mws_gen_aae_spe_ppttaylorrevisited

mws_gen_aae_spe_ppttaylorrevisited - NUMERICAL METHODS:...

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10/14/11 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 ( 29 ( 29 ( 29 ( 29 ( 29 + + + + = + 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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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_aae_spe_ppttaylorrevisited - NUMERICAL METHODS:...

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