
parichaalan ganana

prachaalan cullon, jise prachaalan vishleshan key roop mein bhee jaanaa jaataa haye, ack aisee takneek haye jisake dwara vishleshan mein samasyaon, vishesh roop seey vibhedak samikaranon mein, beejganitiya samasyaon mein badal jaati hain, aamtaur parr ack bahupad sameekaran koo hull karane kii samasya.
itihas.
cullon, vibhedan aur ekikaran kii prakriyaon koo prachaalak key roop mein prastut karane kaa vichaar 
iska ack lamba itihas haye joe gottfried wilheim leibniz taka jaataa haye. ganitshastri lui francois antoine arbogast una pahale logon mein seey ack they jinhone inn prateekon koo usa kaary seey swatantra roop seey herfer kiya thaa jiss parr unhein lagu kiya gayaa thaa.
iss drishtikon koo aage francois-joseph servoice dwara vikasit kiya gayaa thaa jinhone suvidhajanak sanketan vikasit kiye they. servoice key baad charles james hergrave, george bool, bonin, carmichael, dookin, graves, marfi, villium spottiswod aur sylvester sahit british aur ayrish ganitvidon kaa ack school aaya.
sadharan aur aanshik vibhedak samikaranon mein prachaalak vidhiyon key anuprayog kaa varnan karane vaale granth 1855 mein robbert bell carmichael dwara aur 1859 mein bool dwara likhe gaye they.
iss takneek koo poori tarah seey bhautik vigyaani oliver havicide dwara 1893 mein telegraph mein unake kaam key sambandh mein vikasit kiya gayaa thaa. 
usa samay, havicide key tareeke kathor naheen they, aur unake kaam koo ganitvidon dwara aage vikasit naheen kiya gayaa thaa. 
prachaalan cullon koo pahali baar vidyut abhiyaantriki samasyaon mein anuprayog milaa, 
1910 key baad raikhik paripath mein kshansthaayi kii ganana, ernst julius burg, johnn rainshaw carson aur vanever busch key aaveg key tahat.
havicide key sanchaalan vidhiyon kaa ack kathor ganitiya auchitya kewal aaya 
bromwich key kaam key baad joe parichaalan cullon seey sambandhit thaa 
lapless parivartan vidhiyaan (vistrit vyakhya key liye jeffrey, carslau yaa mclachlan kii pustaken dekhein). 
1920 key dashak key madhya mein havicide key sanchaalan vidhiyon koo uchit thaharaane key anya tareeke pesh kiye gaye they. 
samakalan sameekaran takneek (jaisa kii carson dwara kiya gayaa) yaa forier parivartan (jaisa kii norbert weiner dwara kiya gayaa).
1930 key dashak mein polish ganitshastri dwara parichaalan cullon key liye ack alag drishtikon vikasit kiya gayaa thaa. 
beejganitiya tark kaa upayog karate hue zaan mikusinsky.
norbert weiner ney 1926 mein parichaalan cullon kii astitvagat sthiti kii apani sameeksha mein prachaalak siddhant kii neenv rakheeh
siddhant.
prachaalan cullon kaa pramukh tatva vibhedan koo ack prachaalak p = karyon parr kaary karane key roop mein maanana haye. raikhik avkal samikaranon koo phir gyaat falan key barabar agyaat falan parr kaary karane vaale prachaalak pee key "falan" key roop mein punah vyavasthit kiya jaa sakata haye. yahaan, kuchh paribhaashit curr rhaa haye joe ack operator pee mein letaa haye aur dusare operator koo lautaata haye. 
isake baad gyaat falan parr kaary kaa vyutkram prachaalak banaakar samadhan praapt kiye jaate hain. prachaalan cullon koo aam taur parr dou prateekon, prachaalak pee, aur ikai falan 1 dwara vargeekrit kiya jaataa haye. isake upayog mein prachaalak shayed bhautik kii tulanaa mein adhik ganitiya haye, ikai falan ganitiya kii tulanaa mein adhik bhautik haye. havicide cullon mein prachaalak pee shuru mein samay vibhedak kaa pratinidhitva karane key liye haye. isake alawa, yeh vaanchhit haye kii yeh prachaalak parasparik sambandh iss tarah seey rakhta haye kii pee ekikaran key sanchaalan koo darshaata haye.
vidyut paripath siddhant mein, koee bhee aaveg key liye vidyut paripath kii pratikriya nirdhaarit karane kaa prayaas curr rhaa haye. raikhikta key kaaran, ack ikai charan parr vichaar karna paryaapt haih
prachaalan cullon key anuprayog kaa sabse saral udaaharan haih, joe detaa haye
iss udaaharan seey, koee yeh dekhta haye kii sootra _ 2 ekikaran kaa pratinidhitva kartaa haye. isake alawa punaraavritt ekikaran sootra _ 3 dwara darshaaya jaataa haye taaki 
pee koo aise maanana jaari rakhna jaise kii yeh ack charr hoe,
jise jyaamitiya shrinkhala vistaar kaa upayog karke phir seey likhaa jaa sakata haye, 
sootra _ 6
aanshik ansh apghatan kaa upayog karke, koee bhee prachaalak pee mein kissy bhee ansh koo paribhaashit curr sakata haye aur usa parr isaki kaarravaai kii ganana curr sakata haye. 
isake alawa, yadi falan 1/"f" (p) mein roop kaa ack shrinkhala vistaar haye
yeh dhoondhana seedha haye
iss niyam koo lagu karate hue, kissy bhee raikhik avkal sameekaran koo hull karna vishuddh roop seey beejganitiya samasya mein badal jaataa haye.
havicide aage badhaa, aur pee kii aanshik shakti koo paribhaashit kiya, iss prakaar parichaalan cullon aur aanshik cullon key beach ack sambandh sthaapit kiya. 
teller vistaar kaa upayog karke, koee bhee lagrange-bool anuvaad sootra koo bhee satyaapit curr sakata haye, isaliye parichaalan
cullon parimit antar samikaranon aur vilambit sanketon key saath vidyut engineering samasyaon parr bhee lagu hotaa haye.

