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More About This Textbook
Overview
Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.
Product Details
Meet the Author
Anadi Das is a Professor Emeritus at Simon Fraser University, British Columbia, Canada. He earned his Ph.D. in Mathematics and Physics from the National University of Ireland and his D.Sc. from Calcutta University. He has published numerous papers in publications such as the Journal of Mathematical Physics and Foundation of Physics. His book entitled The Special Theory of Relativity: A Mathematical Exposition was published by Springer in 1993.
Table of 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.- Speical Riemannian and Pseudo-Riemannian Manifolds.- Flat Manifolds.- The Space of Constant Curvature.- Extrinsic Curvature.