Details

Tensors

The Mathematics of Relativity Theory and Continuum Mechanics

von: Anadi Jiban Das
106,99 €
Verlag:	Springer
Format:	PDF
Veröffentl.:	05.10.2007
ISBN/EAN:	9780387694696
Sprache:	englisch
Anzahl Seiten:	292

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Beschreibungen

Titelbeschreibung

Tensor algebra and tensor analysis were developed by Riemann, Christo?el, Ricci, Levi-Civita and others in the nineteenth century. The special theory of relativity, as propounded by Einstein in 1905, was elegantly expressed by Minkowski in terms of tensor ?elds in a ?at space-time. In 1915, Einstein formulated the general theory of relativity, in which the space-time manifold is curved. The theory is aesthetically and intellectually satisfying. The general theory of relativity involves tensor analysis in a pseudo- Riemannian manifold from the outset. Later, it was realized that even the pre-relativistic particle mechanics and continuum mechanics can be elegantly formulated in terms of tensor analysis in the three-dimensional Euclidean space. In recent decades, relativistic quantum ?eld theories, gauge ?eld theories, and various uni?ed ?eld theories have all used tensor algebra analysis exhaustively. This book develops from abstract tensor algebra to tensor analysis in va- ous di?erentiable manifolds in a mathematically rigorous and logically coherent manner. The material is intended mainly for students at the fourth-year and ?fth-year university levels and is appropriate for students majoring in either mathematical physics or applied mathematics.

Inhaltsverzeichnis

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.

Autorenportrait

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.

Back cover copy

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.
     Topics covered in this book include, but are not limited to:
-tensor algebra -differential manifold -tensor analysis -differential forms -connection forms -curvature tensors -Riemannian and pseudo-Riemannian manifolds
     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.

Sonderbeitrag

Many known concepts which are scattered in various books are brought together in a rigorous, logical way Chapter 7 contains discussion on extrinsic curvature which is more extensive than in any other book available Tensor analysis is further explained in the book, touching on general differential manifolds, manifolds with connections and manifolds with metrics and connections. Competing books have only Riemannian and Pseudo-Riemannian manifolds discussed Each section of each chapter contains questions and exercises to further enhance understanding of the topics discussed