
leonhard euler

graph sidhaanthatheyum topology kurichulla padanangal sthaapikkukayum vishakalana samkhyaasampradaayam, sankeernamaaya vishakalanam, ananthamaaya calculus thudangiya ganithashaasthrathinte mattu pala shaakhakalilum munnirayilullathum swaadheenamullathumaaya kandethalukal nadathukayum cheytha oru swis ganithashaasthranjanum bhauthikashaasthranjanum jyothishaasthranjanum bhoomishaasthranjanum yukthivaadiyum enchineeyarumaayirunnu leonhard euler (,; 15 epril 1707-18 septambar 1783). ganithashaasthraparamaaya pravartthanam enna ashayam ulppede aadhunika ganithashaasthra padangalum notteshanum addeham avatharippichu. mechanics, fluid dynamics, optiks, jyothishaasthram, sangeetha sidhaantham ennivayile pravarthanangaliloodeyum addeham ariyappedunnu.
charithratthile ettavum mikacha ganithashaasthranjaril oralaayum pathinettaam noottaandile ettavum mikacha ganithashaasthranjanaayum euler kanakkaakkappedunnu. yoolarude maranashesham avarude srishtikal nirmmicha niravadhi mahanaaya ganithashaasthranjar eee mekhalayile addehathinte praadhaanyam thiricharinju, avaril palarudeyum udharanikal kaanikkunnu piyari-saiman laplace ganithashaasthrathil yoolarude swaadheenam prakadippikkunnu "euler vaayikkuka, euler vaayikkuka, addeham namukkellavarkkum maastaraanu."kaal friedrich gass ezhuthi" "yoolarude kruthikalekkurichulla patanam ganithashaasthrathinte vividha mekhalakalkku ettavum mikacha vidyaalayamaayi thudarum, mattonnum athinu pakaramavilla"."euler ettavum samriddhamaayi kanakkaakkappedunnu; addehathinte 866 prasidheekaranangalum kathidapaadukalum" "oormmiya leonhard euler" "enna oopparayil shekharichittundu, athu poortthiyaakumbol 81" "kwarto" "vaalyangal adangiyirikkum". thante praayapoorthiyaaya jeevithathinte bhooribhaagavum addeham chelavazhichathu russiayile sent peettezhsbargilum annathe prashyayude thalasthaanamaaya berlinilumaanu.
oru vrithathinte chuttalavinte vyaasathinte anupaathathe soochippikkunnathinaayi greak akshara soothravaakyam _ 1 (lovercase paii) janapriyamaakkiyathinte bahumati yoolarinund, athupole thanne aadyam oru functionte moolyathinu notteshan soothravaakyam _ 2, saangalppika yoonit soothravaakyam _ 4 prakadippikkaan akshara soothravaakyam _ 3, samgrahangal prakadippikkaan greak akshara soothravaakyam _ 5 (kyaapittal sigma), parimithamaaya vyathyaasangalkk greak akshara soothravaakyam _ 6 (uppercase deltta), konukale valia aksharangalayi prathinidheekarikkunna oru trikonatthinte vashangale prathinidheekarikkunna cheria aksharangal enniva upayogichathinte bahumati addehathinundu. ippol euler nambar ennariyappedunna swaabhaavika logaritham adisthaanamaaya sthiramaaya soothravaakyathinte nilavile nirvachanam addeham nalki.
graph sidhaanthathinte aadya pariseelakan koodiyaayirunnu euler (conigsburghile ezhu paalangalude prashnathinulla parihaaramaayi). mattu pala nettangalkkumoppam, basel prashnam pariharikkunnathilum, squared intejar resiprocalukalude ananthamaaya shreniyude aakethuka krithyamaayi thulyamaanennu theliyichathilum, oru polyhedroninte konukaludeyum mukhangaludeyum koottatthinte koottam mainus arikukal 2 nuu thulyamaanennu kandethiyathilum addeham prashasthanaayi. bhauthikashaasthra mekhalayil, karkkashamaaya vasthukkalude chalanam nannayi vishadeekarikkunnathinaayi euler thante rund vaalyangalulla kruthiyaaya "mechanica" yill nyoottante bhauthikashaasthra niyamangal puthiya niyamangalayi parishkarichu. kharavasthukkalude ilaastik vaikalyangalekkurichulla padanatthinum addeham ganyamaaya sambhavanakal nalki.
aadyakaala jeevitam.
1707 epril 15 nuu swittsarlandile basalil parishkaricha sabhayile paastaraaya pooll moonnaaman yoolarinum klaasikkukalile niravadhi prashastha pandithanmaar ulppetta margaraittinteyum (brucker) makanayi leonhard euler janichu. anna maria, maria magdalana ennee rund ilaya sahodarimaarum johann heinrich enna oru ilaya sahodaranumulla naalu makkalil moothayaalaayirunnu addeham. leonhardinte jananathinu thottupinnaale, euler kudumbam basalil ninnu swittsarlandile raine pattanatthilekku thamasam maari, avide pithaav praadeshika palliyil paastaraayi leonhard thante kuttikkaalatthinte bhooribhaagavum chelavazhichu.
cheruppam muthal thanne, kurachu varshangalkk munbu bassel sarvakalashaalayil jacob bernauliyil ninnu kozhsukal edutha pithaavil ninnu ganithashaasthrathil school vidyaabhyaasam nedi. ettaam vayassil, yoolarine muthasshiyude veettil thamasikkaan ayaykkukayum basalile laattin schoolil cherukayum cheythu. koodaathe, ganithashaasthrathil atheeva thaalpparyamulla yuva daivashaasthranjanaaya johannes burkhardil ninnu addehathinu swakaarya tution labhichu.
1720-ll, pathimoonnaam vayassil, euler basal sarvakalashaalayil chernnu. ithrayum cheruppatthil sarvakalashaalayil cherunnathu akkaalat asaadhaaranamaayirunnilla. maricha jacob bernauliyude (yoolarude pithaavine padippicha) ilaya sahodaran johann bernauliyaanu praadhamika ganithashaasthra kozhs nalkiyathu. johann bernauliyum euler taamasiyaathe parasparam nannayi arian thudangi. euler thante aathmakadhayil bernauliye vivarichittundu
eee samayathaan bernauliyude pinthunayode euler oru paasttarin pakaram oru ganithashaasthranjanaakaan pithaavinte sammatham nediyathu.
