I've watched several of the YouTube videos from MIT's 18.085 math course called
"Computational Science & Engineering". Although Professor Strang may not be the
world's best lecturer, I did like the general flow of the course, which
integrates the infinitesimal calculus side-by-side with finite differences,
aka matrix algebra aka finite element analysis.
Although the course uses MatLab, it could just as easily have used Maxima, and
the symbolic capabilities of Maxima would have enabled closer integration
of the calculus & matrix methods.
Perhaps someone on this list might already be teaching a course similar to
Strang's, but using Maxima instead.
Someone may have to define a small number of functions & operators to make
Maxima "look" more like Matlab & thereby smooth out these differences.