Timeline for Rigorous multivariate differentiation of integral with moving boundaries (Leibniz integral rule)
Current License: CC BY-SA 4.0
10 events
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| Jul 27, 2020 at 19:32 | history | edited | Amir Sagiv | CC BY-SA 4.0 |
typo
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| Feb 6, 2020 at 21:53 | vote | accept | Amir Sagiv | ||
| May 16, 2018 at 17:42 | comment | added | Giuseppe Negro | You can also obtain the formula as an immediate consequence of the pullback formula for the Dirac delta, which does not count as "multivariable calculus", however. Here's some details, again on my personal notes (search for "Reynolds"). HTH | |
| May 16, 2018 at 17:16 | comment | added | Giuseppe Negro | It's §C.4, pag.713 of the second edition, but now that I see it I think that's not what you are looking for, as there's no proof. Sorry. I wrote a proof on my personal notes, based on the derivative of the determinant formula (search "Reynolds transport theorem", towards the end of the page). However, these notes are not meant to be read by anyone except myself. I hope this helps. | |
| May 16, 2018 at 17:03 | answer | added | Michael Bächtold | timeline score: 5 | |
| May 16, 2018 at 14:45 | comment | added | Amir Sagiv | @GiuseppeNegro Thanks! I'm looking at it now, but can't find the theorem. Do you remember where is it? | |
| May 16, 2018 at 14:44 | comment | added | Amir Sagiv | @MichaelBächtold You're on point here, but I wonder if there is a more "elementary" way to do it, given that (a) the differential forms gives much more (b) At least naivly, the theorem can be stated in an elementary way.. | |
| May 16, 2018 at 13:53 | comment | added | Giuseppe Negro | There is a proof of this in the appendix to the book of Evans in PDEs, or have you already checked that? | |
| May 16, 2018 at 13:05 | comment | added | Michael Bächtold | Why do you consider proofs using differential forms far more general than what you need? Or put differently, what is the level you need? | |
| May 16, 2018 at 12:53 | history | asked | Amir Sagiv | CC BY-SA 4.0 |