mws_gen_dif_ppt_discrete

mws_gen_dif_ppt_discrete - 10/14/11...

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Unformatted text preview: 10/14/11 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 Differentiation Discrete Functions http://numericalmethods.eng.usf.edu http://numericalmethods.eng.usf.edu 3 Forward Difference Approximation ( 29 ( 29 ( 29 x x f x x f x x f lim- + = For a finite ' ' x ( 29 ( 29 ( 29 x x f x x f x f - + http://numericalmethods.eng.usf.edu 4 x x+x f(x) Figure 1 Graphical Representation of forward difference approximation of first derivative. Graphical Representation Of Forward Difference Approximation 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 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 http://numericalmethods.eng.usf.edu 6 Example 1 Cont. ( 29 ( 29 ( 29 t t t t a i i i - + 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 http://numericalmethods.eng.usf.edu 7 Example 1 Cont....
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This note was uploaded on 10/14/2011 for the course CEE 305 taught by Professor Nguyen,d during the Spring '08 term at Old Dominion.

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mws_gen_dif_ppt_discrete - 10/14/11...

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