# Periodic functions

1. Dec 14, 2003

### scariari

I'm doing a practice exam for a math test on thursday, wondering if anyone could help figure out how to get from one step to the next. i dont think that the background info is necessary for these two steps.

the file is attached (Adobe acrobat).

what i am wondering about is the answer under (2b).
If the solution for finding (del)u(x,y) were lettered a through d (4 steps, i am wondering how the professer got from b to c.

of course i have emailed him as well.

#### Attached Files:

• ###### examsolutions.pdf
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47.1 KB
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2. Dec 14, 2003

### nbo10

Look in the last line of the 2b) paragraph.
$\Delta \frac{16}{\pi^4 kl(k^2+l^2)}sin(k \pi x)sin(l \pi y) =$
$\frac{16}{\pi^4 kl(k^2+l^2)}(-\pi^2 (k^2 + l^2)sin(k\pi x)sin(l\pi y))$

JMD

Last edited: Dec 14, 2003