Book:B. Hague/An Introduction to Vector Analysis/Fifth Edition
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B. Hague: An Introduction to Vector Analysis for Physicists and Engineers (5th Edition)
Published $\text {1951}$, Methuen
Subject Matter
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
Further Editions
- 1939: B. Hague: An Introduction to Vector Analysis
- 1970: B. Hague and D. Martin: An Introduction to Vector Analysis (6th ed.)
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,
- $\mathbf A \cdot \mathbf B = A B$. $\qquad (2.3)$
Source work progress
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {VI}$: The Theorems of Gauss and Stokes: $1$. The Divergence Theorem of Gauss