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The geometry of physics : an introduction. /Theodore Frankel.

By: Frankel, TheodoreContributor(s): Theodore FrankelMaterial type: Text

TextPublisher number: : Zafaa Books & Distributors | : 313/56F, Anand Nagar, Inderlok, Delhi- 110035Publication details: , Cambridge : Cambridge University Press , 2012Description: lxii, 686 pages : illustrations ; 25 cmISBN: 9781107602601Subject(s): Differentialform | Mathematical physics | Topologie | DifferentialgeometrieDDC classification: 530.15636 FRA

Contents:

Overview: an informal overview of Cartan's exterior differential forms, illustrated with an application to Cauchy's stress tensor t I. Part I: Manifolds and vector fields Tensors and exterior forms Integration of differential forms The Lie derivative The Poincare Lemma and potentials Holonomic and nonholonomic constraints Part II: Geometry and topology R³ and Minkowski space The geometry of surfaces in R³ Covariant differentiation and curvature Geodesics Relativity, tensors, and curvature Curvature and topology: Synge's theorem Betti numbers and De Rham's theorem Harmonic forms Part III: Lie Groups Vector bundles in geometry and physics Fiber bundles, Gauss-Bonnet, and topological quantization Connections and associated bundles The Dirac equation Yang-Mills fields Betti numbers and covering spaces Chern forms and homotopy groups

Summary: "This book is intended to provide 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 the quark model for mesons. Before a discussion of 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. This book will be useful to graduate and advance undergraduate students of physics, engineering or mathematics. It can be used as a course text or for self-study. This third edition includes a new overview of Cartan's exterior differential forms. It previews many of the geometric concepts developed in the text and illustrates their applications to a single extended problem in engineering, namely the Cauchy stresses created by a small twist of an elastic cylindrical rod about its axis"

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Item type	Current library	Call number	Status	Date due	Barcode	Item holds
Books	SNU LIBRARY	530.15636 FRA (Browse shelf(Opens below))	Available		28954

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Previous	530.155353 DOR Dirac structures and integrability of nonlinear evolution equations	530.155353 GUE Partial Differential Equations of Mathematical Physics and Integral Equations	530.15636 FRA The Geometry of Physics : An introduction	530.15636 FRA The geometry of physics : an introduction.	530.157 DUF Differential equations of applied mathematics.	530.159 FOR Hydrodynamic fluctuations, broken symmetry, and correlation functions /	530.159 FOR Hydrodynamic fluctuations, broken symmetry, and correlation functions /	Next

Overview: an informal overview of Cartan's exterior differential forms, illustrated with an application to Cauchy's stress tensor
t I. Part I: Manifolds and vector fields
Tensors and exterior forms
Integration of differential forms
The Lie derivative
The Poincare Lemma and potentials
Holonomic and nonholonomic constraints
Part II: Geometry and topology
R³ and Minkowski space
The geometry of surfaces in R³
Covariant differentiation and curvature
Geodesics
Relativity, tensors, and curvature
Curvature and topology: Synge's theorem
Betti numbers and De Rham's theorem
Harmonic forms
Part III: Lie Groups
Vector bundles in geometry and physics
Fiber bundles, Gauss-Bonnet, and topological quantization
Connections and associated bundles
The Dirac equation
Yang-Mills fields
Betti numbers and covering spaces
Chern forms and homotopy groups

"This book is intended to provide 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 the quark model for mesons. Before a discussion of 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. This book will be useful to graduate and advance undergraduate students of physics, engineering or mathematics. It can be used as a course text or for self-study. This third edition includes a new overview of Cartan's exterior differential forms. It previews many of the geometric concepts developed in the text and illustrates their applications to a single extended problem in engineering, namely the Cauchy stresses created by a small twist of an elastic cylindrical rod about its axis"

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