# Fourier Equations

1. Apr 12, 2012

### Invyz

1. The problem statement, all variables and given/known data

Attached.

2. Relevant equations

3. The attempt at a solution

For #1: I've attempted to use the identity sin(x)sin(y) = 1/2(cos(x-y)-cos(x+y)) and the similar related identities for sin(x)cos(y) and cos(x)cos(y), but I end with answers that are undefined when m = n due to the term (m-n).

For #2: I don't see any derivation in the lecture notes(attached), so I don't know where to start :/ Other than that you probably begin with the summation as n goes to infinity of the fourier constant times the cosine(2*pi*n*t/T)

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• ###### L18_Spectral_Analysis.pdf
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2. Apr 13, 2012

### clamtrox

Do the case m=n separately. You can probably calculate the integral by hand in that case.

Write function f using the Fourier transform, multiply both sides of the equation by cos(2πmx/L). Then integrate both sides using the results you got from #1.