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

Subject Matter

 * Vector Algebra

Contents

 * PREFACE TO THE THIRD EDITION ( Jan. 1945)


 * PREFACE ( 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



Dot Product of Parallel Vectors

 * Chapter $\text {II}$: The Products of Vectors: $2$. The Scalar Product:

Source work progress
* : Chapter $\text {IV}$: The Operator $\nabla$ and its Uses: $7$. Divergence and Curl of $S \mathbf A$: $(4.14)$