978-81-7319-884-7 Publication Year: Reprint 2020
Pages: 176 Binding: Paper Back
About the book
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.
∑ 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.
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, Cramerís 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 / Eulerís Conditions / Geodesics / Riemannian and Geodesic Coordinates / History of Tensor Calculus / Bibliography / Index.