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.

Contenu

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