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February 21st, 2012, 09:38 AM   #1
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Why can a periodic function be written as a Fourier Series?

Hello everyone. The title is self-explanatory. I need help because I've seen this in the ordinary differential equations course I'm taking (yes, the mit one), but it doesn't give any proof.
He simply states that we can express any continuous periodic function as a Fourier Series. Yes, I know that intuitively it makes sense, but I still want the proof.
Is it too hard for a first ordinary differential equations course? If not, does anyone here know this demonstration? If so, does anyone here know in which course I'll be stumbling upon it?

Thanks in advance,
Peter.
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February 21st, 2012, 06:11 PM   #2
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Read Chapter 2 of Fourier Series by I. N. Sneddon for a proof under a slightly more restrictive condition on the function.
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February 22nd, 2012, 09:06 AM   #3
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Re: Why can a periodic function be written as a Fourier Seri

Thank you very much, mate.
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