An Introduction to Vector Analysis de B. Hague

An Introduction to Vector Analysis: For Physicists and Engineers

B. Hague

The principal changes that I have made in preparing this revised edition of the book are the following. (i) Carefuily selected worked and unworked examples have been added to six of the chapters. These examples have been taken from class and degree examination papers set in this University and I am grateful to the University Court for permission to use them. (ii) Some additional matter on the geometrieaI application of veetors has been incorporated in Chapter 1. (iii) Chapters 4 and 5 have been combined into one chapter, some material has been rearranged and some further material added. (iv) The chapter on int~gral theorems, now Chapter 5, has been expanded to include an altemative proof of Gauss's theorem, a treatmeot of Green's theorem and a more extended discussioo of the classification of vector fields. (v) The only major change made in what are now Chapters 6 and 7 is the deletioo of the discussion of the DOW obsolete pot funetioo. (vi) A small part of Chapter 8 on Maxwell's equations has been rewritten to give a fuller account of the use of scalar and veetor potentials in eleetromagnetic theory, and the units emploYed have been changed to the m.k.s. system.

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Cuprins

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.