Calculus (also called "tartar") is a buildup of minerals (chiefly Calcium Phosphate) on the teeth. Minerals are caught in unremoved plaque harden onto the teeth forming tartar, which then forms a rough-surfaced base for more plaque to form.
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Calculus; by a long shot.
Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.
That describes the crusty deposition on your teeth above the gum line. Your dentist uses the pick to scrape it off if you don't brush and floss like you should.
It is certainly used in calculus, just as calculus can be used in trigonometry.