# Difference between revisions of "Stokes' Theorem"

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Stoke's Theorem is a generalization of the [[Fundamental Theorem of Calculus]], which states that if ''M'' is an oriented piece-wise smooth [[manifold]] of [[dimension]] n and <math>\omega</math> is a smooth ''n''−1 form with compact support on ''M''. Let ∂''M'' denotes the boundary of ''M'' with its induced orientation, then | Stoke's Theorem is a generalization of the [[Fundamental Theorem of Calculus]], which states that if ''M'' is an oriented piece-wise smooth [[manifold]] of [[dimension]] n and <math>\omega</math> is a smooth ''n''−1 form with compact support on ''M''. Let ∂''M'' denotes the boundary of ''M'' with its induced orientation, then | ||

− | :<math>\int_M \mathrm{d}\omega = \oint_{\partial M} \omega | + | :<math>\int_M \mathrm{d}\omega = \oint_{\partial M} \omega,\!\,</math> |

where ''d'' is the [[exterior derivative]]. | where ''d'' is the [[exterior derivative]]. | ||

[[category: mathematics]] | [[category: mathematics]] |

## Revision as of 16:21, 22 March 2007

Stoke's Theorem is a generalization of the Fundamental Theorem of Calculus, which states that if *M* is an oriented piece-wise smooth manifold of dimension n and is a smooth *n*−1 form with compact support on *M*. Let ∂*M* denotes the boundary of *M* with its induced orientation, then

where *d* is the exterior derivative.