Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon-delta methods. Students can fully prove fundamental results, such as the

part |2 pages

I Elementary Analysis

chapter 1|34 pages

Basic Concepts

chapter 2|30 pages

Continuity and Limits

chapter 3|32 pages


chapter 4|42 pages

Integration of Continuous Functions

part |2 pages

II Higher Analysis

chapter 5|12 pages

Basic Concepts Revisited

chapter 7|30 pages

Sequences and Series

chapter 8|12 pages

First Order Differential Equations

chapter 9|16 pages


chapter 10|18 pages

Topology of Real Numbers

chapter |28 pages

Answers to Exercises