The hardest (ie, best) math prof I ever had (I was in EE, he was in the math department) used to say that "engineers can teach calculus, but their students cannot go on to teach calculus". I'm impressed by someone who knows a subject deeply enough to take that long of a view.
Personally, I just like the engineering view of dx and dy as simply being new variables (with caveats that we immediately forget). Which is why I'll probably not teach calculus any time soon.
But, still, the best "revelation" moment I had was when he off-handedly said "An integral is the inner product of a function and a suitably-dimensioned unit". Light bulb came on, and I "got" integration for the first time. Too bad they can't lead up to it that way in high school.
(Side rant: why do they teach trig before calculus in high school? That's completely backwards. Trig is a bunch of arbitrary formulas if you don't have the calculus behind them.)
Personally, I just like the engineering view of dx and dy as simply being new variables (with caveats that we immediately forget). Which is why I'll probably not teach calculus any time soon.
But, still, the best "revelation" moment I had was when he off-handedly said "An integral is the inner product of a function and a suitably-dimensioned unit". Light bulb came on, and I "got" integration for the first time. Too bad they can't lead up to it that way in high school.
(Side rant: why do they teach trig before calculus in high school? That's completely backwards. Trig is a bunch of arbitrary formulas if you don't have the calculus behind them.)