When I took DiffEq in undergrad, it was taught as part of an Abstract Algebra class

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Our DiffEq launch is special for me because I’ve been frustrated with DE pedagogy for a long time. This is the course that I wish I and all of my tutoring students had taken.

When I took DiffEq in undergrad, it was taught as part of an Abstract Algebra class.

Abstract Algebra. Let that sink in.

The official title of the course was Algebra 1, and the way that DiffEq was taught in Algebra 1 was kind of like this:

“Speaking of algebraic structures, let’s learn about metric spaces. By the way, differential equations is a thing you can do in metric spaces. Linear independence, Wronskian, yadda yadda. Memorize these proofs. Okay, moving on!”

They said were doing some kind of revamp / reorganization of their math courses, and maybe they were trying to do some kind of “integrated” sequence.

But the bottom line is they gave DiffEq responsibilities to a hardcore algebraist who didn’t want to teach it – so he didn’t. Not really.

Now, I knew my own DiffEq experience was completely whacko, straight out of Alice in Wonderland, but I didn’t expect that so many other people’s DiffEq experiences would be whacko in a different way.

When I did a bunch of tutoring, and talked to people taking DE elsewhere, I realized that pretty much everyone who teaches DiffEq has a different conception of what DiffEq covers.

I mean, sure, there’s a common thread up through 2nd-order homogeneous ODEs via characteristic polynomial, but beyond that, DiffEq class is like a box of chocolates and you never know what you’re gonna get.

I had always assumed that most people taking DE courses were learning it fairly comprehensively: integrating factors, undetermined coefficients, variation of parameters, oscillators, Cauchy-Euler, Bernoulli, systems, Runge-Kutta, power series solutions, Laplace transforms, Fourier series, eigenfunctions, Lotka-Volterra (predatory-prey model), phase portraits, etc.

But what would typically happen instead is, after covering those 2nd-order homogeneous ODEs via characteristic polynomial, the course would shoot off into whatever direction was most applicable to the instructor’s research interest.

And it wouldn’t cover all the other foundational stuff that you would reasonably be expected to know if you took a solid DE course.

Anyway, it feels nice to finally put out a DiffEq course that’s comprehensive and well-scaffolded with plenty of concrete examples.

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