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a. Expand the function f(0)=0² in a Fourier series in the range –r<0

a. Expand the function f(0)=0² in a Fourier series in the range –r<0

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. 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
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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