Timeline for Why are differential forms called closed and exact?
Current License: CC BY-SA 2.5
9 events
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| Mar 3, 2020 at 21:17 | comment | added | C.F.G | What does "exact" and "closed" mean in French? (same terminology that has been used by Poincaré) | |
| Dec 7, 2010 at 14:35 | comment | added | Nikita Kalinin | that is good, but why are they named such way? Did Poincaré be the first who studied exact differential equation? | |
| Dec 7, 2010 at 9:24 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
Link is fixed
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| Dec 7, 2010 at 9:13 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
Links are added, grammar is fixed
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| Dec 7, 2010 at 2:40 | comment | added | Victor Protsak | Pietro, I think that work on integrating systems of first order linear PDEs (Pfaffian systems) predates the development of complex analysis by a long margin. Initially, holomorphic functions were studied using the tools from linear PDEs, cf the history Cauchy-Riemann equations, which had been first considered by D'Alambert (in Russian they are in fact called "D'Alambert-Euler conditions"). | |
| Dec 6, 2010 at 23:00 | comment | added | Pietro Majer | I've always thought that the term exact for differential forms was adopted as a generalization of an older existing term in the theory of complex variable (i.e., $f(z)$ is exact on $\Omega$ iff $f(z)=g′(z)$), and that the usage there had been borrowed from arithmetic, as well as the term residue: $f(z)$ (say a rational function) is exact iff it has no residue, like a quotient is exact iff it has no remainder (lat. residuum). Unfortunately I have no reference for this (which is not in contrast with the above hystorical note). | |
| Dec 6, 2010 at 22:45 | comment | added | Theo Buehler | Thanks for that, Andrey, I didn't know that paper, it sure looks interesting. | |
| Dec 6, 2010 at 22:30 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
added 314 characters in body
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| Dec 6, 2010 at 22:21 | history | answered | Andrey Rekalo | CC BY-SA 2.5 |