Green theorem

*Green's Theorem* (also *the Green Theorem*, but that is easily misunderstood in English) is the classical version of the Stokes Theorem for surfaces in the plane (which just amounts to regions in $\mathbb{R}^2$). It is in a way the most basic form of the Stokes Theorem beyond the Fundamental Theorem of Calculus, containing all of the analytic subtleties. The classical Kelvin–Stokes Theorem (for surfaces in $\mathbb{R}^3$) is a direct corollary (as indeed is the Stokes Theorem for surfaces in any ambient manifold); the other forms are proved in an analogous fashion. Other corollaries include the Cauchy integral theorem and the equality of mixed partial derivatives.

Created on September 17, 2018 at 06:14:43. See the history of this page for a list of all contributions to it.