>> They had the usual examples, like calculating work by integrating the
>> force.
>
> Right. That's the physics I was talking about. I never saw examples in
> our textbooks about *why* you want to do this thing. Just curves, and
> how to figure out the area underneath. Not where the curves came from.

You just needed the right text book.  Our maths was split into pure and 
applied, with separate text books.  Pure had all the theoretical stuff 
for calculus etc, applied had carefully contrived examples of how you 
applied it IRL, things like analysing rockets taking off and various 
mechanisms.

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