mws_gen_dif_ppt_discrete - Differentiation-Discrete...

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1/10/2010 http://numericalmethods.eng.usf.edu 1 Differentiation-Discrete Functions Major: All Engineering Majors Authors: Autar Kaw, Sri Harsha Garapati http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates
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Differentiation –Discrete Functions http://numericalmethods.eng.usf.edu
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http://numericalmethods.eng.usf.edu 3 Forward Difference Approximation ( ) ( ) ( ) x x f x x f x x f Δ Δ 0 Δ lim + = For a finite ' Δ ' x ( ) ( ) ( ) x x f x x f x f +
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http://numericalmethods.eng.usf.edu 4 x x+ Δ x f(x) Figure 1 Graphical Representation of forward difference approximation of first derivative. Graphical Representation Of Forward Difference Approximation
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http://numericalmethods.eng.usf.edu 5 Example 1 The upward velocity of a rocket is given as a function of time in Table 1. Using forward divided difference, find the acceleration of the rocket at . t v(t) s m/s 0 0 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 Table 1 Velocity as a function of time s 16 = t
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http://numericalmethods.eng.usf.edu 6 Example 1 Cont. ( ) ( ) ( ) t t t t a i i i + ν 1 15 = i t 5 15 20 1 = = = + i i t t t To find the acceleration at , we need to choose the two values closest to , that also bracket to evaluate it. The two points are and . s 16 = t s 16 = t s 20 = t s 15 = t 20 1 = + i t s 16 = t Solution
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http://numericalmethods.eng.usf.edu 7 Example 1 Cont. ( ) ( ) ( ) 2 m/s 914 . 30 5 78 . 362 35 . 517 5 15 20 16 ν a
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http://numericalmethods.eng.usf.edu 8 Direct Fit Polynomials ' 1 ' + n ( ) ( ) ( ) ( ) n n y x y x y x y x , , , , , , , , 2 2 1 1 0 0 th n ( ) n n n n n x a x a x a a x P + + + + = 1 1 1 0 ( ) ( ) 1 2 1 2 1 1 2 ) ( + + + + = = n
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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_ppt_discrete - Differentiation-Discrete...

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