Title: Basic Calculus by Way of Infinitesimals
Abstract: Calculus, as initially invented by Leibniz and Newton, relied extensively on the use of infinitesimals. The rigorous justification for the use of infinitesimals was later put into question, and Weierstrass et. al. invented the approach via limits that persists to today. But a rigorous theory of infinitesimals does exist, and the approach to calculus it provides is called "nonstandard analysis", pioneered in the 1960s by Robinson.
In this talk, we will briefly review the historical development of calculus, discuss the issues with infinitesimals as used by the "old masters", and finally sketch the rigorous use of infinitesimals via nonstandard analysis. By the end, we will be able to re-prove basic calculus results such as the Leibniz rule and the chain rule using infinitesimals.
March 30, 2023
6:00 pm - 8:00 pm
PMA 12.166
Participants earn two CPE hours for each session. We request that you register by noon on March 29 so that we have the needed information for your CPE certificate, the food order, and parking validations.
