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 / \ / \ / \ ---------- 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