# Homework Help: Fourier coefficient calculations

1. Feb 2, 2012

### fluidistic

1. The problem statement, all variables and given/known data
I've been following closely a book on PDE's working through lots of steps but here I'm stuck.
Basically I have the relation $f(x)= \sum _{n=1}^\infty F_n \sin \left ( \frac{n\pi x }{L} \right )$. I want to calculate the Fourier coefficients $F_n$.
I look at the definition in the same book and I see that if $f(x)= \sum _{n=1}^\infty c_n g_n(x)$ then $c_n=\frac{1}{||g_n||^2} \int _a ^b f(x)g_n (x)dx$.
Since I'm solving the 1 dimensional wave equation between $x=0$ and $x=L$, the limits of the integral are in my case $0$ and $L$.
I get that $F_n =\frac{1}{|| \sin \left ( \frac{n\pi x }{L} \right )||^2} \int _0^L f(x) \sin \left ( \frac{n\pi x }{L} \right ) dx$. I don't really know how to calculate the modulus squared of the denominator. When I look in the book it says that $F_n=\frac{2}{L} \int _0^L f(x) \sin \left ( \frac{n\pi x }{L} \right ) dx$. I've absolutely no idea how he did this calculation.

2. Relevant equations
I don't know if there are any other than the one I posted.

3. The attempt at a solutionOnly thoughts so far...
Any clarification is welcome.

2. Feb 2, 2012

### jbunniii

What is the definition of the modulus squared of a function?

3. Feb 2, 2012

### fluidistic

Ok thank you, I just found out the result... I didn't know to tell the truth, now I know. Problem solved.