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Tensor Calculus A Concise Course

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ISBN-10: 0486428311

ISBN-13: 9780486428314

Edition: 3rd 2003

Authors: Barry Spain

List price: $9.95
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Description:

A compact exposition of the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry, elasticity, and relativity. Explores tensor algebra, the line element, covariant differentiation, geodesics and parallelism, and curvature tensor. Also covers Euclidean 3-dimensional differential geometry, Cartesian tensors and elasticity, and the theory of relativity. 1960 edition.
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Book details

List price: $9.95
Edition: 3rd
Copyright year: 2003
Publisher: Dover Publications, Incorporated
Publication date: 5/2/2003
Binding: Paperback
Pages: 133
Size: 5.25" wide x 8.00" long x 0.50" tall
Weight: 0.330
Language: English

Tensor Algebra
Introduction
N-Dimensional space
Transformation of co-ordinates
Indicial and summation conventions
Contravariant vectors
Covariant vectors
Invariants
Second order tensors
Higher order tensors
Addition, subtraction and multiplication of tensors
Contraction
Quotient law
Conjugate symmetric tensors of the second order
The Line Element
Fundamental tensor
Length of a Curve
Magnitude of a vector
Associate tensors
Angle between two vectors--orthogonality
Principal directions
Covariant Differentiation
Christoffel symbols
Transformation law of Christoffel symbols
Covariant differentiation of vectors
Covariant differentiation of tensors
Laws of covariant differentiation
Intrinsic derivatives
Geodesics - Parallelism
Geodesics
Null-geodesics
Geodesic coordinates
Parallelism
Covariant derivative
Curvature Tensor
Riemann-Christoffel tensor
Curvature tensor
Ricci tensor--Curvature invariant
Bianchi's identity
Riemannian curvature
Flat space
Space of constant curvature
Euclidean Three-Dimensional Differential Geometry
Permutation tensors
Vector product
Frenet formulae
Surface--First fundamental form
Surface vectors
Permutation surface tensor
Surface covariant differentiation
Geodesic curvature
Normal vector
Tensor derivatives of tensors
Second fundamental form
Third fundamental form
Gauss-Codazzi equations
Normal curvature--asymptotic lines
Principal curvatures--lines of curvature
Cartesian Tensors - Elasticity
Orthogonal transformations
Rotations
Cartesian tensors
Infinitesimal strain
Stress
Equations of equilibrium
Generalised Hooke's law
Isotropic tensors
Homogeneous and isotropic body
Curvilinear coordinates
Mechanics of continuous matter
Theory of Relativity
Special theory
Maxwell's Equations
General theory
Spherically symmetrical metric
Schwarzschild metric
Planetary motion
Einstein's universe
De Sitter's universe
Bibliography
Index