Multivariable Calculus with Nilpotent Infinitesimals: More Smooth Infinitesimal Analysis

This is a continuation of my earlier post on smooth infinitesimal analysis. In this installment, I’ll show how the definition of a “stationary point” in Smooth Infinitesimal Analysis leads directly to a nice substitute for the Lagrange multipliers method. Then I’ll show how you can define differential forms as objects which assign a “signed volume” […]

How can one do calculus with (nilpotent) infinitesimals?: An Introduction to Smooth Infinitesimal Analysis

Many mathematicians, from Archimedes to Leibniz to Euler and beyond, made use of infinitesimals in their arguments. These were later replaced rigorously with limits, but many people still find it useful to think and derive with infinitesimals. Unfortunately, in most informal setups the existence of infinitesimals is technically contradictory, so it can be difficult to […]