File:Fourier constant sides heat plate.png
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Captions
Captions
Solution to the heat equation on a 1x1 square with a boundary condition on three sides
Summary
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English: The Fourier series solution for Laplace's equation on a 1 x 1 square, with the boundary conditions of the top side having a value of 1 and the left and right sides having a value of 0. The bottom side is "floating." The solution is given by
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| Date | |
| Source | Own work |
| Author | AkanoToE |
![{\displaystyle {\frac {4}{\pi }}\sum _{n=0}^{\infty }{\frac {\exp[-(2n+1)\pi y]}{(2n+1)}}\sin[(2n+1)\pi x]={\frac {2}{\pi }}\tan ^{-1}\left({\frac {\sin[\pi x]}{\sinh[\pi y]}}\right).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/912890576ba5271e9063b5dd34f525530034b532)
Licensing
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I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:21, 6 November 2020 | | 2,960 × 2,960 (741 KB) | AkanoToE (talk | contribs) | Uploaded own work with UploadWizard |
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