PlanetPhysics/Stokes Theorem

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

$\int \underset{S}{\int }\mathrm{\nabla }\times 𝐖\cdot d𝐚={\oint }_O𝐖\cdot d𝐫$

On account of its great importance in all branches of [[../PhysicalMathematics2/|mathematical physics]], a number of different proofs of this [[../Formula/|theorem]] will be given.

Proof I.

soon to come...