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E-book
Author Islam, Nazrul.

Title Tensors and their applications / Nazrul Islam
Published New Delhi : New Age International (P) Ltd., Publishers, [2006]
©2006
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Description 1 online resource (xv, 245 pages)
Contents Chapter 1: Preliminaries -- 1.1. n-Dimensional Space -- 1.2. Superscript and Subscript -- 1.3. The Einstein's Summation Convention -- 1.4. Dummy Index -- 1.5. Free Index -- 1.6. Kronecker Delta -- Exercises -- Chapter 2: Tensor Algebra -- 2.1. Introduction -- 2.2. Transformation of Coordinates -- 2.3. Covariant and Contravariant Vectors (Tensor of Rank One) -- 2.4. Contravariant Tensor of Rank Two -- 2.5. Covariant Tensor of Rank Two -- 2.6. Mixed Tensor of Rank Two -- 2.7. Tensor of Higher Order -- 2.8. Scalar or Invariant -- 2.9. Addition and Subtraction of Tensors -- 2.10. Multiplication of Tensors (Outer Product of Tensor) -- 2.11. Contraction of a Tensor -- 2.12. Inner Product of Two Tensors -- 2.13. Symmetric Tensors -- 2.14. Skew-Symmetric Tensor -- 2.15. Quotient Law -- 2.16. Conjugate (or Reciprocal) Symmetric Tensor -- 2.17. Relative Tensor -- Miscellaneous Examples -- Exercises -- Chapter 3: Metric Tensor and Riemannian Metric -- 3.1. The Metric Tensor -- 3.2. Conjugate Metric Tensor: (Contravariant Tensor) -- 3.3. Length of a Curve -- 3.4. Associated Tensor -- 3.5. Magnitude of Vector -- 3.6. Scalar Product of Two Vectors -- 3.7. Angle Between Two Vectors -- 3.8. Angle Between Two Coordinate Curves -- 3.9. Hypersurface -- 3.10. Angle Between Two Coordinate Hyper surface -- 3.11. n-Ply Orthogonal System of Hypersurfaces -- 3.12. Congruence of Curves -- 3.13. Orthogonal Ennuple -- Miscellaneous Examples -- Exercises -- Chapter 4: Christoffel's Symbols and Covariant Differentiation -- 4.1. Christoffel's Symbols -- 4.2. Transformation of Christoffel's Symbols -- 4.3. Covariant Differentiation of a Covariant Vector -- 4.4. Covariant Differentiation of a Contravariant Vector -- 4.5. Covariant Differentiation of Tensors -- 4.6. Ricci's Theorem -- 4.7. Gradient, Divergence and Curl -- 4.8. The Laplacian Operator -- Exercises -- Chapter 5: Riemann-Christoffel Tensor -- 5.1. Riemann-Christoffel Tensor -- 5.2. Ricci Tensor -- 5.3. Covariant Riemann-Christoffel Tensor -- 5.4. Properties of Riemann-Christoffel Tensors of First Kind R [subscript]ijkl -- 5.5. Bianchi Identity -- 5.6. Einstein Tensor -- 5.7. Riemann Curvature of a Vn -- 5.8. Formula for Riemannian Curvature in the Terms of Covariant curvature Tensor of Vn -- 5.9. Schur's Theorem -- 5.10. Mean Curvature -- 5.11. Ricci Principal Directions -- 5.12. Einstein Space -- 5.13. Weyl Tensor or Projective Curvature Tensor -- Exercises -- Chapter 6: The e-Systems and the Generalized Krönecker Deltas -- 6.1. Completely Symmetric -- 6.2. Completely Skew-Symmetric -- 6.3. e-System -- 6.4. Generalised Krönecker Delta -- 6.5. Contraction of ä i jk [over] áǎa -- Exercises -- Chapter 7: Geometry -- 7.1. Length of Arc -- 7.2. Curvilinear Coordinates in E₃ -- 7.3. Reciprocal Base Systems -- 7.4. On the Meaning of Covariant Derivatives -- 7.5. Intrinsic Differentiation -- 7.6. Parallel Vector Fields -- 7.7. Geometry of space curves -- 7.8. Serret-Frenet formulae -- 7.9. Equations of a straight line -- Exercises -- Chapter 8: Analytical mechanics -- Chapter 9: Curvature of a curve, geodesic -- Chapter 10: Parallelism of vectors -- Chapter 11: Ricci-s coefficients of rotation and congruence -- Chapter 12: Hypersurfaces
Summary About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel's Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci's Coefficients of Rotation and Congruence Hyper Surfaces
Notes Print version record
Subject Tensor algebra.
Form Electronic book
ISBN 1282074350
8122427006 (electronic bk.)
9781282074354
9788122427004 (electronic bk.)