Applied Differential Geometry

William L. Burke (Author)

9780521269292, Cambridge University Press

Paperback, published 31 May 1985

436 pages
22.8 x 14.9 x 2.4 cm, 0.57 kg

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.

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.

Subject Areas: Differential & Riemannian geometry [PBMP]