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am confused about the coefficient for the sine term. Since similar previous questions I did, the coefficient for an, bn, or a0 is 1/L. Why is this 2/L? Why is that? Could you please explain? In what circumstance the coefficient will be 2/L? or 1/L?

am confused about the coefficient for the sine term. Since similar previous questions I did, the coefficient for an, bn, or a0 is 1/L. Why is this 2/L? Why is that? Could you please explain? In what circumstance the coefficient will be 2/L? or 1/L?

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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(a) Find the required Fourier series for the given function.

(b) Sketch the function graph to which the series converges over three periods.

I am confused about the coefficient for the sine term. Since similar previous questions I did, the coefficient for an, bn, or a0 is 1/L. Why is this 2/L? Why is that? Could you please explain? In what circumstance the coefficient will be 2/L? or 1/L? 

31. f (x) = 1, 0 < x < n; cosine series, period 27 Answer O Solution (a) L = T. For an even extension of the function, the sine coefficients are zero. The cosine coefficients are given by 2 f(x) dx = dx = 2, ao L and for n > 0, dx L 0. an COS COS пх dr The even extension of the given function is a constant function. As expected, the Fourier cosine series is f(x) = ao :1. 2 (b) 2 1 65
Transcribed Image Text:31. f (x) = 1, 0 < x < n; cosine series, period 27 Answer O Solution (a) L = T. For an even extension of the function, the sine coefficients are zero. The cosine coefficients are given by 2 f(x) dx = dx = 2, ao L and for n > 0, dx L 0. an COS COS пх dr The even extension of the given function is a constant function. As expected, the Fourier cosine series is f(x) = ao :1. 2 (b) 2 1 65
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