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Cover: 9780521468008 | Differential Forms and Connections | R. W. R. Darling | Taschenbuch
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Differential Forms and Connections
Taschenbuch von R. W. R. Darling
Sprache: Englisch

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Beschreibung
This book introduces the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--and covers both classical surface theory, the modern theory of connections, and curvature. Also included is a chapter on applications to theoretical physics. The author uses the powerful and concise calculus of differential forms 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. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. Nearly 200 exercises make the book ideal for both classroom use and self-study for advanced undergraduate and beginning graduate students in mathematics, physics, and engineering.
This book introduces the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--and covers both classical surface theory, the modern theory of connections, and curvature. Also included is a chapter on applications to theoretical physics. The author uses the powerful and concise calculus of differential forms 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. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. Nearly 200 exercises make the book ideal for both classroom use and self-study for advanced undergraduate and beginning graduate students in mathematics, physics, and engineering.
Inhaltsverzeichnis
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.
Details
Medium: Taschenbuch
Seiten: 270
ISBN-13: 9780521468008
ISBN-10: 0521468000
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Darling, R. W. R.
Hersteller: Cambridge University Press
Maße: 254 x 178 x 15 mm
Von/Mit: R. W. R. Darling
Erscheinungsdatum: 28.10.1994
Gewicht: 0,514 kg
preigu-id: 109425840
Inhaltsverzeichnis
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.
Details
Medium: Taschenbuch
Seiten: 270
ISBN-13: 9780521468008
ISBN-10: 0521468000
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Darling, R. W. R.
Hersteller: Cambridge University Press
Maße: 254 x 178 x 15 mm
Von/Mit: R. W. R. Darling
Erscheinungsdatum: 28.10.1994
Gewicht: 0,514 kg
preigu-id: 109425840
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