# Fourier series

f(x)= {0 -2<x<0 f(x+4) = f(x)

{1 0<x<2

I have to find the Fourier series of the problem and sketch the graph of the function at 3 periods. I'm not sure if you need my text and what sections were covering or not so I'll just give it. "Elementary differential equations and boundary value problems" by William E. Boyce and Richard C. Diprima. It's mainly stuff we covered in 10.2-10.5. Thanx a lot for your help.

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#### Solution Preview

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

Checkout the following site:

http://mathworld.wolfram.com/FourierSeries.html

http://mathworld.wolfram.com/FourierSeriesSquareWave.html

http://mathworld.wolfram.com/GibbsPhenomenon.html

Method 1: Brute Force.

Any periodic function in the interval [-L,L] with a period 2L can be expanded ...

#### Solution Summary

This shows how to find Fourier series and sketch a graph.