Dual Complex Numbers and Leibniz's Differentiation Rules - Famous Math Problems

Explore dual complex numbers and Leibniz's differentiation rules in this 27-minute mathematics lecture. Delve into a purely algebraic approach to infinitesimals that extends differential calculus to general fields, including finite fields. Learn about polynumbers, a data structure approach to polynomials, and how they can be evaluated using dual numbers. Examine Leibniz's rules of differentiation and their historical origins with Johann Faulhaber. Gain insights into the algebraic foundations of calculus and the innovative ways of understanding infinitesimals in mathematics.

Introduction
Leibnizs differentiation rules
What is a function
Polynomials
Polynomial Evaluation
Derivative
The hurdle