Tensors The Mathematics of Relativity Theory and Continuum Mechanics
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...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
2007, 2007
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| Edition: | 1st ed. 2007 |
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| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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