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.
For example I taught my daughter factions this way.
Me: "These factions you see them? Now see these decimal points?"
Her: "Yeah I hate factions they are stupid!"
Me: "Factions are the only consistently real numbers below 1 and decimal points for the most part are made up numbers. 1/3 is 1/3 and never .3333."
Her: "I always thought it was the otehr way around."
I wish you would teach me calculus =)
This has nothing to do with calculus, though.
You can construct a complete ordered field from infinite decimals
FYI: infinite sums are calculus.