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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>
:<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]]