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Advanced Engineering Mathematics
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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Q33

The question is asking: 

(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.

I am confused about why the coefficient of bn is 2/L? and how to draw the graph of function. 

0, 0<x < T, 33. f (x) = 1, T < x < 27, sine series, period 67 2, 2т < х < Зт; Answer Solution (a) L = 37. For an odd extension of the function, the cosine coefficients are zero. The sine coefficients are given by 27 37T 2 dx + 3 2 bn i| f(x) sin dx L sin 2 sin dx 3 T 2 cos na – cos(nT/3) – cos(2nn/3) -2- Therefore the Fourier sine series of the specified function is 2nt (2) = - 2 cos na sin 3 + cos COS 3 3 n
Transcribed Image Text:0, 0<x < T, 33. f (x) = 1, T < x < 27, sine series, period 67 2, 2т < х < Зт; Answer Solution (a) L = 37. For an odd extension of the function, the cosine coefficients are zero. The sine coefficients are given by 27 37T 2 dx + 3 2 bn i| f(x) sin dx L sin 2 sin dx 3 T 2 cos na – cos(nT/3) – cos(2nn/3) -2- Therefore the Fourier sine series of the specified function is 2nt (2) = - 2 cos na sin 3 + cos COS 3 3 n
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