Electricity and Magnetism for Mathematicians
A Guided Path from Maxwell's Equations to Yang–Mills
$33.00 ( ) USD
 Author: Thomas A. Garrity, Williams College, Massachusetts
 Date Published: February 2015
 availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
 format: Adobe eBook Reader
 isbn: 9781316236970
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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.
Read more The author is well known among mathematics students for his previous book, All the Mathematics You Missed, which has sold over 20,000 copies
 Does not assume any knowledge of physics, and only basic undergraduate mathematics
 Maxwell's equations are a fascinating topic
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×Product details
 Date Published: February 2015
 format: Adobe eBook Reader
 isbn: 9781316236970
 contains: 81 b/w illus. 2 colour illus. 211 exercises
 availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
1. A brief history
2. Maxwell's equations
3. Electromagnetic waves
4. Special relativity
5. Mechanics and Maxwell's equations
6. Mechanics, Lagrangians, and the calculus of variations
7. Potentials
8. Lagrangians and electromagnetic forces
9. Differential forms
10. The Hodge * operator
11. The electromagnetic twoform
12. Some mathematics needed for quantum mechanics
13. Some quantum mechanical thinking
14. Quantum mechanics of harmonic oscillators
15. Quantizing Maxwell's equations
16. Manifolds
17. Vector bundles
18. Connections
19. Curvature
20. Maxwell via connections and curvature
21. The Lagrangian machine, Yang–Mills, and other forces.
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