# Vector Analysis for Mathematicians, Scientists and Engineers

## 2nd Edition

### The Commonwealth and International Library: Physics Division

Authors:
Editors:
eBook ISBN: 9781483160214
Imprint: Pergamon
Published Date: 1st January 1970
Page Count: 200
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## Description

Vector Analysis for Mathematicians, Scientists and Engineers, Second Edition, provides an understanding of the methods of vector algebra and calculus to the extent that the student will readily follow those works which make use of them, and further, will be able to employ them himself in his own branch of science. New concepts and methods introduced are illustrated by examples drawn from fields with which the student is familiar, and a large number of both worked and unworked exercises are provided. The book begins with an introduction to vectors, covering their representation, addition, geometrical applications, and components. Separate chapters discuss the products of vectors; the products of three or four vectors; the differentiation of vectors; gradient, divergence, and curl; line, surface, and volume integrals; theorems of vector integration; and orthogonal curvilinear coordinates. The final chapter presents an application of vector analysis. Answers to odd-numbered exercises are provided as the end of the book.

## Table of Contents

Preface to the First Edition

Preface to the Second Edition

Chapter 1. Introduction to Vectors

1.1 What is a Vector

1.2 Representation of Vectors

1.3 Addition and Subtraction of Vectors

1.4 Simple Geometrical Applications

1.5 Components of a Vector

Chapter 2. Products of Vectors

2.1 The Scalar Product

2.2 The Vector Product

2.3 Applications of Scalar and Vector Products

Chapter 3. Products of Three or Four Vectors

3.1 The Scalar Triple Product

3.2 The Vector Triple Product

3.3 Products of Four Vectors

Chapter 4. Differentiation of Vectors

4.1 The Derivative of a Vector

4.2 Differentiation of Sums and Products

4.3 Components of a Derivative

4.4 Applications to Mechanics

4.5 Integration of Vectors

4.6 Partial Differentiation

Chapter 5. Gradient, Divergence and Curl

5.1 Vector and Scalar Fields

5.2 The Gradient Operator

5.3 The Divergence Operator

5.4 The Curl Operator

5.5 Grad, Div and Curl of Products

5.6 Double Application of V Operator

5.7 Invariance Properties of V

Chapter 6. Line, Surface and Volume Integrals

6.1 Line Integrals

6.2 Surface Integrals

6.3 Volume Integrals

Chapter 7. Theorems of Vector Integration

7.1 Conservative Vector Fields

7.2 The Divergence Theorem

7.3 Stokes Theorem

Chapter 8. Orthogonal Curvilinear Coordinates

8.1 Vector Components in a General Orthogonal Coordinate System

8.2 Differential Operators for Orthogonal Coordinates

Chapter 9. An Application of Vector Analysis - Electrical Theory

9.1 Electrostatic Field and Potential

9.2 Gauss Theorem

9.3 Poisson's and Laplace's Equations

9.4 Energy of the Electrostatic Field

9.5 Dipoles

9.6 Conductors and Insulators

9.7 Electric Current

9.8 Magnetic Effects of a Current

9.9 Magnetic Vector Potential

9.10 Continuous Current Distributions

9.11 Energy of the Magnetic Field

9.12 Electromagnetic Induction

9.13 The Displacement Current

9.14 Maxwell's Equations

9.15 The Electromagnetic Potentials

9.16 Electromagnetic Waves

Answers to Odd-numbered Exercises

Index

No. of pages:
200
Language:
English
Copyright:
© Pergamon 1970
Published:
Imprint:
Pergamon
eBook ISBN:
9781483160214

## About the Author

### Affiliations and Expertise

Queen Mary College, London, UK