Timeline for Applications needing different constants of integration on different intervals [closed]
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 9 at 3:17 | history | left closed in review |
Alex M. Michael Albanese Brian Hopkins |
Original close reason(s) were not resolved | |
| Oct 8 at 12:57 | comment | added | Chris Sangwin | Thanks @MichaelHardy, yes there are a couple of tutorial examples in textbooks which cover this. E.g. taking $ \tan^{-1}\left(\frac{ax+1}{a-x}\right)$ to be an antiderivative of $ \frac{1}{1+x^2}$ is interesting, and related. All the examples/discussion I've found so far are from a pure mathematics perspective. I'm interested in applications (including pure mathematics techniques) where different constants are needed. | |
| Oct 7 at 16:23 | comment | added | Michael Hardy | The calculus textbook by Salas & Hille set an exercise: find all anti-derivatives of $\sec^2 x.$ It said the answer is $\tan x + C,$ where $C$ is constant. But it should be a piecewise constant, as long as the domain is $\mathbb R$ and not $\mathbb C.$ | |
| Oct 7 at 16:09 | review | Reopen votes | |||
| Oct 9 at 3:17 | |||||
| S Oct 7 at 14:52 | history | unlocked | CommunityBot | ||
| S Oct 7 at 14:52 | history | locked | CommunityBot | ||
| S Oct 7 at 14:52 | history | closed |
Alexandre Eremenko M.G. Jukka Kohonen Robert Israel Daniele Tampieri |
Not suitable for this site | |
| Oct 7 at 14:22 | comment | added | Chris Sangwin | Thanks @RobertIsrael for suggesting MSE. I'm undertaking an educational research project and whether this technical detail from analysis "matters". It would be helpful to ask in a research forum (i.e. here) whether this opportunity with constants on different connected domains is needed/requires in particular situations/applications. I hope I'm not asking an elementary question in the wrong forum. | |
| Oct 7 at 14:06 | comment | added | Robert Israel | Not a research-level question. More appropriate for MSE | |
| Oct 7 at 12:56 | comment | added | R.P. | I think this is a fair question, howbeit of a somewhat elementary nature. I am surprised to see three votes to close within the hour. | |
| Oct 7 at 12:30 | comment | added | Chris Sangwin | Indeed! A point often missed, or quietly passed over in textbooks. My question asks whether this is ever needed or used? | |
| Oct 7 at 12:15 | review | Close votes | |||
| Oct 7 at 14:52 | |||||
| Oct 7 at 12:06 | comment | added | Bertoldo Baccalà | You are computing piecewise derivatives. Your domain is not connected, it is separated by the point 0. So there is no coupling condition between the left and the right part. | |
| Oct 7 at 11:48 | history | asked | Chris Sangwin | CC BY-SA 4.0 |