# Fourier series expansion of periodic function

(See attached file for full problem description)

Consider a periodic function f(x) with period L.

Over one period, f(x) = sin(2*pi*x/L) over the interval -L/4 to L/4, f(x) = 0 over the intervals -L/2 to -L/4, and L/4 to L/2.

Derive an expression for the nth Fourier series coefficient, an.

In the Fourier series expansion

plot for n = -4 to 4 using matlab, and superimpose onto a plot for f(x)

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#### Solution Summary

The solution is comprised of detailed calculation of Fourier series expansion of periodic function. It also includes the Matlab codes to plot the graphs.

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