Stokes' Theorem

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 $\omega$ is a smooth (k−1)-form with compact support on M. Let ∂M denotes the boundary of M with its induced orientation, then

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_M \mathrm{d}\omega = \oint_{\partial M} \omega\!\,} ,

where d is the exterior derivative.