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    I have solved a heat flow PDE in part (a)
    part (b) I am not happy with my solution

    I kinda fudge and take the initial temperature in the midpoint as the average, otherwise I am out by a factor of 2 for the summation deduction.


    Am I fudging or is this valid?

    or worse still have I missed out a factor of 2 in the solution of the PDE
    (Note that the answer at the end of the question is my answer, so it might not be correct)

    many thanks


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    (Original post by TeeEm)
    I have solved a heat flow PDE in part (a)
    part (b) I am not happy with my solution

    I kinda fudge and take the initial temperature in the midpoint as the average, otherwise I am out by a factor of 2 for the summation deduction.


    Am I fudging or is this valid?

    or worse still have I missed out a factor of 2 in the solution of the PDE
    (Note that the answer at the end of the question is my answer, so it might not be correct)

    many thanks


    PDF.pdf
    It's valid. If a function is discontinuous somewhere, then its Fourier series assumes the value which is the average of the limits approached from each side.
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    (Original post by Smaug123)
    It's valid. If a function is discontinuous somewhere, then its Fourier series assumes the value which is the average of the limits approached from each side.
    This (PRSOM).

    (Original post by TeeEm)
    ..
    It's a bit of nasty hack, especially when it comes up in a question, but at the same time, if you are taking advantage of symmetry when setting up a question with discontinuities, it's pretty common that the natural "summation point" (i.e. the value(s) of x that mean you can eliminate the sin/cos terms from the Fourier series) fall on the discontinuities, so it happens enough that you should be aware of it.
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    (Original post by Smaug123)
    It's valid. If a function is discontinuous somewhere, then its Fourier series assumes the value which is the average of the limits approached from each side.

    (Original post by DFranklin)
    This (PRSOM).



    It's a bit of nasty hack, especially when it comes up in a question, but at the same time, if you are taking advantage of symmetry when setting up a question with discontinuities, it's pretty common that the natural "summation point" (i.e. the value(s) of x that mean you can eliminate the sin/cos terms from the Fourier series) fall on the discontinuities, so it happens enough that you should be aware of it.
    thanks for the response.


    I thought of that after I spending ages looking for that factor of 2 at the actual solution, so at the end I vaguely remembered something about the average value which I put down but I wanted to make sure before I add the question to my resources.

    Thanks again
 
 
 
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