Differential Equations is taught completely wrong. It should start with them handing you a flow chart telling you how to recognize a differential equation, how to tell if it's ordinary or not, then give you yes/no questions on what techniques would be used. The rest of the semester could be spent breaking down and teaching those techniques.
In practice, we can only solve rigorously about 5% of the differentials that come up. Number techniques will be used almost exclusively (even for the ones we could solve). It's an exercise in learning with very little applicable technique.
Now that I'm old, the Internet is a wonder for independently learning these things. Stuff that the old coots could never explain to me properly when I was paying them can now be taught easily and for free in ways that I can follow. Trying to finally nail down vector math led me to linear algebra in higher than 3 dimensions, which led me to exploring graph theory and now topology. It seems to incorporate a whole lot of interesting concepts. I can't think of a practical application for most of it, but it's fun to learn in the spare time.
