| Description |
ix, 324 pages : illustrations ; 21 cm |
| Series |
Mathematical expositions ; v. 5
|
| Contents |
Machine derived contents note: Table of contents for Tensor calculus / by J. L. Synge and A. Schild. -- -- -- Bibliographic record and links to related information available from the Library of Congress catalog -- Information from electronic data provided by the publisher. May be incomplete or contain other coding. -- -- 1. Spaces and Tensors 1.1 The generalized idea of a space 1.2 Transformation of coordinates. Summation convention 1.3 Contravariant vectors and tensors. Invariants 1.4 Covariant vectors and tensors. Mixed tensors 1.5 Addition, multiplication, and contraction of tensors 1.6 Tests for tensor character 1.7 Compressed notation Summary I, Exercises III. Basic Operations in Riemannian Space 2.1 The metric tensor and the line element 2.2 The conjugate tensor. Lowering and raising suffixes 2.3 Magnitude of a vector. Angle between vectors 2.4 Geodesics and geodesic null lines. Christoffel symbols 2.5 Derivatives of tensors 2.6 Special coordinate systems 2.7 Frenet formulae Summary II, Exercises IIIII. Curvature of Space 3.1 The curvature tensor 3.2 The Ricci tensor, the curvature invariant, and the Einstein tensor 3.3 Geodesic deviation 3.4 Riemannian curvature 3.5 Parallel propagation Summary III, Exercises IIIIV. Special Types of Space 4.1 Space of constant curvature 4.2 Flat space 4.3 Cartesian tensors 4.4 A space of constant curvature regarded as a sphere in a flat space Summary IV, Exercises IVV. Applications to Classical Dynamics 5.1 Physical components of tensors 5.2 Dynamics of a particle 5.3 Dynamics of a rigid body 5.4 Moving frames of reference 5.5 General dynamical systems Summary V, Exercises VVI. Applications to hydrodynamics, elasticity, and electromagnetic radiation 6.1 Hydrodynamics 6.2 Elasticity 6.3 Electromagnetic radiation Summary VI, Exercises VIVII. Relative Tensors, Ideas of Volume, Green-Stokes Theorems 7.1 Relative tensors, generalized Kronecker delta, permutation symbol 7.2 Change of weight. Differentiation 7.3 Extension 7.4 Volume 7.5 Stokes' theorem 7.6 Green's theorem Summary VII, Exercises VIIVIII. Non-Riemannian spaces 8.1 Absolute derivative. Spaces with a linear connection. Paths 8.2 Spaces with symmetric connection. Curvature 8.3 Weyl spaces. Riemannian spaces. Projective spaces Summary VIII, Exercises VIIIAppendix A. Reduction of a Quadratic FormAppendix B. Multiple integration Bibliography, Index -- -- Library of Congress subject headings for this publication: Calculus of tensors |
| Analysis |
Tensor analysis |
| Notes |
Includes index |
|
Reprint of the 1969 ed. published by University of Toronto Press, Toronto, which was issued as v. 5 of Mathematical expositions |
| Bibliography |
Bibliography: page 319 |
| Subject |
Calculus of tensors.
|
| Author |
Schild, Alfred, 1921- author
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| LC no. |
77094163 |
| ISBN |
0486636127 |
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