Fourier series confusion and pre/post-integration substitution dilemmas.

September 13, 2009 1:10 AM

Asking for a friend: With the use of Fourier series, I'm trying to solve an ODE of the form L*y'' + R*y' + y/C = r(x), where r(x) = 1 - x^2 for |x| <= 1, i.e. has a period of 2. To do so I need to represent 1 - x^2 as a Fourier series. In doing so I have to integrate e^(-n * i * pi * x), but I've reached a stumbling block.

I'm stuck because I noticed that substituting n = 0 before the integration yielded a different result to substituting post-integration (ie. Divide by zero). What am I doing wrong? Both in regards to what I'm trying to achieve overall and as a stand alone problem, how would I deal with the such integrals when substituting in for the case n = 0?

posted by PuGZ to Education (2 answers total)

I might not be understanding the issue, but why not just substitute before the integration? n=0 corresponds to the area under the curve, so y for the n=0 term would just be a constant.
posted by UrineSoakedRube at 2:18 AM on September 13, 2009

Yes; break the infinite sum up into an n=0 term and a sum for n != 0.
posted by fatllama at 3:31 AM on September 13, 2009