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• catalog abstract ""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 (in flat and curved space), 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 be of interest also 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."--BOOK JACKET.".
• catalog contributor b10591797.
• catalog created "1997.".
• catalog date "1997".
• catalog date "1997.".
• catalog dateCopyrighted "1997.".
• catalog description ""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 (in flat and curved space), 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 be of interest also 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."--BOOK JACKET.".
• catalog description "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 Nonholonomic Constraints -- II. Geometry and Topology. 7. R[superscript 3] and Minkowski Space. 8. The Geometry of Surfaces in R[superscript 3]. 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 -- 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 -- App. Forms in Continuum Mechanics.".
• catalog description "Includes bibliographical references (p. 639-641) and index.".
• catalog extent "xxii, 654 p. :".
• catalog issued "1997".
• catalog issued "1997.".
• catalog language "eng".
• catalog publisher "Cambridge, United Kingdom ; New York : Cambridge University Press,".
• catalog subject "530.1/5636 20".
• catalog subject "Geometry, Differential.".
• catalog subject "Mathematical physics.".
• catalog subject "QC20 .F7 1997".
• catalog tableOfContents "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 Nonholonomic Constraints -- II. Geometry and Topology. 7. R[superscript 3] and Minkowski Space. 8. The Geometry of Surfaces in R[superscript 3]. 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 -- 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 -- App. Forms in Continuum Mechanics.".
• catalog title "The geometry of physics : an introduction / Theodore Frankel.".
• catalog type "text".