Vectors in Three-Dimensional Space

J. S. R. Chisholm

doi:10.1017/CBO9780511569494

This book deals with vector algebra and analysis and with their application to three-dimensional geometry and the analysis of fields in three dimensions. While many treatments of the application of vectors have approached the fundamentals of the subject intuitively, assuming some prior knowledge of Euclidean and Cartesian geometry, Professor Chrisholm here bases the subject on the axioms of linear space algebra, which are fundamental to many branches of mathematics. While developing the properties of vectors from axioms, however, he continually emphasizes the geometrical interpretation of vector algebra in order to build up intuitive relations between the algebraic equations and geometrical concepts. Throughout, examples are used to illustrate the theory being developed; several sets of problems are incorporate in each chapter, and outline answers to many of these are given. Written primarily for undergraduate mathematicians in the early part of their courses, this lucidly written book will also appeal to mathematical physicists and to mathematically inclined engineers.

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Vectors in Three-Dimensional Space

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-xii

1 - Linear spaces and displacements
pp 1-23

2 - Scalar products and components
pp 24-56

3 - Other products of vectors
pp 57-86

4 - Transformations of vectors
pp 87-134

5 - Curves and surfaces; vector calculus
pp 135-202

6 - Vector analysis
pp 203-252

Appendix A - Some properties of functions of two variables
pp 253-262

Appendix B - Proof of Stokes' theorem
pp 263-268

Reference list
pp 269-270

Outline solutions to selected problems
pp 271-284

Index
pp 285-293

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