I took, we called it Diff-e-q, my freshman year in college and the professor died a couple weeks into the course and the new guy was not pleased about having to teach it. We did the applied aspects with the springs and the little ants running away from a candle heating the corner of a plate.

What I didn't like about it was just all the memorization. I had no desire to memorize a bunch of formulas that I knew full well in the real world I'd look up in a table or type into a computer. What I wanted to learn how to do was solve problems using math, not memorize patterns of formulas to apply to problems.

So I didn't memorize them and instead went to work and earned money to pay for college. Still passed the class but it was one of my lowest grades. It's a hard class even without the memorization.

It's a little spooky that the author, Gian-Carlo Rota, passed away the night before teaching a class.

That is spooky. Both from heart problems too. Maybe the stress of teaching the class takes a toll. Heart attacks are pretty common among men of that age, though.

Coincidence, of course. Spooky. For sure.

Strongly agree. The way ODEs are taught at the sophomore level violates the beauty of math by teaching a plug-and-pray method of solution. For this form of equation, try this form of solution, if it doesn't work, try this one, then this. If none work, oops. At least once the Laplace method is taught things get a little better.

While I didn't exactly enjoy my course taught that way, as a human plugging in those methods manually, it was sort of interesting from the perspective of later being a fairly heavy user of computer algebra systems (CASs). The bag-of-tricks approach they teach in school is really how such systems work in practice, and tons of practical problems will be solved that way, either with you doing it by hand, or using software that does it for you. Software like Maxima, Maple, Mathematica, Sage, etc. consists of a huge pile of case analysis techniques and methods that pattern-match on specific equation forms that can be solved with the method in question. A CAS does feel a bit more satisfying because it feels like the pile of techniques is at least being given some kind of formalization and order, versus me just trying to remember them. Although the amount of order is not quite as much as one might like; even using a CAS there's still a lot poring over documentation to find the function that works in your case, which will go a bit faster if you remember enough of the textbook methods to recognize what you're looking for.

That's not to say this is anything like what mathematicians do, especially PhD mathematics researchers. But a lot of applied mathematics in engineering is not that far off from what's taught in a university ODE class.

Heh, all these years I thought it was just me.

Hated sophomore ODEs.

Much later took a mathematical physics course that actually taught me ODEs. Also took a year of applied mathematics that really solidified PDEs and taught me complex analysis. Took another graduate course in calculus of variations that was useful. Another very senior-level physics course taught me greens functions, method of steepest descent, etc.

The Physics and Applied Math profs were vastly better at teaching Math than the Math profs. Only real problem was in the freshman Physics courses where they taught you sloppy vector calculus before you'd seen that from the freshman calculus courses (and generally if you tried to pick up Math directly from the Physics courses that were teaching concepts it was all sloppy physics math -- it worked but you never quite understood why...)

I wonder if there are people that really click and appreciate purely abstract definitions of mathematical concepts. Many books and courses (especially in Europe it seems, watching U.S.A classes, Strang's for instance, feel a lot more pragmatic and applied). Sure after a few years of confusion one might finally click and realize all that was hidden behind a lemma, an identity or a symbol, and then that definition goes from painful to beautiful.

I hated ODEs until I took MIT's robotics course and had to solve non-linear ones using non-linear optimization techniques. Since then I love them ;-)

This has to be Russell Tedrake's Underactuated Robotics class right? Love that course, there's an online version now if I remember correctly.