Analysis with relative infinitesimals
Time and place
1 PM on Thursday, November 20th, 2008;
Karel Hrbacek (CCNY)
Abstract
Use of infinitesimals in Analysis dates back to Leibniz and Euler. The modern, rigorous theory of infinitesimals, known as "Nonstandard Analysis," is due to Abraham Robinson. Its methods have been instrumental in proofs of a number of new results in many branches of mathematics, but they have not made much impact on the teaching of Analysis, in main part, because of the technical machinery they require.
In the talk I will present a simple intuitive framework for infinitesimal methods and illustrate its use by giving simple proofs of some basic theorems of Calculus (Extreme Value Theorem, L'Hospital's Rule, Continuity implies Uniform Continuity on Closed Intervals, Fundamental Theorem,...). The talk should be accessible to Advanced Calculus students. The pilot project to teach Calculus based on this approach is currently being implemented at some high schools in Geneva.
