Analytical and Computational Methods in Electromagnetics

Basic Principles of Electromagnetic Theory
- Maxwell’s Equations
- Constitutive Relations
- Electrical Properties of the Medium
- Interface and Boundary Conditions
- Skin Depth
- Poynting Vector and Power Flow
- Image Currents and Equivalence Principle
- Reciprocity Theorem
- Differential Equations in Electromagnetics
- Electric and Magnetic Vector Potentials
- Wave Types and Solutions
- Phase Velocity, Dispersion, and Group Velocity
- Characteristics of Transmission Lines
- Charge and Current Singularities
- Classification of Methods of Analysis
- Mathematical Framework in Electromagnetics
- Overview of Analytical and Computational Methods
Analytical Methods and Orthogonal Functions
- Introduction
- Method of Separation of variables
- Orthogonality Condition
- Sturn-Liouville Differential Equation
  - Orthogonallity of Eigenfunctions
  - Boundary Condition for Orthogonal Functions
  - Examples of Sturn-Liouville Type of Differential Equations
- Eigenfunction Expansion Method
- Vector Space/Function Space
  - Operators
  - Matrix representation of Operators
- Delta-Function and Source representations
Green’s Function
- Introduction
- Direct Construction Approach for Green’s Function
  - Eqn(3.5) to Eqn(3.18)
  - Green’s Function for the Sturm-Liouville Differential Equations
    - Eqn(3.19) to Eqn(3.24)
  - Green’s Function for a Loaded transmission Line
    - Eqn(3.25a-b) to Eqn(3.38a-b)
- Eigenfunction Expansion of Green’s Function
Contour Integration and Conformal Mapping
Fourier Transform Method
Introduction to Computational Methods
Method of Finite Differences
Finite-Difference Time-Domain Analysis
Variational Methods
Finite Element Method
Method of Moments
Appendix A
- Solution Methods for the Set of Simultaneous Equations
Appendix B
- Evaluation of Singular Integrals