1723-ll, rene descartesinteyum isak nyoottaninteyum thathwachinthakale thaarathamyam cheiyunna oru prabandhathode ularinu thathwachinthayil oru maasttar labhichu. pinneedu addeham basal sarvakalaashaalayile daivashaasthra faakkalttiyil chernnu.
1726-ll, euler shabdathinte prachaaranathekkurichulla oru prabandham "dii sono" enna thalakkettode poortthiyaakki, athil addeham basal sarvakalashaalayil oru sthaanam nedaan parajayappettu. 1727-ll addeham aadyamaayi paarees akkadami sammana malsarathil (1720-ll aarambhicha akkadami prathivarshavum pinneedu dvivarshavum vaagdaanam cheiyunnu) praveshichu. kappalil maastukal sthaapikkaanulla ettavum nalla maargam kandethuka ennathaayirunnu aaa varsham uyarnnuvanna prashnam. naavika vaasthuvidyayude pithaav" ennariyappettirunna piyari bogger vijayichu, euler randaam sthaanathethi. varshangalolam, euler 15 thavana eee malsarathil praveshichu, athil 12 ennam nedi.
currier.
sent peettezhsburg.
johann bernauliyude rund aanmakkalaaya danielum nicolas 1725-ll sent peettezhsbargile imperial russian akkadami oof sciencesil sevanathil praveshichu, avar labhyamaakumbol oru thasthikayilekku addehathe shupaarsha cheiyumennu ularinu urappu nalki. 1726 juulai 31nuu russiayil oru varshathil thaazhe samayam chelavazhicha nicolas appendicitis baadhichu marichu. danielle ganithashaasthram/bhauthikashaasthram vibhaagathil sahodarante sthaanam etteduthappol, thaan ozhinjukidanna physiologyile tasthika thante suhruthu euler nikathanamennu addeham shupaarsha cheythu. 1726 novemberil, euler eee vaagdaanam aakaamkshayode sweekarichu, pakshe bassel sarvakalashaalayil physics professorshipinu apekshichappol sent peettezhsbargilekkulla yaatra vaikippichu.
1727 meyy maasathil euler sent peettezhsbargil ethi. academyude medical vakuppile juuniyar thasthikayil ninnu ganithashaasthra vibhaagathile oru sthaanathekku sthaanakkayattam labhichu. addeham danielle bernauliyumaayi adutha sahakaranathode jolie cheythu. euler russian bhashayil praaveenyam nedukayum sent peettezhsbargil sthirathaamasamaakkukayum russian navikasenayil vaidyanaayi oru adhika jolie ettedukkukayum cheythu.
peettar dhii grettu sthaapicha sent peettezhsbargile akkadami russiayile vidyaabhyaasam mechappeduthunnathinum padinjaaran europpumaayulla shaasthreeya vidavu nikathunnathinum uddeshichullathaayirunnu. thalphalamaayi, eularineppolulla videsha pandithanmaarkk ithu prathyekichum akarshakamaakki. antharicha bharthaavinte purogamana nayangal thudarnna academyude sahayiyaaya catherine onnaaman, euler sent peettezhsbargilethunnathu munbu marichu. panthrand vayassulla peettar randaamante aarohanathode russian yaadhaasthithika prabhukkanmaar adikaaram nedi. academyude videsha shaasthranjare samshayicha prabhukkanmaar, yoolarinum sahapravarthakarkkumulla dhanasahayam vettikkuraykkukayum videsha, aristokratik vidyaarthikalude jimneshyathilekkum sarvakalaashaalakalilekkum praveshanam thadayukayum cheythu.
1730ll peettar randaamante maranashesham sthithigathikal alpam mechappedukayum russiayile jarmman swaadheenamulla anna adhikaaramelkkukayum cheythu. euler academyile raankukaliloode athivegam uyarukayum 1731-ll bhauthikashaasthra professoraayi niyamikkappedukayum cheythu. leftanantaayi sthaanakkayattam nirasichu addeham russian navikasena vittu. rund varshathinu sesham, sent peettezhsbargil thaan neritta sensorshippilum shathruthayilum madutha danielle bernauli basalilekku pooyi. ganithashaasthravibhaagathinte thalavanayi euler addehathinte pingamiyaayi. 1734 januvariyil addeham jorg jisellinte makalaaya catherina jisel (1707-1773) neey vivaham kazhichu. 1740-ll puthuthayi sthaapithamaaya berlin academyil yoolarude sevanangalkkayi recruit cheyyaan frederic randaaman shramichuvenkilum euler thudakkathil sent peettezhsbargil thamasikkaan eshtappettu. ennaal anna chakravarty marichathinushesham frederic randaaman 1600 iii. sii. yuu (russiayil euler sambaadichathinu thulyamaayathu) nalkaan sammathikkukayum addeham berlinilekk marran sammathikkukayum cheythu. 1741-ll, kaazhchaykk mithamaaya kaalavastha aavasyamaanennu vaadichu addeham berlinilekk pookaan anumathi abhyarthichu. russian akkadami athinte sammatham nalkukayum athinte sajeeva amgangalil oralaayi prathivarsham 200 rubles nalkukayum cheythu.
berlin.
russiayile thudarchayaaya prakshubdhathayekkurichu aashankaakulanaaya euler sent. 1741 juunil peettezhsburg berlin academyil oru tasthika ettedukkaan, athu prashyayile mahanaaya frederic addehathinu vaagdaanam cheythirunnu. addeham 25 varsham berlinil thaamasichu, avide addeham noorukanakkinu lekhanangal ezhuthi. 1748-ll "aamukham analysine infinittoram" enna peril pravarthanangalekkurichu addehathinte paatam prasidheekarikkukayum 1755-ll deferential kaalkkulasinekkurichula "institutions kalkuli differentialis" enna oru paatam prasidheekarikkukayum cheythu. 1755ll royal sweedish akkadami oof sciencesilum franch akkadami oof sciencesilum videsha amgamaayi thiranjedukkappettu. berlinile yoolarinte sradheyamaaya vidyaarthikalil stepaan rumovsky ulppedunnu, pinneedu aadyathe russian jyothishaasthranjanaayi kanakkakkappettu. 1748-ll aduthide marichupoya johann bernauliyude pingamiyaayi basal sarvakalashaalayil ninnulla oru vaagdaanam addeham nirasichu. 1753ll addeham charlottenbergil oru veedu vaangi, athil addeham kudumbathodum vidhavayaya ammayodum oppam thaamasichu.
