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Concept
Generalized Stokes theorem
Summary
In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus. In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, Green’s theorem and Stokes' theorem are the cases of a surface in \R^2 or \R^3, and the divergence theorem is the case of a volume in \R^3. Hence, the theorem is sometimes referred to as the Fundamental Theorem of Multivariate Calculus.
Stokes' theorem says that the integral of a differential form \omega over the boundary \partial\Omega of some orientable manifold \Omega is equal to the integral of its exterior derivative d\omega over the whole of \Omeg
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