Wave Propagation in Electromagnetic Media
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 c...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1990, 1990
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| Edition: | 1st ed. 1990 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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
- 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
- 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