Calculus was invented by Newton and Leibniz, motivated by problems in mechanics and analytic geometry. The main concept of calculus is that of derivative of a function which we briefly review here.
Definition 42.1. Let F : R → R be a map and a0 ∈ R. We say F is differentiable at a0 if there exists a real number (denoted by) F
′(a0) ∈ R such that for any sequence an → a0 with an 6= a0 we have
F (an)− F (a0) an − a0 → F