unhault-desoyude rajakumary frederikkinte anantharavalumaaya brandenberg-shwedinte friederic chaarlottinte adthyaapakanaayi euler maari. 1760-kalude thudakkathil addeham avarkk 200-ladhikam kathukal ezhuthi, avaa pinneedu "prakrithi thathwachinthayile vividha vishayangalekkurichulla oormmappeduthal kathukal" enna peril oru jarmman rajakumari abhisambodhana cheyth oru vaalyamaayi samaaharichu. bhauthikashaasthravum ganithashaasthravumaayi bandhapetta vividha vishayangalekkurichulla yoolarude vivaranam ulkkollunna eee kruthi yoolarude vyakthithvatheyum mathavishwaasangaleyum kurichu vilapetta ulkkazhchakal nalki. ithu onniladhikam bhaashakalilekku vivarthanam cheyyappedukayum europiludaneelam amerikkayilum prasidheekarikkappedukayum addehathinte ganithashaasthra kruthikalekkaal vyaapakamaayi vaayikkappedukayum cheythu. aksharangalude" janapreeti shaasthreeya karyangal oru saadhaarana prekshakarumaayi phalapradamaayi ashayavinimayam nadathaanulla yoolarude kazhivinu saakshyam vahikkunnu, ithu oru samarppita gaveshana shaasthranjante apoorva kazhivaanu.
academyude antassinu euler nalkia aparamaaya sambhaavanakalum athinte president sthaanathekkulla sthaanaarthiyaayi jeane leeii rondu dii alambert munnottuvachenkilum frederic randaaman athinte presidentaayi svayam namakaranam cheythu. prussian rajaavinu thante kottaaratthil budhijeevikalude oru valia sarkkil undaayirunnu, ganithashaasthranjane aadhunikanallaathavanum akkangalkkum akkangalkkum atheethamaaya kaaryangalil arivillaathavanumaayi addeham kandethi. nilavilulla saamoohika kramatheyo parambaraagatha vishwaasangaleyo orikkalum chodyam cheyyaatha lalithavum bhakthiyullathumaya oru mathavishwaasiyaayirunnu euler. frederikkinte kottaaratthil uyarnna anthass aasvadichirunna addeham pala tharatthil volteyarinte vipareethamaayi pravarthichu. euler oru vidagdha samvaadakanallathathinaal thanikk adhikam ariyaatha vishayangal tharkkikkunnath palappozhum volteyarinte budhiyude pathiv lakshyamakki. frederic yoolarude praayogika enchiniyaring kazhivukalil nirasha prakadippikkukayum paranju
berlinile thante thaamasatthiludaneelam, sent euler academyumaayi sakthamaaya bandham nilanirtthi. peettezhsburg russiayil 109 prabandhangal prasidheekarikkukayum cheythu. sent vidyaarthikaleyum addeham sahayichu. peettezhsburg academy chilappol russian vidyaarthikaleyum berlinile addehathinte veettil thaamasippichirunnu. 1760ll, ezhu varshathe yuddham pottippurappettathode, russian sainyathe munnott kondupoyi charlottenbergile yoolarude phaam kollayadikkappettu. eee sambhavathekkurichu arinja general ivan petrovich saltikov yoolarude estettinu sambhavicha naashanashtatthinu nashtapariharam nalki, russiayile chakravarthini elisabath pinneedu 4000 rubles koodi nalki-akkaalathe amithamaya thuka. 1766ll berlin vittu russiayilekku madangaan euler theerumaanichu.
berlin varshangalil (1741-1766), euler thante uthppaadanakshamathayude unnathiyilaayirunnu. addeham 380 kruthikal rachichu, athil 275 ennam prasidheekarikkappettu. berlin academyile 125 oormmakkurippukalum sent berlin academyilekku ayacha nooriladhikam oormmakkurippukalum ithil ulppedunnu. addehathe amgamaayi nilanirthukayum vaarshika stipend nalkukayum cheytha peettezhsburg akkadami. 1748-ll yoolarude "aamukham analysine infinittoram" rund bhagangalaayi prasidheekarichu. swantham gaveshanathinu purame, library, nireekshanaalayam, botanical garden, akkadami varumanam nediya kalandarukaludeyum bhoopadangaludeyum prasidheekaranam ennivayude melnottam euler vahichu. raajaavinte venalkkaala kottaramaaya sansochiyile jaladhaarakalude roopakalppanayil polum addeham earppettirunnu.
russia enna thaalilekku madanguka.
catherine dhii grettu simhaasanathileriyathinushe russiayile rashtreeya sahacharyam sthiratha kaivarichu, athinaal 1766-ll euler sent lekkulla madakkathinulla kshanam sweekarichu. peettezhsburg akkadami. 3000 rubles vaarshika shambalam, bhaaryaykk pension, makkalkk uyarnna raankilulla niyamanangal enniva vaagdaanam cheythukondu addehathinte avasthakal valare amithamaayirunnu. sarvakalashaalayil addehathe sahaayichath addehathinte vidyaarthi aandezhs johann lexalaanu. sent. 1771-leeii peettezhsburg theepidutthatthil addehathinte veedu nashichu.
vyakthiparamaaya jeevitam.
