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Homework Help: Solving Coefficient not using Fourier Series coefficient

  1. May 4, 2016 #1
    Given the Laplace's equation with several boundary conditions. finally i got the general solution u(x,t).
    One of the condition is that:

    After working on this I finally got:
    ∑An sin(π n y )sinh (π n) = y(1-y)

    However, i was asked to find An, by not using Fourier series coefficient, Is it possible to do so? Cheers
  2. jcsd
  3. May 5, 2016 #2


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    No, I don't think so. That hint usually arises in a situation where, if your equation were$$\sum_{n=1}^\infty A_n\sinh(\pi n)\sin(n\pi y) = 5\sin(3\pi y)$$where you could immediately say$$A_3 \sinh(3\pi) = 5$$ and all the other ##A_n=0##.
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