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Differentiable Manifolds: A Theoretical Physics Approach

Differentiable Manifolds: A Theoretical Physics Approach
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Field name Details
Dewey Class 516.36
Title Differentiable Manifolds ([Ebook]) : A Theoretical Physics Approach / by Gerardo F. Torres del Castillo.
Author Torres del Castillo, G. F. (Gerardo Francisco) , 1956-
Other name(s) SpringerLink (Online service)
Publication Boston : Birkhäuser , 2012.
Physical Details VIII, 275 pages, 20 illus. : online resource.
ISBN 9780817682712
Summary Note This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The workâs first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations (Chapter 4), connections (Chapter 5), Riemannian manifolds (Chapter 6), Lie groups (Chapter 7), and Hamiltonian mechanics (Chapter 8). Throughout, the book contains examples, worked out in detail, as well as exercises intended to show how the formalism is applied to actual computations and to emphasize the connections among various areas of mathematics. Differentiable Manifolds is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and (for the last chapter) a basic knowledge of analytical mechanics.:
Contents note Preface.-1 Manifolds.-  2 Lie Derivatives -- 3 Differential Forms -- 4 Integral Manifolds -- 5 Connections -- 6. Riemannian Manifolds -- 7 Lie Groups -- 8 Hamiltonian Classical Mechanics -- References.-Index.
System details note Online access is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-0-8176-8271-2
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