Author Topic: HA 6, sections 4.3-4.5, problem 6  (Read 142 times)

Shaghayegh A

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HA 6, sections 4.3-4.5, problem 6
« on: November 14, 2016, 02:18:44 PM »
http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter4/S4.5.P.html

For problem 6f, I get $b_n=0$, which I know is wrong.
I have $$b_n=\frac{2}{\pi} \int_0 ^{\pi} \sin((m-1/2)x) \sin((n+1/2)x) dx \\
=1/pi \int_0 ^{\pi} \cos((m-n-1)x) -\cos((m+n)x) dx =0$$
Separately for $n \neq m-1$ and $n=m-1$. Why am I getting b_n=0?

Victor Ivrii

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Re: HA 6, sections 4.3-4.5, problem 6
« Reply #1 on: November 15, 2016, 07:03:03 AM »
The last line of calculations is wrong. We already counted
$\in_0^\pi \cos (kx)\,dx$