# Book:B. Hague/An Introduction to Vector Analysis/Fifth Edition

## B. Hague: An Introduction to Vector Analysis for Physicists and Engineers (5th Edition)

Published $\text {1951}$, Methuen

### Contents

PREFACE TO THE THIRD EDITION (Glasgow Jan. 1945)
PREFACE (Glasgow June 1938)
$\text{I} \quad$ DEFINITIONS. ELEMENTS OF VECTOR ALGEBRA
1. Scalar and Vector Quantities. 2. Graphical Representation of Vectors. 3. Addition and Subtraction of Vectors. 4. Components of a Vector. 5. Scalar and Vector Fields
$\text{II} \quad$ PRODUCTS OF VECTORS
1. General. 2. The Scalar Product. 3. Line and Surface Integrals as Scalar Products. 4. The Vector Product. 5. Vector Area. 6. Application to Vector Products. 7. Products of Three Vectors. 8. Summary
$\text{III} \quad$ THE DIFFERENTIATION OF VECTORS
1. Scalar Differentiation. 2. Differentiation of Sums and Products. 3. Partial Differentiation
$\text{IV} \quad$ THE OPERATOR $\nabla$ AND ITS USES
1. The Operator $\nabla$. 2. The Gradient of a Scalar Field. 2a. The operation $\nabla S$. 3. The Divergence of a Vector Field. 3a. The Operation $\nabla \cdot \mathbf V$. 4. The Curl of a Vector Field. 4a. The Operation $\nabla \times \mathbf V$. 5. Simple Examples of Curl. 6. Divergence of a Vector Product. 7. Divergence and Curl of $S \mathbf A$
$\text{V} \quad$ FURTHER APPLICATIONS OF THE OPERATOR $\nabla$
1. The Operator $\operatorname{div} \, \operatorname{grad}$. 2. The Operator $\operatorname{curl} \, \operatorname{grad}$. 3. The Operator $\nabla^2$ with Vector Operand. 4. The Operator $\operatorname{grad} \, \operatorname{div}$. 5. The Operator $\operatorname{div} \, \operatorname{curl}$. 6. The Operator $\operatorname{curl} \, \operatorname{curl}$. 7. The Classification of Vector Fields. 8. Two Useful Divergence Formulae. 9. The Vector Field $\operatorname{grad} (k/r)$
$\text{VI} \quad$ INTEGRAL THEOREMS
1. The Divergence Theorem of Gauss. 2. Gauss's Theorem and the Inverse Square Law. 3. Stokes's Theorem. 4. Invariance of Divergence and Curl
$\text{VII} \quad$ THE SCALAR POTENTIAL FIELD
1. General Properties. 2. The Inverse Square Law. Point Sources. 3. Volume Distributions. 4. The Potential Operation. 5. Multivalued Potentials
$\text{VIII} \quad$ THE VECTOR POTENTIAL FIELD
1. The Magnetic Field of a Steady Current. 2. The Vector Potential. 3. The Potential Operation 4. Linear Currents. 5. Simple Examples of Vector Potential
$\text{IX} \quad$ THE ELECTROMAGNETIC FIELD EQUATIONS OF MAXWELL
1. General. 2. Maxwell's Equations. 3. Conducting Media. 4. Energy Considerations
$\text{X} \quad$ ELEMENTARY PROPERTIES OF THE LINEAR VECTOR FUNCTION
1. The Linear Vector Function. 2. Simple Types of Tensors. 3. The Symmetrical Tensor. 4. Resolution of a Tensor. 5. Repeated Tensor Operations. 6. The Dyadic. 7. Application of Linear Vector Functions
POLAR CO-ORDINATES
PROPERTIES OF $\nabla$ AS A FORMAL VECTOR
BIBLIOGRAPHY
NOTATION
NOTE ON MAXWELL'S EQUATIONS
INDEX

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## Errata

### Dot Product of Parallel Vectors

Chapter $\text {II}$: The Products of Vectors: $2$. The Scalar Product:
When two vectors are perpendicular, therefore,
$\mathbf A \cdot \mathbf B = 0$, $\qquad (2.2)$
and when they are parallel,
$\mathbf A \cdot \mathbf B = A B$. $\qquad (2.3)$