# general Stokes theorem

Let $M$ be an oriented $r$-dimensional differentiable manifold with a piecewise differentiable boundary $\partial M$. Further, let $\partial M$ have the orientation induced by $M$. If $\omega$ is an $(r-1)$-form on $M$ with compact support, whose components have continuous first partial derivatives in any coordinate chart, then

 $\int_{M}\mathrm{d}\omega=\int_{\partial M}\omega.$
Title general Stokes theorem GeneralStokesTheorem 2013-03-22 12:44:52 2013-03-22 12:44:52 matte (1858) matte (1858) 11 matte (1858) Theorem msc 58C35 Stokes theorem DifferentialForms GaussGreenTheorem ClassicalStokesTheorem