Very much yes. I am currently trying to tutor my daughter through college-level calculus. She wants to be a civil engineer. Civil engineers, obviously, need to know calculus. But calculus is not being taught to her by engineers. It is being taught by mathematicians. And as part of teaching it, they are attempting to instill a "mathematical mindset". Which means, in practice, that it is an entry to proofs. Every proof…
You can't hope to understand first year physics without calculus. To be a reasonable civil engineer, don't you need to understand structural engineering, including dynamics, which requires differential equations? On the other hand, what do I know? The civil engineering plans for our place had glaring errors that the construction workers caught after doing half the earthmoving. Even after it was fixed, the results las…
Yes, but memorizing a bag of tricks for hand solving integrals and ODEs that you will never see in symbolic form without more than a passing exposure to the underlying concepts doesn't help anyone understand anything.
Learning mathematical thinking and getting into the groove of that style of problem solving is equally as important (although much less concrete in its applicability for an engineer). But conflating rote memorization of the 'trick' to integrate cos(x)sin(x) with either helps nobody.
A first year physics course is a better venue for teaching actual understanding of what derivative means than a purely symbolic presentation of the chain and product rules followed by presentation of a 'quotient rule' as a separate thing to memorize rather than a trivial combination of the other two. As is implementing some simulations of simple dynamical systems. As is intro to epidemiology or ecology. As is playing cookie clicker.
Get students to visualise things, and actually experience them rather than memorize symbols. Then formalize themand introduce the language so they can express what they've learnt