This is what I wish I learned from in my freshman year of college. Honestly, the third of it that is about linear algebra is one of the best linear algebra resources out there.

It doesn't pull any punches for the pure math students, but unlike many books with that target audience it stays grounded in frequent numerical examples and scientific applications. The culmination to the generalized Stokes' theorem, as well as the way to frame Maxwell's equations with differential forms, are particularly satisfying.