Timeline for How should one present curl and divergence in an undergraduate multivariable calculus class?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| S Jan 7, 2018 at 5:54 | history | suggested | Toby Bartels | CC BY-SA 3.0 |
technical correction to statement of theorem
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| Jan 7, 2018 at 5:04 | comment | added | Toby Bartels | A technicality: if you want the curl to be continuous as you state (which is certainly beneficial to ensure that its integrals are defined and well behaved), then you need the original vector field to be continuously differentiable, not just differentiable. (I have edited the hypothesis of the theorem to reflect this, but my edit is still under review.) | |
| Jan 7, 2018 at 4:58 | review | Suggested edits | |||
| S Jan 7, 2018 at 5:54 | |||||
| Apr 20, 2010 at 18:37 | comment | added | Willie Wong | An old officemate of mine tried to teach his multivariate calc course this way (integrals first, then the derivative operators). The students who were taking simultaneously a physics course which "counted on div,grad,curl being taught first" (of course the physics department never bothered to communicate that fact to the maths department) were understandably confused and upset. So just as a protocol I suggest checking with departmental administrators before changing the order of the course too much! | |
| Apr 20, 2010 at 0:05 | comment | added | Deane Yang | This is exactly how I learned about div and curl in my physics course on electromagnetic theory, where they talk about the integral form of Maxwell's equations (which we call Stokes' theorem) and take a limit to derive the differential form of Maxwell's equations (containing the div and curl). Although I generally do not like the way physicists present mathematics, this is one case, where I think the physicists do it better. | |
| Apr 19, 2010 at 21:17 | comment | added | some guy on the street | oh! me too, for not thoroughly investigating what other people already said... | |
| Apr 19, 2010 at 21:14 | comment | added | Kevin H. Lin | Thanks. Yeah, I think your the idea of your proposal is essentially contained in the wikipedia links in Qiaochu's answer. (Sigh -- another example of me not first looking things up on wikipedia before asking on MO -- sorry.) | |
| Apr 19, 2010 at 21:07 | history | answered | some guy on the street | CC BY-SA 2.5 |