An Introduction to Vector Analysis

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 ? and Its Uses. - 1. The Operator ?. - 2. The Gradient of a Scalar Field. - 3. The Divergence of a Vector Field. - 4. The Operator div grad. - 5. The Operator ?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 SA. - 10. The Operator curl grad. - 11. The Operator grad div. - 12. The Operator div curl. - 13. The Operator curl curl. - 14. The Vector Field 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. Language: English