As an undergrad I tutored folks in a sort of “calculus for non-STEM students” class that focused more on practical stuff and applications… and TBH I think trying to shield them from the complexity didn’t really do them any favors. I often found that they had some practical algorithm memorized step-by-step and some graphical or conceptual intuition, but when the steps and intuition betrayed them we’d end up spending a while backtracking to find where they lost track of the concrete rules, and then we could work our way forward to catch up to their intuition. Practical results are good guideposts but don’t replace full understanding I think.

That’s just my perspective, though, I have a pretty simplistic, algebraic way of looking at math. I could never be a mathematician or see true beauty in math, it is just a bunch of little rules to me.

IMO calculus class is fundamentally just relatively abstract compared to the stuff before it. But once you’ve finished it, your engineering and science classes should be full of practical, reinforcing applications, right?

The valuable part of calculus to me was understanding the concepts of limits, differentiation, integration, and a tiny bit of differential equations.

Learning how to actually solve integrals or differential equations was useless other than it teaching me more about calculus and how it is useful. For calculations in practice I will turn to wolfram alpha, but it has some value to understand what wolfram alpha is doing under the hood.

I think a calculus course whose tests defocusses calculations might be very valuable for practically minded people. Knowing to think about derivatives is much more useful in practice than actually being able to calculate a derivative.