
chee-varg vitaran seey sambandhit pramaan

nimnalikhit chee-varg vitaran seey sambandhit kaee visheshtaon key pramaan hain.
pee. dee. aff. kii vyutpatti.
ack degree off friedam key liye pdf kii vyutpatti.
yaadrichhik charr "y" koo "y" = "x" 2 key roop mein paribhaashit kiya jaae jahan "x" kaa ausat 0 aur vicharan 1 (joe "x" ~ "n" (0,1) haye) key saath samanya vitaran haye.
taba, <bee. aar.>
sootra _ 1
jahan sootra _ 3 aur sootra _ 4 sambandhit yaadrichhik charr key cdf aur pdf hain.
phir sootra _ 5
parivartaniya sootra key parivartan kaa upayog karke seedhe vaikalpik pramaan.
ack monotonic parivartan sootra _ 6 key liye parivartaniya sootra (oopar nihit roop seey vyutpann) kaa parivartan haih 
iss mamle mein parivartan acrus naheen haye, kyonki sootra _ 8 key pratyek moolya mein sootra _ 9 (ack sakaratmak aur nakaratmak) key dou sambandhit moolya hain. haalaanki, samroopata key kaaran, donon bhaag samaan roop seey badal jaayenge, i.ee.
iss mamle mein, parivartan haih sootra _ 11, aur iska vyutpann haye
sootra _ 12
tou yahaanh
aur ack koo chee-varg vitaran milata haye, gaama function key guna koo dhyaan mein rakhate hueh sootra _ 14.
dou degree off friedam key liye pdf kii vyutpatti.
2 degree off friedam key saath chee-varg vitaran praapt karane key kaee tareeke hain. yahaan 1 degree off friedam key saath vitaran parr adharit haye.
maan leejiye kii sootra _ 15 aur sootra _ 16 dou swatantra charr hain joe sootra _ 17 aur sootra _ 18 koo santusht karate hain, taaki sootra _ 15 aur sootra _ 16 key sambhaavyata ghanatva kaary kramshah hainh
aur
buss, humm sootra _ 15 aur sootra _ 16 key sanyukt vitaran koo praapt curr sakate hainh
jahan sootra _ 26 koo sootra _ 27 dwara pratisthaapit kiya jaataa haye. aage, sootra _ 28 aur sootra _ 29, humm praapt curr sakate hainh
aur
yaa, vipareet roop seey
aur
choonki dou parivartaniya parivartan neetiyaan samamit hain, isaliye humm oopari ack lete hain aur parinam koo 2 seey gunaa karate hain. jacobian nirdhaarak kii ganana iss prakaar kii jaa sakati haih
abb humm sootra _ 35 koo sootra _ 36 mein badal sakate hainh
jahan pramukh sthiraank 2 donon parivartaniya parivartan neetiyon koo dhyaan mein rakhna haye. anta mein, humm sootra 39, i kaa vitaran praapt karane key liye sootra 38 koo ekikrit karate hain.ee. sootra _ 40:
sootra _ 42 koo iss sameekaran mein badala jaa sakata haih
tou parinam haih
key" degree off friedam key liye pdf kii vyutpatti.
key"-ayami sthaan mein ack bindu kaa pratinidhitva karane key liye "key" namoonon key sootra _ 45 parr vichaar karein. key" degree off friedam key liye chee varg vitaran taba iss prakaar diyaa jaaegaah
jahan sootra _ 47 maanak samanya vitaran haye aur sootra _ 48 "q" ("x") parr vaha maulik khol aayatan haye, joe "k"-sthaan mein ("k" −1)-ayami satah key samanupati haye jisake liye
yeh dekhaa jaa sakata haye kii yeh satah ack "k"-ayami gend kii satah haye yaa, vaikalpik roop seey, ack n-kshetra haye jahan "n" = "k"-1 trijya sootra _ 50 key saath, aur ghatank mein shabd koo kewal "q" key sandarbh mein vyakt kiya jaataa haye. choonki yeh ack sthiraank haye, isaliye ise samakalan key ander seey hataaya jaa sakata haye.
samakalan abb kewal ("k" −1) kaa satah kshetra "a" haye-gole kii aseem motai kaa goal gunaa joe haye
a ("k" −1)-kshetra kaa kshetrafal haih
usa sootra koo pratisthaapit karna, usa sootra koo mahsoos karna aur sharton koo radd karane seey laabh hotaa haih

