# Orthogonal series and boundary value problems
Solving the wave equation by separating the variables

This is an evaluated *Mathematica* notebook. If you have
*Mathematica* or *MathReader* (which is available free from WRI, you may download the
notebook file. This notebook contains some *Mathematica*
calculations for chapter IV,
*Calculating Fourier series* of Harrell's WWW textbook.

# Solution to Problem IV.5

### Solution by Richard W. Cowan, April 1996, edited for length by

Evans M. Harrell, II, (c) copyright 1996, all rights reserved

Calculate the Fourier Series for the functions f(x) = x^2, x^3, and x^4.
Calculate them

on the intervals a) [-Pi, Pi] and b) [0,1]
The formulae for these coefficients are:

a[0] := (1/L) Integrate[f[x], {x,0,L}] (the average of f)

a[m] := (2/L) Integrate[f[x] Cos[2 Pi m x/L], {x,0,L}], m = 1, 2, ...

b[n] := (2/L) Integrate[f[x] Cos[2 Pi n x/L], {x,0,L}], n = 1, 2, ...

Up to chapter IV!

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