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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
This question is asking
(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?
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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