Kelvin–Stokes theorem

Stokes' theorem is a theorem in vector calculus which relates a closed line integral over a vector field to a surface integral over the curl of the vector field, with the boundary of the surface being the path of the line integral. Mathematically, it is stated as:

$\oint_C \vec{F} \cdot d \vec{r} = \iint_S \nabla \times \vec{F} \cdot d \vec{S}$

Stoke's theorem is essentially a higher dimensional equivalent to Green's theorem. Both of these theorems, along with the divergence theorem, are special cases of the generalized Stokes' theorem.