The Fourier series for the function f(x) = x, -T < x < T is sin nx E(-1)"-1; n n=1 a) Sketch the graph of the function fp which is the pointwise sum of the series on R. b) Use Parseval's formula to show that = 5. c) Use the integration theorem to show that 2 (7? – 3a²) = E(-1)"-108 næ -T < x < T n2 n=1 and n*(r² – x²) = E(-1)"-1 sin næ -T < x
The Fourier series for the function f(x) = x, -T < x < T is sin nx E(-1)"-1; n n=1 a) Sketch the graph of the function fp which is the pointwise sum of the series on R. b) Use Parseval's formula to show that = 5. c) Use the integration theorem to show that 2 (7? – 3a²) = E(-1)"-108 næ -T < x < T n2 n=1 and n*(r² – x²) = E(-1)"-1 sin næ -T < x
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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Solve the last part
Transcribed Image Text:1. The Fourier series for the function f(x) = ;x, –T < x < r is
sin nx
n
n=1
a) Sketch the graph of the function fp which is the pointwise sum of the
series on R.
b) Use Parseval's formula to show that E = .
n=1
c) Use the integration theorem to show that
COS nx
(7? – 30²) = E(-1)"-1
n2
-T < x < T
n=1
and
sin nx
* (r² – a²) = E(-1)"-1;
-T < x < T
n3
n=1
d) Discuss whether the sum of each Fourier series in c) is piecewise
continuous, continuous, piecewise C1 or C1 on R. Sketch the graphs
of the sum functions.
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