Lessons I Wish I Had Learned Before Teaching Differential Equations (1997) [pdf]
I TA&#x27;d for an undergrad ODE course for two semesters. I&#x27;m a grad student at a public university with very good undergrad engineering students. Nonetheless, with the course I taught, at least, the main problem was that WAY too much was packed into a single semester. I suspect that this is the same everywhere. For example, about a month and a half of the course was devoted to systems of linear equations. These were students who, a priori, knew basically no linear algebra, being asked to understand an entire linear algebra course, with some extra stuff thrown in (you know, the differential equations), in six weeks. In order to solve a general system of constant coefficient linear odes, you have to take a matrix and compute its Jordan canonical form. The students I taught were performing this calculation by the end of the unit, but it was of course a joke. On their exam, they were asked to do this calculation (in differential equations language), and most of them were able to do it because they were good students and had memorized the procedure. Then, in another question, they were presented a 5x5 matrix, told that its only eigenvalues were 2 and -2, and asked if it was invertable. I don&#x27;t think anyone gave a reasonable answer.<p>What is the point of that?<p>Edit: Everyone should be aware of this amazing Gian-Carlo Rota quote, the entirety of a book review on contemporary philosophers: &quot;When pygmies cast such long shadows, it must be very late in the day.&quot;