On the general Stokes formula (Q1358181)

A new proof of the general Stokes formula (gSf) is given. The modern exposition of proofs of various versions of the gSf usually involves applying rather advanced theory of exterior differential forms and integrals of exterior forms over surfaces. This proof of gSf uses essentially the same methods as in the classical proof for dimension three. The main difficulty is constructing the system of necessary concepts (parametrization of a surface, the correlation between the orientations of a surface and its boundary, constructing surfaces by ``glueing'' images of convex sets along the common parts of their boundaries that are oppositely oriented). The proof itself is very simple.