lecture24bw - LECTURE 24 DERIVATIVE = SLOPE f(x) Numerical...

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LECTURE 24 Numerical Differentiation inite Differences Finite Differences Textbook: Section 8.3 E7, Fall 2008, M. Frenklach DERIVATIVE = SLOPE f ( x ) x 0 a ( ) ( ) ( ) lim f af a fxa δ +− == 0 2 NUMERICAL DIFFERENTIATION f ( x ) x 0 Δ x 1 ' ii yy y x + Δ = ( ) 1 fx x xx + Δ− 3 FINITE DIFFERENCES y 0 0 x 1 1 7 8 2 64 4 27 3 125 5 # # 4
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FIRST DIFFERENCE y 0 0 x Δ y 1 x y 1 1 7 7 8 2 19 64 4 27 3 1 37 125 5 # 61 # # 5 SECOND DIFFERENCE y 2 0 0 x Δ y Δ y 1 1 1 7 2 6 7 8 2 19 18 12 64 4 27 3 1 37 24 125 5 # 61 # # # 6 NUMERICAL DIFFERENTIATION y y Δ () 1 ' ii yy yy fx x xh + ΔΔ ≈= = Δ 1 xx + Δ 22 1 1 '' " i i y y y yy y x x x + + −Δ Δ = = = ( ) 1 x h x + Δ 7 Taylor Series a f a ′′ ( ) ( ) ( ) ( ) ( ) ( ) 2 12 fa f xf a x a x a !! =+ + + ( ) ( ) n n x a ! 1 n n n! = a= 0 ( ) ( ) 1 0 0 n n f f x = ( ) 0 n n f y x + 0 1 n =
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Newton’s Interpolation Formula 0 n f Δ ( ) ( ) ( ) ( )( ) ( ) 1 01 2 1 n f x f xx x x n n! = =+ + " () () 00 n x ff ⎛⎞ Δ ⎜⎟ 1 n n = ⎝⎠ 0 12 1 n y y x x x x n Δ + " ( )( ) ( ) 0 1 n yy = 9 MATLAB FUNCTIONS iff diff olyder polyder polyval conv, roots,. ..
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This note was uploaded on 11/01/2009 for the course ENGLISH 7 taught by Professor Sengupta during the Spring '09 term at University of California, Berkeley.

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lecture24bw - LECTURE 24 DERIVATIVE = SLOPE f(x) Numerical...

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