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

$${\int }_{M}d\omega ={\int }_{\partial M}\omega .$$

Title	general Stokes theorem
Canonical name	GeneralStokesTheorem
Date of creation	2013-03-22 12:44:52
Last modified on	2013-03-22 12:44:52
Owner	matte (1858)
Last modified by	matte (1858)
Numerical id	11
Author	matte (1858)
Entry type	Theorem
Classification	msc 58C35
Synonym	Stokes theorem
Related topic	DifferentialForms
Related topic	GaussGreenTheorem
Related topic	ClassicalStokesTheorem