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Electricity and Magnetism for Mathematicians - A Guided Path from Maxwell's Equations to Yang-Mills (Hardcover)
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Electricity and Magnetism for Mathematicians - A Guided Path from Maxwell's Equations to Yang-Mills (Hardcover)
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This text is an introduction to some of the mathematical wonders of
Maxwell's equations. These equations led to the prediction of radio
waves, the realization that light is a type of electromagnetic
wave, and the discovery of the special theory of relativity. In
fact, almost all current descriptions of the fundamental laws of
the universe can be viewed as deep generalizations of Maxwell's
equations. Even more surprising is that these equations and their
generalizations have led to some of the most important mathematical
discoveries of the past thirty years. It seems that the mathematics
behind Maxwell's equations is endless. The goal of this book is to
explain to mathematicians the underlying physics behind electricity
and magnetism and to show their connections to mathematics.
Starting with Maxwell's equations, the reader is led to such topics
as the special theory of relativity, differential forms, quantum
mechanics, manifolds, tangent bundles, connections, and curvature.
General
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