Table of Contents
Preface.
1. Linear Analysis.
1.1 Linear Spaces.
1.2 Linear Transformations.
1.3 The Inversion Problem.
1.4 Greens Functions.
1.5 Reciprocity.
1.6 Greens Dyadics.
1.7 Convergence of a Series.
1.8 Eigenfunctions.
1.9 Integral Operators.
1.10 Eigenfunction Expansions.
1.11 Discretization.
1.12 Matrices.
1.13 Solution of Matrix Equations: Stability.
1.14 Finite Differences.
1.15 Perturbations.
2. Variational Techniques.
2.1 Stationary functionals.
2.2 A Suitable Functional for the String Problem.
2.3 Functionals for the General L Transformation.
2.4 Eulers Equations of Some Important Functionals.
2.5 Discretization of the Trial Functions.
2.6 Simple Finite Elements for Planar Problems.
2.7 More Finite Elements.
2.8 Direct Numerical Solution of Matrix Problems.
2.9 Iterative Numerical Solution of Matrix Problems.
3. Electrostatic Fields in the Presence of Dielectrics.
3.1 Volume Charges in Vacuum.
3.2 Greens Function for Infinite Space.
3.3 Multipole Expansion.
3.4 Potential Generated by a Single Layer of Charge.
3.5 Potential Generated by a Double Layer of Charge.
3.6 Potential Generated by a Linear Charge.
3.7 Spherical Harmonics.
3.8 Dielectric Materials.
3.9 Cavity Fields.
3.10 Dielectric Sphere in an External Field.
3.11 Dielectric Spheroid in an Incident Field.
3.12 Numerical Methods.
4. Electrostatic Fields in the Presence of Conductors.
4.1 Conductivity.
4.2 Potential Outside a Charged Conductor.
4.3 Capacitance Matrix.
4.4 The Dirichlet Problem.
4.5 The Neumann Problem.
4.6 Numerical Solution of the Charge Density Problem.
4.7 Conductor in an External Field.
4.8 Conductors in the Presence of Dielectrics.
4.9 Current Injection into a Conducting Volume.
4.10 Contact Electrodes.
4.11 Chains of Conductors.
5. Special Geometries for the Electrostatic Field.
5.1 TwoDimensional Potentials in the Plane.
5.2 Field Behavior at a ConductingWedge.
5.3 Field Behavior at a DielectricWedge.
5.4 Separation of Variables in Two Dimensions.
5.5 TwoDimensional Integral Equations.
5.6 Finite Methods in Two Dimensions.
5.7 Infinite Computational Domains.
5.8 More TwoDimensional Techniques.
5.9 Layered Media.
5.10 Apertures.
5.11 Axisymmetric Geometries.
5.12 Conical Boundaries.
6. Magnetostatic Fields.
6.1 Magnetic Fields in Free Space: Vector Potential.
6.2 Fields Generated by Linear Currents.
6.3 Fields Generated by Surface Currents.
6.4 Fields at Large Distances from the Sources.
6.5 Scalar Potential in Vacuum.
6.6 Magnetic Materials.
6.7 Permanent Magnets.
6.8 The Limit of Infinite Permeability.
6.9 TwoDimensional Fields in the Plane.
6.10 Axisymmetric Geometries.
6.11 Numerical Methods: Integral Equations.
6.12 Numerical Methods: Finite Elements.
6.13 Nonlinear Materials.
6.14 Strong Magnetic Fields and ForceFree Currents.
7. Radiation in Free Space.
7.1 Maxwells Equations.
7.2 TheWave Equation.
7.3 Potentials.
7.4 Sinusoidal Time Dependence: Polarization.
7.5 Partially Polarized Fields.
7.6 The Radiation Condition.
7.7 TimeHarmonic Potentials.
7.8 Radiation Patterns.
7.9 Greens Dyadics.
7.10 Multipole Expansion.
7.11 Spherical Harmonics.
7.12 Equivalent Sources.
7.13 LinearWire Antennas.
7.14 CurvedWire Antennas: Radiation.
7.15 Transient Sources.
8. Radiation in a Material Medium.
8.1 Constitutive Equations.
8.2 PlaneWaves.
8.3 Ray Methods.
8.4 Beamlike Propagation.
8.5 Greens Dyadics.
8.6 Reciprocity.
8.7 Equivalent Circuit of an Antenna.
8.8 Effective Antenna Area.
9. Plane Boundaries.
9.1 PlaneWave Incident on a Plane Boundary.
9.2 Propagation Through a Layered Medium.
9.3 The Sommerfeld Dipole Problem.
9.4 Multilayered Structures.
9.5 Periodic Structures.
9.6 Field Penetration Through Apertures.
9.7 Edge Diffraction.
