VADODARA INSTITUTE OF ENGINEERINGKUSHWAHA AKHILESH(16COMP021)RAMI JAY (16COMP022)PATEL TINKEL(16COMP023)BHATT DHURATI(16COMP024)

CONTENT

APPLICATION OF PARTIAL DERIVATIVE

1.JACOBBIAN2.TAYLOR SERIES

JACOBIAN FORMUALEFOR TWO VARIABLE

FOR THREE VARIABLE

PROPERTIES OF JACOBIAN1. J x J* = 12.IF u AND v ARE FUNCTION OF x AND y,AND x AND y IS A FUNCTION OF r,t THEN ∂(u,v/r,t) = ∂(u,v/x,y)* ∂(x,y/r,t)

EXAMPLE OF JACOBIAN

TAYLOR SERIESIF A FUNCTION F(X) HAS DERIVATIVES

OF ALL ORDERS AT X = C, THEN THE SERIES

IS CALLED THE TAYLOR SERIES FOR F(X) AT C.

IF C = 0, THE SERIES IS THE MACLAURIN SERIES FOR F .

( )2

0

( ) "( )( ) ( ) '( )( ) ( ) ...! 2!

nn

n

f c f cx c f c f c x c x cn

EXAMPLE OF TAYLOR SERIES