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Book Cover
E-book
Author Das, Anadijiban.

Title Tensors : the mathematics of relativity theory and continuum mechanics / Anadijiban Das
Published New York ; London : Springer, 2007
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Description 1 online resource (xii, 289 pages) : illustrations
Contents Finite- Dimensional Vector Spaces and Linear Mappings -- Fields -- Finite-Dimensional Vector Spaces -- Linear Mappings of a Vector Space -- Dual or Covariant Vector Space -- Tensor Algebra -- The Second Order Tensors -- Higher Order Tensors -- Exterior or Grassmann Algebra -- Inner Product Vector Spaces and the Metric Tensor -- Tensor Analysis on a Differentiable Manifold -- Differentiable Manifolds -- Vectors and Curves -- Tensor Fields over Differentiable Manifolds -- Differential Forms and Exterior Derivatives -- Differentiable Manifolds with Connections -- The Affine Connection and Covariant Derivative -- Covariant Derivatives of Tensors along a Curve -- Lie Bracket, Torsion, and Curvature Tensor -- Riemannian and Pseudo-Riemannian Manifolds -- Metric, Christoffel, Ricci Rotation -- Covariant Derivatives -- Curves, Frenet-Serret Formulas, and Geodesics -- Special Coordinate Charts -- Special Riemannian and Pseudo-Riemannian Manifolds -- Flat Manifolds -- The Space of Constant Curvature -- Extrinsic Curvature
Summary "Tensors: The Mathematics of Relativity Theory and Continuum Mechanics, by Anadijiban Das, emerged from courses taught over the years at the University College of Dublin, Carnegie-Mellon University and Simon Fraser University. This book will serve readers well as a modern introduction to the theories of tensor algebra and tensor analysis. Throughout Tensors, examples and worked-out problems are furnished from the theory of relativity and continuum mechanics. The extensive presentation of the mathematical tools, examples and problems make the book a unique text for the pursuit of both the mathematical relativity theory and continuum mechanics."--Jacket
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Tensor algebra.
Calculus of tensors.
Riemannian manifolds.
Form Electronic book
LC no. 2006939203
ISBN 9780387694696
0387694692
9780387694689 (hbk.)
0387694684 (hbk.)