Author | Hague, B. author |
---|---|
Title | An Introduction to Vector Analysis For Physicists and Engineers [electronic resource] / by B. Hague |
Imprint | Dordrecht : Springer Netherlands, 1970 |
Connect to | http://dx.doi.org/10.1007/978-94-009-5841-8 |
Descript | X, 122 p. online resource |
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. Gaussโs Theorem and the Inverse Square Law -- 3. Greenโs Theorem -- 4. Stokesโs 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. Maxwellโs Equations -- 3. Energy Considerations -- Miscellaneous Exercises VIII -- Answers to Exercises