The Differential Calculus for Curves - Lagrange's Algebraic Approach - Lecture 4

This lesson presents Lagrange’s algebraic approach to differential calculus, using translations and truncated Taylor expansions to study polynomial functions near a point. It develops sub-derivatives and applies them to finding tangent lines and higher-order tangent curves.

Syllabus

Correction: At the formula for D2pq should be D2pq=D1D1pq=pD2q+2*D1p*D2q+qD2p as noted by Faraz Sahba thanks!
The algebraic approach to Calculus
Euler and Lagrange
Reviewing the standard approach to calculus
Lagrange's approach
Pascal's array
Taylor expansions and product rules
The shape of curves near a point
Truncating to find approximations
Tangents and equation of a line
Problem: Calculate & graph the tangent curves to a curve at a point