Comments on: Fourier series confusion and pre/post-integration substitution dilemmas.
http://ask.metafilter.com/132705/Fourier-series-confusion-and-prepostintegration-substitution-dilemmas/
Comments on Ask MetaFilter post Fourier series confusion and pre/post-integration substitution dilemmas.Sun, 13 Sep 2009 02:18:56 -0800Sun, 13 Sep 2009 02:18:56 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: Fourier series confusion and pre/post-integration substitution dilemmas.
http://ask.metafilter.com/132705/Fourier-series-confusion-and-prepostintegration-substitution-dilemmas
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. <br /><br /> 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?post:ask.metafilter.com,2009:site.132705Sun, 13 Sep 2009 01:10:41 -0800PuGZintegrationfourierseriesmathematicscalculusconundrumBy: UrineSoakedRube
http://ask.metafilter.com/132705/Fourier-series-confusion-and-prepostintegration-substitution-dilemmas#1895846
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.comment:ask.metafilter.com,2009:site.132705-1895846Sun, 13 Sep 2009 02:18:56 -0800UrineSoakedRubeBy: fatllama
http://ask.metafilter.com/132705/Fourier-series-confusion-and-prepostintegration-substitution-dilemmas#1895859
Yes; break the infinite sum up into an n=0 term and a sum for n != 0.comment:ask.metafilter.com,2009:site.132705-1895859Sun, 13 Sep 2009 03:31:23 -0800fatllama