Tensor Calculus Made Simple

This book is about tensor analysis. It consists of 169 pages. The language and method used in presenting the ideas and techniques of tensors make it very suitable as a textbook or as a reference for an introductory course on tensor algebra and calculus or as a guide for self-studying and learning. The book contains many exercises. The detailed solutions of all these exercises are available in another book by the author (Solutions of Exercises of Tensor Calculus Made Simple). Preface Nomenclature 1: Preliminaries 1.1: Historical Overview of Development & Use of Tensor Calculus 1.2: General Conventions 1.3: General Mathematical Background 1.3.1: Coordinate Systems 1.3.2: Vector Algebra and Calculus 1.3.3: Matrix Algebra 1.4: Exercises 2: Tensors 2.1: General Background about Tensors 2.2: General Terms and Concepts 2.3: General Rules 2.4: Examples of Tensors of Different Ranks 2.5: Applications of Tensors 2.6: Types of Tensor 2.6.1: Covariant and Contravariant Tensors 2.6.2: True and Pseudo Tensors 2.6.3: Absolute and Relative Tensors 2.6.4: Isotropic and Anisotropic Tensors 2.6.5: Symmetric and Anti-symmetric Tensors 2.7: Exercises 3: Tensor Operations 3.1: Addition and Subtraction 3.2: Multiplication of Tensor by Scalar 3.3: Tensor Multiplication 3.4: Contraction 3.5: Inner Product 3.6: Permutation 3.7: Tensor Test: Quotient Rule 3.8: Exercises 4: delta and epsilon Tensors 4.1: Kronecker delta 4.2: Permutation epsilon 4.3: Useful Identities Involving delta or/and epsilon 4.3.1: Identities Involving delta 4.3.2: Identities Involving epsilon 4.3.3: Identities Involving delta and epsilon 4.4: Generalized Kronecker delta 4.5: Exercises 5: Applications of Tensor Notation and Techniques 5.1: Common Definitions in Tensor Notation 5.2: Scalar Invariants of Tensors 5.3: Common Differential Operations in Tensor Notation 5.3.1: Cartesian Coordinate System 5.3.2: Cylindrical Coordinate System 5.3.3: Spherical Coordinate System 5.3.4: General Orthogonal Coordinate System 5.4: Common Identities in Vector and Tensor Notation 5.5: Integral Theorems in Tensor Notation 5.6: Examples of Using Tensor Techniques to Prove Identities 5.7: Exercises 6: Metric Tensor 6.1: Exercises 7: Covariant Differentiation 7.1: Exercises References Footnotes