Tensor Calculus

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Tensor Calculus while presenting the concepts and Techniques begins with a brief introduction and history of tensors, followed by the study of systems of different orders, Einstein summation convention, kronecker symbol leading to the concepts of tensor algebra and tensor calculus. The authors conclude with a stimulating study in Riemannian geometry. Key Features Self-contained.  Basic Concepts of Vectors and Matrices Explained.  Unique Presentation to Understand the Theory.  Illuminating Examples New To The Second Edition:  Several new problems alongwith a stimulating study in Riemannian geometry. Table of Contents Preface to the Second Edition Preface to the First Edition Introduction Some Preliminaries: Introduction Systems of Different Orders Summation Convention Kronecker Symbols Some Results of Determinants Differentiation of a Determinant Linear Equations, Cramer’s Rule Examples Exercises Tensor Algebra: Introduction n-dimensional Space Transformation of Coordinates in Sn Invariants Vectors Tensors of Second Order Mixed Tensors of Type (p, q) Zero Tensor Tensor Field Algebra of Tensors Equality of Two Tensors Symmetric and Skew-symmetric Tensors Outer Multiplication and Contraction Inner Multiplication Quotient Law of Tensors Reciprocal Tensor of a Tensor Relative Tensor Cross Product or Vector Product of Two Vectors Examples Exercises Tensor Calculus: Introduction Riemannian Space Christoffel Symbols and their Properties Covariant Differentiation of Tensors Riemann-Christoffel Curvature Tensor Intrinsic Differentiation Geodesics, Riemannian Coordinates and Geodesic Coordinates: Introduction Calculus of Variations Families of Curves Euler’s Conditions Geodesics Riemannian and Geodesic Coordinates History of Tensor Calculus Bibliography Index.