Wave Propagation in Electromagnetic Media

01.12.1989

Englisch

9780387970660

Springer US

Nein

Julian L. Davis

294

Gebundene Ausgabe

mechanics, dynamics, physics, Maxwell's equations, hyperbolic equation, wave, hyperbolic partial differential equation, wave equation, electromagnetic wave, quantum mechanics

PHDS - Wellenmechanik (Vibration und Akustik) TBC - Ingenieurswesen, Maschinenbau allgemein TJF - Elektronik PHD - Klassische Mechanik

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.

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