Talk:Divergence theorem

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This article is based on the GFDL article from PlanetMath at http://planetmath.org/encyclopedia/Divergence.html

That's my contribution for the day done. The Anome

Re: removal of the condition that the region S be compact - I doubt that one can do this unconditionally.

Charles Matthews 18:53, 6 Feb 2004 (UTC)

You are correct. Either the manifold must be compact, or the integrand must have compact support. sorry for the sloppiness. i think i will just change it back.

Re: Infinite plane of mass

The behavior is an approximative case only. It is the closest to "ideal" when you are very close to the black hole's event horizon. At least that is what I remember from a website which I'll need to look up. :-)

--24.84.203.193 28 June 2005 14:17 (UTC)

Contents

[edit] Remarks about links

(Moved from my talk page)

Thank you for your changes to divergence theorem. However, I have some remarks about links.

First, one should not link to plural, rather to singular, so it's got to be [[divergence]]s and not [[divergences]]. Second, you should wonder if links are actually needed, a link to sink does not make any sence in that article.

Third, one should check where the links point to. Instead of boundary one should link to [[boundary (topology)|boundary]]. Fourth, a link to "conservation law" should be instead conservation law, because, as you notice, those two words go together.

These are minor things, but it helps give value to the links. Thanks. Oleg Alexandrov (talk) 10:38, 29 October 2005 (UTC)

Yes thanks for advice!--Light current 19:32, 29 October 2005 (UTC)

[edit] Example

By symmetry,

\iiint\limits_W y dV = \iiint\limits_W z dV = 0

Why? --Abdull 19:30, 2 June 2006 (UTC)

A sphere looks the same if you look at its z-axis as if you look at its y-axis. Rotational symmetry. -lethe talk + 20:05, 2 June 2006 (UTC)

[edit] Generalization of the divergence theorem to tensors

Could somebody with the requisite mathematical expertise please fill this in?

I copied a sentence into the intro, specifying the article wherein the generalization of this theorem can be found. I don't think this page itself is the right place to go into it. --Steve (talk) 21:08, 1 April 2008 (UTC)

[edit] Conditions for the Divergence theorem

The condition of the div theorem says that F must be C1. How can the theorem be applied then for example, for u \nabla G , where G is a Green's function? Typically, Green's functions have a singularity, so they are not C1. Does this mean the divergence theorem can be extended? --Janzz2k 17:21, 19 April 2007 (UTC)

[edit] Clarified the spherical symmetry case

I have added a bit of clarification to the section for spherical symmetry. I was prompted by a change provided by 83.30.188.66 (talk · contribs), which was aiming for clarity, but technically introduced an error. I hope the rewording I have now supplied makes it a bit clearer. Further suggestions very welcome. —Duae Quartunciae (talk · cont) 11:48, 5 August 2007 (UTC)

[edit] WikiProject class rating

This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:48, 10 November 2007 (UTC)

[edit] Moved content off of page

I made dedicated articles for Gauss's law for magnetism and Gauss's law for gravity, and accordingly moved some material from here to those pages. (I went through and updated the links for hopefully all of the other wikipedia articles citing this material.) By the way, anyone interested in contributing to those articles is encouraged to do so. :-) --Steve (talk) 21:08, 1 April 2008 (UTC)

[edit] Do N-dimensional integrals need to have N squiggly integral signs? (N=2 or 3)

On the plus side, it helps people who only know a little calculus, and aren't familiar with the idea of one squiggly-integral sign denoting anything other than a one-dimensional integral. On the minus side, it makes equations harder to read and generally more cluttered. On the plus side, anyone who can understand it with one integral sign can understand it with three, but not necessarily vice-versa. On the minus side, I don't think any professional mathematician or physicist would write it this way (except maybe when they're writing introductory textbooks), and at least the physics articles I've seen on Wikipedia don't write it that way either.

Has anyone thought about this issue, pro and/or con? I have mixed feelings, myself. --Steve (talk) 21:07, 8 April 2008 (UTC)