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mws_gen_dif_ppt_discrete

mws_gen_dif_ppt_discrete - DISCRETE FUNCTIONS

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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
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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 ( 29 ( 29 ( 29 x x f x x f x x f Δ Δ 0 Δ lim - + = For a finite ' Δ ' x ( 29 ( 29 ( 29 x x f x x f x f - +
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                                            http://numericalmethods.eng.usf.edu 4 x x+Δx 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.                                     ( 29 ( 29 ( 29 t t t t a i i i - + ν 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.
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