Wave Propagation in Electromagnetic Media

1 Time-Varying Electromagnetic Fields.- 1.1. Maxwell’s Equations.- 1.2. Conservation Laws.- 1.3. Scalar and Vector Potentials.- 1.4. Plane Electromagnetic Waves in a Nonconducting Medium.- 1.5. Plane Waves in a Conducting Medium.- 2 Hyperbolic Partial Differential Equations in Two Independent Variables.- 2.1. General Solution of the Wave Equation.- 2.2. D’Alembert’s Solution of the Cauchy Initial Value Problem.- 2.3. Method of Characteristics for a Single First-Order Equation.- 2.4. Method of Characteristics for a First-Order System.- 2.5. Second-Order Quasilinear Partial Differential Equation.- 2.6. Domain of Dependence and Range of Influence.- 2.7. Some Basic Mathematical and Physical Principles.- 2.8. Propagation of Discontinuities.- 2.9. Weak Solutions and the Conservation Laws.- 2.10. Normal Forms for Second-Order Partial Differential Equations.- 2.11. Riemann’s Method.- 2.12. Nonlinear Hyperbolic Equations in Two Independent Variables.- 3 Hyperbolic Partial Differential Equations in More Than Two Independent Variables.- 3.1. First-Order Quasilinear Equations in n Independent Variables.- 3.2. First-Order Fully Nonlinear Equations in n Independent Variables.- 3.3. Directional Derivatives in n Dimensions.- 3.4. Characteristic Surfaces in n Dimensions.- 3.5. Maxwell’s Equations.- 3.6. Second-Order Quasilinear Equation in n Independent Variables.- 3.7. Geometry of Characteristics for Second-Order Systems.- 3.8. Ray Cone, Normal Cone, Duality.- 3.9. Wave Equation in n Dimensions.- Appendix: Similarity Transformations and Canonical Forms.- 4 Variational Methods.- 4.1. Principle of Least Time.- 4.2. One-Dimensional Calculus of Variations, Euler’s Equation.- 4.3. Generalization to Functionals with More Than One Dependent Variable.- 4.4. Special Case.- 4.5.Hamilton’s Variational Principle and Configuration Space.- 4.6. Lagrange’s Equations of Motion.- 4.7. D’Alembert’s Principle, Constraints, and Lagrange’s Equations.- 4.8. Nonconservative Force Field, Velocity-Dependent Potential.- 4.9. Constraints Revisited, Undetermined Multipliers.- 4.10. Hamilton’s Equations of Motion.- 4.11. Cyclic Coordinates.- 4.12. Principle of Least Action.- 4.13. Lagrange’s Equations of Motion for a Continuum.- 4.14. Hamilton’s Equations of Motion for a Continuum.- 5 Canonical Transformations and Hamilton—Jacobi Theory.- I. Canonical Transformations.- II. Hamilton—Jacobi Theory.- 6 Quantum Mechanics—A Survey.- 7 Plasma Physics and Magnetohydrodynamics.- 7.1. Fluid Dynamics Equations—General Treatment.- 7.2. Application of Fluid Dynamics Equations to Magnetohydrodynamics.- 7.3. Application of Characteristic Theory to Magnetohydrodynamics.- 7.4. Linearization of the Field Equations.- 8 The Special Theory of Relativity.- 8.1. Collapse of the Ether Theory.- 8.2. The Lorentz Transformation.- 8.3. Maxwell’s Equations with Respect to a Lorentz Transformation.- 8.4. Contraction of Rods and Time Dilation.- 8.5. Addition of Velocities.- 8.6. World Lines and Light Cones.- 8.7. Covariant Formulation of the Laws of Physics in Minkowski Space.- 8.8. Covariance of the Electromagnetic Equations.- 8.9. Force and Energy Equations in Relativistic Mechanics.- 8.10. Lagrangian Formulation of Equations of Motion in Relativistic Mechanics.- 8.11. Covariant Lagrangian.