For this engineering, I think calculus is not the main proficiency enhancer you claim it to be. Linear Algebra, combinatorics, probability and number theory are more relevant.
Calculus was important during the world wars because it means we could throw shells to the enemy army better, and that was an important issue during that period.
Nowadays, calculus is just a stepping stone to more relevant mathematics.
Todays ML frameworks grapple with the problem of “jacobian-vector products” & “vector-jacobian product” as a consequence of understanding the interplay between gradients & derivative; and the application of the “chain rule”. All of those 3 concepts are fundamentally understood by being proficient in calculus.
While I’m being the hype-man for calculus I don’t mean to say proficiency in linear algebra or statistics is in any “less necessary” or “less useful” or “less challenging” or “less..” in any way.
I’m merely stating that, historically, calculus has been the unique branch of study for engineering. Statistics has always found value in many fields — business, finance, government policy etc.
Sure Linear algebra is one of those unique fields too — I kinda like to think of it as “algebra” in general and perhaps its utility has flowed in tandem with calculus. Idk. I haven’t thought super hard about it.
Calculus was important during the world wars because it means we could throw shells to the enemy army better, and that was an important issue during that period.
Nowadays, calculus is just a stepping stone to more relevant mathematics.