Elementary explorations in Tangents to a Cubic Polynomial
Channel: Abraximus
Date: 07/01/2018

*Correction* Dnx (x^k) = (k choose n) (x^k-n) and the same for Dnr.

Thanks to professor Norman J Wildberger for all his effort

This video shows how to find tangent vectors, lines, and parabolas to a Cubic polynomial. What is novel is that this is done without a prior theory of limits or real numbers, and is valid over a general field. In future videos, I will go over general cubic curves, surfaces, and parametric functions.

Geogebra Document
https://docs.google.com/document/d/1gn3Ig1HCADV9Y3TeBLvwfr13DNS4EnlmpTF4_G9MAW4/edit?usp=sharing

Binomial theorem Worksheet
https://docs.google.com/document/d/1ZcaJUaEDGGv8VQLRiNp7Jh2Rqep0gyNzvnL_bJ1NLdQ/edit?usp=sharing

Cavalieri's Quadrature Formula
https://www.researchgate.net/publication/266256869_A_New_Proof_of_Cavalieri%27s_Quadrature_Formula

Algebraic Calculus One
https://www.openlearning.com/courses/algebraic-calculus-one/HomePage

Differential Geometry through Algebra 
https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP