FOUNDATIONS OF APPLIED ELECTRODYNAMICS -- Contents -- Preface -- 1 Maxwell Equations -- 1.1 Experimental Laws -- 1.1.1 Coulomb's Law -- 1.1.2 Amp`ere's Law -- 1.1.3 Faraday's Law -- 1.1.4 Law of Conservation of Charge -- 1.2 Maxwell Equations, Constitutive Relation, and Dispersion -- 1.2.1 Maxwell Equations and Boundary Conditions -- 1.2.2 Constitutive Relations -- 1.2.3 Wave Equations -- 1.2.4 Dispersion -- 1.3 Theorems for Electromagnetic Fields -- 1.3.1 Superposition Theorem -- 1.3.2 Compensation Theorem -- 1.3.3 Conservation of Electromagnetic Energy -- 1.3.4 Conservation of Electromagnetic Momentum -- 1.3.5 Conservation of Electromagnetic Angular Momentum -- 1.3.6 Uniqueness Theorems -- 1.3.7 Equivalence Theorems -- 1.3.8 Reciprocity -- 1.4 Wavepackets -- 1.4.1 Spatial Wavepacket and Temporal Wavepacket -- 1.4.2 Signal Velocity and Group Velocity -- 1.4.3 Energy Density for Wavepackets -- 1.4.4 Energy Velocity and Group Velocity -- 1.4.5 Narrow-band Stationary Stochastic Vector Field -- 2 Solutions of Maxwell Equations -- 2.1 Linear Space and Linear Operator -- 2.1.1 Linear Space, Normed Space and Inner Product Space -- 2.1.2 Linear and Multilinear Maps -- 2.2 Classification of Partial Differential Equations -- 2.2.1 Canonical Form of Elliptical Equations -- 2.2.2 Canonical Form of Hyperbolic Equations -- 2.2.3 Canonical Form of Parabolic Equations -- 2.3 Modern Theory of Partial Differential Equations -- 2.3.1 Limitation of Classical Solutions -- 2.3.2 Theory of Generalized Functions -- 2.3.3 Sobolev Spaces -- 2.3.4 Generalized Solutions of Partial Differential Equations -- 2.4 Method of Separation of Variables -- 2.4.1 Rectangular Coordinate System -- 2.4.2 Cylindrical Coordinate System -- 2.4.3 Spherical Coordinate System -- 2.5 Method of Green's Function -- 2.5.1 Fundamental Solutions of Partial Differential Equations.

2.5.2 Integral Representations of Arbitrary Fields -- 2.5.3 Integral Representations of Electromagnetic Fields -- 2.6 Potential Theory -- 2.6.1 Vector Potential, Scalar Potential, and Gauge Conditions -- 2.6.2 Hertz Vectors and Debye Potentials -- 2.6.3 Jump Relations in Potential Theory -- 2.7 Variational Principles -- 2.7.1 Generalized Calculus of Variation -- 2.7.2 Lagrangian Formulation -- 2.7.3 Hamiltonian Formulation -- 3 Eigenvalue Problems -- 3.1 Introduction to Linear Operator Theory -- 3.1.1 Compact Operators and Embeddings -- 3.1.2 Closed Operators -- 3.1.3 Spectrum and Resolvent of Linear Operators -- 3.1.4 Adjoint Operators and Symmetric Operators -- 3.1.5 Energy Space -- 3.1.6 Energy Extension, Friedrichs Extension and Generalized Solution -- 3.2 Eigenvalue Problems for Symmetric Operators -- 3.2.1 Positive-Bounded-Below Symmetric Operators -- 3.2.2 Compact Symmetric Operators -- 3.3 Interior Electromagnetic Problems -- 3.3.1 Mode Theory for Waveguides -- 3.3.2 Mode Theory for Cavity Resonators -- 3.4 Exterior Electromagnetic Problems -- 3.4.1 Mode Theory for Spherical Waveguides -- 3.4.2 Singular Functions and Singular Values -- 3.5 Eigenfunctions of Curl Operator -- 4 Antenna Theory -- 4.1 Antenna Parameters -- 4.1.1 Radiation Patterns and Radiation Intensity -- 4.1.2 Radiation Efficiency, Antenna Efficiency and Matching Network Efficiency -- 4.1.3 Directivity and Gain -- 4.1.4 Input Impedance, Bandwidth and Antenna Quality Factor -- 4.1.5 Vector Effective Length, Equivalent Area and Antenna Factor -- 4.1.6 Polarization and Coupling -- 4.2 Properties of Far Fields -- 4.3 Spherical Vector Wavefunctions -- 4.3.1 Field Expansions in Terms of Spherical Vector Wavefunctions -- 4.3.2 Completeness of Spherical Vector Wavefunctions -- 4.4 Foster Theorems and Relationship Between Quality Factor and Bandwidth.

4.4.1 Poynting Theorem and the Evaluation of Antenna Quality Factor -- 4.4.2 Equivalent Circuit for Transmitting Antenna -- 4.4.3 Foster Theorems for Ideal Antenna and Antenna Quality Factor -- 4.4.4 Relationship Between Antenna Quality Factor and Bandwidth -- 4.5 Minimum Possible Antenna Quality Factor -- 4.5.1 Spherical Wavefunction Expansion for Antenna Quality Factor -- 4.5.2 Minimum Possible Antenna Quality Factor -- 4.6 Maximum Possible Product of Gain and Bandwidth -- 4.6.1 Directive Antenna -- 4.6.2 Omni-Directional Antenna -- 4.6.3 Best Possible Antenna Performance -- 4.7 Evaluation of Antenna Quality Factor -- 4.7.1 Quality Factor for Arbitrary Antenna -- 4.7.2 Quality Factor for Small Antenna -- 4.7.3 Some Remarks on Electromagnetic Stored Energy -- 5 Integral Equation Formulations -- 5.1 Integral Equations -- 5.2 TEM Transmission Lines -- 5.3 Waveguide Eigenvalue Problems -- 5.3.1 Spurious Solutions and their Discrimination -- 5.3.2 Integral Equations Without Spurious Solutions -- 5.4 Metal Cavity Resonators -- 5.5 Scattering Problems -- 5.5.1 Three-Dimensional Scatterers -- 5.5.2 Two-Dimensional Scatterers -- 5.5.3 Scattering Cross-Section -- 5.5.4 Low Frequency Solutions of Integral Equations -- 5.6 Multiple Metal Antenna System -- 5.7 Numerical Methods -- 5.7.1 Projection Method -- 5.7.2 Moment Method -- 5.7.3 Construction of Approximating Subspaces -- 6 Network Formulations -- 6.1 Transmission Line Theory -- 6.1.1 Transmission Line Equations -- 6.1.2 Signal Propagations in Transmission Lines -- 6.2 Scattering Parameters for General Circuits -- 6.2.1 One-Port Network -- 6.2.2 Multi-Port Network -- 6.3 Waveguide Junctions -- 6.4 Multiple Antenna System -- 6.4.1 Impedance Matrix -- 6.4.2 Scattering Matrix -- 6.4.3 Antenna System with Large Separations -- 6.5 Power Transmission Between Antennas.

