Level:

Graduate

Semester:

Fall 2015

Topics covered:

1. Introduction: Maxwell’s equations, constitutive relationships, time-harmonic fields, Poynting’s theorem.
2. Radiation and EM principles: scalar & vector potentials, free-space Green’s function, dipole radiation, uniqueness, image theory, reciprocity, duality, equivalence principle.
3. Transmission lines and planewaves: polarization, reflection & transmission, Fresnel coefficiens, Brewster’s angle.
4. Guided waves: TE/TM/TEM modes, parallel-plate/rectangular/circular waveguides, mode orthogonality, waveguide excitation.

Level:

Graduate

Semester:

Winter 2014

Topics covered:

1. Review of basic electromagnetic theory
2. Inverse problems
   • Classification of inverse problems: inverse source, inverse scattering
   • Formulation of forward and inverse scattering problems: integral and differential
   • Inverse problem solution: existence, uniqueness, minimum-norm, least-squares, regularization
3. Inversion methods
   • Direct approximate methods: Born and extended Born approximations, 2-D diffraction tomography
   • Direct iterative methods: distorted Born iterative method (DBIM)
   • Optimization methods: contrast source inversion method (CSI)
4. A software implementation of 2-D TM forward solver, min-norm, least-squares, regularized least squares, 2-D diffraction tomography, DBIM, and CSI.

Level:

Undergraduate

Semester:

Fall 2012, Fall 2013

Topics covered:

1. Electrostatics:
• Coulomb’s law, electric force, the electric field
• Gauss’s law, electric flux density, electric polarization, dielectric material, capacitance
• Electrostatic potential, boundary conditions, Laplace’s and Poisson’s equations
• Solving boundary value problems: finite differences and the method of images
• Energy in electrostatic systems
2. Magnetostatics
• Biot-Savart law, magnetic force, the magnetic field
• Ampère’s circuital law, magnetic flux density, inductance
• Magnetic potential, boundary conditions, magnetostatic boundary value problems
• Energy in magnetostatic systems
3. Electromagnetic Fields
• Maxwell’s equations in differential and integral form
• Time-harmonic electromagnetic fields and plane waves
• Power and Poynting’s theorem
4. Electromagnetics of Circuits
• Circuit theory from electromagnetic field theory
• Mutual capacitance and inductance

Level:

Undergraduate

Semester:

Fall 2011, Winter 2012, Fall 2013, Winter 2014

Topics covered:

Mathematical induction, sigma notation, complex numbers, polynomial equations, vector geometry in 2-D and 3-D, systems of linear equations, determinant, matrix inverse, linear transformations, eigenpairs.

Level:

Undergraduate

Semester:

Winter 2012, Summer 2012, Fall 2012, Winter 2013, Summer 2013, Fall 2013

Topics covered:

Systems of linear equations and matrices, determinants, Cramer’s rule, vectors and geometry in multidimensional space, linear transformations, eigenvalues and eigenvectors.

Level:

Undergraduate

Semester:

Fall 2012, Winter 2013, Winter 2014

Topics covered:

Introduction to differential and integral calculus: limit of a function, derivative, implicit differentiation, max&min problems, optimization, mean value theorem, function graph sketching, anti-derivatives, fundamental theorem of calculus.

Level:

Undergraduate

Semester:

Winter 2013