Mws_gen_dif_spe_forw - Forward Divided Difference Topic Differentiation Major General Engineering Authors Autar Kaw Sri Harsha Garapati

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5/21/2008 http://numericalmethods.eng.usf.edu 1 Forward Divided Difference Topic: Differentiation Major: General Engineering Authors: Autar Kaw, Sri Harsha Garapati
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http://numericalmethods.eng.usf.edu 2 Definition i x . () ( )( ) x x f x x f x x f Δ Δ 0 Δ lim + = f(x) Slope at x y i x
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http://numericalmethods.eng.usf.edu 3 Forward Divided Difference x x Δ + x x () ( ) x x f x x f x f Δ Δ + ( ) x x f x x f x f i i i Δ Δ + ) ( x f
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http://numericalmethods.eng.usf.edu 4 Example Example : The velocity of a rocket is given by () 30 0 , 8 . 9 2100 10 14 10 14 ln 2000 4 4 × × = t t t t ν where given in m/s and t is given in seconds . Use forward difference approximation of the first derivative of ( ) t ν to calculate the acceleration at . 16 s t = Use a step size of . 2 s t = Δ ( ) t t ν t ν t a i i i Δ 1 + Solution: 16 = i t
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http://numericalmethods.eng.usf.edu 5 2 Δ = t t t t i i Δ 1 + = + 18 2 16 = + = () 2 16 18 16 ν = a 18 8 . 9 18 2100 10 14 10 14 ln 2000 18 4 4 × × = s m / 02 . 453 = 16 8 . 9 16 2100 10 14 10 14
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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Mws_gen_dif_spe_forw - Forward Divided Difference Topic Differentiation Major General Engineering Authors Autar Kaw Sri Harsha Garapati

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