Anadi Jiban Das

Tensors (eBook, PDF)

The Mathematics of Relativity Theory and Continuum Mechanics

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 290
• Erscheinungstermin: 5. Oktober 2007
• Englisch
• ISBN-13: 9780387694696
• Artikelnr.: 37286029

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

From the reviews: "This book is a very nice introduction to the theory of tensor analysis on differentiable manifolds. It is intended mainly for students, but it can also be useful to everyone interested in the tensor analysis on differentiable manifolds and its application to the relativity theory and continuum mechanics." (Cezar Dumitru Oniciuc, Zentralblatt MATH, Vol. 1138 (16), 2008)