Home : Book details : Book description

Description of  Theory and Computation of Electromagnetic Fields,1st Edition

0470533595 pdf Mathematics is a grand subject in the way it can be applied to various problems in science and engineering. To use mathematics, one needs to understand the physical context. The author uses mathematical techniques along with observations and experiments to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow. Equal emphasis is placed on the mathematical formulation of the problem and the interpretation of the results. In the sections on mechanical vibrations and population dynamics, the author emphasizes the nonlinear aspects of ordinary differential equations and develops the concepts of equilibrium solutions and their stability. He introduces phase plane methods for the nonlinear pendulum and for predator-prey and competing species models PREFACE. ACKNOWLEDGMENTS. PART I ELECTROMAGNETIC FIELD THEORY. CHAPTER 1 BASIC ELECTROMAGNETIC THEORY. 1.1 Review of Vector Analysis. 1.1.1 Vector Operations and Integral Theorems. 1.1.2 Symbolic Vector Method. 1.1.3 Helmholtz Decomposition Theorem. 1.1.4 Green's Theorems. 1.2 Maxwell's Equations in Terms of Total Charges and Currents. 1.2.1 Maxwell's Equations in Integral Form. 1.2.2 Maxwell's Equations in Differential Form. 1.2.3 Current Continuity Equation. 1.2.4 The Lorentz Force Law. 1.3 Constitutive Relations. 1.3.1 Electric Polarization. 1.3.2 Magnetization. 1.3.3 Electric Conduction. 1.3.4 Classifi cation of Media. 1.4 Maxwell's Equations in Terms of Free Charges and Currents. 1.5 Boundary Conditions. 1.6 Energy, Power, and Poynting's Theorem. 1.7 Time-Harmonic Fields. 1.7.1 Time-Harmonic Fields. 1.7.2 Fourier Transforms. 1.7.3 Complex Power. 1.7.4 Complex Permittivity and Permeability. CHAPTER 2 ELECTROMAGNETIC RADIATION IN FREE SPACE. 2.1 Scalar and Vector Potentials. 2.1.1 Static Fields. 2.1.2 Time-Harmonic Fields and the Lorenz Gauge Condition. 2.2 Solution of Vector Potentials in Free Space. 2.2.1 Delta Function and Green's Function. 2.2.2 Green's Function in Free Space. 2.2.3 Field-Source Relations in Free Space. 2.2.4 Why Use Auxiliary Potential Functions. 2.2.5 Free-Space Dyadic Green's Functions. 2.3 Electromagnetic Radiation in Free Space. 2.3.1 Infi nitesimal Electric Dipole. 2.3.2 Finite Electric Dipole. 2.3.3 Far-Field Approximation and the Sommerfeld Radiation Condition. 2.3.4 Circular Current Loop and Magnetic Dipole. 2.4 Radiation by Surface Currents and Phased Arrays. 2.4.1 Radiation by a Surface Current. 2.4.2 Radiation by a Phased Array. CHAPTER 3 ELECTROMAGNETIC THEOREMS AND PRINCIPLES. 3.1 Uniqueness Theorem. 3.2 Image Theory. 3.2.1 Basic Image Theory. 3.2.2 Half-Space Field-Source Relations. 3.3 Reciprocity Theorems. 3.3.1 General Reciprocity Theorem. 3.3.2 Lorentz Reciprocity Theorem. 3.3.3 Rayleigh-Carson Reciprocity Theorem. 3.4 Equivalence Principles. 3.4.1 Surface Equivalence Principle. 3.4.2 Application to Scattering by a Conducting Object. 3.4.3 Application to Scattering by a Dielectric Object. 3.4.4 Volume Equivalence Principle. 3.5 Duality Principle. 3.6 Aperture Radiation and Scattering. 3.6.1 Equivalent Problems. 3.6.2 Babinet's Principle. 3.6.3 Complementary Antennas. CHAPTER 4 TRANSMISSION LINES AND PLANE WAVES. 4.1 Transmission Line Theory. 4.1.1 Governing Differential Equations and General Solutions. 4.1.2 Refl ection and Transmission. 4.1.3 Green's Function and Eigenfunction Expansion. 4.2 Wave Equations and General Solutions. 4.2.1 Wave Equations and Solution by Separation of Variables. 4.2.2 Characteristics of a Plane Wave. 4.2.3 Wave Velocities and Attenuation. 4.2.4 Linear, Circular, and Elliptical Polarizations. 4.2.5 Wave Propagation in Metamaterials. 4.3 Plane Waves Generated by A Current Sheet. 4.4 Refl ection and Transmission. 4.4.1 Refl ection and Transmission at Normal Incidence. 4.4.2 Refl ection and Transmission at Oblique Incidence. 4.4.3 Total Transmission and Total Reflection. 4.4.4 Transmission into a Left-Handed Medium. 