I totally agree. I've always longed for a class called "differential reasoning" that focuses on building differential equations, proofs with differentials, and

I totally agree. I've always longed for a class called "differential reasoning" that focuses on building differential equations, proofs with differentials, and tricky arguments and mathematical justifications for all the stuff physics professors say "is technically invalid, but works". In my engineering program, they did something like this, though it was weak on the differential reasoning part. And heavy in hand-coding numerical solvers in FORTRAN.