Sep 27, 2004
Fourier series notes
This is a *very* sketchy version of the last stuff
I did on the blackboard Please refer to your own notes to flesh this out.
I) /\ y=H
/ \
/ \
/ \
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x=0 x=L
Let y(x) be a triangle function, as above.
We want to express this as a sum of sine waves.
The boundary conditions y(0)=y(L)=0 imply that the sinusoids are
sin( 2 pi n x/(2L) ) where n=1,2,3,4,5,...
So the problem is to find (A1, A2, A3, ...) such that
y(x) = sum [ An sin( 2 pi n x/(2L) ) ] for n=1,2,3,...
where y(x) = x 2H/L for 0 < x < L/2,
y(x) = (L-x) * 2H/L for L/2 < x < L
Using the fact that integral( sin( 2 pi n x/(2L) ) dx ) for 0