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# Fourier Series and Fourier Sine and Cosine Series

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1.) Find fourier series of f(x)=4, x greater than -3 and less than 3

and

2.) Find fourier series of f(x) = x^2-x+3, x greater than -2 and less than 2

and

3.) Write the cosine and sine fourier series f(x)=x^2 for x greater than 0 and less than 2

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#### Solution Preview

For a function periodic on an interval instead of , a simple change of variables can be used to transform the interval of integration from to . Let

(11)

(12)
Solving for gives , and plugging this in gives

(13)
Therefore,

(14)

(15)

(16)

1. , ...

#### Solution Summary

Fourier Series and Cosine and Sine Fourier Series are found. The solution is detailed and well presented.

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