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Features

Offers a balanced view of techniques for solving electromagnetic problems
Covers separation of variables, series expansion, conformal transformation, and perturbation methods
Illustrates Fourier sine and cosine, two-sided Fourier, Laplace, Hankel, and Mellin transform techniques
Uses simple examples, worked-out problems, and end-of-chapter exercises to demonstrate applications
Provides an appreciation of the kinds of electromagnetic problems that can be solved exactly
Summary

Analytical Techniques in Electromagnetics is designed for researchers, scientists, and engineers seeking analytical solutions to electromagnetic (EM) problems. The techniques presented provide exact solutions that can be used to validate the accuracy of approximate solutions, offer better insight into actual physical processes, and can be utilized in finding precise quantities of interest over a wide range of parameter values.

Beginning with a review of basic EMs, the text:

Describes the use of the separation of variables technique in Laplace, heat, and wave equations, covering rectangular, cylindrical, and spherical coordinate systems
Explains the series expansion method, providing the solution of Poisson´s equation in a cube and in a cylinder, and scattering by cylinders and spheres, as examples
Addresses the conformal transformation technique, offering a visual display of conformal mapping and a brief introduction to the Schwarz-Christoffel transformation
Employs worked-out problems to demonstrate various applications of Fourier sine and cosine, two-sided Fourier, Laplace, Hankel, and Mellin transform techniques
Discusses perturbation techniques, supplying examples of perturbed results degenerating to their unperturbed versions as the perturbation parameters tend to zero
Analytical Techniques in Electromagnetics maintains a balanced view of techniques for solving EM problems, refusing to overemphasize the importance of analytical methods at the expense of numerical techniques. Carefully selected topics give readers an appreciation of the kinds of EM problems that can be solved exactly.



Table of Contents

Review of Electromagnetics
Maxwell´s Equations
Constitutive Relations
Boundary Conditions
Power and Energy
Vector and Scalar Potentials
Time Harmonic Fields
Wave Equations
Diffusion Equation
Classification of EM Problems
References
Problems

Separation of Variables
Conditions for Complete Separability
Rectangular Coordinates
Cylindrical Coordinates
Spherical Coordinates
Conclusion
References
Problems

Series Expansion Method
Generalized Fourier Series
Poisson´s Equation in a Cube
Poisson´s Equation in a Cylinder
Strip Transmission Line
Scattering by a Conducting Cylinder
Scattering by a Dielectric Sphere
Conclusion
References
Problems

Conformal Transformation
Complex Variables
Functions of a Complex Variable
Derivative of a Complex Function
Conformal Mapping
Complex Electric Potential
Coplanar Strips at Fixed Potentials
Evaluation of Capacitance per Unit Length
The Schwarz-Christoffel Transformation
Strip Lines and Microstrip Lines
Strip with Finite Ground Plane
Strip Line with Elliptical Center Conductor
Conclusion
References
Problems

Transform Methods
The Fourier Transform
The Fourier Sine and Cosine Transforms
The Hankel Transform
The Mellin Transform
Laplace Transform
Conclusion
References
Problems

Perturbation Methods
Introduction
The Underlying Technique
Electromagnetic Cavities
Material Perturbations
Conclusion
References
Problems