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
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 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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