Differential Forms And The Geometry Of General Relativity PDF Download

Differential Forms and the Geometry of General Relativity PDF
Author: Tevian Dray
Publisher: CRC Press
Size: 57.27 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 321
View: 5714

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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.

Formulations Of General Relativity PDF Download

Formulations of General Relativity PDF
Author: Kirill Krasnov
Publisher: Cambridge University Press
Size: 14.11 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 404
View: 2419

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Carefully documenting the different formulations of general relativity, the author reveals valuable insight into the nature of the gravitational force and its interaction with matter. This book will interest graduate students and researchers in the fields of general relativity, gravitational physics and differential geometry.

Differential Geometry For Physicists And Mathematicians PDF Download

Differential Geometry for Physicists and Mathematicians PDF
Author: José G Vargas
Publisher: World Scientific
Size: 53.23 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 312
View: 1354

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This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative — almost like a story being told — that does not impede sophistication and deep results. It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter. In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose. Contents:Introduction:OrientationsTools:Differential FormsVector Spaces and Tensor ProductsExterior DifferentiationTwo Klein Geometries:Affine Klein GeometryEuclidean Klein GeometryCartan Connections:Generalized Geometry Made SimpleAffine ConnectionsEuclidean ConnectionsRiemannian Spaces and Pseudo-SpacesThe Future?:Extensions of CartanUnderstand the Past to Imagine the FutureA Book of Farewells Readership: Physicists and mathematicians working on differential geometry. Keywords:Differential Geometry;Differential Forms;Moving Frames;Exterior CalculusKey Features:Reader FriendlyNaturalnessRespect for the history of the subject and related incisiveness

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Author: Карлос Кастанеда
Publisher: Family Leisure Club
Size: 63.57 MB
Format: PDF
Category :
Languages : uk
Pages :
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Колись шамани древньої Мексики вірили, що простір і час ― це єдине ціле. Час вони уявляли як нескінченний тунель із дзеркальними борознами. Пересічна людина потягом життя може споглядати тільки одну таку борозну, потрапляючи у своєрідну пастку, і лиш обраним до снаги дивитися на будь-яку з них і обертати те, що зветься колесом часу. Мудрість, пронесена крізь віки й зібрана на сторінках цієї книжки, відчиняє двері у магічний світ Карлоса Кастанеди. Роздуми письменника про людське життя та призначення, свободу, гармонію і самопізнання, пошук істини та власного шляху — заповітні ключі, здатні допомогти нам стати володарями свого часу та своєї долі. Цитати й афоризми немовби намотуються на химерну спіраль. Спіраль, яку древні шамани називали колесом часу…

Tensors Differential Forms And Variational Principles PDF Download

Tensors  Differential Forms  and Variational Principles PDF
Author: David Lovelock
Publisher: Courier Corporation
Size: 14.40 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 400
View: 4209

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Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

General Relativity PDF Download

General Relativity PDF
Author: Norbert Straumann
Publisher: Springer Science & Business Media
Size: 29.12 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 736
View: 2438

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This book provides a completely revised and expanded version of the previous classic edition ‘General Relativity and Relativistic Astrophysics’. In Part I the foundations of general relativity are thoroughly developed, while Part II is devoted to tests of general relativity and many of its applications. Binary pulsars – our best laboratories for general relativity – are studied in considerable detail. An introduction to gravitational lensing theory is included as well, so as to make the current literature on the subject accessible to readers. Considerable attention is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel’s proof of his uniqueness theorem, and a derivation of the basic laws of black hole physics. Part II ends with Witten’s proof of the positive energy theorem, which is presented in detail, together with the required tools on spin structures and spinor analysis. In Part III, all of the differential geometric tools required are developed in detail. A great deal of effort went into refining and improving the text for the new edition. New material has been added, including a chapter on cosmology. The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It utilizes a very well structured approach, which should help it continue to be a standard work for a modern treatment of gravitational physics. The clear presentation of differential geometry also makes it useful for work on string theory and other fields of physics, classical as well as quantum.

First Steps In Differential Geometry PDF Download

First Steps in Differential Geometry PDF
Author: Andrew McInerney
Publisher: Springer Science & Business Media
Size: 46.95 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 410
View: 2013

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Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.

Introduction To General Relativity PDF Download

Introduction to General Relativity PDF
Author: Lewis Ryder
Publisher: Cambridge University Press
Size: 62.70 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 441
View: 4073

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Student-friendly, well illustrated textbook for advanced undergraduate and beginning graduate students in physics and mathematics.

The Development Of Mathematics PDF Download

The Development of Mathematics PDF
Author: E. T. Bell
Publisher: Courier Corporation
Size: 60.28 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 656
View: 5169

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Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.

The Geometry Of Physics PDF Download

The Geometry of Physics PDF
Author: Theodore Frankel
Publisher: Cambridge University Press
Size: 34.28 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 694
View: 6403

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This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the deformation tensors of elasticity, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers, quarks, and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should be of interest also to mathematics students. Ideal for graduate and advanced undergraduate students of physics, engineering and mathematics as a course text or for self study.