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Math Help - Fourier Series, Sketch and Compute

  1. #1
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    Question Fourier Series, Sketch and Compute

    See figure attached for problem statement as well as my attempt.

    I'm not entirely sure if I've done the sketch in part a) correctly, can someone verify this for me?

    Also, when solving for a_{n} I noticed that all even values of n will give me 0. I tried to rewrite this so that only odd n's are valid.

    Can I do this, and am I correct in doing so?

    Can anyone else spot any other problems?

    Thanks again!
    Attached Thumbnails Attached Thumbnails Fourier Series, Sketch and Compute-2007q3.jpg  
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  2. #2
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    Quote Originally Posted by jegues View Post
    See figure attached for problem statement as well as my attempt.

    I'm not entirely sure if I've done the sketch in part a) correctly, can someone verify this for me?

    Also, when solving for a_{n} I noticed that all even values of n will give me 0. I tried to rewrite this so that only odd n's are valid.

    Can I do this, and am I correct in doing so?

    Can anyone else spot any other problems?

    Thanks again!

    Assuming you evaluated correctly the corresponding integrals (and it looks like you did it correctly, indeed. It's

    only that I didn't check them), your result looks fine.

    Just do not write in the last line "f(x)=..." since you still have to calculate the coefficients of the sines...

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    Assuming you evaluated correctly the corresponding integrals (and it looks like you did it correctly, indeed. It's

    only that I didn't check them), your result looks fine.

    Just do not write in the last line "f(x)=..." since you still have to calculate the coefficients of the sines...

    Tonio
    The only reason I stated the last line was because the question stated NOT to calculate the coefficients of the sine series. Is it still unacceptable to write f(x) = ... ?
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  4. #4
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    Quote Originally Posted by jegues View Post
    The only reason I stated the last line was because the question stated NOT to calculate the coefficients of the sine series. Is it still unacceptable to write f(x) = ... ?

    Of course, since the equality (within the limits of the theorem about Fourieri series) follows whn you have the whole

    Fourier series on the right. That you didin't calculate the sines' coefficients doesn't necessarily mean they equal zero,

    which would follow from your equality...

    Tonio
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  5. #5
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    Quote Originally Posted by tonio View Post
    Of course, since the equality (within the limits of the theorem about Fourieri series) follows whn you have the whole

    Fourier series on the right. That you didin't calculate the sines' coefficients doesn't necessarily mean they equal zero,

    which would follow from your equality...

    Tonio
    Makes sense, much more clear now.

    Thanks!
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