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Tensors The Mathematics of Relativity Theory and Continuum Mechanics

:	Anadi Jiban Das
:	Tensors The Mathematics of Relativity Theory and Continuum Mechanics
:	Springer-Verlag
:	9780387694696
:	1
:	CHF 82.70
:

:	Allgemeines, Lexika
:	English

:	290
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

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 theJournal of Mathematical PhysicsandFoundation of Physics. His book entitledThe Special Theory of Relativity: A Mathematical Expositionwas published by Springer in 1993.

	Preface	6
	Finite-Dimensional Vector Spaces and Linear Mappings	12
	Fields	12
	Finite-Dimensional Vector Spaces	14
	Linear Mappings of a Vector Space	20
	Dual or Covariant Vector Spaces	22
	Tensor Algebra	27
	Second-Order Tensors	27
	Higher-Order Tensors	35
	Exterior or Grassmann Algebra	42
	Inner Product Vector Spacesand the Metric Tensor	53
	Tensor Analysis on a Differentiable Manifold	63
	Differentiable Manifolds	63
	Tangent Vectors, Cotangent Vectors, and Parametrized Curves	71
	Tensor Fields over Differentiable Manifolds	80
	Differential Forms and Exterior Derivatives	91
	Differentiable Manifolds with Connections	103
	The Affine Connection and Covariant Derivative	103
	Covariant Derivatives of Tensors along a Curve	112
	Lie Bracket, Torsion, and Curvature Tensor	118
	Riemannian and Pseudo-Riemannian Manifolds	132
	Metric Tensor, Christoffel Symbols, and Ricci Rotation Coefficients	132
	Covariant Derivatives and the Curvature Tensor	146
	Curves, Frenet-Serret Formulas,and Geodesics	168
	Special Coordinate Charts	192
	Special Riemannian and Pseudo-Riemannian Manifolds	211
	Flat Manifolds	211
	The Space of Constant Curvature	216
	Einstein Spaces	225
	Conformally Flat Spaces	227
	Hypersurfaces, Submanifolds, and Extrinsic Curvature	236
	Two-Dimensional Surfaces Embedded in a Three-Dimensional Space	236
	(N-1)-Dimensional Hypersurfaces	244
	D-Dimensional Submanifolds	256
	Appendix I Fibre Bundles	267
	Appendix II Lie Derivatives	268
	Answers and Hints to Selected Exercises	281
	References	285
	List of Symbols	288
	Index	291