In vector calculus and differential geometry, the **generalized Stokes' theorem** or just **Stokes' theorem** relates the integral of a function over the boundary of a manifold to the integral of the function's exterior derivative on the manifold itself. Mathematically, it is stated as

The fundamental theorem of calculus, gradient theorem, Green's theorem, divergence theorem, and Kelvin–Stokes theorem are all special cases of Stokes' theorem.