10. Resonators.
10.1 Eigenvectors for an Enclosed Volume.
10.2 Excitation of a Cavity.
10.3 Determination of the Eigenvectors.
10.4 Resonances.
10.5 Open Resonators: Dielectric Resonances.
10.6 Aperture Coupling.
10.7 Greens Dyadics.
11. Scattering: Generalities.
11.1 The Scattering Matrix.
11.2 Cross Sections.
11.3 Scattering by a Sphere.
11.4 Resonant Scattering.
11.5 The Singularity Expansion Method.
11.6 Impedance Boundary Conditions.
11.7 Thin Layers.
11.8 Characteristic Modes.
12. Scattering: Numerical Methods.
12.1 The Electric Field Integral Equation.
12.2 The Magnetic Field Integral Equation.
12.3 The TMatrix.
12.4 Numerical Procedures.
12.5 Integral Equations for Penetrable Bodies.
12.6 Absorbing Boundary Conditions.
12.7 Finite Elements.
12.8 Finite Differences in the Time Domain.
13. High and LowFrequency Fields.
13.1 Physical Optics.
13.2 Geometrical Optics.
13.3 Geometric Theory of Diffraction.
13.4 Edge Currents and Equivalent Currents.
13.5 Hybrid Methods.
13.6 LowFrequency Fields: The Rayleigh Region.
13.7 NonConducting Scatterers at Low Frequencies.
13.8 Perfectly Conducting Scatterers at Low Frequencies.
13.9 Good Conductors.
13.10 Stevensons Method Applied to Good Conductors.
13.11 Circuit Parameters.
13.12 Transient Eddy Currents.
14. TwoDimensional Problems.
14.1 E and H Waves.
14.2 Scattering by Perfectly Conducting Cylinders.
14.3 Scattering by Penetrable Circular Cylinders.
14.4 Scattering by Elliptic Cylinders.
14.5 Scattering byWedges.
14.6 Integral Equations for Perfectly Conducting Cylinders.
14.7 Scattering by Penetrable Cylinders.
14.8 LowFrequency Scattering by Cylinders.
14.9 Slots in a Planar Screen.
14.10 More Slot Couplings.
14.11 Termination of a Truncated Domain.
14.12 Line Methods.
15. CylindricalWaveguides.
15.1 Field Expansions in a ClosedWaveguide.
15.2 Determination of the Eigenvectors.
15.3 Propagation in a Closed Waveguide.
15.4 Waveguide Losses.
15.5 Waveguide Networks.
15.6 Aperture Excitation and Coupling.
15.7 GuidedWaves in General Media.
15.8 Orthogonality and Normalization.
15.9 DielectricWaveguides.
15.10 Other Examples ofWaveguides.
16. Axisymmetric and Conical Boundaries.
16.1 Field Expansions for Axisymmetric Geometries.
16.2 Scattering by Bodies of Revolution: Integral Equations.
16.3 Scattering by Bodies of Revolution: Finite Methods.
16.4 Apertures in Axisymmetric Surfaces.
16.5 The ConicalWaveguide.
16.6 Singularities at the Tip of a Cone.
16.7 Radiation and Scattering from Cones.
17. Electrodynamics of Moving Bodies.
17.1 Fields Generated by a Moving Charge.
17.2 The Lorentz Transformation.
17.3 Transformation of Fields and Currents.
17.4 Radiation from Sources: the Doppler Effect.
17.5 Constitutive Equations and Boundary Conditions.
17.6 Material Bodies Moving Uniformly in Static Fields.
17.7 Magnetic Levitation.
17.8 Scatterers in Uniform Motion.
17.9 Material Bodies in Nonuniform Motion.
17.10 Rotating Bodies of Revolution.
17.11 Motional Eddy Currents.
17.12 Accelerated Frames of Reference.
17.13 Rotating Comoving Frames.
Appendix 1. Vector Analysis in Three Dimensions.
Appendix 2. Vector Operators in Several Coordinate Systems.
Appendix 3. Vector Analysis on a Surface.
Appendix 4. Dyadic Analysis.
Appendix 5. Special Functions.
Appendix 6. Complex Integration.
Appendix 7. Transforms.
Appendix 8. Distributions.
Appendix 9. Some Eigenfunctions and Eigenvectors.
Appendix 10. Miscellaneous Data.
Bibliography.
General Texts on Electromagnetic Theory.
Texts that Discuss Particular Areas of Electromagnetic Theory.
General Mathematical Background.
Mathematical Techniques Specifically Applied to Electromagnetic Theory.
Acronyms and Symbols.
Author Index.
Subject Index.