6.5.1 Universal Power Transmission Formula -- 6.5.2 Power Transmission Between Two Planar Apertures -- 6.5.3 Power Transmission Between Two Antenna Arrays -- 6.6 Network Parameters in a Scattering Environment -- 6.6.1 Compensation Theorem for Time-Harmonic Fields -- 6.6.2 Scattering Parameters in a Scattering Environment -- 6.6.3 Antenna Input Impedance in a Scattering Environment -- 6.7 RLC Equivalent Circuits -- 6.7.1 RLC Equivalent Circuit for a One-Port Microwave Network -- 6.7.2 RLC Equivalent Circuits for Current Sources -- 7 Fields in Inhomogeneous Media -- 7.1 Foundations of Spectral Analysis -- 7.1.1 The Spectrum -- 7.1.2 Spectral Theorem -- 7.1.3 Generalized Eigenfunctions of Self-Adjoint Operators -- 7.1.4 Bilinear Forms -- 7.1.5 Min-Max Principle -- 7.1.6 A Bilinear Form for Maxwell Equations -- 7.2 Plane Waves in Inhomogeneous Media -- 7.2.1 Wave Equations in Inhomogeneous Media -- 7.2.2 Waves in Slowly Varying Layered Media and WKB Approximation -- 7.2.3 High Frequency Approximations and Geometric Optics -- 7.2.4 Reflection and Transmission in Layered Media -- 7.3 Inhomogeneous Metal Waveguides -- 7.3.1 General Field Relationships -- 7.3.2 Symmetric Formulation -- 7.3.3 Asymmetric Formulation -- 7.4 Optical Fibers -- 7.4.1 Circular Optical Fiber -- 7.4.2 Guidance Condition -- 7.4.3 Eigenvalues and Essential Spectrum -- 7.5 Inhomogeneous Cavity Resonator -- 7.5.1 Mode Theory -- 7.5.2 Field Expansions -- 8 Time-domain Theory -- 8.1 Time-domain Theory of Metal Waveguides -- 8.1.1 Field Expansions -- 8.1.2 Solution of the Modified Klein-Gordon Equation -- 8.1.3 Excitation of Waveguides -- 8.2 Time-domain Theory of Metal Cavity Resonators -- 8.2.1 Field in Arbitrary Cavities -- 8.2.2 Fields in Waveguide Cavities -- 8.3 Spherical Wave Expansions in Time-domain -- 8.3.1 Transverse Field Equations -- 8.3.2 Spherical Transmission Line Equations.

8.4 Radiation and Scattering in Time-domain -- 8.4.1 Radiation from an Arbitrary Source -- 8.4.2 Radiation from Elementary Sources -- 8.4.3 Enhancement of Radiation -- 8.4.4 Time-domain Integral Equations -- 9 Relativity -- 9.1 Tensor Algebra on Linear Spaces -- 9.1.1 Tensor Algebra -- 9.1.2 Tangent Space, Cotangent Space and Tensor Space -- 9.1.3 Metric Tensor -- 9.2 Einstein's Postulates for Special Relativity -- 9.2.1 Galilean Relativity Principle -- 9.2.2 Fundamental Postulates -- 9.3 The Lorentz Transformation -- 9.3.1 Intervals -- 9.3.2 Derivation of the Lorentz Transformation -- 9.3.3 Properties of Space-Time -- 9.4 Relativistic Mechanics in Inertial Reference Frame -- 9.4.1 Four-Velocity Vector -- 9.4.2 Four-Momentum Vector -- 9.4.3 Relativistic Equation of Motion -- 9.4.4 Angular Momentum Tensor and Energy-Momentum Tensor -- 9.5 Electrodynamics in Inertial Reference Frame -- 9.5.1 Covariance of Continuity Equation -- 9.5.2 Covariance of Maxwell Equations -- 9.5.3 Transformation of Electromagnetic Fields and Sources -- 9.5.4 Covariant Forms of Electromagnetic Conservation Laws -- 9.5.5 Total Energy-Momentum Tensor -- 9.6 General Theory of Relativity -- 9.6.1 Principle of Equivalence -- 9.6.2 Manifolds -- 9.6.3 Tangent Bundles, Cotangent Bundles and Tensor Bundles -- 9.6.4 Riemannian Manifold -- 9.6.5 Accelerated Reference Frames -- 9.6.6 Time and Length in Accelerated Reference Frame -- 9.6.7 Covariant Derivative and Connection -- 9.6.8 Geodesics and Equation of Motion in Gravitational Field -- 9.6.9 Bianchi Identities -- 9.6.10 Principle of General Covariance and Minimal Coupling -- 9.6.11 Einstein Field Equations -- 9.6.12 The Schwarzschild Solution -- 9.6.13 Electromagnetic Fields in an Accelerated System -- 10 Quantization of Electromagnetic Fields -- 10.1 Fundamentals of Quantum Mechanics -- 10.1.1 Basic Postulates of Quantum Mechanics.

10.1.2 Quantum Mechanical Operators.