Lectures related to Implicit Functions Theorem

Nature of Extremum Points

Explores the nature of extremum points in functions of class e² around the point (0,0), emphasizing the importance of understanding their behavior in the vicinity.

Implicit Function Theorem: Local Extrema

Explores the Implicit Function Theorem, local extrema, supporting hyperplanes, and higher-order derivatives.

Local Extremum Conditions: n=2 and n=3

Explains local extremum conditions for n=2 and n=3, critical points, and stationary points.

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Analyse II: Stationary Points Classification

Covers the classification of stationary points in functions of two variables using the Hessian matrix.

Stationary Points: Necessary Conditions and Examples

Covers necessary conditions for extrema and provides illustrative examples.

Extrema of Functions

Covers the concept of extrema of functions, including local and global maxima and minima.

Stationary Points Analysis

Covers the analysis of stationary points in functions, focusing on optimization methods.

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Extreme Points and Function Extrema

Explores finding extrema of functions over compact sets and edge parametrization.