PlanetPhysics/Stokes Theorem

{\mathbf Stokes' theorem}:\, The surface integral of the curl of a vector function is equal to the line integral of that vector function taken around the closed curve bounding that surface.

$\int \int _{S}\nabla \times {\mathbf {W} }\cdot d{\mathbf {a} }=\oint _{O}{\mathbf {W} }\cdot d{\mathbf {r} }$

On account of its great importance in all branches of mathematical physics, a number of different proofs of this theorem will be given.

Proof I.

soon to come...