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Short Fourier series question

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data

    ynms7.jpg

    2. Relevant equations

    Usual equations for calculating fourier series coefficients

    3. The attempt at a solution

    Well essentially I don't know what to let f(x) equal to for calculating the coefficients a0, an and bn. Should I use 1 + x/pi or 1 - x/pi? And what about the limits? I was thinking maybe between -pi and pi.

    Anyway here's my progress thus far, I think the graph is ok anyways.

    519dnb.jpg

    Thanks dudes. I would use latex but I suck at it :yuck:
     
  2. jcsd
  3. Dec 7, 2011 #2

    I like Serena

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    Homework Helper

    Looks fine.
    Just start with the generic formula for a0.
    The integral can be calculated by splitting it into the sum of 2 integrals.
     
  4. Dec 7, 2011 #3
    Take for example:

    [tex]a_1=\frac{1}{\pi}\int_{-\pi}^{\pi} f(x)\cos(x)dx[/tex]

    now, I want to integrate that function between -pi and pi but it's defined differently in two intervals. Why not just split up the intervals and write:

    [tex]a_1=\frac{1}{\pi}\left(\int_{-\pi}^{0} (1+x\pi)\cos(x)dx+\int_{0}^{\pi} (1-x\pi)\cos(x)dx\right)[/tex]

    However it is an even function so there are short-cuts for computing them. But for now, you may want to just do it this way.
     
  5. Dec 7, 2011 #4
    Great I understand completely now, thanks everyone. :smile:
     
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