Most mathematics taught in universities at the undergraduate level is the mathematics for non-mathematicians. The typical calculus, ODE, PDE, vector calculus, complex variable stream taught for engineers and scientist is not at all rigorous, and misses a lot of the interesting details (for mathematicians) in order to speed up and cover more practical results.

It sounds like you ended up in the wrong numerical methods course, which is unfortunate. But there is a lot of the system is actually oriented exactly at what you are asking for.