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(d) Briefly explain why the Dirichlet conditions hold. (e) By evaluating f(x) at a suitable value of r, find 1 (2m – 1)2 m=1 (f) Given n=1 using Parseval's theorem and the value of (1), deduce that 1 (2m – 1)4 96 m=1

(d) Briefly explain why the Dirichlet conditions hold. (e) By evaluating f(x) at a suitable value of r, find 1 (2m – 1)2 m=1 (f) Given n=1 using Parseval's theorem and the value of (1), deduce that 1 (2m – 1)4 96 m=1

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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part D E F

Consider the period 4 function -2 < x < 0 0 <x < 2 ( f(x+4) otherwise. f(r) = {2 – x (a) Sketch three periods of f(x). (b) Show that the Fourier coefficients b1, b2, ... may be written as 1 bam-1 = 0 , bzm for m = 1, 2, .... (c) Knowing the Fourier coefficients 4 a2m = 0 , d2m-1= (2m – 1)272 for m = 1,2, ..., write down the Fourier series corresponding to f(r). (d) Briefly explain why the Dirichlet conditions hold. (e) By evaluating f(x) at a suitable value of r, find 1. (2m – 1)2 (f) Given n=1 using Parseval's theorem and the value of (1), deduce that 1. (2m – 1)4
Transcribed Image Text:Consider the period 4 function -2 < x < 0 0 <x < 2 ( f(x+4) otherwise. f(r) = {2 – x (a) Sketch three periods of f(x). (b) Show that the Fourier coefficients b1, b2, ... may be written as 1 bam-1 = 0 , bzm for m = 1, 2, .... (c) Knowing the Fourier coefficients 4 a2m = 0 , d2m-1= (2m – 1)272 for m = 1,2, ..., write down the Fourier series corresponding to f(r). (d) Briefly explain why the Dirichlet conditions hold. (e) By evaluating f(x) at a suitable value of r, find 1. (2m – 1)2 (f) Given n=1 using Parseval's theorem and the value of (1), deduce that 1. (2m – 1)4
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