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Examples for non-math department students to be used for Calculus course

This semester I am a teaching assistant for Calculus. There are many students from different departments like International Relations, Economics and more taking the course. The course is comprehensive....
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Should you keep a notebook of example problems while going through science and engineering courses?

I find myself constantly being told I should not intentionally jot down example problems but understand the core logic of a topic. But some of my high level math classes tend to have very few examples ...