Introduction to Vector and Tensor Analysis

by Wrede, Robert C.

• ISBN13: 9780486618791
• ISBN10: 048661879X
• Format: Paperback
• Copyright: 1972-06-01
• Publisher: Dover Publications

Summary

Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more.

Table of Contents

the algebra of vectors	1	(123)
Historical summary	1	(6)
Introductory concepts	7	(16)
Linear dependence or independence of a set of number n-tuples	23	(12)
Transformation equations relating rectangular Cartesian coordinate systems	35	(16)
Definitions of Cartesian scalar and vector	51	(5)
The inner product	56	(9)
General Cartesian coordinates	65	(20)
&epsis; systems and determinants	85	(11)
The cross product	96	(15)
&epsis; systems and the cross product in general Cartesian systems	111	(3)
The algebra of matrices	114	(9)
the differentiation of vectors	123	(73)
The differentiation of vectors	123	(16)
Geometry of space curves	139	(8)
Kinematics	147	(8)
Moving frames of reference	155	(11)
A tensor formulation of the theory of rotating frames of reference	166	(5)
Newtonian orbits	171	(5)
An introduction to Einstein's special theory of relativity	176	(20)
partial differentiation and associated concepts	196	(58)
Surface representations	196	(9)
Vector concepts associated with partial differentiation	205	(13)
Identities involving ∇	218	(2)
Bases in general coordinate systems	220	(17)
Vector concepts in curvilinear orthogonal coordinate systems	237	(8)
Maxima and minima of functions of two variables	245	(9)
integration of vectors	254	(50)
Line integrals	255	(15)
Surface integrals	270	(12)
An introduction to surface tensors and surface invariants	282	(6)
Volume integrals	288	(3)
Integral theorems	291	(13)
tensor algebra and analysis	304	(79)
Fundamental notions in n-space	305	(10)
Transformations and tensors	315	(9)
Riemannian geometry	324	(7)
Tensor processes of differentiation	331	(10)
Geodesics	341	(7)
The parallelism of Levi-Civita	348	(6)
The curvature tensor	354	(7)
Algebraic properties of the curvature tensor	361	(10)
An introduction to the general theory of relativity	371	(12)
answers to odd-numbered problems	383	(28)
index	411