Applicable Differential Geometry

Applicable Differential Geometry

by M. Crampin, F. A. E. Pirani, F. A. Pirani
     
 

ISBN-10: 0521231906

ISBN-13: 9780521231909

Pub. Date: 04/28/1987

Publisher: Cambridge University Press

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

Overview

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.

Product Details

ISBN-13:
9780521231909
Publisher:
Cambridge University Press
Publication date:
04/28/1987
Series:
London Mathematical Society Lecture Note Series, #59
Edition description:
New Edition
Pages:
404
Product dimensions:
5.98(w) x 8.98(h) x 0.91(d)

Table of Contents

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.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >