Three Useful Theorems from Vector Calculus

In a second year Calculus class, one is usually introduced to vector fields which are so important in Physics. The theorems of Green, Gauss and Stokes are the classic trio which tie together line and surface integrals with ordinary double and triple integrals involving such fields. An illuminating application of Stokes' Theorem is found in my earlier blog on surface tension.

The Theorems of Green, Gauss, and Stokes: A Study Guide from First Principles is a paper I wrote in 2014 to review the mathematical tools necessary to establish these theorems. As such, the paper might be used as a handy study guide for reviewing many of the key aspects of basic Calculus.


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