Tensors and Manifolds: With Applications to Physics / Edition 2

by Robert H. Wasserman

Overview

This book is a new edition of "Tensors and Manifolds: With Applications to Mechanics and Relativity" which was published in 1992. It 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 the basic courses and the highly technical and specialized courses which both mathematics and physics students require in their 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 basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. He existing material from the first edition has been reworked and extended in some sections to provide extra clarity, as well as additional 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 rigor combined with an informal style makes this a very accessible book and will provide the reader with an enjoyable panorama of interesting mathematics and physics.

Product Details

ISBN-13:	9780198510598
Publisher:	Oxford University Press
Publication date:	07/08/2004
Edition description:	REV
Pages:	464
Product dimensions:	6.20(w) x 9.30(h) x 1.30(d)

About the Author

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

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 differentialforms13. The flow and the Lie derivative of a vector field14. Integrability conditions for distributions and forpfaffian 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