Tensors and Manifolds: With Applications to Physics

Paperback | May 20, 2009

byRobert H. Wasserman

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This second edition of Tensors and Manifolds is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between thebasic courses and the highly technical and specialised courses which both mathematics and physics students require in ther advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other's discipline. The book sets forth the basicprinciples of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. The existing material from the first edition has been reworked and extended in some sections to provide extra clarity, withadditional problems. Four new chapters on Lie groups and fibre bundles have been included, leading to an exposition of gauge theory and the standard model of elementary particle physics. Mathematical rigour combined with an informal style makes this a very accessible book and will provide the readerwith an enjoyable panorama of interesting mathematics and physics.

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From the Publisher

This second edition of Tensors and Manifolds is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between thebasic courses and the highly technical and spe...

Robert H. Wasserman is Professor Emeritus of Mathematics at Michigan State University, USA.

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Format:PaperbackDimensions:464 pages, 9.21 × 6.14 × 0.68 inPublished:May 20, 2009Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199564825

ISBN - 13:9780199564828

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Table of Contents

1. Vector spaces2. Multilinear mappings and dual spaces3. Tensor product spaces4. Tensors5. Symmetric and skew-symmetric tensors6. Exterior (Grassmann) algebra7. The tangent map of real cartesian spaces8. Topological spaces9. Differentiable manifolds10. Submanifolds11. Vector fields, 1-forms and other tensor fields12. Differentiation and integration of differential forms13. The flow and the Lie derivative of a vector field14. Integrability conditions for distributions and for pfaffian systems15. Pseudo-Riemannian manifolds16. Connection 1-forms17. Connection on manifolds18. Mechanics19. Additional topics in mechanics20. A spacetime21. Some physics on Minkowski spacetime22. Einstein spacetimes23. Spacetimes near an isolated star24. Nonempty spacetimes25. Lie groups26. Fiber bundles27. Connections on fiber bundles28. Gauge theory

Editorial Reviews

Review from previous edition: "Clearly written and self-contained and, in particular, the author has succeeded in combining mathematical rigor with a certain degree of informality in a satisfactory way. As such, this work will certainly be appreciated by a wide audience." --Mathematical Reviews