
bhaagon dwara yog

ganit mein, bhaagon dwara yog anukramon key utpaadon key yog koo anya yogon mein badal detaa haye, joe aksar ganana yaa (vishesh roop seey) kuchh prakaar key yogon key anuman koo saral banaata haye. ise ebel kaa lemma yaa ebel parivartan bhee kahaa jaataa haye, jiska naam niels heinrich ebel key naam parr rakhaa gayaa haye, jinhone ise 1826 mein pesh kiya thaa.
bayaan.
maan leejiye kii sootra _ 1 aur sootra _ 2 dou anukram hain. taba,
forward difference operator sootra _ 4 kaa upayog karke, ise adhik sankshipt roop seey kahaa jaa sakata haye
bhaagon dwara yog bhaagon dwara ekikaran key liye ack anuroop haih
yaa aabel key yog sootra key liyeh
ack vaikalpik kathan haye
joe ardh-martingles key liye bhaagon key sootra dwara ekikaran key anuroop haye.
haalaanki anuprayog lagbhag hamesha anukramon key abhisaran seey sambandhit hotey hain, lekin kathan vishuddh roop seey beejganitiya haye aur kissy bhee kshetra mein kaam karega. yeh taba bhee kaam karega jaba ack anukram vector sthaan mein hoga, aur doosara scalar key praasangik kshetra mein hoga.
neuton shrinkhala.
sootra kabhi-kabhi inmein seey kissy ack mein diyaa jaataa haye-thodaa alag-roop
joe adhik samanya niyam key ack vishesh mamle (sootra _ 10) kaa pratinidhitva karate hain
donon praarambhik sootra key punaraavritt anuprayog kaa parinam hain. sahayak maatraaen neuton shrinkhala hainh
aur 
ack vishesh (sootra _ 15) parinam pehchaan haye
yahaan, sootra _ 17 dwipad gunank haye.
vidhi.
dou diye gaye anukram sootra _ 18 aur sootra _ 19 key liye, sootra _ 20 key saath, koee nimnalikhit shrinkhala key yog kaa adhyayan karna chaahata haih sootra _ 21
yadi humm sootra _ 22 koo paribhaashit karate hain tou pratyek sootra _ 23 sootra _ 24 key liye aur
sootra _ 25
sootra _ 26
anta mein sootra _ 27
iss prakriya, jise ebel parivartan kahaa jaataa haye, kaa upayog sootra _ 28 key liye abhisaran key kaee maandandon koo saabit karane key liye kiya jaa sakata haye.
bhaagon dwara ekikaran key saath samaantaa.
bhaagon dwara ekikaran kaa sootra sootra _ 29 haye.
seema sharton key alawa, humm dekhate hain kii pahale samakalan mein dou gunit kaary hotey hain, ack joe antim samakalan mein ekikrit hotaa haye (sootra _ 30 sootra _ 31 bunn jaataa haye) aur ack joe vibhedak hotaa haye (sootra _ 32 sootra _ 33 bunn jaataa haye).
ebel parivartan" kii prakriya samaan haye, kyonki dou praarambhik anukramon mein seey ack kaa yog kiya jaataa haye (sootra 34 sootra 35 bunn jaataa haye) aur doosara bhinn hotaa haye (sootra 36 sootra 37 bunn jaataa haye).
aavedan.
aabel key pareekshan kaa pramaan. bhaagon dwara yog detaa haye
sootra _ 43
jahan "a" sootra _ 41 kii seema haye. kyonki sootra _ 40 abhisari haye, sootra _ 46 sootra _ 47 seey swatantra roop seey bandha huaa haye, maan leejiye sootra _ 48 dwara. sootra _ 49 shoonya parr jaataa haye, isaliye pahale dou shabdon parr jaaen. teesara pada sootra _ 40 key liye kauchi mandand dwara shoonya parr jaataa haye. shesh yog dwara seemit haye
sootra _ 51
sootra _ 41 kii ekarasata seey, aur sootra _ 53 key roop mein shoonya parr bhee jaataa haye.
oopar diye gaye samaan pramaan kaa upayog karke, koee yeh dikhaa sakata haye kii yadi
phir sootra _ 42 abhisaran kartaa haye.
donon hii mamalon mein, shrinkhala kaa yog santusht kartaa haih sootra _ 61
uchch crum seemit antar vidhiyon key liye yog-darr-bhaag prachaalak.
ack yog-darr-bhaag (aiss. bee. pee.) seemit antar prachaalak mein paaramparik roop seey ack kendrit antar aantarik yojana aur vishisht seema stancil hotey hain joe sambandhit ekikaran-darr-bhaag nirmaan key vyavhaaron kii nakal karate hain. seema kii shartein aamtaur parr ack saath-abhigrahan-avadhi (aiss. aeye. tii.) takneek dwara lagu kii jaati hain. aiss. bee. pee.-sait kaa sanyojan seema upchaar key liye ack shaktishali dhancha haye. vidhi koo lambe samay taka anukaran aur sateekta key uchch crum key liye achchi tarah seey saabit sthirata key liye prathamikta dee jaati haye.