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Fourier series expansions

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1. Find the Fourier series expansions of f(x) = Co + C1x^2 with respect to the following two orthonormal bases on the interval [0,L] (L>0)

a) {(1/L)^.5, (2/L)^.5*cos*((k*pi*x)/L)|k=1,2,...}
b) {(2/L)^.5*sin*((k*pi*x)/L)|k=1,2,....}.

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Solution Summary

This solution shows how to find Fourier series expansions for the given equation.

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Fourier Series Expansion: Example Problem

Please see the attached file for the fully formatted problems.

See f(x) in the file.
1. Sketch f(x) over -3<x<3
2. Is f(x) odd, even or neither?
3. Solve for the Fourier coefficients.
4. Write out the Fourier series expansion up to n=3

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