Understanding the Fourier Series for Solving Laplace's Equation on a Plate

[zheng89120]

The question involved solving the "T" on a plate sized from (0,0) to (1,2). Any ways, I will spare you of the details and get to the line in the solution I was confused with:

Bottom: T(x,0) = 1-x = B_n (sinh 2n∏) (sin n∏x) = b_n (sin n∏x)

The next line confused me: b_n = 2 ₀∫¹ (1-x) sin n∏x dx

How did they arrive at that equation to solve for b_n? thanks(forgot to read the stickies, move this post if you wish, thanks)

 

[I like Serena]

Hi zheng89120!

That looks like the Fourier series instead of the Laplace transform.
http://en.wikipedia.org/wiki/Fourier_series



Btw, this looks like homework/coursework.
Is it?
If so, you should post in the homework section.