The Differential Calculus for Curves - Differential Geometry
Offered By: Insights into Mathematics via YouTube
Course Description
Overview
Explore the differential calculus for algebraic curves in this advanced mathematics lecture. Extend Lagrange's approach to study tangent lines, tangent conics, and higher-order approximations for general curves of the form p(x,y)=0. Examine the lemniscate of Bernoulli in detail, learning to classify curve points as elliptic, parabolic, or hyperbolic based on the nature of the quadratic approximation. Discover how this strategy generalizes to investigate algebraic surfaces in three-dimensional space, opening the door to a more comprehensive differential study of algebraic curves.
Syllabus
Introduction
The ordinary calculus
Solving for u
Algebraic Approach
General curves
Special cases
Example
Tangent line
Tangent conic
Discriminant conic
Taught by
Insights into Mathematics
Related Courses
Intro to PhysicsUdacity College Readiness Math MOOC
University of Wisconsin–La Crosse via Desire2Learn Matemáticas y Movimiento
Tecnológico de Monterrey via Coursera Mathe-MOOC: Mathematisch denken!
iversity Introduzione alla matematica per l'università: Pre-Calculus
Politecnico di Milano via Polimi OPEN KNOWLEDGE