Timeline for Polar Coordinate Variable Transformations
Current License: CC BY-SA 3.0
8 events
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| Aug 22, 2021 at 20:52 | history | edited | kjetil b halvorsen♦ |
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| Nov 30, 2017 at 17:36 | comment | added | whuber♦ | Some people think the approach in my link is "very basic." :-) It has been in wide use in mathematics for over 120 years. | |
| Nov 30, 2017 at 16:35 | comment | added | DanRoDuq | This seems great. I would still be happy to see a more traditional approach this question as it seems like a very basic thing to know. | |
| Nov 30, 2017 at 16:07 | comment | added | whuber♦ | I have pasted a link into that comment twice, and twice it has vanished! Let's try here: stats.stackexchange.com/a/154298/919. The methods shown there don't use Jacobians directly--they are designed to avoid them altogether. | |
| Nov 30, 2017 at 15:58 | comment | added | DanRoDuq | Thanks would you be able to link me to your answer. I have seen a few answers that make use of the $rdrd\theta=dxdy$ however, I am not completely clear why it should still work if that equality comes from the change of variable theorem for double integrals as well which involves a jacobian and so should fall into the same issue. | |
| Nov 30, 2017 at 15:32 | comment | added | whuber♦ | The detailed example in my answer shows $rdr\wedge d\theta=dx\wedge dy$ for the transformation $(x,y)\leftrightarrow(r,\theta)$. For $r\gt 0, \theta\in [0,2\pi)$ this transformation is one-to-one with the punctured plane. The result is immediate. Note how the use of differential forms eliminates the somewhat shaky use of inverse tangents. | |
| Nov 30, 2017 at 15:26 | history | edited | DanRoDuq | CC BY-SA 3.0 |
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| Nov 30, 2017 at 15:18 | history | asked | DanRoDuq | CC BY-SA 3.0 |