هذا بدي
+
+436
+00:48:08,790 --> 00:48:17,470
+اعطينا ان ال order للواحد زائد اتنين minus ال one-
+
+437
+00:48:17,470 --> 00:48:24,630
+I بد يساوي واحد or خمسة طيب إذا استبعدنا الواحد يا
+
+438
+00:48:24,630 --> 00:48:32,110
+بنات؟ ماظنش إلا مين؟ إذا ال order يساوي خمسة وإذا
+
+439
+00:48:32,110 --> 00:48:36,210
+ال order يساوي خمسة وعدد العناصر في ال ring اللي
+
+440
+00:48:36,210 --> 00:48:41,410
+كاتبينه خمسةيبقى بالفعل هذا الكلام يكون generator
+
+441
+00:48:41,410 --> 00:48:47,630
+وبالتالي ماعنديش إلا الخمسة عناصر هذه فقط غابة طب
+
+442
+00:48:47,630 --> 00:48:51,930
+ليش مستبعد الواحد؟ فاستنى شوية نشوفوا مهوطة كم
+
+443
+00:48:51,930 --> 00:48:55,470
+order فينا ال element؟ واحد طبعا ليش الواحد مش
+
+444
+00:48:55,470 --> 00:48:58,750
+واحد؟ قيمة واحدة، عددية، يبقى ده استبعدنا واحدة،
+
+445
+00:48:58,750 --> 00:49:03,950
+بتثبت التالية، مظبوط؟ طيب تعالى نشوف كيف قلنا ممكن
+
+446
+00:49:03,950 --> 00:49:13,180
+نستبعد الواحد، فبروح بقولهif ال order لمن؟ للواحد
+
+447
+00:49:13,180 --> 00:49:19,240
+زائد ال principle ideal generated by اتنين زائد I
+
+448
+00:49:19,240 --> 00:49:27,800
+يساوي واحد كويس؟ يبقى then الواحد
+
+449
+00:49:27,800 --> 00:49:33,360
+في الواحد زائد ال principle ideal generated by
+
+450
+00:49:33,360 --> 00:49:44,990
+اتنين-I بده يساوي 2-I يعني صار الواحد زي ال
+
+451
+00:49:44,990 --> 00:49:53,910
+principle ideal generated بده يساوي 2-I هذا الكلام
+
+452
+00:49:53,910 --> 00:50:00,410
+صحيح معناته ان الواحد موجود في ال principle ideal
+
+453
+00:50:00,410 --> 00:50:09,730
+generated by 2-Iطيب مدام واحد طب هذا عناصره
+
+454
+00:50:09,730 --> 00:50:16,570
+element من ال ring الأصلية مضروف element من هنا صح
+
+455
+00:50:16,570 --> 00:50:23,890
+ولا لا؟ يبقى هذا معناه إيش؟ معناته أن الواحد هذا
+
+456
+00:50:23,890 --> 00:50:30,120
+بده يساوي element من ال ring الأصليةمع الإثنين
+
+457
+00:50:30,120 --> 00:50:38,840
+ناقص I في مين؟ في الـ A زائد بي R سجة
+
+458
+00:50:38,840 --> 00:50:46,220
+الشعور الواحد موجود هنا صح؟ هذه من عناصرها ال
+
+459
+00:50:46,220 --> 00:50:51,800
+principle هذه بدي أجيب element من R و أضربه في
+
+460
+00:50:51,800 --> 00:50:57,320
+مين؟ في اللي هو ال element اللي عندنا هذا صح ولا
+
+461
+00:50:57,320 --> 00:51:04,040
+لا؟ماذا تعريف ال principle ideal generated by A؟
+
+462
+00:51:04,040 --> 00:51:08,820
+مش AR صحيح نايت ال R موجود في R يعني جبنا element
+
+463
+00:51:08,820 --> 00:51:13,440
+من R و جبنا element من A و ضربناهم في بعض أنا عندي
+
+464
+00:51:13,440 --> 00:51:18,600
+الواحد موجود في ال ring اللي عندنا هذه صح ولا لأ؟
+
+465
+00:51:18,600 --> 00:51:22,940
+مدام الواحد موجود في اللي جاخد في ال ideal الواحد
