Book:B. Hague/An Introduction to Vector Analysis

Subject Matter

 * Vector Algebra

Contents

 * PREFACE TO THE REVISED EDITION (D. Martin)


 * PREFACE (B. Hague)


 * 1 DEFINITIONS. ADDITION OF VECTORS
 * 1. Scalar and Vector Quantities. 2. Graphical Representation of Vectors. 3. Addition and Subtraction of Vectors. 4. Components of a Vector. 5. Geometrical Applications. 6. Scalar and Vector Fields. Miscellaneous Exercises I.


 * 2 PRODUCTS OF VECTORS
 * 1. General. 2. The Scalar Product. 3. The Vector Product. 4. Vector Area. 5. Application to Vector Products. 6. Products of Three Vectors. 7. Line and Surface Integrals as Scalar Products. Miscellaneous Exercises II.


 * 3 THE DIFFERENTIATION OF VECTORS
 * 1. Scalar Differentiation. 2. Differentiation of Sums and Products. 3. Partial Differentiation. Miscellaneous Exercises III.


 * 4 THE OPERATOR $\nabla$ AND ITS USES
 * 1. The Operator $\nabla$. 2. The Gradient of a Scalar Field. 3. The Divergence of a Vector Field. 4. The Operator $\operatorname{div} \, \operatorname{grad}$. 5. The Operator $\nabla^2$ with Vector Operand. 6. The Curl of a Vector Field. 7. Simple Examples of the Curl of a Vector Field. 8. Divergence of a Vector Product. 9. Divergence and Curl of $S \mathbf A$. 10. The Operator $\operatorname{curl} \, \operatorname{grad}$. 11. The Operator $\operatorname{grad} \, \operatorname{div}$. 12. The Operator $\operatorname{div} \, \operatorname{curl}$. 13. The Operator $\operatorname{curl} \, \operatorname{curl}$. 14. The Vector Field $\operatorname{grad} (k/r)$. 15. Vector Operators in Terms of Polar Co-ordinates. Miscellaneous Exercises IV.


 * 5 INTEGRAL THEOREMS
 * 1. The Divergence Theorem of Gauss. 2. Gauss's Theorem and the Inverse Square Law. 3. Green's Theorem. 4. Stokes's Theorem. 5. Alternative Definitions of Divergence and Curl. 6. Classification of Vector Fields. Miscellaneous Exercises V.


 * 6 THE SCALAR POTENTIAL FIELD
 * 1. General Properties. 2. The Inverse Square Law. Point Sources. 3. Volume Distributions. 4. Multi-valued Potentials.


 * 7 THE VECTOR POTENTIAL FIELD
 * 1. The Magnetic Field of a Steady Current. 2. The Vector Potential. 3. Linear Currents. 4. Simple Examples of Vector Potential.


 * 8 THE ELECTROMAGNETIC FIELD EQUATIONS OF MAXWELL
 * 1. General. 2. Maxwell's Equations. 3. Energy Considerations. Miscellaneous Exercises VIII.


 * ANSWERS TO EXERCISES


 * BIBLIOGRAPHY


 * INDEX