Explore an algebraic infinitesimal approach to product and chain rules in calculus without relying on limits or real numbers. Learn about dual complex numbers and bi-polynumbers as foundational concepts for understanding derivatives in a general field F. Discover the Derivative theorem and its applications to the Product Rule and Chain Rule in a broad mathematical context. Gain insights into this novel approach to calculus, which will be further developed in the Algebraic Calculus Two online course.
An Algebraic Infinitesimal Approach to Product and Chain Rules - N J Wildberger
Insights into Mathematics via YouTube
Overview
Syllabus
Introduction
Field F
Bipoly numbers
Example
Bipoly number algebra
Derivative theorem
Product rule
Substitution rule
Chain rule
Taught by
Insights into Mathematics
