Classical Stokes’ Theorems
Manifolds and boundaries
Vector-valued functions on manifolds
Function’s average over a boundary
= Derivative’s average over interior
Stokes’ Theorem, in all of its many manifestations, comes down to equating the average of a function on the boundary of some geometric object with the average of its derivative (in a suitable sense) on the interior of the object. Of course, a correct statement about averages must be put into the language of integrals. This theorem provides ...