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Fourier Series

  1. Mar 16, 2007 #1
    can anyone help me interpret what exactly this question is asking as i am quite unawares

    By direct substitution into the heat equation and calculation of boundary values,
    verify that the solution u(x, t) for a metal rod of length L which satisfies
    the initial temperature u(x, 0) = f(x) and the boundary conditions
    u(0, t) = u(L, t) = 0 is given by

    u(x, t) = (sum)B(n)sin(npix/L)Dx

    NB: Do not re-derive this formula, just verify that it satisfies the equation and
    boundary conditions!]

    i dont know how to do this without rederiving this equation,i do not know how to answer this question ,could anyone help
  2. jcsd
  3. Mar 16, 2007 #2


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    Homework Helper

    ie. put your given solution into the equation and show that LHS =RHS
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