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

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The discussion focuses on solving the Fourier series for the temperature distribution T on a plate defined by the coordinates (0,0) to (1,2). The equation T(x,0) = 1-x = Bn (sinh 2n∏) (sin n∏x) leads to the calculation of the Fourier coefficients bn, specifically bn = 2 ∫(0 to 1) (1-x) sin(n∏x) dx. This equation is derived from the application of Fourier series principles rather than Laplace transforms, clarifying the method used for solving the problem.

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zheng89120
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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 = Bn (sinh 2n∏) (sin n∏x) = bn (sin n∏x)

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

How did they arrive at that equation to solve for bn? thanks(forgot to read the stickies, move this post if you wish, thanks)
 
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Hi zheng89120! :smile:

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.
 

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