mws_gen_aae_spe_ppttaylorrevisited(1)

mws_gen_aae_spe_ppttaylorrevisited(1) - Taylor Series...

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1/11/2010 http://numericalmethods.eng.usf.edu 1 Taylor Series Revisited Major: All Engineering Majors Authors: Autar Kaw, Luke Snyder http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates
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Taylor Series Revisited http://numericalmethods.eng.usf.edu
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http://numericalmethods.eng.usf.edu 3 What is a Taylor series? Some examples of Taylor series which you must have seen + + = ! 6 ! 4 ! 2 1 ) cos( 6 4 2 x x x x + + = ! 7 ! 5 ! 3 ) sin( 7 5 3 x x x x x + + + + = ! 3 ! 2 1 3 2 x x x e x
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http://numericalmethods.eng.usf.edu 4 General Taylor Series The general form of the Taylor series is given by ( ) ( ) ( ) ( ) ( ) + + + + = + 3 2 ! 3 ! 2 h x f h x f h x f x f h x f provided that all derivatives of f(x) are continuous and exist in the interval [x,x+h] What does this mean in plain English? As Archimedes would have said, “Give me the value of the function at a single point, and the value of all (first, second, and so on) its derivatives at that single point, and I can give you the value of the function at any other point” ( fine print excluded )
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http://numericalmethods.eng.usf.edu
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mws_gen_aae_spe_ppttaylorrevisited(1) - Taylor Series...

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