4.4.5 Plane Waves versus Transmission Lines. 4.5 Plane Waves in Anisotropic and Bi-Isotropic Media. 4.5.1 Plane Waves in Uniaxial Media. 4.5.2 Plane Waves in Gyrotropic Media. 4.5.3 Plane Waves in Chiral Media. CHAPTER 5 FIELDS AND WAVES IN RECTANGULAR COORDINATES. 5.1 Uniform Waveguides. 5.1.1 General Analysis. 5.1.2 General Characteristics. 5.1.3 Uniform Rectangular Waveguide. 5.1.4 Losses in Waveguides and Attenuation Constant. 5.2 Uniform Cavities. 5.2.1 General Theory. 5.2.2 Rectangular Cavity. 5.2.3 Material and Geometry Perturbations. 5.3 Partially Filled Waveguides and Dielectric Slab Waveguides. 5.3.1 General Theory. 5.3.2 Partially Filled Rectangular Waveguide. 5.3.3 Dielectric Slab Waveguide on a Ground Plane. 5.4 Field Excitation in Waveguides. 5.4.1 Excitation by Planar Surface Currents. 5.4.2 Excitation by General Volumetric Currents. 5.5 Fields in Planar Layered Media. 5.5.1 Spectral Green's Function and Sommerfeld Identity. 5.5.2 Vertical Electric Dipole above a Layered Medium. 5.5.3 Horizontal Electric Dipole above a Layered Medium. 5.5.4 Dipoles on a Grounded Dielectric Slab. CHAPTER 6 FIELDS AND WAVES IN CYLINDRICAL COORDINATES. 6.1 Solution of Wave Equation. 6.1.1 Solution by Separation of Variables. 6.1.2 Cylindrical Wave Functions. 6.2 Circular and Coaxial Waveguides and Cavities. 6.2.1 Circular Waveguide. 6.2.2 Coaxial Waveguide. 6.2.3 Cylindrical Cavity. 6.3 Circular Dielectric Waveguide. 6.3.1 Analysis of Hybrid Modes. 6.3.2 Characteristics of Hybrid Modes. 6.4 Wave Transformation and Scattering Analysis. 6.4.1 Wave Transformation. 6.4.2 Scattering by a Circular Conducting Cylinder. 6.4.3 Scattering by a Circular Dielectric Cylinder. 6.4.4 Scattering by a Circular Multilayer Dielectric Cylinder. 6.5 Radiation by Infi nitely Long Currents. 6.5.1 Line Current Radiation in Free Space. 6.5.2 Radiation by a Cylindrical Surface Current. 6.5.3 Radiation in the Presence of a Circular Conducting Cylinder. 6.5.4 Radiation in the Presence of a Conducting Wedge. 6.5.5 Radiation by a Finite Current. CHAPTER 7 FIELDS AND WAVES IN SPHERICAL COORDINATES. 7.1 Solution of Wave Equation. 7.1.1 Solution by Separation of Variables. 7.1.2 Spherical Wave Functions. 7.1.3 TEr and TMr Modes. 7.2 Spherical Cavity. 7.3 Biconical Antenna. 7.3.1 Infi nitely Long Model. 7.3.2 Finite Biconical Antenna. 7.4 Wave Transformation and Scattering Analysis. 7.4.1 Wave Transformation. 7.4.2 Expansion of a Plane Wave. 7.4.3 Scattering by a Conducting Sphere. 7.4.4 Scattering by a Dielectric Sphere. 7.4.5 Scattering by a Multilayer Dielectric Sphere. 7.5 Addition Theorem and Radiation Analysis. 7.5.1 Addition Theorem for Spherical Wave Functions. 7.5.2 Radiation of a Spherical Surface Current. 7.5.3 Radiation in the Presence of a Sphere. 7.5.4 Radiation in the Presence of a Conducting Cone. PART II ELECTROMAGNETIC FIELD COMPUTATION. CHAPTER 8 THE FINITE DIFFERENCE METHOD. 8.1 Finite Differencing Formulas. 8.2 One-Dimensional Analysis. 8.2.1 Solution of the Diffusion Equation. 8.2.2 Solution of the Wave Equation. 8.2.3 Stability Analysis. 8.2.4 Numerical Dispersion Analysis. 8.3 Two-Dimensional Analysis. 8.3.1 Analysis in the Time Domain. 8.3.2 Analysis in the Frequency Domain. 8.4 Yee's FDTD Scheme. 8.4.1 Two-Dimensional Analysis. 8.4.2 Three-Dimensional Analysis. 8.5 Absorbing Boundary Conditions. 8.5.1 One-Dimensional ABC. 8.5.2 Two-Dimensional ABCs. 8.5.3 Perfectly Matched Layers. 8.6 Modeling of Dispersive Media. 8.6.1 Recursive Convolution Approach. 8.6.2 Auxiliary Differential Equation Approach. 8.7 Wave Excitation and Far-Field Calculation. 8.7.1 Modeling of Wave Excitation. 8.7.2 Near-to-Far Field Transformation. 8.8 Summary. CHAPTER 9 THE FINITE ELEMENT METHOD. 9.1 Introduction to the Finite Element Method. 9.1.1 The General Principle. 9.1.2 One-Dimensional Example. 9.2 Finite Element Analysis of Scalar Fields. 9.2.1 The Boundary-Value Problem. 9.2.2 Finite Element Formulation. 9.2.3 Application Examples. 9.3 Finite Element Analysis of Vector Fields. 9.3.1 The Boundary-Value Proble