Differential Forms and Connections

This 1994 book introduces the tools of modern differential geometry, exterior calculus, manifolds, vector bundles and connections.

R. W. R. Darling (Author)

9780521468008, Cambridge University Press

Paperback, published 22 September 1994

270 pages
25.2 x 17.7 x 2.6 cm, 0.579 kg

"...a good introduction to differential geometry and its applications to physics by using the calculus of differential forms...Nearly 200 exercises and many examples will help the reader's understanding...this book can be recommended as a good textbook for advanced undergraduate and beginning graduate students in mathematics, physics, and engineering." Akira Asada, Mathematical Reviews

This 1994 book introduces the tools of modern differential geometry, exterior calculus, manifolds, vector bundles and connections, to advanced undergraduate and beginning graduate students in mathematics, physics and engineering. The book covers both classical surface theory and the modern theory of connections and curvature, and includes a chapter on applications to theoretical physics. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. The powerful and concise calculus of differential forms is used throughout. Through the use of numerous concrete examples, the author develops computational skills in the familiar Euclidean context before exposing the reader to the more abstract setting of manifolds. There are nearly 200 exercises, making the book ideal for both classroom use and self-study.

Preface
1. Exterior algebra
2. Exterior calculus on Euclidean space
3. Submanifolds of Euclidean spaces
4. Surface theory using moving frames
5. Differential manifolds
6. Vector bundles
7. Frame fields, forms and metrics
8. Integration on oriented manifolds
9. Connections on vector bundles
10. Applications to gauge field theory
Bibliography
Index.

Subject Areas: Maths for engineers [TBJ], Maths for scientists [PDE], Differential & Riemannian geometry [PBMP], Calculus & mathematical analysis [PBK]