Discrete differential geometry preliminary entry 38, 

Автор: Sussman Gerald Jay
Название: Functional Differential Geometry
ISBN: 0262019345 ISBN-13(EAN): 9780262019347
Издательство: MIT Press
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Цена: 62070.00 T
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An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory.

Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Miserables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level.

The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.

Автор: Sharpe
Название: Differential Geometry
ISBN: 0387947329 ISBN-13(EAN): 9780387947327
Издательство: Springer
Цена: 55850.00 T
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Описание: Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections.

Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces generalises" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.

Автор: Lipschutz, Martin M.
Название: Schaum`s outline of differential geometry
ISBN: 0070379858 ISBN-13(EAN): 9780070379855
Издательство: McGraw-Hill
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Цена: 32020.00 T
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Описание: Schaum`s Outlines present all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

Автор: Snygg
Название: A New Approach to Differential Geometry using Clifford`s Geometric Algebra
ISBN: 0817682821 ISBN-13(EAN): 9780817682828
Издательство: Springer
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Цена: 74530.00 T
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Описание: A New Approach to Differential Geometry using Clifford`s Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra.