Calculus with Integral Polynumbers - Arithmetic and Geometry Math Foundations 70

Explore calculus through the lens of integral polynumbers in this comprehensive video lecture. Begin with a review of Pascal's Array and binomial coefficients before delving into the Taylor bipolynumber of polynumbers. Learn how to derive the standard form for polynomial derivatives and discover a lesser-known formula for second subderivatives. Master important rules for finding subderivatives of sums and products of polynumbers. Gain insights into alternative approaches to calculus that challenge traditional mathematical education methods. Study notation for binomial coefficients and examine proofs for key theorems. This fundamental lecture offers a fresh perspective on calculus, suitable for both teachers and students seeking a deeper understanding of mathematical foundations.

Intro to integral polynumbers and Calculus with them
Reviewing Pascal's Array
What the Taylor polynumber looks like
Derivative formula
Notation for binomial coefficients
Proof of the second subderivative theorem
Addition rule for subderivatives
Multiplication rule for subderivatives
Formula for the second subderivative of a product