a. Expand the function f(0)=0² in a Fourier series in the range –r<0
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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Transcribed Image Text:a. Expand the function f(0)=0² in a Fourier series in the range –A<0<n. Sketch the
function within and outside of the given range.
b. For the Fourier Series obtained, let 0 = T and deduce the series for E
n²
c. Determine the Fourier series for the function f (0)=02 in the range -A <0 <T. The
function has a period of 27. Sketch the graph over the given period and extend it to
outside the range
d. For the Fourier series mentioned in part c above , let 0 = T and show that E÷=-
n2
%3D
ao =
2n
f (x) dr
E s(x)cosnxdx
an=
(n=1,2,3,...)
1
b,=-/ sx)sin nrdr
- s(x)sin nxdx
and
(n=1,2,3, ...)
2nd pic as reference for solving the question
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