Thomas A. Garrity (Massachusetts Williams College)

Electricity and Magnetism for Mathematicians

• Broschiertes Buch

Produktbeschreibung

Almost all current descriptions of the fundamental laws of the universe can be viewed as deep generalizations of Maxwell's equations, which have led to some of the most important mathematical discoveries of the past thirty years. This text introduces some of the mathematical wonders of these equations.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 300
• Erscheinungstermin: 19. März 2015
• Englisch
• Abmessung: 229mm x 152mm x 16mm
• Gewicht: 412g
• ISBN-13: 9781107435162
• ISBN-10: 1107435161
• Artikelnr.: 41612068

Autorenporträt

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.

Inhaltsangabe

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.