Vector Analysis for Mathematicians, Scientists and Engineers

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