Tensors and Manifolds: With Applications to Physics (2nd edition)

ISBN : 9780199564828

Robert H. Wasserman
464 Pages
155 x 234 mm
Pub date
Apr 2009
Send mail

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 specialised 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. The 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 rigour 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.


1. Vector spaces
2. Multilinear mappings and dual spaces
3. Tensor product spaces
4. Tensors
5. Symmetric and skew-symmetric tensors
6. Exterior (Grassmann) algebra
7. The tangent map of real cartesian spaces
8. Topological spaces
9. Differentiable manifolds
10. Submanifolds
11. Vector fields, 1-forms and other tensor fields
12. Differentiation and integration of differential forms
13. The flow and the Lie derivative of a vector field
14. Integrability conditions for distributions and for pfaffian systems
15. Pseudo-Riemannian manifolds
16. Connection 1-forms
17. Connection on manifolds
18. Mechanics
19. Additional topics in mechanics
20. A spacetime
21. Some physics on Minkowski spacetime
22. Einstein spacetimes
23. Spacetimes near an isolated star
24. Nonempty spacetimes
25. Lie groups
26. Fiber bundles
27. Connections on fiber bundles
28. Gauge theory

About the author: 

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

The price listed on this page is the recommended retail price for Japan. When a discount is applied, the discounted price is indicated as “Discount price”. Prices are subject to change without notice.