Tensor Calculus A Concise Course

Name: Tensor Calculus A Concise Course
Price: 5.98 USD
Availability: InStock
ISBN: 9780486428314

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.

Book details

List price: $9.95
Edition: 3rd
Copyright year: 2003
Publisher: Dover Publications, Incorporated
Publication date: 5/2/2003
Binding: Paperback
Pages: 144
Size: 5.24" wide x 7.99" long x 0.31" tall
Weight: 0.418
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