Stokes' theorem

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.

$\displaystyle \int \int_S \nabla \times {\bf W} \cdot d {\bf a} = \oint_O {\bf W} \cdot d {\bf r}$ (1)

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...



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