An Introduction to Riemannian Geometry

With Applications to Mechanics and Relativity

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Author: Leonor Godinho,José Natário

Publisher: Springer

ISBN: 3319086669

Category: Mathematics

Page: 467

View: 4439

Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Compact Riemann Surfaces

An Introduction to Contemporary Mathematics

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Author: Jürgen Jost

Publisher: Springer Science & Business Media

ISBN: 3662034468

Category: Mathematics

Page: 295

View: 2970

This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Riemannian Geometry and Geometric Analysis

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Author: Jürgen Jost

Publisher: Springer Science & Business Media

ISBN: 3662223856

Category: Mathematics

Page: 458

View: 3307

FROM REVIEWS OF THE FIRST EDITION "a very readable introduction to Riemannian geometry...it is most welcome...The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references."-MATHEMATICAL REVIEWS

Tensor Geometry

The Geometric Viewpoint and its Uses

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Author: C. T. J. Dodson,Timothy Poston

Publisher: Springer Science & Business Media

ISBN: 3642105149

Category: Mathematics

Page: 434

View: 1717

This treatment of differential geometry and the mathematics required for general relativity makes the subject accessible, for the first time, to anyone familiar with elementary calculus in one variable and with some knowledge of vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the many illustrations presenting figures of three and more dimensions as closely as the book form will allow.

Aspects of Brownian Motion

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Author: Roger Mansuy,Marc Yor

Publisher: Springer Science & Business Media

ISBN: 9783540499664

Category: Mathematics

Page: 200

View: 3262

Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about Brownian motion and related processes. This book focuses on special classes of Brownian functionals, including Gaussian subspaces of the Gaussian space of Brownian motion; Brownian quadratic funtionals; Brownian local times; Exponential functionals of Brownian motion with drift; Time spent by Brownian motion below a multiple of its one-sided supremum.

Ordinary differential equations

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Author: Vladimir Igorevich Arnolʹd

Publisher: Springer Verlag

ISBN: 9783540345633

Category: Mathematics

Page: 334

View: 2961

There are dozens of books on ODEs, but none with the elegantgeometric insight of Arnol'd's book. Arnol'd puts a clear emphasis on the qualitative andgeometric properties of ODEs and their solutions, ratherthan on theroutine presentation of algorithms for solvingspecial classes of equations.Of course, the reader learnshow to solve equations, but with much more understandingof the systems, the solutions and the techniques. Vector fields and one-parameter groups of transformationscome right from the startand Arnol'd uses this "language"throughout the book. This fundamental difference from thestandard presentation allows him to explain some of the realmathematics of ODEs in a very understandable way and withouthidingthe substance. The text is also rich with examples and connections withmechanics. Where possible, Arnol'd proceeds by physicalreasoning, using it as a convenient shorthand for muchlonger formal mathematical reasoning. This technique helpsthe student get a feel for the subject. Following Arnol'd's guiding geometric and qualitativeprinciples, there are 272 figures in the book, but not asingle complicated formula. Also, the text is peppered withhistoricalremarks, which put the material in context,showing how the ideas have developped since Newton andLeibniz. This book is an excellent text for a course whose goal is amathematical treatment of differential equations and therelated physical systems.

Books in Print

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Author: R.R. Bowker Company

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 4394

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Newsletter

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Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1051