Wave Propagation in Electromagnetic Media

ISBN-13: 9781461279501 / Angielski / Miękka / 2011 / 294 str.

Julian L. Davis

Opis

This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical tech niques, and on showing how these methods of mathematical physics can be effective in unifying the physics of wave propagation in electromagnetic media. Chapter 1 presents the theory of time-varying electromagnetic fields, which involves a discussion of Faraday's laws, Maxwell's equations, and their appli cations to electromagnetic wave propagation under a variety of conditions."

Spis treści

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.- 3A.1. Geometric Considerations.- 3A.2. Orthogonal Transformations and Eigenvectors in Relation to Similarity Transformations.- 3A.3. Diagonalization of A?.- 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.- 5.1. Equations of Canonical Transformations and Generating Functions.- 5.2. Some Examples of Canonical Transformations.- II. Hamilton—Jacobi Theory.- 5.3. Derivation of the Hamilton—Jacobi Equation for Hamilton’s Principle Function.- 5.4. S Related to a Variational Principle.- 5.5. Application to Harmonic Oscillator.- 5.6. Hamilton’s Characteristic Function.- 5.7. Application to n Harmonic Oscillators.- 5.8. Hamilton—Jacobi Theory Related to Characteristic Theory.- 5.9. Hamilton—Jacobi Theory and Wave Propagation.- 5.10. Hamilton—Jacobi Theory and Quantum Mechanics.- 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.