Generalized Stokes theorem

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 {\displaystyle \mathbb {R} ^{2}} or ⁠ R 3 {\displaystyle \mathbb {R} ^{3}} ⁠, and the divergence theorem is the case of a volume in ⁠ R 3 {\displaystyle \mathbb {R} ^{3}} ⁠.

Source: Wikipedia — Generalized Stokes theorem (CC BY-SA 4.0)

Generalized Stokes theorem

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 {\displaystyle \mathbb {R} ^{2}} or ⁠ R 3 {\displaystyle \mathbb {R} ^{3}} ⁠, and the divergence theorem is the case of a volume in ⁠ R 3 {\displaystyle \mathbb {R} ^{3}} ⁠.

Source: Wikipedia "Generalized Stokes theorem" · CC BY-SA 4.0

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