Applicable Differential Geometry - Brossura

Crampin, M.

Brossura

ISBN 10: 0521231906 ISBN 13: 9780521231909

Casa editrice: Cambridge University Press, 1987

Riassunto

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.

Su questo libro

Descrizione del libro:

Applicable Differential Geometry is an introduction to geometrical topics which are useful in applied mathematics and theoretical physics. It discusses the geometry of affine spaces which is appropriate for the theory of special relativity as well as to Newtonian mechanics, as well as the geometry of manifolds, employed in general relativity and gauge field theory.

Contenuti:

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.

Su questa edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 1987
• ISBN 10: 0521231906
• ISBN 13: 9780521231909
• Rilegatura: Copertina flessibile
• Numero di pagine: 400