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che132a-rec-5

# che132a-rec-5 - Chemical Engineering 132A Analytical...

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Chemical Engineering 132A Analytical Methods of Chemical Engineering Professor Mike Gordon, Fall 2011 Mathematica Assignment #5: Fourier Series 1) Which of the following functions are orthogonal on the domain [-L,L]? Hint : directly integrate all possible pairings of functions for n m and n m = . cos , sin , cos , sin n x n x m x m x L L L L π Which combinations give you non-zero results? 2) Consider the following function on the domain [-2,2]: 3 0 0 ( ) 1 0 x f x x x < = - a) How could you represent f(x) in compact form? Plot this function on the domain [-2,2]. b) Define new functions an(x,L) and bn(x,L) which compute the a n and b n Fourier coefficients for f(x) via direct integration. c) If we want to make a Fourier series for f(x) on the domain [-2,2], what should you use for L? Make two tables of the first four a

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che132a-rec-5 - Chemical Engineering 132A Analytical...

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