Applied Differential Geometry

Erscheinungsjahr 2003
ISBN: 978-0-521-26929-2
Verlag: Cambridge University Press

Buch, Englisch, 416 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 704 g

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.

Autoren/Hrsg.

Burke, William L.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

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.