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T w i e r d z e n i e ( R ó w n o [c i S c h w a r z a )
n
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z a c h o d z r ó w n o [c i :
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( P ) = ( P ) , i , j = 1 , 2 , . . . , n , i `" j
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w r a z z e w s z y s t k i m i s w o i m i p o c h o d n y m i c z s t k o w y m i a | d o r z d u m w Bc z n i e w A .
T w i e r d z e n i e ( T a y l o r a )
n n
" " " + " + ‚" +
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m - 1
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Bc z c y p u n k t y P , P + h z a w i e r a s i w A ) . J e |e l i f : A ’! j e s t k l a s y C w A
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o r a z d l a k a |d e g o x n a l e |c e g o d o o d c i n k a P , P + h i s t n i e j e d x f , t o i s t n i e j e ± " 0 , 1
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t a k i e , |e
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f ( P + h ) = f ( P ) + d P f ( h ) + d P f ( h ) + . . . + d P m - 1 ) f ( h ) + d P m ) f ( h )
+ = + + + + +
+ = + + + + +
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+ ±h
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2 ! ( m - 1 ) ! m !
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T w i e r d z e n i e ( T a y l o r a z r e s z t P a e a n o )
n n
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m - 1 m
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C w A o r a z i s t n i e j e d P f , t o
1 1 1
2 ( - (
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f ( P + h ) = f ( P ) + d P f ( h ) + d P f ( h ) + . . . + d P m - 1 ) f ( h ) + d P m ) f ( h ) + É( P , h ) | | h | | m
+ = + + + + + +
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2 ! ( m - 1 ) ! m !
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g d z i e É( P , h )
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f u n k c j i j e d n e j z m i e n n e j , t z n .
n
f : t o p " A ’! "
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