Khan Q. Tensor Analysis and Its Applications 2015 torrent

Textbook in PDF format

Preface
Preliminaries
N - Dimensional Space
Superscript and Subscript
Einstein’s Summation Convention
Dummy Suffix and Real Suffix
Transformation of Coordinates
Kronecker Delta
Matrices and Determinants
Tensor Algebra and Its Calculus
Tensors
Operations on Tensors
Addition and Subtraction of Tensors
Multiplication of Tensors
Contraction
Inner Product or Scalar Product
Quotient Law
Extension of Rank of a Tensor
Types of Tensors
Invariant Tensors and Equality of Tensors
Fundamental Tensor
Symmetric Tensor and Anti - Symmetric (skew - Symmetric) Tensor
Reciprocal Tensor
Reducible Tensor and Irreducible Tensor
Relative Tensor
Raising and Lowering Suffix: Associated Tensors
Christoffel’s Symbols and Their Properties
Christoffel’s Symbols or Christoffel’s Brackets
Symmetric Properties of Christoffel’s Symbols
Tensor Laws of Transformation of Christoffel’s Symbols
Transitive Property for Laws of Transformation of Christoffel’s Symbols
Covariant Differentiation of Tensors and Their Properties
Comma Notation
Covariant Differentiation of Vectors (tensors of Rank One)
Covariant Derivative of a Covariant Tensor of Rank Two
Covariant Derivative of a Contravariant Tensor of Rank Two
Covariant Derivative of a Mixed Tensor of Rank Two
Covariant Derivative of the Fundamental Tensors
Laws of Covariant Differentiation
Covariant Derivative of an Invariant (or a Scalar)
Tensor Form of Gradient, Divergence, Laplacian and Curl
Divergence of a Tensor
Intrinsic Derivatives
Parallel Displacement of Vectors
Riemannian Symbols and Its Properties
Riemannian Symbols of Second Kind
Properties of the Riemann Curvature Tensor 
Contraction of the Riemann Curvature Tensor 
Riemannian Symbols of First Kind
Properties of Covariant Curvature Tensor 
Contraction of Bianchi’s Identities (einstein Tensor)
Riemannian Curvature
Flat Space
Uniform Vector Field
Conditions for Flat Space - Time
Space of Constant Curvature
Einstein Space
Application of Tensor Calculus
Introduction
Application of Tensor Calculus
Tensor Calculus and Differential Geometry
Tensor Calculus and Riemannian Geometry
Tensor Calculus and Theory of Relativity
Tensor Calculus and Elasticity
Tensor Calculus and Physics
Tensor Calculus and Other Fields Like Economics, Probability and Engineering
Bibliography