Foundations of Arithmetic Differential Geometry, Alexandru Buium

Автор: Tu, Loring W.
Название: Differential Geometry
ISBN: 3319550829 ISBN-13(EAN): 9783319550824
Издательство: Springer
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Цена: 59620.00 T
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Описание: Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein`s general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory.

Автор: Dray Tevian
Название: Differential Forms and the Geometry of General Relativity
ISBN: 1466510005 ISBN-13(EAN): 9781466510005
Издательство: Taylor&Francis
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Цена: 112290.00 T
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Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity.

The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of index gymnastics as much as possible.

The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.

Автор: Lee, J.M.
Название: Manifolds and Differential Geometry. Graduate Studies in Mathematics, 107.
ISBN: 0821848151 ISBN-13(EAN): 9780821848159
Издательство: Mare Nostrum (Eurospan)
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Цена: 83600.00 T
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Описание: Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and structures of modern differential geometry. It includes the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, and de Rham cohomology.

Название: Nonlinear Systems and Their Remarkable Mathematical Structures
ISBN: 1138601004 ISBN-13(EAN): 9781138601000
Издательство: Taylor&Francis
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Цена: 224570.00 T
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Описание: The book aims to describe some recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete).

Автор: Elhadj, Zeraoulia (university Of Tebessa, Algeria)
Название: Theories and applications
ISBN: 0367137046 ISBN-13(EAN): 9780367137045
Издательство: Taylor&Francis
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Цена: 224570.00 T
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Описание: This book presents the latest investigations in the theory of chaotic systems and their dynamics. It covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. The book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.

Автор: Liu, Qing
Название: Algebraic Geometry and Arithmetic Curves
ISBN: 0199202494 ISBN-13(EAN): 9780199202492
Издательство: Oxford Academ
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Цена: 80250.00 T
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Описание: This new-in-paperback edition provides an introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. Clear explanations of both theory and applications, and almost 600 exercises are included in the text.

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.