The World of Limits

Limits are where calculus actually begins. Before a limit, a function is just a curve; after it, the function has derivatives, integrals, and series that can be computed. This course moves in the order a working mathematician would: establish the basic concept and the two special quantities, the infinitesimal and the infinity; work through the rules for manipulating limits; use the Cauchy criterion, the monotone-bounded criterion, and the squeeze theorem to answer whether a limit exists at all; derive the few limit values worth memorising; and finally turn them into methods you can execute directly. By the end you should be able to decide independently whether a limit exists and, when it does, compute it.