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This 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. 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.Read more
- 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
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- Edition: 3rd Edition
- Date Published: December 2011
- format: Paperback
- isbn: 9781107602601
- length: 748 pages
- dimensions: 248 x 174 x 33 mm
- weight: 1.44kg
- contains: 260 b/w illus. 205 exercises
- availability: Available
Table of Contents
Preface to the Third Edition
Preface to the Second Edition
Preface to the revised printing
Preface to the First Edition
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
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.
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