Talk:Divergence theorem

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

Compactness
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)

Just go to pornhub and fap to it — Preceding unsigned comment added by 2A00:23C7:7201:8D01:51A8:2E54:1548:C1AC (talk) 17:01, 1 November 2021 (UTC)

Generalization
5.95.187.184 (talk)I would like to recall your attention about this section, in particular about the first subsection: Multiple dimensions. In fact, I think that this one would actually benefit in being inserted as a sub-subsection of the generalization to the Riemaniann Manifold, for which the equation is: $${\int_{M}\text{div}(X)\ \nu_g=\int_{\partial M}\nu_{\hat{g}}}$$, where $$\nu$$ is for the riemaniann volume form of the riemannian Manifolds, namely, $$(M,g)$$ and $$(\partial M, \hat{g})$$ (the last one considered as a submanifold of $$M$$ with the inclusion as embedding), $$X$$ is a vector field, and $$N$$ is the versor normal field defined on $$\partial M$$. Considered this equation, the subsection Multiple dimensions is just a corollary, with $$M$$ considered as a submanifold of $$\mathbb{R}^n$$

Divergence theorem
vect 41.79.120.17 (talk) 20:51, 17 March 2023 (UTC)

Vector calcuis
divergence theorem 41.79.120.17 (talk) 20:52, 17 March 2023 (UTC)