2019/01/27 by Pinelis, Iosif
#53A04 #53A05 #53A45 #FOS: Mathematics #History and Overview (math.HO)
paper · doi:10.48550/arxiv.1901.09295
Oftentimes, Stokes' theorem is derived by using, more or less explicitly, the invariance of the curl of the vector field with respect to translations and rotations. However, this invariance -- which is oftentimes described as the curl being a "physical" vector -- does not seem quite easy to verify, especially for undergraduate students. An even bigger problem with Stokes' theorem is to rigorously define such notions as ``the boundary curve remains to the left of the surface''. Here an apparently simpler and more general approach is suggested.