This is exactly why I gave up on higher level calculus. It was full of highly illogical "tricks" in a way diametrically opposite to go how physics is rarely ill

This is exactly why I gave up on higher level calculus. It was full of highly illogical "tricks" in a way diametrically opposite to go how physics is rarely illogical. That plus the fact that even with fairly low power computers available then, it was apparent numerical methods would very soon become good enough. Fully agree mathematics for non math majors the should not be taught by mathematics departments in college. Today in a very similar way I find data science is not effective when taught by college professors and their TAs and instead we get our own courses created by people with practical experience.