Electricity and Magnetism for Mathematicians: A Guided Path from Maxwell's Equations to Yang-Mills

Electricity and Magnetism for Mathematicians: A Guided Path from Maxwell's Equations to Yang-Mills

by Thomas A. Garrity

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Product Details

ISBN-13: 9781107078208
Publisher: Cambridge University Press
Publication date: 01/31/2015
Pages: 304
Product dimensions: 5.98(w) x 8.98(h) x 0.91(d)

About the Author

Thomas A. Garrity is the William R. Kenan, Jr Professor of Mathematics at Williams College, where he was the director of the Williams College Project for Effective Teaching for many years. He has written a number of research papers and has authored or coauthored two other books, All the Mathematics You Missed (But Need to Know for Graduate School) and Algebraic Geometry: A Problem Solving Approach. Among his awards and honors is the MAA Deborah and Franklin Tepper Haimo Award for outstanding college or university teaching.

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 two-form; 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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