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YouTube

Tangent Conics and Tangent Quadrics - Differential Geometry

Insights into Mathematics via YouTube

Overview

Explore an advanced lecture on differential geometry that delves into Lagrange's algebraic approach to calculus. Learn how to associate polynomial functions with tangent lines, conics, and higher-order approximations using only elementary high school math. Discover the concept of sub-derivatives and their importance in differential geometry. Examine the quadratic approximation and tangent conics, including a beautiful theorem about cubic polynomials. Extend these concepts to multivariable functions and surfaces, using the Folium of Descartes as an example. Gain insights into a powerful alternative approach to understanding functions and their geometric properties.

Syllabus

Introduction
Taylor polynomials
Example
Scale
Theorem
Generalisation
Tangent plane

Taught by

Insights into Mathematics

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