Tensor Calculus
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Tensor Calculus

Tensor Calculus


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About the Book

Table of Contents:
Introduction / Some Preliminaries: Introduction / Systems of Different Orders / Sumination Convention / Kronecker Symbols / Some Results of Determinant / Differentiation of a Determinant / Linear Equations, Cramer's Rule / Examples / Exercises / Tensor Algebra: Introduction / n-dimensional Space / Transformation of Coordinates in Sn / Invariants / Vectors / Covariant Vectors / Contravariant Vectors / Tensors of Second Order / Contravariant Tensors of Order Two / Convariant Tensors of Order Two / Mixed Tensors of Order Two / Mixed Tensors of Type (p,q) / Zero Tensor / Tensor Field / Algebra of Tensors / Equality of Two Tensors / Symmetric and Skew-symmetric Tensors / Symmetric Tensors /Skew-symmetric Tensors / Outer Multiplications and Contraction / Outer Multiplications / Contraction / Quotient Law of Tensors / Quotient Law of Tensors of First Order and Type (0,1) / Quotient Law for Tensors of First Order and Type (1,0) / Quotient Law for Convariant Tensors of Second Order or of Type (0,2) / Quotient Law for Contravariant Tensors of Second Order or of Type (2,0) / Quotient Law in General Form / Reciprocal Tensor of a Tensor / Relative Tensor / Cross Product or Vector Product of Two Vectors / Examples / Exercises / Tensor Calculus: Introduction / Riemannian Space / Riemannian Metric / reciprocal or Conjugate Tensor of the Fundamental Metric Tensor gij / Associated Tensors, Lowering and Raising Indices / Magnitude or Length of a Vector / Unit Vector / Null Vector / Angle Between Two Non-null Vectors / Orthogonal Vectors / Christoffel Symbols and their Properties / Christoffel Symbols of First Kind / Christoffel Symbols of Second Kind / Properties of Christoffel Symbols / Law of Transformation of Christoffel Symbols of First Kind / Law of Transformation of Christoffel Symbols of Second Kind / Covariant Differentiation of Tensors / Covariant Differentiation of a Covariant Vector / Covariant Differentiation of a Contravariant Vector / Covariant Differentiation of Tensors of Type (0,2) / Covariant Derivative of a Tensor of Type (2,0) / Covariant Derivative of a Mixed tensor of type (1,1) / Covariant Derivate of a Mixed Tensor of Type (p,q) / Ricci's Theorem / Gradient of a Scalar / Divergence of a Contravariant Vector / Divergence of a Covariant Vector / Conservative Vector / Divergence of a Contravariant Tensor of Order Two / Divergence of a Mixed Tensor of Type (1,1) / Laplacian of an Invariatn / Curl of a Covariant Vector / Riemann-Christoffel Curvature Tensor / Definition / Properties of Tiemann-Christoffel Curvature Tensor / Rcci Tensor / Scalar Curvature / Einstein Space / Einstein Space / Einstein Tensor / Intrinsic Differentiation / Geodesics, Riemannian Coordinates and Geodesic Coordinates: Calculus of Variations / Families of Curves / Euler's Conditions / Geodesics / Riemannian and Geodesic Coordinates / History of Tensor Calculus


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Product Details
  • ISBN-13: 9781842651902
  • Publisher: Alpha Science International Ltd
  • Publisher Imprint: Alpha Science International Ltd
  • Height: 240 mm
  • ISBN-10: 1842651900
  • Publisher Date: 20 Sep 2004
  • Binding: Hardback
  • Width: 160 mm


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