Computationally based proofs of Stokes's theorem and Gauss's theorem

Abstract

Relative to perhaps forty years ago, the current undergraduate curriculum in physics and in mathematics often contains less rigourous proof and more computation. As a consequence, by the time physics majors take a junior level course in electricity and magnetism, many of them have not been exposed to proofs of Gauss's theorem and Stokes's theorem; indeed, their very knowledge of these essential theorems may even be questioned. However, it is straightforward to establish these theorems with computationally based proofs. Stokes's theorem is proved by considering a small arbitrary triangle, from which an arbitrary surface can be approximated. Gauss's theorem is proved by considering a small arbitrary tetrahedron, from which an arbitrary volume can be approximated.