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Can somebody check my work on this Fourier Series problem?

  1. Nov 29, 2015 #1
    1. The problem statement, all variables and given/known data
    pix.jpg

    2. Relevant equations

    img1.gif
    img3.gif


    3. The attempt at a solution

    Since P=2L, L=1 ?

    a_o = 1/2 [ ∫(from -1 to 0) -dx + ∫(from 0 to 1) dx ] = 1/2 [ (0-1) + (1-0) ] = 1/2(0) = 0

    a_n = - ∫ (from -1 to 0) cosnπx dx + ∫ (from 0 to 1) cosnπx dx = 0

    b_n = - ∫ (from -1 to 0) sinnπx dx + (from 0 to 1) sinnπx dx = 2/nπ - 2/nπ*(cosnπ) = 2nπ / (1-cosnπ) = { 4/nπ n is odd ; 0 is even



    The problem is my teacher has this as his answer:
    pic2.jpg

    Am i doing something incorrectly?
     
    Last edited: Nov 29, 2015
  2. jcsd
  3. Nov 29, 2015 #2
    Why not check by graphing the original function and the Fourier series?
     
  4. Nov 29, 2015 #3
    I understand you can check through graphing, but I just wanted some verification that my math is correct?
     
  5. Nov 29, 2015 #4
    Wait L is suppose to equal 2 correct? Not 1?
     
  6. Nov 29, 2015 #5

    Ray Vickson

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    If you mean that one period of the function goes from ##-L## to ##+L## then yes, of course ##L = 2##. That was implied in the question.
     
  7. Nov 29, 2015 #6
    I figured...
    For my b_n I got 2/(n*pi) [1 - cos(n*pi / 2 ).

    Is this correct?
     
  8. Nov 29, 2015 #7

    vela

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    Why don't you do as suggested and graph the resulting series? That'll tell you immediately if you got the right series. If you still want someone to check your work, you need to show it. Just posting the answer is next to useless.
     
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