Enhanced descriptions from Syndetics:

This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

Table of contents provided by Syndetics

• Preface
• Glossary of notation
• Introduction
• 1 Tensors in linear spaces
• 2 Manifolds
• 3 Transformations
• 4 The calculus of differential forms
• 5 Applications of the exterior calculus
• 6 Classical electrodynamics
• 7 Dynamics of particles and fields
• 8 Calculus on fiber bundles
• 9 Gravitation
• Bibliography
• Index

Reviews provided by Syndetics

CHOICE Review

The two outstanding features of Burke's book are its large number of figures and its examples. Pictures are used extensively throughout to illustrate analytical discussions, and they are particularly helpful in giving insight into abstract concepts. Many are associated with the worked examples. The book is divided into three main sections. The first (roughly the first half of the book) is basically mathematical-an introduction to manifolds and transformations. Topics such as the Lie derivative and fiber bundles are discussed. The heart of the book is, in a sense, the long, excellent chapter on the calculus of differential forms. It leads to a final section on the applications of the techniques to thermodynamics, electrodynamics, field theory, and so on. Burke ends with a chapter on general relativity. Much of this material could be obtained in a more concentrated form from books such as C.W. Misner, K.S. Thorne, and J.A. Wheeler's Gravitation (CH, Apr '74) but there is no other book that explains the ideas so clearly and in such detail. Also, the book is not weighted with mathematical proofs; the emphasis throughout is on geometrical structure and applications. Level: advanced undergraduate and graduate.-B.R. Parker, Idaho State University