+
+466
+00:51:22,940 --> 00:51:28,280
+موجود في ال idealيبقى الواحدة دي حيث ويحصل ضرب
+
+467
+00:51:28,280 --> 00:51:35,060
+element من هنا في element من ال ring صح ولا لا؟
+
+468
+00:51:35,060 --> 00:51:43,600
+مصبوط؟ يبقى بالبناء العليه بتسوى وهاديها for some
+
+469
+00:51:43,600 --> 00:51:53,470
+ال a زائد bi اللي موجودة في z of i تمام؟بدنا نضرب
+
+470
+00:51:53,470 --> 00:52:03,150
+هدول في بعض يبقى هذا الكلام بيساوي 2A زائد B زائد
+
+471
+00:52:03,150 --> 00:52:15,010
+زائد هذه بيصير عند اللي في I يبقى هذه 2B اتنين بيه
+
+472
+00:52:15,010 --> 00:52:23,080
+وناقص ال A كل هذا الكلام في ال I بيساوي واحدهذا
+
+473
+00:52:23,080 --> 00:52:29,140
+سيقودنا إلى معادلتين المعادلة الأولى 2A زائد B
+
+474
+00:52:29,140 --> 00:52:35,280
+يساوي واحد والتانية 2B ناقص ال A بده يساوي Zero
+
+475
+00:52:35,280 --> 00:52:39,260
+لإن ال real بده يساوي ال real و ال complex بده
+
+476
+00:52:39,260 --> 00:52:43,200
+يساوي ال complex ماعنديش جهدك ب Zero طيب نحل
+
+477
+00:52:43,200 --> 00:52:49,240
+المعادلة هذه هذا بده يعطينا 2A زائد B يساوي واحد
+
+478
+00:52:49,240 --> 00:52:55,120
+وهذه بتضربها في اتنينيبقى أربعة B نقص اتنين A
+
+479
+00:52:55,120 --> 00:53:00,580
+يساوي Zero أجمع هذه و هذه بروحوا مع بعض بظل عندنا
+
+480
+00:53:00,580 --> 00:53:08,940
+مين؟ أربعة B قبل خمسة B خمسة اللي هو B تساوي
+
+481
+00:53:08,940 --> 00:53:17,200
+الواحد يبقى ال B تساوي كدهش؟ كدهش؟ واحد على خمسة
+
+482
+00:53:17,200 --> 00:53:22,350
+طب اللي هو ال B و اين موجودة هدول؟to z يبقى هذا
+
+483
+00:53:22,350 --> 00:53:28,370
+does not belong to z يبقى ال order يساوي واحد كلام
+
+484
+00:53:28,370 --> 00:53:35,670
+غلط مش صحيح انه قادني الى نتيجة خاطية يبقى ساعة ال
+
+485
+00:53:35,670 --> 00:53:41,010
+order لواحد زي ال principle ideal generated لا
+
+486
+00:53:41,010 --> 00:53:47,550
+يمكن ان يساوي الواحد هذا معناتهإن ال order للواحد
+
+487
+00:53:47,550 --> 00:53:54,370
+زي اتنين ناقص I بده يسوي خمسة وعدد العماصر هنا
+
+488
+00:53:54,370 --> 00:53:58,250
+كتبناهم طلع خمسة إذا لا يمكن لهذا اللي يكون
+
+489
+00:53:58,250 --> 00:54:07,730
+generator ومافيش غيرهم يبقى هنا therefore ولهذا
+
+490
+00:54:07,730 --> 00:54:16,300
+اللي هو ال .. هذه مش واحد يا بنات هذه واحدهنا نوعا
+
+491
+00:54:16,300 --> 00:54:22,060
+يبقى therefore الواحد زي ال principle ideal
+
+492
+00:54:22,060 --> 00:54:33,740
+generated by اتنين minus ال I is a generator يبقى
+
+493
+00:54:33,740 --> 00:54:41,700
+هدفه يعطينا ان ال order لمين لزد of I مدير ال
+
+494
+00:54:41,700 --> 00:54:48,290
+principle ideal generatedباعي هذا بيسوي خمسة عناصر
+
+495
+00:54:48,290 --> 00:54:56,390
+تبع زعمنا قبل قليل يبقى هذه خمسة عناصر فقط زاغية
+