The Geometry of Physics
The Geometry of Physics
$92.99
USDThis book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are helpful for a deeper understanding of both classical and modern physics and engineering. It is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study.
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A main addition introduced in this Third Edition is the inclusion of an Overview, which can be read before starting the text. This appears at the beginning of the text, before Chapter 1. Many of the geometric concepts developed in the text are previewed here and these are illustrated by their applications to a single extended problem in engineering, namely the study of the Cauchy stresses created by a small twist of an elastic cylindrical rod about its axis.
- Develops geometric intuition
- Presents physical applications
- Highly readable and includes over 200 exercises
Reviews & endorsements
"It contains a wealth of interesting material for both the beginning and the advanced levels. The writing may feel informal but it is precise - a masterful exposition. Users of this "introduction" will be well prepared for further study of differential geometry and its use in physics and engineering.
As did earlier editions, this third edition will continue to promote the language with which mathematicians and scientists can communicate."
Jay P. Fillmore, University of California, San Diego for SIAM Review
Product details
December 2011Paperback
9781107602601
748 pages
248 × 174 × 33 mm
1.44kg
260 b/w illus. 205 exercises
Available
Table of Contents
- Preface to the Third Edition
- Preface to the Second Edition
- Preface to the revised printing
- Preface to the First Edition
- Overview
- Part I. Manifolds, Tensors, and Exterior Forms:
- 1. Manifolds and vector fields
- 2. Tensors and exterior forms
- 3. Integration of differential forms
- 4. The Lie derivative
- 5. The Poincaré Lemma and potentials
- 6. Holonomic and nonholonomic constraints
- Part II. Geometry and Topology:
- 7. R3 and Minkowski space
- 8. The geometry of surfaces in R3
- 9. Covariant differentiation and curvature
- 10. Geodesics
- 11. Relativity, tensors, and curvature
- 12. Curvature and topology: Synge's theorem
- 13. Betti numbers and De Rham's theorem
- 14. Harmonic forms
- Part III. Lie Groups, Bundles, and Chern Forms:
- 15. Lie groups
- 16. Vector bundles in geometry and physics
- 17. Fiber bundles, Gauss–Bonnet, and topological quantization
- 18. Connections and associated bundles
- 19. The Dirac equation
- 20. Yang–Mills fields
- 21. Betti numbers and covering spaces
- 22. Chern forms and homotopy groups
- Appendix A. Forms in continuum mechanics
- Appendix B. Harmonic chains and Kirchhoff's circuit laws
- Appendix C. Symmetries, quarks, and Meson masses
- Appendix D. Representations and hyperelastic bodies
- Appendix E. Orbits and Morse–Bott theory in compact Lie groups.
