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Bachman, David

A Geometric Approach to Differential Forms (Kartoniert / Broschiert / Paperback)

Springer Basel AG, Birkhäuser Boston, Dezember 2011


133 S. - Sprache: Englisch - 39 illustrations - 241x161x17 mm

ISBN: 0817683038 EAN: 9780817683030

This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.

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Produktdetails

This text presents differential forms from a geometric perspective accessible at the undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Containing excellent motivation, numerous illustrations and solutions to selected problems in an appendix, the material has been tested in the classroom along all three potential course tracks.

Inhaltsverzeichnis

Preface.- Guide to the Reader.-Multivariable Calculus.- Parameterizations.- Introduction to Forms.- Forms.- Differential Forms.- Differentiation of Forms.- Stokes' Theorem.- Applications.- Manifolds.- Non-linear Forms.- References.- Index.- Solutions.

ISBN 0-817683-03-8, ISBN 0-81-768303-8, ISBN 0-81768-303-8, ISBN 0-817-68303-8, ISBN 0-8176-8303-8

ISBN 978-0-817683-03-0, ISBN 978-0-81-768303-0, ISBN 978-0-81768-303-0, ISBN 978-0-817-68303-0, ISBN 978-0-8176-8303-0

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