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