Tensors The Mathematics of Relativity Theory and Continuum Mechanics /

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Das, Anadijiban (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2007.
• Θέματα: Physics.; Human physiology.; Theoretical, Mathematical and Computational Physics.; Mathematical Methods in Physics.; Human Physiology.

  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. 

 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.