1734 januvari 7nuu addeham sent peettezhsbargile akkadami jimneshyathile chithrakaaranaaya jorg gsellinte makalaaya catherina gselline (1707-1773) vivaham kazhichu. yuvadambathikal neva nadiyude theerathu oru veedu vaangi.
avarude pathimoonnu makkalil moonnu aanmakkalum rund penmakkalum ulppede anchu perr maathramaan kuttikkalam athijeevichathu. avarude aadya makan johann aalbrekt euler aayirunnu, addehathinte godfather kristhyan goldback aayirunnu.
1773-ll bhaaryayude maranathinu moonnu varshathinu sesham, euler avarude ardhasahodariyaaya salomi abigale jisel (1723-1794) neey vivaham kazhichu. 1783ll addehathinte maranam vare eee vivaham thudarnnu.
addehathinte sahodaran johann heinrich sent. 1735ll peettezhsburg academyil chithrakaaranaayi jolie cheythu.
kaazhchashakthi kurayunnu.
ganithashaasthrajeevithathilas yoolarude kaazhchashakthi vashalayi. 1738-ll, panii baadhichu ekadesham moonnu varshathinu sesham, addeham thante valath kannin eathaandu andhanayi. thaan avatharippicha cartography sent ennu euler kuttappedutthi. addehathinte avasthayekkurichu peettezhsburg akkadami, pakshe addehathinte andhathayude kaaranam oohaapohangalude vishayamaayi thudarunnu. germmaniyile thaamasatthiludaneelam yoolarude kannile kazhcha moshamaayathode frederic addehathe "cyclops" ennu vilichirunnu. thante kazhcha nashtappedunnathinekkur euler abhiprayappettu, "ippol enikku shradha vyathichalikkal kuravaayirikkum."1766ll addehathinte idathu kannil oru timiram kandethi. thimiratthinte kidakka thaalkkaalikamaayi kazhcha mechappeduthiyenkilum, sankeernathakal aathyanthikamayi idathu kannilum addehathe eathaandu poornnamaayum andhanakki. ennirunnaalum, addehathinte avastha addehathinte uthppaadanakshamathaye kaaryamaayi baadhichillennu thonni. thante ezhuthukaarude sahaayathode, padanatthinte pala mekhalakalilum yoolarinte uthppaadanakshamatha vardhichu; 1775-ll addeham oro aazhchayum sharashari oru ganithashaasthra prabandham nirmmichu.
maranam.
sent. 1783 septambar 18 nuu peettezhsburg, kudumbathodoppam uchabhakshanathinu sesham, puthuthayi kandethiya euranus grahathekkurichum athinte bhramanapathathekkurichum aandezhs johann lexalumaayi charcha cheyyave addeham thalachorile rakthasraavathe thudarnnu kuzhanjuveenu marichu. russian akkadami oof sayansinu vendi oru hraswa anushochanam ezhuthukayum yoolarude shishyanmaril oralaaya russian ganithashaasthranjanaaya nicolas phas kooduthal vishadamaaya oru sthuthilekhanam ezhuthukayum athu addeham oru smaaraka yogathil nalkukayum cheythu. franch academy prashamsichukondu franch ganithashaasthranjanum thathwachinthakanumaaya markvis dii contorsettu ezhuthi
vasiliyevsky dveepile smollensk lutheran semitheriyil kaatharinaykk sameepam yoolarine samskarichu. 1837-ll russian akkadami oof sciences addehathinte valarnnukidakkunna shavakudeera phalakathinu pakaram oru puthiya smaarakam sthaapichu. 1957ll yoolarude 250-aamm janmavaarshikathodanubandhi addehathinte shavakudeeram alexander nevsky aashramathile lazarevsko semitheriyilekku maatti.
ganithashaasthrathilum bhauthikashaasthrathilum sambhavanakal.
jyamiti, ananthamaaya calculus, trikonamithi, beejaganitam, samkhya sidhaantham, thudarchayaaya bhauthikashaasthram, chandra sidhaantham, bhauthikashaasthrathinte mattu mekhalakal ennivayulppede ganithashaasthrathinte mikkavarum ellah mekhalakalilum euler pravarthichu. ganithashaasthra charithratthile oru pradhana vyakthiyaan addeham; achadikkappettaal, adisthaana thaalpparyamulla addehathinte kruthikalil palathum 60 muthal 80 kwarto vaalyangal vare ulkkollum. yoolarude peru niravadhi vishayangalumayi bandhappettirikkunnu. 1725 muthal 1783 vare prathivarsham sharashari 800 pejukalulla yoolarude kruthikalum 4500-ladhikam kathukalum noorukanakkinu kayyezhuthuprathikalum addeham ezhuthiyittundu. pathinettaam noottaandil ganitham, bhauthikashaasthram, mechanics, jyothishaasthram, naavigeshan ennivayile samyojitha aouttputtinte naalilonn leonard euleraanu rachichathennu kanakkaakkappedunnu.
ganithashaasthraparamaaya notteshan.
euler thante niravadhi, vyaapakamaayi pracharikkappedunna paatapusthakangaliloode niravadhi notteshanal kanvenshanukal avatharippikkukayum janapriyamaakkukayum cheythu. ettavum shradheyamaayi, addeham oru function enna ashayam avatharippikkukayum "x" enna vaadathil prayogikkunna "f" functione soochippikkunnathinu "f" ("x") ezhuthiya aadya vyakthiyaan. trikonamitheeya pravarthanangalkkulla aadhunika notteshan, swaabhaavika logarithathinte aditharaykkulla aksharam (ippol yoolarude nambar ennum ariyappedunnu), yogangalkkulla greak aksharam σ, saangalppika yoonittine soochippikkunnathinul aksharam ennivayum addeham avatharippichu. velsh ganithashaasthranjanaaya vilyam jonsil ninnaan ithu uthbhavichathenkilum oru vrithathinte chuttalavum vyaasavum thammilulla anupatham soochippikkaan greak aksharamaaya "π" upayogichathum euler janapriyamakki.
vishakalanam.
