A Brief Introduction to Infinitesimal Calculus

Section 2: Keisler's Axioms

The following presentation of Keisler's foundations for Robinson's Theory of Infinitesimals is explained in more detail in either of the (free .pdf) files: on my web site and the Epilog to Keisler's text,   on his web site.

Small, Medium, and Large Hyperreal Numbers

Keisler's Function Extension Axiom

Continuity & Extreme Values

Microscopic tangency in one variable

The Fundamental Theorem of Integral Calculus

The Local Inverse Function Theorem

Second Differences and Higher Order Smoothness


Created by Mathematica  (September 22, 2004)