Classical Vector Algebra  book cover
1st Edition

Classical Vector Algebra

  • Available for pre-order. Item will ship after December 22, 2022
ISBN 9781032380995
December 22, 2022 Forthcoming by Chapman and Hall/CRC
154 Pages 90 B/W Illustrations

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Book Description

Every physicist, engineer, and certainly a mathematician, would undoubtedly agree that vector algebra is a part of basic mathematical instruments packed in their toolbox.

Classic Vector Algebra should be viewed as a prerequisite, an introduction, for other mathematical courses dealing with vectors, following typical form and appropriate rigor of more advanced mathematics texts.

Vector algebra discussed in this book briefly addresses vectors in general 3-dimensional Euclidian space, and then, in more detail, vectors in Cartesian □□3 space. These vectors are easier to visualize, their operational techniques are relatively simple, but they are necessary for the study of Vector Analysis. In addition, this could also serve as a good intuition build up for more abstract structures of □□-dimensional vector spaces.

Definition, theorem, proof, corollary, example, etc. is not useless formalism, even in an introductory treatise -- it is the way mathematical thinking has to be structured. In other words, "introduction" and "rigor" should not exclude one another.

The material in this book is not difficult nor easy. The text is a serious exposition of a part of mathematics students need to master in order to be proficient in their field. In addition to the detailed outline of the theory, the book contains literally hundreds of corresponding examples/exercises.


Table of Contents

1.    Introduction
2.    Vector Space – Definitions, Notation and Examples

3.     Three – dimensional Vector Space V
3.1    Definition and Basic Features of V
3.2   Multiplication of a Vector by a Scalar
3.3   Collinear and Coplanar Vectors
3.4   Addition of Vectors
3.5    Basis of a Vector Space

4.   Vectors in R^3 Space
4.1     {i,j,k} - basis of R^3 Space
4.2    Multiplication by a Scalar and Addition of Vectors in R^3 Space
4.3     Scalar (dot) Product of Vectors
4.4     Cross (vector) Product of Vectors
4.5     Mixed Product of Vectors
4.6.    Triple Cross Product of Vectors
4.7    The Quadruple Dot - Quadruple Cross Product

5.      Elements of Analytic Geometry
5.1    Some Preliminary Remarks
5.2   Equations of a Line
5.3   The Angle Between Two Lines
5.4   The Distance Between Two Lines
5.5     Equations of a Plane
5.6    Angle Between two Planes

Appendix A
Appendix B
Appendix C

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Vladimir Lepetic is Professor in the Department of Mathematical Sciences, DePaul University. Research interests include mathematical physics, set theory, foundation and philosophy of mathematics.