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#### CHAPTER 1 - INTRODUCTION

Pages 1-7 - Book chapterAbstract only
#### CHAPTER 2 - FUNCTIONS OF SEVERAL INDEPENDENT VARIABLES

Pages 8-33 - Book chapterAbstract only
#### CHAPTER 3 - LINE INTEGRALS

Pages 34-49 - Book chapterAbstract only
#### CHAPTER 4 - MULTIPLE INTEGRALS

Pages 50-91 - Book chapterAbstract only
#### CHAPTER 5 - SURFACE INTEGRALS

Pages 92-110 - Book chapterAbstract only
#### CHAPTER 6 - VECTOR FIELD THEORY (1)

Pages 111-146 - Book chapterAbstract only
#### CHAPTER 7 - VECTOR FIELD THEORY (2)

Pages 147-196 - Book chapterAbstract only
#### CHAPTER 8 - APPLICATIONS OF VECTOR FIELD THEORY

Pages 197-254 - Book chapterNo access
#### ANSWERS TO EXERCISES

Pages 255-261 - Book chapterNo access
#### Index

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#### Inside Back Matter

Page ibc1

## About the book

### Description

THIS book falls naturally into two parts. In Chapters 1-5 the basic ideas and techniques of partial differentiation, and of line, multiple and surface integrals are discussed. Chapters 6 and 7 give the elements of vector field theory, taking the integral definitions of the divergence and curl of a vector field as their starting points; the last chapter surveys very briefly some of the immediate applications of vector field theory to five branches of applied mathematics. Throughout I have given numerous worked examples. In these I have paid particular attention to those points which in my own experience I have found to give most difficulty to students. In the text I have denoted spherical polar coordinates by (/-, 0, ψ)9 and cylindrical polar coordinates by (p, ψ, ζ), so that ψ measures the same angle in both systems. Since there is no one standard notation for these systems, the reader will meet different notations in the course of his reading, and in quoting examination questions in the exercises I have kept to the notation of the originals. The Exercises at the end of each section are intended to give practice in the basic techniques just discussed. The Miscellaneous Exercises are more varied, and contain many examination questions.

THIS book falls naturally into two parts. In Chapters 1-5 the basic ideas and techniques of partial differentiation, and of line, multiple and surface integrals are discussed. Chapters 6 and 7 give the elements of vector field theory, taking the integral definitions of the divergence and curl of a vector field as their starting points; the last chapter surveys very briefly some of the immediate applications of vector field theory to five branches of applied mathematics. Throughout I have given numerous worked examples. In these I have paid particular attention to those points which in my own experience I have found to give most difficulty to students. In the text I have denoted spherical polar coordinates by (/-, 0, ψ)9 and cylindrical polar coordinates by (p, ψ, ζ), so that ψ measures the same angle in both systems. Since there is no one standard notation for these systems, the reader will meet different notations in the course of his reading, and in quoting examination questions in the exercises I have kept to the notation of the originals. The Exercises at the end of each section are intended to give practice in the basic techniques just discussed. The Miscellaneous Exercises are more varied, and contain many examination questions.

## Details

### ISBN

978-1-4831-6785-5

### Language

English

### Published

1966

### Copyright

Copyright © 1966 Elsevier Ltd. All rights reserved.

### Imprint

Pergamon