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Fourier series problem

  1. Dec 2, 2013 #1
    1. The problem statement, all variables and given/known data
    https://wiki.math.ntnu.no/_media/tma4120/2013h/tma4120_h11.pdf

    Check out the solution to problem 4b)

    My question is: Why do they set ##b_n = \frac{2}{\pi} \int_{0}^{\pi}(...)dx## instead of ##b_n = \frac{1}{\pi} \int_{0}^{\pi} (...)dx##?

    Ie, why did they multiply the integral with 2? Did they find the fourier integral to the odd expansion of ##sin(x)^2##? Because that's the only way for sin(x)^2 to be defined by solely a sine fourier expansion?

    EDIT: Ooops, posted in wrong section. Please move to calculus and beyond homework forum! sorry!
     
    Last edited: Dec 2, 2013
  2. jcsd
  3. Dec 2, 2013 #2

    LCKurtz

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    Yes, that's exactly it. Since they only have sine functions for the eigenfunction expansion, the FS must represent an odd function so they take the odd extension of ##\sin^2(x)## and use the half range formulas.
     
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