What I learned by teaching Numerical Methods in Electromechanics


At the moment, this post has taken me more than one month to write, so let’s get the most important lesson out of the way before anything else:

There’s no perfect time for anything – just start.

Someone (can’t remember where I first read this, so that’s the best attribution I can manage) learned this after becoming a father. I can now wholeheartedly second that opinion. If five minutes are all you’ve got, you’ve better utilize those five minutes in a damn efficient fashion.

Alright, let’s move on to the actual post.

Teaching experiences

Hi all! This year, I got to lecture an entire university course for the first time

Well, the course is just about finished now, so I thought it might be a good idea to  wrap it up with a dedicated post. Here, I’ll share some of my experiences, muse on what I learned, and maybe try to figure out what I might do differently next time.

So on we go!

Course debriefing

Cross-section of a loaded synchronous machine. Screenshot from the course slides.


The course I taught was called Numerical Methods in Electromechanics. It’s a 5 ECTS course (for comparison, a Bachelor’s degree is 180, and Master’s is 120), nominally aimed at second-year Master’s students. I use the word word nominally because university studies are still quite flexible here, although there has been some rigidification since my days…damn I feel old already. Meaning there might be some younger students present, as well as older ones. But you get the point.

Anyways, as the name suggests, Numerical Methods focused on the use of finite element method for analysing electrical machines. It covered topics such as the basic principles of FEM, implementation aspects, higher-order and isoparametric shape functions, and nonlinear problems. Furthermore, more machine-specific stuff like circuit coupling and loss computation were examined, as were 3D problems albeit briefly.

It was a roughly five-week-long course. It consisted of bi-weekly lectures of about two hours each. So, ten of those in total. In addition, there were weekly exercise sessions, plus two home assignments that were graded, and then of course an exam. I was responsible for the lectures, preparing the assignments, and the exam as a whole.

Now, some details and lessons for me.

What I did

As mentioned just moments ago, I was responsible for giving the course lectures.

Besides that, I also updated the lecture slides. That was purely my personal choice – I could have used existing material. But, that simply didn’t match my personal preferences. I wanted to approach things from a different direction, in a different order.

For example, I pretty much skipped the energy minimization aspects of FEM. You know, how the solution minimizes an energy functional? Except for when it doesn’t, like in time-harmonic analysis. Instead, I focused purely on the Galerkin’s method, since that can be applied whenever you have a residual to weigh. Basically always.

I also cut back on the attention given to the conjugate gradient method, and instead briefly considered iterative solvers in general. With the time saved, I was able to introduce both multigrid and domain decompositions methods, at least on the operating principle level. I could argue that knowing about their existence is more important than the details of conjugate gradients.

My goal was to make the course somewhat more approachable, and I’d like to think I succeeded.

But let’s move on.

What did I learn from making others learn?

It’s rough on your voice

Lecturing, I mean. Speaking for two hours straight is not something many of us routinely do.

On the other hand, speaking is really all it takes. No need to raise your voice higher than normally (I was earlier quilty of this). The students will listen, if you’re worth listening.

It takes time

Teaching takes a lot of invisible time.

Even the lectures themselves – roughly two hours in total, twice a week – take one tenth of the workweek. Add the time to walk back and forth across the campus, and you’re looking at one extra hour per week. But alright, that’s not bad. And really gets associated to teaching in most people’s minds.

But the lion’s share is still spent on preparation. Simply learning the material and taking a wild, educated guess on your student’s probably sticking points takes at least as much as the lectures themselves. If you’re actually making said material, you can at least double the number. Add the weekly quizzes, some extra contact teaching, plus all the miscellaneous administrative stuff, and more than half your work week is suddenly spent.

What was difficult

Numerical Methods is a difficult course to learn, and perhaps even more so teach. Of course I understand the topic, having worked on it for years. But making others understand what you do is often easier said than done.

Chalkboard after an exercise session (from 2016, when I was giving the exercises rather than lecturing).

The worst difficulties related to the theoretical nature of the course – it wasn’t Comsol in Electromechanics, after all. And many people instinctively associate the word theoretical with boring, difficult, or unuseful. Rather than e.g. fundamental, foundation-laying, or path-opening. It’s an understandable bias, and something that I’m also guilty of when dealing with matters outside my own specialty.

Another complication were the different backgrounds of all the international and exhange students. Different universities have wildly different foci in teaching, and often mathematics is not one of them. (By contrast, their Bachelors would probably wipe the table with as Finns when it comes to practical knowledge.)

How I did

Despite all the difficulties, I’d like to think I did okay. I think everybody who clearly put some effort into the course, also passed it. Often with good grades, even.

Feedback was also nice; I mean having one’s teaching described as awesome is, well, awesome.

How I could do better

If something is clear, is the fact that the course has to be steered more to the practical direction. Not by too much, mind you. It’s still a theoretical course, and will remain as such. But maybe some exercises could be more of a hands-on-software type. Or something like that.

Wanna learn numerical methods yourself?

I already sent some material to one interested person. If you’d like to receive your copy, get in touch and we’ll see what can be done.

Or, if that’s a little too much for you, at least get the free 20-page guide ‘Boundary Conditions in Magnetic FEA’.


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Lessons from Teaching, and More

2 thoughts on “Lessons from Teaching, and More

  • Hey Antti!

    It’s great that you did your first lecture. Each new class you teach it is rough the first time (well maybe 2 times) but after a while it gets better – hang in there!

    1. Yeah it certainly does. I’d had some prior experience, but those were limited to giving exercise sessions, or stepping in for a lecture or two at most.

      But, in general teaching is one of the best ways to deepen your own understanding.

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