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 Nov 20 comment Why the method of separation of variables works? @ChrisWhite There are theoretical and mathematical physicists here who might know the answer to my question and who might not be following math stackexchange regularly. I want to maximize my chances to get an answer so I posted my question here and there. Sorry for offending anybody. Jul 14 comment A little integration paradox Interesting. I do not remember that is written in my calculus books, not even a warning :( Jul 14 comment A little integration paradox Yeah got it thanks. So the antiderivative must be continuous across the domain of integration to be able to substitute with the integral limits, right? Jan 3 comment Where is the flaw in evaluating the following integral? Excellent explanation, thank you so much. I am wondering why such subtleties are not taught in calculus courses? Do you know any book that cover similar subtleties? Jan 3 comment Where is the flaw in evaluating the following integral? @cardinal Please point out where it was used incorrectly as this is exactly my question. Jan 3 comment Where is the flaw in evaluating the following integral? @J.M. $dy=\cos\theta d\theta$ where $\cos\theta=\sqrt{1-y^2}$ Nov 18 comment Fourier-like expansion of a closed curve in 2D @twistor59 I never said the closed curve can be represented by a single valued function, but anyway can a double valued function be expanded in terms of some set of "orthogonal double valued functions"? Nov 18 comment Fourier-like expansion of a closed curve in 2D @DavidZaslavsky Why it should be moved to mathematics? Some shape in space can be built out of spherical harmonics which has so many applications, similarly the concepts of multipole moments and expansion which all have physics applications. If we can expand closed surface, why cannot we expand a closed line?