This book is intended to provide 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 essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism, thermodynamics, the deformation tensors of elasticity, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should also be of interest to mathematics students. This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics. It can be used as a course text or for self study.
Rezensionen / Stimmen
' ... extremely helpful for students in physics and engineering ... recommended to a wide audience ...' European Mathematical Society 'The layout, the typography and the illustrations of this advanced textbook on modern mathematical methods are all very impressive and so are the topics covered in the text.' Zentralblatt fuer Mathematik und ihre Grenzgebiete
Sprache
Verlagsort
Zielgruppe
Illustrationen
120 Line drawings, unspecified
Maße
Höhe: 263 mm
Breite: 185 mm
Dicke: 37 mm
Gewicht
ISBN-13
978-0-521-38334-9 (9780521383349)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
University of California, San Diego
Preface; 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 Poincare Lemma and potentials; 6. Holonomic and non-holonomic 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: forms in continuum mechanics.
