Tensor calculus and applications : simplified tools and techniques /: simplified tools and techniques. ([2019])

• Record Type: Book
• Further Information: Note: Authored by Bhaben Chandra Kalita.
• Authors: Kalita, Bharat Chandra, 1937-
• Contents: Exercises4. Christoffel Three-Index Symbols (Brackets) and Covariant Differentiation; 4.1 Christoffel Symbols (or Brackets) of the First and Second Kinds; 4.2 Two Standard Applicable Results of Christoffel Symbols; 4.3 Evolutionary Basis of Christoffel Symbols (Brackets); 4.4 Use of Symmetry Condition for the Ultimate Result; 4.5 Coordinate Transformations of Christoffel Symbols; 4.5.1 Transformation of the First Kind [sub(ij, k)]; 4.5.2 Transformation of the Second Kind [sup(ij)][sub(k)]; 4.6 Covariant Derivative of Covariant Tensor of Rank One 2.4 Operations on Tensors2.5 Symmetric and Antisymmetric (or Skew-Symmetric) Tensors; 2.6 Quotient Law; Exercises; 3. Riemannian Metric and Fundamental Tensors; 3.1 Riemannian Metric; 3.2 Cartesian Coordinate System and Orthogonal Coordinate System; 3.3 Euclidean Space of n Dimensions, Euclidean Co-Ordinates, and Euclidean Geometry; 3.4 The Metric Functions g[sub(ij)] Are Second-Order Covariant Symmetric Tensors; 3.5 The Function g[sub(ij)] Is a Contravariant Second-Order Symmetric Tensor; 3.6 Scalar Product and Magnitude of Vectors; 3.7 Angle Between Two Vectors and Orthogonal Condition 4.7 Covariant Derivative of Contravariant Tensor of Rank One4.8 Covariant Derivative of Covariant Tensor of Rank Two; 4.9 Covariant Derivative of Contravariant Tensor of Rank Two; 4.10 Covariant Derivative of Mixed Tensor of Rank Two; 4.10.1 Generalization; 4.11 Covariant Derivatives of g[sub(ij)] g[sup(ij)] and also g[sub(i)][sub(j)]; 4.12 Covariant Differentiations of Sum (or Difference) and Product of Tensors; 4.13 Gradient of an Invariant Function; 4.14 Curl of a Vector; 4.15 Divergence of a Vector; 4.16 Laplacian of a Scalar Invariant; 4.17 Intrinsic Derivative or Derived Vector of v 4.18 Definition: Parallel Displacement of Vectors4.18.1 When Magnitude Is Constant; 4.18.2 Parallel Displacement When a Vector Is of Variable Magnitude; Exercises; 5. Properties of Curves in V[sub(n)] and Geodesics; 5.1 The First Curvature of a Curve; 5.2 Geodesics; 5.3 Derivation of Differential Equations of Geodesics; 5.4 Aliter: Differential Equations of Geodesics as Stationary Length; 5.5 Geodesic Is an Autoparallel Curve; 5.6 Integral Curve of Geodesic Equations; 5.7 Riemannian and Geodesic Coordinates, and Conditions for Riemannian and Geodesic Coordinates Cover; Half Title; Series Page; Title Page; Copyright Page; Contents; Preface; About the Book; Author; Part I: Formalism of Tensor Calculus; 1. Prerequisites for Tensors; 1.1 Ideas of Coordinate Systems; 1.2 Curvilinear Coordinates and Contravariant and Covariant Components of a Vector (the Entity); 1.3 Quadratic Forms, Properties, and Classifications; 1.4 Quadratic Differential Forms and Metric of a Space in the Form of Quadratic Differentials; Exercises; 2. Concept of Tensors; 2.1 Some Useful Definitions; 2.2 Transformation of Coordinates; 2.3 Second and Higher Order Tensors
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2019
• Copyright Date: 2019
• Extent: 1 online resource
• Subjects: 515/.63; Calculus of tensors; Geometry, Differential; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; TECHNOLOGY -- Engineering -- Industrial; TECHNOLOGY -- Operations Research; MATHEMATICS -- Applied; Calculus of tensors; Geometry, Differential; Electronic books
• Languages: English
• ISBNs: 9780429028670; 0429028679; 9780429644924; 0429644922; 9780429647567; 0429647565; 9780429650208; 0429650205
• Related ISBNs: 9780367138066
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (EBSCO, viewed March 18, 2019)
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.