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Cambridge University Press
25 May 1987
Mathematics & Sciences; Differential & Riemannian geometry
This is an introduction to geometrical topics that are useful in applied mathematics and theoretical physics, including manifolds, metrics, connections, Lie groups, spinors and bundles, preparing readers for the study of modern treatments of mechanics, gauge fields theories, relativity and gravitation. The order of presentation corresponds to that used for the relevant material in theoretical physics: the geometry of affine spaces, which is appropriate to special relativity theory, as well as to Newtonian mechanics, is developed in the first half of the book, and the geometry of manifolds, which is needed for general relativity and gauge field theory, in the second half. Analysis is included not for its own sake, but only where it illuminates geometrical ideas. The style is informal and clear yet rigorous; each chapter ends with a summary of important concepts and results. In addition there are over 650 exercises, making this a book which is valuable as a text for advanced undergraduate and postgraduate students.
By:   M. Crampin (The Open University Milton Keynes), F. A. E. Pirani (University of London)
Other adaptation by:   N. J. Hitchin
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Volume:   59
Dimensions:   Height: 229mm,  Width: 152mm,  Spine: 23mm
Weight:   590g
ISBN:   9780521231909
ISBN 10:   0521231906
Series:   London Mathematical Society Lecture Note Series
Pages:   404
Publication Date:   25 May 1987
Audience:   College/higher education ,  Professional and scholarly ,  Primary ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
The background: vector calculus; 1. Affine spaces; 2. Curves, functions and derivatives; 3. Vector fields and flows; 4. Volumes and subspaces: exterior algebra; 5. Calculus of forms; 6. Frobenius's theorem; 7. Metrics on affine spaces; 8. Isometrics; 9. Geometry of surfaces; 10. Manifolds; 11. Connections; 12. Lie groups; 13. The tangent and cotangent bundles; 14. Fibre bundles; 15. Connections revisited.

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