The Fourier expansion of an odd function F(1) must use sines instead of cosines: 2nnI 2nRI dr Ffr)-Σ Β, sin F(r) sin with %3D %3D n=0 ere, the B are the Fourier coefficients. Consider the square wave shown below as an example ol E periodic odd function F(r). (a) Write down an expression for F(r) valid for the range 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The Fourier expansion of an odd function F(1) must use sines instead of cosines:
2.
2nRI
de
F(r) = Bn sin
with
Bn =
F(x) sin
%3D
%3D
nere, the B are the Fourier coefficients. Consider the square wave shown below as an example of a
periodic odd function F(r). (a) Write down an expression for F(r) valid for the range 0<r< A. (b) by
evaluating the integral in the equation above, show that the Fourier coefficients B, for this square wave
are given by
f(r)
a = X/2
0.
for even n
Bn =
%3D
A
4A
for odd n
nR
Transcribed Image Text:The Fourier expansion of an odd function F(1) must use sines instead of cosines: 2. 2nRI de F(r) = Bn sin with Bn = F(x) sin %3D %3D nere, the B are the Fourier coefficients. Consider the square wave shown below as an example of a periodic odd function F(r). (a) Write down an expression for F(r) valid for the range 0<r< A. (b) by evaluating the integral in the equation above, show that the Fourier coefficients B, for this square wave are given by f(r) a = X/2 0. for even n Bn = %3D A 4A for odd n nR
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