Anecdotally, as an engineer in industry, I use very little of the engineering math. Number sense and sort of general quantitative reasoning are used.
Let's suppose for sake of argument that I actually used engineering math though. Analytic solutions to derivatives and integrals (2 semesters of calculus) are largely useless because of applications like Wolfram Alpha that will solve these problems for you. The small class of ODE/PDE problems that are handled by analytic undergrad math classes will most often be solved using numerical methods such as Runge Kutta. Linear algebra is actually super useful in practice because you can use matrix solvers to solve systems of linear equations -- but a first course in undergraduate linear algebra is often just basic by-hand computations on matrix systems, and don't discuss higher order concepts at more than a shallow level (spans, invertibility, spectral decomposition, canonical forms, etc.)
Number theory is also a huge bore
Because they're for math majors. And less-advanced ones are filters for potential math majors. Me, I hated that stuff. Engineering math actually taught useful skills.
> I’m cynical about students. The vast majority are philistines.
I was a horrible TA. I was mainly an RA, but had to TA one semester. I had no patience for the "what do I need to know for the test?" ones. Especially pre-meds. But ~five kids loved me, because we all cared about the ideas.
It was actually easier as a professor, because I had TAs to deal with most students. Only the ones who cared bothered to see me personally. Or maybe I was just too rude to the others.