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1 Burnside Mathematics- Calculus

Dover Pictorial Archives #5: Tensor Calculus

by

Dover Pictorial Archives #5: Tensor Calculus Cover

ISBN13: 9780486636122
ISBN10: 0486636127
Condition: Standard
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Synopses & Reviews

Publisher Comments:

"This book is an excellent classroom text, since it is clearly written, contains numerous problems and exercises, and at the end of each chapter has a summary of the significant results of the chapter." — Quarterly of Applied Mathematics. Fundamental introduction for beginning student of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, special types of space, relative tensors, ideas of volume, and more.

Synopsis:

Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more.

Synopsis:

Widely used introductory text covers spaces and tensors, basic operations in Riemannian space, non-Riemannian spaces, etc.

Table of Contents

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 I

II. 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 II

III. 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 III

IV. 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 IV

V. 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 V

VI. Applications to hydrodynamics, elasticity, and electromagnetic radiation

  6.1 Hydrodynamics

  6.2 Elasticity

  6.3 Electromagnetic radiation

  Summary VI, Exercises VI

VII. 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 VII

VIII. 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 VIII

Appendix A. Reduction of a Quadratic Form

Appendix B. Multiple integration

  Bibliography, Index

What Our Readers Are Saying

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Average customer rating based on 1 comment:

asfar.nisar, November 23, 2007 (view all comments by asfar.nisar)
The topics are in very much arranged order its very worthwhile from my point view to have such books
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Product Details

ISBN:
9780486636122
With:
Schulb, A.
Author:
Schulb, A.
Author:
Schild
Author:
Schild, A.
Author:
Mathematics
Author:
Synge, L.
Author:
Synge, J. L.
Publisher:
Dover Publications
Location:
New York :
Subject:
Mathematics
Subject:
Calculus
Subject:
Vector Analysis
Subject:
Calculus of tensors
Subject:
General Mathematics
Subject:
Mathematics : Vector Analysis
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
5
Publication Date:
19780731
Binding:
TRADE PAPER
Grade Level:
General/trade
Language:
English
Illustrations:
Yes
Pages:
324
Dimensions:
8.25 x 5.63 in 0.8 lb

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Related Subjects


Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Mathematics » Vector Analysis
Science and Mathematics » Nature Studies » General

Dover Pictorial Archives #5: Tensor Calculus Used Trade Paper
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Product details 324 pages Dover Publications - English 9780486636122 Reviews:
"Synopsis" by ,
Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more.
"Synopsis" by , Widely used introductory text covers spaces and tensors, basic operations in Riemannian space, non-Riemannian spaces, etc.

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