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A function is defined over (0,3) by We then extend it to an even periodic function of period 6 and its graph is displayed below. The function may be approximated by the Fourier series bn = ao = 0 a2k-1= ww a2k= f(x) = = for k= 1, 2,... f(x) = ap +2=1 (an x + 2. an cos where L is the half-period of the function. NTX Use the fact that f(x) sin( is an odd functions, enter the value of bn in the box below. L & P for n = 0,1,2,... Hence besides the constant term, the Fourier series made up entirely of cosines. Ⓡa 5 Calculate the following coefficients of the Fourier series and enter them below in Maple syntax. X 10 ηπα ηπε ¹T²) + bn sin (¹T² )), 15

A function is defined over (0,3) by We then extend it to an even periodic function of period 6 and its graph is displayed below. The function may be approximated by the Fourier series bn = ao = 0 a2k-1= ww a2k= f(x) = = for k= 1, 2,... f(x) = ap +2=1 (an x + 2. an cos where L is the half-period of the function. NTX Use the fact that f(x) sin( is an odd functions, enter the value of bn in the box below. L & P for n = 0,1,2,... Hence besides the constant term, the Fourier series made up entirely of cosines. Ⓡa 5 Calculate the following coefficients of the Fourier series and enter them below in Maple syntax. X 10 ηπα ηπε ¹T²) + bn sin (¹T² )), 15

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 function is defined over (0,3) by We then extend it to an even periodic function of period 6 and its graph is displayed below. The function may be approximated by the Fourier series bn = where I is the half-period of the function. Use the fact that f(x) sin( NTX L ww ao = 0 a2k-1 = f(2)=/2+2. a2k = for k= 1, 2, ... f(x) = ao + ₁ (an cos ( nTx L Hence besides the constant term, the Fourier series made up entirely of cosines. X + bn sin (¹T²)), L 1, for n=0,1,2,... 10 is an odd functions, enter the value of bn in the box below. Calculate the following coefficients of the Fourier series and enter them below in Maple syntax. 15
Transcribed Image Text:A function is defined over (0,3) by We then extend it to an even periodic function of period 6 and its graph is displayed below. The function may be approximated by the Fourier series bn = where I is the half-period of the function. Use the fact that f(x) sin( NTX L ww ao = 0 a2k-1 = f(2)=/2+2. a2k = for k= 1, 2, ... f(x) = ao + ₁ (an cos ( nTx L Hence besides the constant term, the Fourier series made up entirely of cosines. X + bn sin (¹T²)), L 1, for n=0,1,2,... 10 is an odd functions, enter the value of bn in the box below. Calculate the following coefficients of the Fourier series and enter them below in Maple syntax. 15
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