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arXiv · 1901.09295

A simple and more general approach to Stokes' theorem

Iosif Pinelis
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Abstract

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.

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Iosif Pinelis. 2019-01-27. A simple and more general approach to Stokes' theorem. https://arxiv.org/abs/1901.09295

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