L value

[Chad S]

I'm a little confused on the value of L. I'll use problem 12 in
section 9.5 as an example. The problem says Ut = Uxx , 0<x<100, ... In
this case I believe we set the value of L = 100. However, when finding
the fourier series of f(x), I was under the impression we set L = to
half the period, so in this case 50. But when we do this, I don't
think f(x) would match up with u(x,0). How am I thinking of this wrong?

[Professor Laugesen]

Remember that if you are using a sine series or a cosine series on
0<x<L, then after doing an odd or even *extension*, you see that the
full period interval is -L<x<L. So the period is 2L, or in other
words, L is half the period,

[Chad S]

ohh, ok that makes sense, thanks