ourier Sine and Cosine Series. In each of Problems 29 througn 36: (a) Find the required Fourier series for the given function. (b) Sketch the graph of the function to which the series converges over three periods. ´1, 0 Answer V Solution (a) Using Equation (29) with L = 2, we have 2 sin(nt/2) ao = dx = 1 and dx = 2 an = Cos 2/nn for n = 1,5, 9, ... and an = -2/nn for n = 3,7,11,.... Hence we may write a2n = 0 and - 1)T, which when substituted into the series gives the desired answer. We obtain that Thus, an = 0 for n even, an = a2n-1 = 2(-1)*+1/(2n f(=) =- (-1)" Cos 2n – 1 1 2 (2n – 1)Tx 2 (b)
ourier Sine and Cosine Series. In each of Problems 29 througn 36: (a) Find the required Fourier series for the given function. (b) Sketch the graph of the function to which the series converges over three periods. ´1, 0 Answer V Solution (a) Using Equation (29) with L = 2, we have 2 sin(nt/2) ao = dx = 1 and dx = 2 an = Cos 2/nn for n = 1,5, 9, ... and an = -2/nn for n = 3,7,11,.... Hence we may write a2n = 0 and - 1)T, which when substituted into the series gives the desired answer. We obtain that Thus, an = 0 for n even, an = a2n-1 = 2(-1)*+1/(2n f(=) =- (-1)" Cos 2n – 1 1 2 (2n – 1)Tx 2 (b)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help with this one. After computing the an, how do we get rid of the sin on the final answer? I did not get it. Please show me the work and give me as many details as possible. And how to draw the graph? should we just draw the even extension?
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