> 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.

Yep, Diff Eq 1 (ODEs) and Diff Eq 2 (PDEs) for us as undergrads were exercises in memorization, even as a math major. I didn't really understand them until after I took a (well, several) linear algebra classes, after which it clicked that it was basically all the same theory.