Talk:Divergence theorem

Licensing

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

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: ${\int _{M}{\text{div}}(X)\ \nu _{g}=\int _{\partial M}<X,N>\nu _{\hat {g}}}$, 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)

n=3 versus general n

The current description following `Mathematical statement' is inconsistent: it starts by assuming that $V$ is a subset of $\mathbb {R} ^{n}$, but then states the identity in notation that presupposes that $V\subset \mathbb {R} ^{3}$: the three integrals on the left and the two integrals on the right are specific for dimension three. Proposal: state first the general case, and then explain that in three space dimensions the integrals are more commonly formatted as ... (etc.). Markpeletier (talk) 20:05, 31 January 2026 (UTC)