Toronto Math Forum
APM3462016F => APM346Lectures => Chapter 4 => Topic started by: Shaghayegh A on November 14, 2016, 02:18:44 PM

http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter4/S4.5.P.html
For problem 6f, I get $b_n=0$, which I know is wrong.
I have $$b_n=\frac{2}{\pi} \int_0 ^{\pi} \sin((m1/2)x) \sin((n+1/2)x) dx \\
=1/pi \int_0 ^{\pi} \cos((mn1)x) \cos((m+n)x) dx =0$$
Separately for $n \neq m1$ and $n=m1$. Why am I getting b_n=0?

The last line of calculations is wrong. We already counted
$\in_0^\pi \cos (kx)\,dx$