Foundations of Applied Electrodynamics

1 Maxwell Equations.

1.1 Experimental Laws.

1.2 Maxwell Equations, Constitutive Relation, and Dispersion.

1.3 Theorems for Electromagnetic Fields.

1.4 Wavepackets.

2 Solutions of Maxwell Equations.

2.1 Linear Space and Linear Operator.

2.2 Classification of Partial Differential Equations.

2.3 Modern Theory of Partial Differential Equations.

2.4 Method of Separation of Variables.

2.5 Method of Green’s Function.

2.6 Potential Theory.

2.7 Variational Principles.

3 Eigenvalue Problems.

3.1 Introduction to Linear Operator Theory.

3.2 Eigenvalue Problems for Symmetric Operators.

3.3 Interior Electromagnetic Problems.

3.4 Exterior Electromagnetic Problems.

3.5 Eigenfunctions of Curl Operator.

4 Antenna Theory.

4.1 Antenna Parameters.

4.2 Properties of Far Fields.

4.3 Spherical Vector Wavefunctions.

4.4 Foster Theorems and Relationship Between Quality Factor and Bandwidth.

4.5 Minimum Possible Antenna Quality Factor.

4.6 Maximum Possible Product of Gain and Bandwidth.

4.7 Evaluation of Antenna Quality Factor.

5 Integral Equation Formulations.

5.1 Integral Equations.

5.2 TEM Transmission Lines.

5.3 Waveguide Eigenvalue Problems.

5.4 Metal Cavity Resonators.

5.5 Scattering Problems.

5.6 Multiple Metal Antenna System.

5.7 Numerical Methods.

6 Network Formulations.

6.1 Transmission Line Theory.

6.2 Scattering Parameters for General Circuits.

6.3 Waveguide Junctions.

6.4 Multiple Antenna System.

6.5 Power Transmission Between Antennas.

6.6 Network Parameters in a Scattering Environment.

6.7 RLC Equivalent Circuits.

7 Fields in Inhomogeneous Media.

7.1 Foundations of Spectral Analysis.

7.2 Plane Waves in Inhomogeneous Media.

7.3 Inhomogeneous Metal Waveguides.

7.4 Optical Fibers.

7.5 Inhomogeneous Cavity Resonator.

8 Time-domain Theory.

8.1 Time-domain Theory of Metal Waveguides.

8.2 Time-domain Theory of Metal Cavity Resonators.

8.3 Spherical Wave Expansions in Time-domain.

8.4 Radiation and Scattering in Time-domain.

9 Relativity.

9.1 Tensor Algebra on Linear Spaces.

9.2 Einstein’s Postulates for Special Relativity.

9.3 The Lorentz Transformation.

9.4 Relativistic Mechanics in Inertial Reference Frame.

9.5 Electrodynamics in Inertial Reference Frame.

9.6 General Theory of Relativity.

10 Quantization of Electromagnetic Fields.

10.1 Fundamentals of Quantum Mechanics.

10.2 Quantization of Free Electromagnetic Fields.

10.3 Quantum Statistics.

10.4 Interaction of Electromagnetic Fields with the Small Particle System.

10.5 Relativistic Quantum Mechanics.

Appendix A: Set Theory.

A.1 Basic Concepts.

A.2 Set Operations.

A.3 Set Algebra.

Appendix B: Vector Analysis.

B.1 Formulas from Vector Analysis.

B.2 Vector Analysis in Curvilinear Coordinate Systems.

Appendix C: Special Functions.

C.1 Bessel Functions.

C.2 Spherical Bessel Functions.

C.3 Legendre Functions and Associated Legendre Functions.

Appendix D: SI Unit System.

Bibliography.

Index.