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Applicable Differential Geometry : London Mathematical Society Lecture Notes - M. Crampin

Applicable Differential Geometry

London Mathematical Society Lecture Notes

Paperback

Published: 25th May 1987
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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.

The background: vector calculus
Affine spaces
Curves, functions and derivatives
Vector fields and flows
Volumes and subspaces: exterior algebra
Calculus of forms
Frobenius's theorem
Metrics on affine spaces
Isometrics
Geometry of surfaces
Manifolds
Connections
Lie groups
The tangent and cotangent bundles
Fibre bundles
Connections revisited
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521231909
ISBN-10: 0521231906
Series: London Mathematical Society Lecture Notes
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 404
Published: 25th May 1987
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.39  x 2.54
Weight (kg): 0.63