18-aamm noottaandile ganithashaasthra gaveshanathil ananthamaaya kaalkkulasinte vikasanam munpanthiyilaayirunnu, koodaathe eee mekhalayile aadyakaala purogathikku kaaranam bernaulis-yoolarinte kudumbasuhrithukkal-aayirunnu. avarude swaadheenathaal, calculus padikkunnathu yoolarude kruthiyude pradhana kendramaayi maari. ganithashaasthrathinte kaadinyatthinte aadhunika maanadandangal (prathyekichu beejaganithatthinte saamaanyathayude thathwathe addeham aashrayikkunnath) yoolarude chila thelivukal sweekaaryamallengilum, addehathinte ashayangal niravadhi valia purogathikku kaaranamaayi.
oolar thante pathiv upayogathinum power seereesinte vikasanathinum vishakalanathil ariyappedunnu, functionukalude aavishkaaram ananthamaaya niravadhi padangalude thukayayi, udaaharanathina
soothravaakyam _ 8
1735-ll prashasthamaaya basal prashnam pariharikkan yoolarude power seerees upayogam addehathe praapthanakki (1741-ll addeham kooduthal vishadamaaya oru vaadam nalki):
formula _ 9
addeham sthiratha avatharippichu
soothravaakyam _ 10
ippol ulers konsttant allengil euler-masheroni konsttant ennariyappedunnu, koodaathe harmonic seerees, gaama function, riman seetta functionte moolyangal ennivayumaayulla athinte bandham padichu.
vishakalana thelivukalil exponential function logaritham upayogikkunnathum euler avatharippichu. power seerees upayogichu vividha logaritham functionukal prakadippikkaanulla vazhikal addeham kandethi, koodaathe negatteevu, complexes samkhyakalkkulla logaritham vijayakaramaayi nirvachichu, angane logaritham ganithashaasthra prayogangalude vyaapthi valareyadhikam vipuleekarichu. sankeernna samkhyakalkkulla exponential function addeham nirvachikkukayum trikonamitheeya functionukalumaayulla athinte bandham kandethukayum cheythu. eathenkilum yadhaartha samkhyaykku (radian aayi kanakkaakkappedunnu), sankeernamaaya exponential function thripthippeduthunnuvennu yoolarinte soothravaakyam prasthaavikkunnu.
soothravaakyam _ 11
ithine "ganithashaasthrathile ettavum sradheyamaaya soothravaakyam" ennu richard pii. fainman.
melpparanja soothravaakyathinte oru prathyeka cases yoolarude aidantitti ennariyappedunnu.
soothravaakyam _ 12
gamma function avatharippichu uyarnna ateendriya functionukalude sidhaantham euler vishadeekarikkukayum quartic samavaakyangal pariharikkunnathinulla oru puthiya reethi avatharippikkukayum cheythu. aadhunika sankeernamaaya vishakalanathinte vikasanathinu munkootty kaanikkunna sankeernamaaya paridhikalulla integralukal kanakkakkaanulla oru maargam addeham kandethi. addeham vyathiyaanangalude calculus kandupidikkukayum eee mekhalayile opttimaiseshan prasnangal kuraykkunnathinu deferential samavaakyangalude parihaaratthilekku euler-lagranch samavaakyam roopappeduthukayum cheythu.
samkhyaa sidhaantha prasnangal pariharikkunnathin vishakalana reethikal upayogikkunnathinu euler thudakkamittu. angane cheiyunnathiloode addeham ganithashaasthrathinte rund vyathyastha shaakhakale onnippikkukayum vishakalana samkhya sidhaantham enna puthiya patana mekhala avatharippikkukayum cheythu. eee puthiya feeldinu adithara paakunnathil, hypergiometric seerees, kyu-seerees, hyperbolic trikonamithika pravartthanangal, thudarchayaaya bhinnasamkhyakalude vishakalana sidhaantham enniva euler srishtichu. udaaharanathinu, harmonic shreniyude vyathichalipp upayogichu addeham avibhaajyasamkhyakalude anantatha theliyikkukayum avibhaajyasankhyakal vitharanam cheiyunna reethiyekkurich kurachu dhaarana nedunnathinu vishakalana reethikal upayogikkukayum cheythu. eee mekhalayile yoolarude pravartthanangal prime nambar sidhaanthathinte vikasanathilekku nayichu.
nambar sidhaantham.
samkhyaa sidhaanthathodulla yoolarude thaalparyam addehathinte suhruthaaya kristhyan goldbaakkinte swaadheenathil ninnu kandethanakum. peettezhsburg akkadami. samkhyaa sidhaanthathekkurichulla yoolarude aadyakaala pravarthanangalil bhooribhaagavum piyar dii fermattinte pravartthanatthe adisthaanamaakkiyullathaayinu. euler fermattinte chila ashayangal vikasippikkukayum formula _ 13 (fermatt samkhyakal) enna roopathile ellah samkhyakalum avibhaajyamaanenna addehathinte anumaanam polulla chila anumanangal nirasikkukayum cheythu.
euler pradhana vitharanathinte swabhaavathe vishakalanathile aashayangalumayi bandhippichu. avibhaajyasamkhyakalude parasparasamkhyakalude aakethuka vyathyaasappedunnuvennu addeham theliyichu. angane cheyyumbol, riman seetta function prime nambarukalum thammilulla bandham addeham kandethi; ithu riman seetta functionte euler prodakt formula ennariyappedunnu.
n" ennathinekkaal kuranjatho thulyamo aaya poornnasankhyayaaya "n" ennathinekkaal thulyamo aaya positteev poornnasamkhyakalude ennamaaya tottiyant function φ ("n") yaanu euler kandupidichathu. eee functionte gunangal upayogichu addeham fermattinte cheria sidhaanthathe ippol euler sidhaantham ennariyappedunnathinu saamaanyavalkkarichu. euclid muthal ganithashaasthranjare aakarshicha thikanja samkhyakalude sidhaanthathinu addeham ganyamaaya sambhavana nalki. poornnasamkhyakalum mersen primukalum (addeham neratthe theliyicha) thammilulla bandham onnumuthal onnuvare aanennu addeham theliyichu, athinte phalam euclid-euler sidhaantham ennariyappedunnu. quadratic resiprosittiyude niyamavum euler oohichu. eee ashayam samkhyaa sidhaanthathinullile oru adisthaana sidhaanthamaayi kanakkaakkappedunnu, addehathinte ashayangal kaal friedrich gaasinte, prathyekichu "ganithashaasthrathinte vishakalanathin" vazhiyorukki. 1772 aayappozhekkum ooyilar theliyikkunnathu, mersen prime aanu, athaayath, mersen prime ennathu, athaayath, mersen prime aanu. 1867 vare ariyappedunna ettavum valia prime aayirikkam ithu.
oru poornnasamkhyayude vibhajana sidhaanthathinu euler pradhana vikasanangal sambhavana cheythu.
graph sidhaantham.
1735ll conigsburghile ezhu paalangal ennariyappedunna prashnathinu oru pariharam euler avatharippichu. prashyayile conigsburg nagaram prejel nadiyil sthithicheyyukayum athil ezhu paalangalal parasparam bandhippicha rund valia dveepukalum pradhana bhoopradesavum ulppedunnu. oro paalavum krithyamaayi oru thavana kadannu arambha poyintilekku madangunna oru paatha pinthudaraan kazhiyumo ennu theerumaanikkuka ennathaanu prashnam. athu saadhyamalla eularian surcuted illa. eee pariharam graph sidhaanthathinte aadya sidhaanthamaayi kanakkaakkappedunnu.
oru convex polyhedroninte konukal, arikukal, mukhangal ennivayude ennavumaayi bandhapetta formula formula _ 14 yum euler kandethi, athinaal oru planner graph. eee soothravaakyathile sthiraangam ippol graafinte (allengil mattu ganithashaasthra vasthukkalude) euler swabhaavam ennariyappedunnu, ithu vasthuvinte janussumayi bandhappettirikkunnu. eee soothravaakyathinte padanavum saamanyavalkkaranavum, prathyekichu kauchiyum ell 'huilier, topology uthbhavasthaanathaanu.
bhauthikashaasthram, jyothishaasthram, enchiniyaring.
yadhaartha loka prasnangal vishakalanaparamayi pariharikkunnathilum bernauli samkhyakal, forrier seerees, euler samkhyakal, sthiraangangal, thudarchayaaya bhinnasamkhyakal, integralukal ennivayude niravadhi prayogangal vivarikkunnathilum yoolarinte ettavum valia vijayangalil chilath undaayirunnu. addeham lebnisinte deferential calculusine nyoottante flection reethiyumaayi samyojippikkukayum shaareerika prashnangalkk calculus prayogikkunnathu eluppamaakkunna upakaranangal vikasippikkukayum cheythu. ippol euler ekadesha kanakkukal ennariyappedunnava kandupidichukondu integralukalude samkhyaa ekadesha kanakk mechappeduthunnathil addeham valia munnettangal nadatthi. eee ekadesha kanakkukalil ettavum sradheyamaayathu euler reethiyum euler-maclorin soothravaakyavumaanu.
enchineeyaringinte moolakkallaayi marria euler-bernauli beam samavaakyam vikasippikkaan euler sahayichu. classical mechanicsile prashnangalkk thante vishakalana upakaranangal vijayakaramaayi prayogikkunnathinu purame, euler eee saankethikavidyakal aakasha prasnangalkkum prayogichu. jyothishaasthrathile addehathinte pravartthanangal addehathinte kariyaril onniladhikam paarees akkadami sammanangalaal amgeekarikkappettu. dhoomakethukkaludeyum mattu aakasha vasthukkaludeyum bhramanapathangal valare krithyathayode nirnnayikkuka, dhoomakethukkalude swabhaavam manasilakkuka, sooryante paralax kanakkaakkuka enniva addehathinte nettangalil ulppedunnu. krithyamaaya rekhamsha pattikakalude vikasanathinu addehathinte kanakkukoottalukal sambhavana cheythu.
opttiksil euler pradhana sambhavanakal nalki. akkaalathe nilavilulla sidhaanthamaaya nyoottante prakaashatthinte corpuscular sidhaanthathodu addeham viyojichu. kristhyan hyujans nirddeshicha prakaashatthinte taranga sidhaantham prakaashatthinte kwaandam sidhaantham vikasikkunnathuvare prabalamaaya chinthaadhaarayaayi maarumennu urappakkaan 1740-kalile opttiksinekkurichu addehathinte prabandhangal sahayichu.
draavaka chalanathmakathayil, pathonpathaam noottaandinte avasaanathil athinte aadya nireekshanatthinu valare munbuthanne 1754 ll arukkal prathibhasam aadyamaayi pravachichathu euleraanu, koodaathe draavaka pravaaha kanakkukoottalukalil upayogikkunna euler nambar turbineukalude kaaryakshamathayekkurichulla addehathinte anubandha pravarthanangalil ninnaan varunnath. 1757-ll addeham draavaka chalanaathmakathayile adrishyamaaya ozhukkinulla oru pradhana samavaakyangal prasidheekarichu, avaa ippol euler samavaakyangal ennariyappedunnu.
euler structural enchineeyaringil ariyappedunnathu, yoolarinte critical looad nalkunna formulayude perilaanu, ithu oru anuyojyamaaya strattinte critical buckling looad aanu, ithu athinte neelatheyum flexeral kaadinyatheyum maathram aasrayichirikkunnu.
yukthiprakaram.
sylogistic reasoning (1768) chithreekarikkaan clossed karvukal upayogichathinte bahumati ularinu labhikkunnu. eee rekhaachitrangal euler rekhaachitrangal ennariyappedunnu.
settukaleyum avayude bandhangaleyum prathinidheekarikkunnathinu oru rekhaachithra maargamaan euler diagram. euler rekhaachitrangalil settukale chithreekarikkunna prathalatthile lalithamaaya adacha valavukal (saadhaaranayaayi vrithangal) adangiyirikkunnu. oro euler karvum thalathe rund mekhalakalaayo "sonukalaayo" vibhajikkunnu settinte gadakangale pratheekaathmakamaayi prathinidheekarikkunna interior, settile amgangalallaatha ellah gadakangaleyum prathinidheekarikkunna eksteeriyar. vakrangalude valuppamo aakruthiyo pradhaanamalla; avaa engane ovarlaappu cheiyunnu ennathilaanu rekhaachithrathinte praadhaanyam. oro vakravum (ovarlaappu, kandeynment allengil randum) kondu chuttapetta pradeshangal thammilulla speshyal bandhangal settu-theoritic bandhangalumayi (intersection, subset, disjointness) poruthappedunnu. interior sonukal murichukadakkaatha valavukal disjoyint settukale prathinidheekarikkunnu. interior sonukal murichukadakkunna rund valavukal pothuvaaya gadakangalulla settukale prathinidheekarikkunnu; rund valavukalkkullile mekhala rund settukalkkum pothuvaaya gadakangalude koottatthe prathinidheekarikkunnu (settukalude intersection). mattonninte aantharika mekhalaykkullil poornnamaayum adangiyirikkunna oru vakram athinte oru upavibhaagathe prathinidheekarikkunnu.
