The Course

In fall 2016, as part of my UofT M.Eng (course based engineering master’s), I took Electromagnetic Theory (ECE1228H), and have and have PDF notes for that course available (redacted: 183 pages, full version 256 pages).

This course was taught by Prof. M. Mojahedi.

The official course description at the time was:

Fundamentals: Maxwell’s equations, constitutive relations and boundary conditions, wave polarization. Field representations: potentials, Green’s functions and integral equations. Theorems and concepts: duality, uniqueness, images, equivalence, reciprocity and Babinet’s principles. Plane, cylindrical and spherical waves and waveguides. radiation and scattering.

New material in this course was limited to:

  • dispersion relations.
  • Druid-Lorentz model
  • quadropole moments
  • magnetic moments, magnetostatic force, and torque (mentioned in class without details, but studied from Jackson)
  • matrix representation of transmission and reflection through multiple interfaces

Mathematica notebooks associated with this course are also available.

Review of this course.

This course, despite being offered as a grad course, turned out to be largely an introductory course, and was very disappointing. I’d seen fundamentals in the course description, but assumed that this would be a more in depth attack on those fundamentals. In particular, I mistakenly assumed this would be on par with phy1510, the grad physics electromagnetism course, which also covers fundamentals, and is known as one of the most difficult grad physics courses.

Phy1510 is the electromagnetism course I really wanted to take, but I felt forced to take this one to satisfy the M.Eng graduation requirements (a quota of ECE courses was required.)  In retrospect I shouldn’t have bothered wasting my time caring about actually graduating from the M.Eng program since my initial purpose for enrolling in that program was just as a vector to take grad physics courses (there was no part time grad physics option available, and this allowed me to mix and match).  If I’d been sensible, and not cared about credentials, as I hadn’t when I took all the undergrad physics courses as a non-degree student, I wouldn’t have wasted so much time and money on this sub-par ECE electromagnetism course.   The part time M.Eng ECE fees were $2500 per term.  I definitely did not get my money’s worth out of this course!  As it turned out, I was disappointed in almost all the ECE courses I took — the only exception was multiphysics modelling, taught by Prof Triverio.  In contrast, I was not disappointed in any of the grad physics courses I took, all of which were superb.

I did not think that this course was taught badly.  However, it has no place in a graduate electrical engineering (electromagnetism) program!


Should you wish to actively contribute typo fixes (or additions, editing, …) to these notes, you can do so by contacting me with suggested changes, or by forking your own copy of the associated git repositories and building the book pdf from source, and submitting a subsequent merge request.

git clone peeterjoot
cd peeterjoot
submods="figures/ece1228-electromagnetic-theory mathematica ece1228-electromagnetic-theory latex"
for i in $submods ; do
   git submodule update --init $i
   (cd $i && git checkout master)

export PATH=`pwd`/latex/bin:$PATH
cd ece1228-electromagnetic-theory

I reserve the right to impose dictatorial control over any editing and content decisions, and may not accept merge requests as-is, or at all. That said, I’ll probably not refuse reasonable suggestions or merge requests.


  • Copyright
  • Document Version
  • Dedication
  • Preface
  • Contents
  • List of Figures
  • Lecture Notes
  • 1 Introduction
  • 2 Boundaries
  • 2.1 Problems
  • 3 Electrostatics and dipoles.
  • 3.1 Problems
  • 4 Magnetic moment, and Boundary value conditions
  • 4.1 Problems
  • 5 Poynting vector, and time harmonic (phasor) fields.
  • 5.1 Problems
  • 5.2 Problems
  • 6 Druid model
  • 6.1 Problems
  • 7 Wave equation
  • 7.1 Problems
  • 8 Wave equation solutions
  • 8.1 Problems
  • 9 Wave equation solutions
  • 9.1 Problems
  • 10 Quadrupole expansion
  • 10.1 Problems
  • 11 Fresnel relations
  • 11.1 Single interface TE mode.
  • 11.2 Single interface TM mode.
  • 11.3 Normal transmission and reflection through two interfaces.
  • 11.4 Total internal reflection
  • 11.5 Brewster’s angle
  • 11.6 Problems
  • 12 Gauge freedom.
  • 12.1 Problems
  • Appendices
  • A Useful formulas and review
  • B Geometric Algebra
  • C Jackson’s electrostatic self energy analysis
  • D Magnetostatic force and torque.
  • E Line charge field and potential
  • F Gradient, divergence, curl and Laplacian in cylindrical coordinates.
  • G Gradient, divergence, curl and Laplacian in spherical coordinates.
  • H vector wave equation in spherical coordinates
  • I Transverse gauge
  • J Mathematica notebooks
  • Bibliography