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February 21st, 2012, 08:38 AM  #1 
Newbie Joined: Feb 2012 Posts: 20 Thanks: 0  Why can a periodic function be written as a Fourier Series?
Hello everyone. The title is selfexplanatory. 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. 
February 21st, 2012, 05:11 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1385 
Read Chapter 2 of Fourier Series by I. N. Sneddon for a proof under a slightly more restrictive condition on the function.

February 22nd, 2012, 08:06 AM  #3 
Newbie Joined: Feb 2012 Posts: 20 Thanks: 0  Re: Why can a periodic function be written as a Fourier Seri
Thank you very much, mate.


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fourier, function, periodic, series, written 
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