Turns out that mathematics pedagogy is poor, in general. Especially for geometry and vector calculus, where it's either obsolete, busted systems or incredibly abstruse ones.

Skipping over div/grad/curl and Gibbs-Heaviside vector calculus by going straight to differential forms and Clifford algebras (geometric calc) would save a bunch of heartache and pointless effort.

Linear algebra is essential since the whole point of differentiation is to construct linear approximations of functions...among other things.