Here's a nice page: List of topics named after Carl Friedrich Gauss. Perhaps Gauss theorem and related terms should redirect there instead? Or at least a disambiguating note at the top of this article? --Steve 01:03, 20 September 2008 (UTC) Conditions for the Divergence theorem. The condition of the div theorem says that F must be C 1.
The divergence theorem can also be used to evaluate triple integrals by turning them into surface integrals. This depends on finding a vector field whose divergence is equal to the given function.
Math · Multivariable calculus · Green's, Stokes', and the divergence theorems · Divergence theorem (articles) 3D divergence theorem Also known as Gauss's theorem, the divergence theorem is a tool for translating between surface integrals and triple integrals. Example of calculating the flux across a surface by using the Divergence Theorem If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. The divergence theorem is an equality relationship between surface integrals and volume integrals, with the divergence of a vector field involved. It often arises in mechanics problems, especially so in variational calculus problems in mechanics. The equality is valuable because integrals often arise that are difficult to evaluate in one form ... The divergence theorem was derived by many people, perhaps including Gauss. I don't think it is appropriate to link only his name with it. Actually all the statements you give for the divergence theorem render it useless for many physical situations, including many implementations of Gauss's law, where E is not finite everywhere.
Fundamental Theorem of Divergence - Gauss Theorem Consider a closed surface in vector field. The volume integral of the divergence of the associated vector function carried within a enclosed volume is equal to the surface integral of the normal component of the associated vector function carried over an enclosing surface.