I felt I didn't really learn calculus in calculus class, but rather in physics class. In fact I remember distinctly setting up my first differential equation "from scratch" (i.e. from a problem that was stated without equations or variables), and solving it, in a physics exam. A lightbulb went on for me at that moment. I remember thinking afterwards "so this is what this calculus thing is all about!"

I've told this story to others, and many of them reply that they too had similar epiphanies about calculus in physics class.

Calculus books, even the best of them, focus on the formalism of calculus, as they should. It is difficult for such a book to challenge students with calculus problems as they appear "in the wild", without everything already translated to the terms of the formalism.

Unfortunately, this translation process is half the battle! One can ace one's calculus class without yet mastering the skill of performing such a translation. (I realize that this problem pervades mathematics education, not just calculus, but here I want to focus on basic calculus, good ol' freshman-level differential + integral calculus.)

Does anyone know of a good collection of problems intended to exercise this skill of translating a problem as it appears "in the wild" to something that requires freshman calculus to solve?

(Freshman physics books would be an OK fallback, but even they do a lot of the translation for the student.)


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