John L. Bell is Professor of Philosophy at the University of Western Ontario. He is the author of 7 other books, including Models and Ultraproducts with A. B. Slomson, A Course in Mathematical Logic with M. Machover, Logical Options with D. DeVidi and G. Solomon, Set Theory: Boolean-Valued Models and Independence Proofs, and The Continuous and the Infinitesimal in Mathematics and Philosophy.
Introduction
1. Basic features of smooth worlds
2. Basic differential calculus
3. First applications of the differential calculus
4. Applications to physics
5. Multivariable calculus and applications
6. The definite integral: Higher order infinitesimals
7. Synthetic geometry
8. Smooth infinitesimal analysis as an axiomatic system
Appendix
Models for smooth infinitesimal analysis.
