Timeline for How do I make the conceptual transition from multivariable calculus to differential forms?
Current License: CC BY-SA 3.0
29 events
| when toggle format | what | by | license | comment | |
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| Jul 23, 2019 at 17:37 | answer | added | Michael Engelhardt | timeline score: 1 | |
| Jul 23, 2019 at 16:17 | answer | added | Georg Essl | timeline score: 2 | |
| Jul 3, 2017 at 4:17 | answer | added | Phil Harmsworth | timeline score: 5 | |
| Sep 23, 2015 at 7:42 | comment | added | user13113 | I personally find multivariable calculus already better formulated in terms of covectors rather than vectors; IMO the exterior derivative is more natural than directional derivatives, especially in terms of symbolic calculation, and furthermore $\mathrm{d}(xy)$ is always $y \mathrm{d}x + x \mathrm{d}y$, whereas there are several relevant ways in which $\frac{\partial}{\partial x}(xy)$ won't be $y$ (e.g. if $y$ depends on $x$, or you are working in different coordinates and mean to hold $x-y$ constant rather than holding $y$ constant). | |
| May 31, 2015 at 19:03 | comment | added | Norbert | @StevenGubkin I was waiting for this explanation for years! | |
| Oct 7, 2013 at 2:46 | history | edited | Ricardo Andrade |
replaced tag 'tag-removed'
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| Oct 7, 2013 at 2:26 | answer | added | Douglas Lind | timeline score: 6 | |
| Oct 6, 2013 at 22:30 | history | edited | Michael Albanese | CC BY-SA 3.0 |
Replace   by \ so math would render properly. There should probably be some wedges in there as well, but I wasn't sure if the OP was supressing specific notation for the multiplicative structure on \Omega(M).
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| Jul 7, 2012 at 10:52 | answer | added | Mirco A. Mannucci | timeline score: 42 | |
| Dec 1, 2011 at 2:42 | answer | added | Phil Isett | timeline score: 12 | |
| Jan 27, 2011 at 20:25 | comment | added | Steven Gubkin | A 1-form is a function which grows proportionally to how fast you are moving. Thus it doesn't matter how you parametrize the curve you are moving on - you either end up integrating a smaller function for a longer period of time, or a bigger function for a shorter period of time. This is why you can't integrate functions on manifolds - they have no intrinsic "unit speeds", because there are many choices of local coordinates - but you can still integrate differential forms. k-forms just generalize this to higher dimensions. | |
| Jul 12, 2010 at 7:15 | answer | added | Jonathan Fischoff | timeline score: 6 | |
| Feb 11, 2010 at 17:01 | answer | added | Olivier | timeline score: 10 | |
| Jan 14, 2010 at 22:53 | comment | added | B. Bischof | +1 for "I freaking love this question". | |
| Jan 3, 2010 at 22:32 | history | made wiki | Post Made Community Wiki by Qiaochu Yuan | ||
| Jan 3, 2010 at 21:21 | answer | added | Mike Shulman | timeline score: 9 | |
| Jan 3, 2010 at 19:04 | answer | added | Ilya Grigoriev | timeline score: 28 | |
| Jan 3, 2010 at 15:43 | answer | added | pmoduli | timeline score: 7 | |
| Jan 3, 2010 at 15:28 | comment | added | Akhil Mathew | Have you seen From Calculus to Cohomology by Madsden and Tornehave? It's not really about physical intuition (which is why I'm making this a comment), but it might be helpful. | |
| Jan 3, 2010 at 15:24 | answer | added | S. Carnahan♦ | timeline score: 5 | |
| Jan 3, 2010 at 15:22 | answer | added | Matt Noonan | timeline score: 8 | |
| Jan 3, 2010 at 15:04 | answer | added | David Lehavi | timeline score: 6 | |
| Jan 3, 2010 at 14:26 | answer | added | José Figueroa-O'Farrill | timeline score: 116 | |
| Jan 3, 2010 at 13:52 | answer | added | Deane Yang | timeline score: 7 | |
| Jan 3, 2010 at 13:17 | answer | added | Steve Huntsman | timeline score: 5 | |
| Jan 3, 2010 at 13:12 | answer | added | Harrison Brown | timeline score: 23 | |
| Jan 3, 2010 at 12:22 | comment | added | Pete L. Clark | This is nitpicky, but it is traditional to denote the product structure on differential forms with a $\wedge$ ("wedge product"). | |
| Jan 3, 2010 at 10:55 | answer | added | Thomas Sauvaget | timeline score: 12 | |
| Jan 3, 2010 at 10:11 | history | asked | Qiaochu Yuan | CC BY-SA 2.5 |