Orthogonal series and boundary value problems
Solving the wave equation by separating the variables
This is an evaluated Mathematica notebook. If you have
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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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Part a) Find the Fourier Series for the functions f(x)=x^2, x^3, and x^4 on the interval [-Pi,Pi]