Mathematical Background: Foundations of Infinitesimal Calculus

This book of mathematical 'background' shows how to fill in the mathematical details of the main topics from the course. These proofs are completely rigorous in the sense of modern mathematics - technically bulletproof.

We wrote this book of foundations in part to provide a convenient reference for a student who might like to see the "theorem - proof" approach to calculus.

This book also shows how the pathologies arise in the traditional approach (we left pointwise pathology out of the main text, but present it here for the curious and for comparison). Perhaps only math majors ever need to know about these sorts of examples, but they are fun in a negative sort of way.