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From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the nineteenth century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.
—Richard Feynman
The Special Theory of Relativity owes its origins to Maxwell’s Equations\(\ldots\)
—Albert Einstein
We are now prepared to tie together vector differential calculus and vector integral calculus. This will be done by means of the important theorems of Green, Gauss, and Stokes. We shall also point out some of the physical applications of these theorems to the study of gravitation, electricity, and magnetism.
The basic integral theorems in vector analysis had their origins in applications. For example, Green’s theorem, discovered about 1828, arose in connection with potential theory (this includes gravitational and electrical potentials). Gauss’ theorem—the divergence theorem—arose in connection with the study of capillarity (this theorem should be jointly credited to the Russian mathematician Ostrogradsky, who discovered the theorem around the same time as Gauss). Stokes’ theorem was first suggested in a letter to Stokes from the physicist Lord Kelvin in 1850 and was used by Stokes on the examination for the Smith Prize in 1854.