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This textual content material is an introduction to a number of of the mathematical wonders of Maxwell's equations. These equations led to the prediction of radio waves, the assumption that light is a sort of electromagnetic wave, and the invention of the actual idea of relativity. Truly, nearly all current descriptions of the basic authorized tips of the universe might be seen as deep generalizations of Maxwell's equations. Rather more surprising is that these equations and their generalizations have led to a number of of probably the most important mathematical discoveries of the earlier thirty years. It seems that evidently the arithmetic behind Maxwell's equations is infinite. The purpose of this book is to make clear to mathematicians the underlying physics behind electrical power and magnetism and to current their connections to arithmetic. Starting with Maxwell's equations, the reader is led to such topics as a result of the actual precept of relativity, differential varieties, quantum mechanics, manifolds, tangent bundles, connections, and curvature.
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