
laghuganak vyutpann

ganit mein, vishesh roop seey cullon aur jatil vishleshan mein, ack falan "f" key laghuganak vyutpann koo sootra dwara paribhaashit kiya jaataa haye.
sootra _ 1
jahan sootra _ 2 "f" kaa vyutpann haye. sahaj gyaan seey, yeh "f" mein aseem saapeksh parivartan haye; arthaat, "f" mein aseem nirpeksh parivartan, arthaat sootra _ 3 koo "f" key vartamaan moolya dwara maapa jaataa haye."
jaba "f" ack vaastavik charr "x" kaa falan "f" ("x") haye, aur vaastavik, sakhti seey sakaratmak maan letaa haye, tou yeh ln ("f") key vyutpann, yaa "f" key praakritik laghuganak key barabar hotaa haye. yeh seedhe shrinkhala niyam seey nimnalikhit haih
sootra _ 4
buniyaadi guna.
vaastavik laghuganak key kaee guna laghuganak vyutpann parr bhee lagu hotey hain, taba bhee jaba falan sakaratmak vaastavik mein maan naheen letaa haye. udaaharan key liye, choonki kissy utpaad kaa laghuganak karakon key laghuganak kaa yog haye, isaliye hamaare paas haye
sootra _ 5
isaliye sakaratmak-vaastavik-moolya vaale karyon key liye, ack utpaad kaa laghuganak vyutpann karakon key laghuganak vyutpannon kaa yog haye. lekin humm kissy utpaad key vyutpann key liye leibniz kaanoon kaa bhee upayog curr sakate hain
sootra _ 6
iss prakaar, yeh "kissy bhee" falan key liye sach haye kii kissy utpaad kaa laghuganak vyutpann karakon key laghuganak vyutpannon kaa yog haye (jaba way paribhaashit kiye jaate hain).
iska ack upsamhaar yeh haye kii ack falan key parasparik kaa laghuganak vyutpann falan key laghuganak vyutpann kaa nishedh haih
sootra _ 7
jaise ack dhanaatmak vaastavik sankhya key parasparik kaa laghuganak sankhya key laghuganak kaa nishedh haye.
adhik aam taur parr, ack bhagfal kaa laghuganak vyutpann labhansh aur bhaajak key laghuganak vyutpann kaa antar haih
sootra _ 8
jaise bhagfal kaa laghuganak labhansh aur bhaajak key laghuganak kaa antar haye.
ack anya disha mein saamaanyikaran karate hue, ack shakti kaa laghuganak vyutpann (sthir vaastavik pratipaadak key saath) ghatank kaa utpaad haye aur aadhar kaa laghuganak vyutpann haih
sootra _ 9
jaise kii ack shakti kaa laghuganak ghatank aur aadhar kaa laghuganak kaa utpaad haye.
sankshep mein, vyutpann aur laghuganak donon mein ack utpaad niyam, ack parasparik niyam, ack bhagfal niyam aur ack shakti niyam (laghuganak pehchaan kii soochi kii tulanaa karein) hotaa haye; niyamon kii pratyek jodee laghuganak vyutpann key madhyam seey sambandhit hoti haye.
laghuganak vyutpannon kaa upayog karke sadharan vyutpannon kii ganana karna.
logridmic vyutpann samaan parinam utpann karate hue utpaad niyam kii aavashyakta vaale vyutpannon kii ganana koo saral banaa sakate hain. prakriya iss prakaar haih maan leejiye kii humm sootra _ 10 kii ganana karna chaahte hain. ise seedhe ganana karane key bajaay, humm isake laghuganak vyutpann kii ganana karate hain. arthaat, humm ganana karate hainh
sootra _ 11
aff ganana dwara gunaa karnaah
sootra _ 12
yeh takneek sabse adhik upayogi hoti haye jaba f badee sankhya mein karakon kaa utpaad hotaa haye. iss takneek seey pratyek kaarak key laghuganak vyutpann kii ganana karke, yog karke aur gunaa karke ganana karna sambhav hoe jaataa haye.
udaaharan key liye, humm sootra _ 13 key laghuganak vyutpann kii ganana sootra _ 14 key roop mein curr sakate hain.
kaarak ekikrit karna.
laghuganak vyutpann vichaar pratham-crum avkal samikaranon key liye samakalan kaarak vidhi seey nikatata seey judaa huaa haye. prachaalak key shabdon mein, sootra _ 15 likhein aur "m" koo kissy diye gaye falan "g" ("x") dwara gunan key prachaalak koo darshaane dein. phir sootra _ 16 koo (utpaad niyam dwara) sootra _ 17 key roop mein likhaa jaa sakata haye jahan sootra _ 18 abb logridmic vyutpann sootra _ 19 dwara gunan prachaalak koo darshaata haye.
vyavhaar mein hamein ack operator diyaa jaataa haye jaise kii
sootra _ 20
aur samikaranon koo hull karna chaahte hain
sootra _ 21
falan "aich" key liye, "aff" diyaa gayaa haye. yeh taba hull karane key liye cumm hoe jaataa haye
sootra _ 22
jiska samadhan haye
sootra _ 23
f" key kissy bhee anishchit samakalan key saath.
jatil vishleshan.
jaisa kii diyaa gayaa sootra adhik vyaapak roop seey lagu kiya jaa sakata haye; udaaharan key liye yadi "f" ("z") ack meromorphic function haye, tou yeh "z" key sabhi jatil moolyon parr samajh mein aataa haye jiss parr "f" kaa naa tou shoonya haye aur naa hii ack dhruv haye. isake alawa, ack shoonya yaa ack dhruv parr laghuganak vyutpann iss tarah seey vyavhaar kartaa haye jiska aasaani seey vishesh mamle key sandarbh mein vishleshan kiya jaataa haye.
aine" ack purnank key saath. logridmic vyutpann taba haye
sootra _ 24
aur koee bhee samanya nishkarsh nikaal sakata haye kii "f" meromorphic key liye, "f" key laghuganak vyutpann kii vilakshantaaen sabhi "saral" dhruv hain, jisamen shoonya crum "n" seey avashesh "n", anukram "n" key dhruv seey avashesh-"n" hain. tark siddhant dekhein. iss jaankaari kaa aksar samocch ekikaran mein upayog kiya jaataa haye.
nevanlinna siddhant key kshetra mein, ack mahatvapurna lemma bataata haye kii ack laghuganak vyutpann kaa nikatata kaary mool kaary kii nevanlinna visheshta key sambandh mein chhota haye, udaaharan key liye sootra _ 25.
gunak samooh.
laghuganak vyutpann key upayog key peechhe "jee. ell." 1 key baare mein dou buniyaadi tathya hain, joe kii vaastavik sankhyaon yaa anya kshetra kaa gunak samooh haye. vibhedak prachaalak
sootra _ 26
failaav key tahat aparivartaniya haye ("a" sthiraank key liye "x" koo "aksh" seey pratisthaapit karna). aur vibhedak sootra _ 27 bhee isi tarah aparivartaniya haye. kaary "f" key liye gl1 mein, sootra
isaliye sootra _ 28 aparivartaniya roop kaa ack "pullback" haye.

