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Math Help - Fourier Series

  1. #1
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    Fourier Series

    Hello,

    Can anyone please help me with the attached file. Questions (iv) to (vi). Its related to Fourier Series.
    Attached Thumbnails Attached Thumbnails Fourier Series-fourier6.jpg  
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  2. #2
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    Quote Originally Posted by atwinix View Post
    Hello,

    Can anyone please help me with the attached file. Questions (iv) to (vi). Its related to Fourier Series.
    What is the problem with these? The third line in each tells you that the function is periodic with period
    2 \pi so any interval of that length is what you use in the integrations and the basis functions are
    \sin(nx) and \cos(nx).

    RonL
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  3. #3
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    Yes, I know how the Fourier series expansion work.

    I am having problem with the integration between the limits for question 6 (iv) as you get something like:

    ∫ (π+t) cos (nt) dt + ∫ (π-t) cos (nt) dt
    Last edited by atwinix; August 17th 2007 at 08:40 PM.
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  4. #4
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    Quote Originally Posted by atwinix View Post
    Yes, I know how the Fourier series expansion work.

    I am having problem with the integration between the limits for question 6 (iv) as you get something like:

    ∫ (π+t) cos (nt) dt + ∫ (π-t) cos (nt) dt
    Using integration by parts with u=(\pi-t) and dv=\cos(nt):

    \int_0^\pi (\pi-t) \cos(nt)~dt = \left[ \frac{(\pi-t)}{n} \sin(nt) \right]_0^{\pi}+\int_0^{\pi}\frac{1}{n^2} \sin(nt)~dt =\frac{1}{n^2}(1-(-1)^n)

    which is 2/n^2,\ n=1, 3, 5, .. and 0,\ n=2,4,..

    RonL
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  5. #5
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    Oh!!! So that's the catch! I shall try it.

    Thanks loads.
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