Lec17 - Lecture 17 Differentiation Analytical Numerical...

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Lecture 17 Numerical Differentiation 1 Lecture 17 Differentiation Analytical Numerical Motivation – why? Forward, central and backward difference An example

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Lecture 17 Numerical Differentiation 2 0 ) ( 1 1 + + = - - m n bmx anx dx x df c bx ax x f m n + + = ) ( Analytical Derivative Rules for simple functions ) sin( ) ( x x f = ) cos( ) ( x dx x df = ) cos( ) ( x x f = ) sin( ) ( x dx x df - = x e x f = ) ( x e dx x df = ) ( ) ln( ) ( x x f = x dx x df 1 ) ( =
Lecture 17 Numerical Differentiation 3 -6 -4 -2 0 2 4 6 8 10 12 3 4 5 6 7 2 54 . 0 ) ( 2 - - = x x dx x df 1 2 5 . 0 18 . 0 ) ( 2 3 + - - = x x x x f Analytical Derivative example 50 . 6 2 5 ) 5 ( 54 . 0 ) ( 2 = - - = dx x df 64 . 2 2 4 ) 4 ( 54 . 0 ) ( 2 = - - = dx x df

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Lecture 17 Numerical Differentiation 4 -6 -4 -2 0 2 4 6 8 10 12 3 4 5 6 7 1 2 5 . 0 18 . 0 ) ( 2 3 + - - = x x x x f Numerical Differentiation Methods h x f h x f dx x df ) ( ) ( ) ( - + = Forward difference h h x f h x f dx x df 2 ) ( ) ( ) ( - - + = Central difference h h x f x f dx x df ) ( ) ( ) ( - - = Backward difference h
Lecture 17 Numerical Differentiation 5 -6 -4 -2 0 2 4 6 8 10 12 3 4 5 6 7 Numerical Differentiation – the numbers Forward difference Central difference 96 . 5 25 . 0

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This note was uploaded on 02/26/2008 for the course ENGR 1 taught by Professor X during the Spring '07 term at Lehigh University .

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Lec17 - Lecture 17 Differentiation Analytical Numerical...

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