1960-kalil puthiya ganitha prasthaanatthinte bhaagamaayi settu sidhaanthathile nirddeshathinte bhaagamaayi euler rekhaachithrangalum (wenn rekhaachithrangalilekkulla avayude parishkkaranavum) ulppeduthi. athinusesham, savisheshathakalude samyojanam drishyavalkkarikkunnathinu oru maargamaayi avaa vyaapakamaayi upayogathilaayi.
samgeetham.
samgeethathil ganithashaasthra aashayangalude prayogamaayirunnu yoolarude asaadhaaranamaaya thaalpparyangalilonn. 1739-ll addeham "tentamen noway theoria myoosikke" ("samgeethathinte oru puthiya sidhaanthathilekkulla sramam") ezhuthi, oduvil sangeetha sidhaanthathe ganithashaasthrathinte bhaagamaayi ulppeduthaamenna pratheekshayil. ennirunnaalum, addehathinte kruthiyude eee bhagam valia shradha nediyilla, samgeethajnjarkku valare ganithashaasthraparavum ganithashaasthranjarkku valare samgeethaparavumaanennu orikkal visheshippikkappettu. samgeethavumaayi edapedumbol polum, yoolarude sameepanam pradhaanamaayum ganithashaasthramaanu, udaaharanathinu, ashtakangalude upavibhaagathe bhinnabhagangalaayi samkhyaaparamaayi vivarikkunnathinulla oru maargamaayi addeham bainari logaritham avatharippichu. samgeethathekkurichulla addehathinte rachanakal prathyekichum ennamattathalla (eathaanum noorukanakkinu pejukal, addehathinte motham nirmmaanatthil ekadesham muppathinayiram pejukal), pakshe avaa aadyakaalathe oru tirakkum jeevithathiludaneelam addehathodoppam nilaninnirunna oru kaaryavum prathifalippikkunnu.
yoolarude sangeetha sidhaanthathinte aadya pooyint "vibhaagangalude" nirvachanamaan, athaayath.iii. 3, 5 ennee prime nambarukal upayogichu ashtakathinte saadhyamaaya vibhajanangalude ennam. 2ma enna pothuvaaya nirvachanathode, atharam 18 vibhaagangale euler vivarikkunnu, avide a ennathu eee vibhaagathinte "ghaathakam" aanu (i.iii. 3, 5 ennivayude ghaathaamkangaludeyum 2 meterinteyum ("m ennathu oru anischitha samkhyayaayirikkumbol, shabdangal thirichariyaan kazhiyunnathra kaalam cherutho valutho aakunnu") koottuka, bandhapetta ashtakangalude ennathil ninnu swathanthramaayi bandham nilanilkkunnuvennu prakadippikkunnu. a = 1 ulla aadya vibhaagam ashtakam (allengil athinte thanippakarpukal) aanu; randaamathe vibhaagam, 2m3, anchaam (anchaamathe + naalaamathe, c-g-c) kondu harikkappedunna ashtakam; moonnaamathe tharam 2m5, mejar moonnaamathe + minor aaraamathe (c-e-c); naalaamathethu 2m.32, naalil rund, oru toonn (c-f-b-c); anchaamathethu 2m.3.5 (c-e-g-b-c); muthalaayava. 12 (2m.33.5), 13 (2m.32.52), 14 (2m.3.53) ennee vibhagangal yathaakramam dietonic, chrometic, enharmonic ennivayude thiruthiya pathippukalaanu. 18-aamm tharam (2m.33.52) "dietonico-chrometic" aanu, "ellah rachanakalilum saadhaaranayaayi upayogikkunnu", ithu johann maathasan vivaricha sisttavumaayi saamyamullathayi maarunnu. 7-aamm nambar ulppedeyulla vibhaagangale vivarikkanulla saadhyatha euler pinneedu vibhavanam cheythu.
dietonico-chrometic vibhaagathe chithreekarikkunnathinaayi euler oru prathyeka graph, "speculum myoosikkam", aavishkarikkukayum conigsburghile ezhu paalangalodulla thante thaalparyam oormmippichukondu prathyeka edavelakalkkaayi eee graphile pathakal charcha cheyyukayum cheythu (mukalil kaanuka). neo-remanian sidhaanthathil tonnetts enna nilayil eee upakaranam puthiya thaalparyam aakarshichu (laattis (samgeetham) ennivayum kaanuka).
edavelakalil ninnum cordukalil ninnum avayude pradhana gadakangalil ninnu "gradus suvithattis" (swaabhittiyude alavu, sammathathinte alavu) ennathinte oru vyulppannam nirddeshikkaan euler "eksponant" enna thathwam upayogichu-oraal oormmikkendathu addeham kevalam swaram, athaayath, pariganichu ennaanu.iii. 1 umm 3 umm 5 umm mathramulla pradhana samkhyakal. eee samvidaanam ethra abhaajyasamkhyakalilekkum vyaapippikkaan soothravaakyangal nirddeshikkappettittund, udha.jii. roopathil
soothravaakyam _ 15
ivide "p" "i" ennathu prime nambarukalum "k" "i" avayude eksponantukalumaanu.
vyakthiparamaaya thathwachinthayum mathavishwaasangalum.
