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I think it would be a good idea. I'm going to add a section on the applicability of separation of variables which will include the translated material and also explain the link to the spectral theorem for PDEs (which subsumes the
Fourier series case). I think an example where separation of variables
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In the article it is stated that solutions to PDEs can be expressed as a sum in which each term is a product of several functions which each depend on only one variable. For example, given the equation
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The German language version of this article includes a theorem (and proof) about when the method is actually applicable. Would it be a good idea to translate this and add it to the
English version?
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I have never seen separation of variables using sums before, but this should of course not be a problem. However (and this connects to a remark below) the space of functions of the form
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700:{\displaystyle \Psi (x,y)=\sum _{m,n=-\infty }^{\infty }c_{mn}~e^{2\pi i(mx+ny)}=\sum _{m,n=-\infty }^{\infty }c_{mn}~e^{2\pi imx}e^{2\pi iny}}
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The two examples are redundant! It would make more sense to have either one example or two different examples. I am going to erase one ...
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can be expressed as a
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324:{\displaystyle ({\frac {\partial }{\partial x}}^{2}+{\frac {\partial }{\partial y}}^{2})\Psi (x,y)=0}
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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This should be explained. The explanation is really quite simple. Since any function
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is inapplicable would be good too, but I can't think of one at the moment.
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which is a sum of products of functions depending on x and y independently.
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http://www-fourier.ujf-grenoble.fr/~parisse/giac/cascmd_en.pdf
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is not dense in the space of functions of three variables
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Why can solutions to PDEs be written as sums of products?
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we are told to assume that the solution can be written
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Xcas does separation of variables with this command:
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