Yeah, I might have been guilty of some hyperbole. I remember a nasty integral on the Linear Systems midterm. It probably would have taken an hour or so if I didn't make any mistakes; but you could transform it and solve it as a linear equation in 10 seconds.

That was the point of the class, that there area two kinds of problems, linear problems and problems you can't solve.

I'm not in the least suggesting that an engineer shouldn't go through three semesters of Calculus, Linear Algebra+DiffEq and a Discrete Math course.