leybnisinte monadisathinteyum kristhyan wolfinte thathwashaasthrathinteyum aashayangale euler ethirthu. monadisathinum volfian shaasthrathinum nalkaan kazhiyaatha krithyamaaya alavukolukalude adisthaanathilaanu arivu bhaagikamaayi sthaapikkappettrikkunnathu euler urappichu paranju. wolfinte aashayangale "anyamathakkaarum nireeshwaravaadikalum" ennum euler visheshippichu.
jeevithathiludaneelam oru mathavishwaasiyaayirunnu euler. yoolarude mathavishwaasangalekkurichu ariyappedunnathil bhooribhaagavum addehathinte "oru jarmman rajakumariykku ezhuthiya kathukalil" ninnum "rettang derr gottlichen offenberang gegen dye inverf derr freejisttar" ("swathanthrachinthakarude athirppukalkkethire daivika velipaadinte prathirodham") enna muun kruthiyil ninnum oohikkaam. baibil prachodithamaanennu vishwasichirunna oru bhakthanaya kristhyaaniyaayirunnu euler ennu eee kruthikal kaanikkunnu; "retung" praadhamikamaayi thiruvezhuthukalude divya prachodanatthinulla oru vaadamaayirunnu.
mathathekkurichulla mathethara thathwachinthakarumaayulla yoolarude vaadangalil ninnu prachodanam ulkkonda oru prashasthamaaya aitihyam undu, ithu sent yoolarinte randaam bharanakaalathaanu. peettezhsburg akkadami. franch thathwachinthakanaaya denis dederot catherine dhii grettinte shanaprakaaram russia sandarshikkukayaayirunnu. ennirunnaalum, nireeshwaravaadathekkurichallu thathwachinthakante vaadangal thante kottaaratthile amgangale swaadheenikkunnuvennu chakravarthini ashankaakulayaayi, athinaal franchukaarane neridaan ulerinode aavasyappettu. oru pandita ganithashaasthranjan daivathinte asthithvathinte thelivu hajaraakkiyathaayi diderottine ariyichu kodathiyil avatharippichathupole thelivu kaanaan addeham sammathichu. euler prathyakshappedukayum dederotylake munnerukayum thikanja bodhyathode eee noonn-seekwar prakhyapikkukayum cheythu "sarr, formula 16, athinaal daivam nilanilkkunnu-utharam!"
ellah ganithashaasthravum (katha parayunnu) asambandhamaayirunna dederot, kodathiyil ninnu chiri pottippurappettappol viddiyaayi ninnu. lajjayode addeham russia vidaan aavasyappettu, eee abhyarthana chakravarthini dayaapoorvam amgeekarichu. eee katha rasakaramaanengilum, dederot thanne ganithathil gaveshanam nadathiyathinaal ithu apraamaanikamaan.
augustus dii morgan alankarichukondu deodon tiboltaanu eee aitihyam aadyamaayi paranjathu.
anusmaranangal.
swis 10-frank baanknottinte aaraamatheyum ezhaamatheyum parambarayilum niravadhi swis, jarmman, russian tapal staambukalilum euler pradharshippichirunnu. 1782ll american akkadami oof arts aandu sayansasinte videsha oonarari amgamaayi addeham thiranjedukkappettu. 2002-leeii chhinnagrahathinu addehathinte bahumaanaartham euler ennu namakaranam cheythu.
thiranjeduttha grandhasoochika.
eulerinu vipulamaaya grandhasoochikayundu. addehathinte pusthakangalil iva ulppedunnu
pooll heinrich voonn phas (yoolarinte cherumakanum nicolas fasinte makan) kandethiya 61 prasidheekarikkappedaathu kruthikalude oru adhika baachu 1862-ll oru shekharamaayi prasidheekarikkukayum cheythukondu, yoolarinte maranananthara kruthikalil bhooribhaagavum vyakthigathamayi prasidheekarikkaan 1830 vare samayameduthu. yoolarinte kruthikalude oru kaalakrama pattika sweedish ganithashaasthranjanaaya gustaf enestrome samaharikkukayum 1910 muthal 1913 vare prasidheekarikkukayum cheythu. enestrome soochika ennariyappedunna kaattalog, e1 muthal e866 vareyulla numpers yoolarude kruthikal. amerikkayude ganithashaasthra associationilekkum 2017-ll ettavum aduthide pasaphik sarvakalaashaalayilekkum maarunnathin munbu dartmouth kolejilaanu euler archive aarambhichath.
1907-ll swis akkadami oof sciences euler kammeeshan roopeekarikkukayum yoolarude samboornna kruthikal prasidheekarikkaanulla chumatala athinu nalkukayum cheythu. pathonpathaam noottaandile niravadhi kaalathaamasangalkk sesham, "ooppara oomniya" yude aadya vaalyam 1911-ll prasidheekarichu. ennirunnaalum, puthiya kayyezhuthuprathikalude kandethal eee padhathiyude vyaapthi vardhippikkunnathu thudarnnu. bhagyavashaal, 2006-oode 70-ladhikam vaalyangalum (sharashari 426 pejukal veetham) 2022-oode 80 vaalyangalum prasidheekarichukondu yoolarude ooppara oomniyayude prasidheekaranam sthiramaaya purogathi kaivarichu. eee vaalyangal naalu seereesukalaayi krameekarichirikkunnu. aadya parambara vishakalanam, beejaganitam, samkhyaa sidhaantham ennivayekkurichulla kruthikal samaaharikkunnu; ithil 14,000 pejukalilaayi 29 vaalyangalum akkangalum adangiyirikkunnu. randaam shreniyude 31 vaalyangalil 10,660 pejukalulla mechanics, jyothishaasthram, enchiniyaring ennivayekkurichulla kruthikal adangiyirikkunnu. moonnaam shreniyil bhauthikashaasthrathekkurislathu 12 vaalyangalund. valia alavil yoolarude kathidapaadukal, prasidheekarikkappedaathu kayyezhuthuprathikal, kurippukal enniva ulkkollunna parambara IV 1967 ll maathramaan samahaaram aarambhichath. eee parambara 16 vaalyangal vyaapippikkumenn prathekshikkunnu, athil ettu vaalyangal puratthirangi.