Local Extremums of Functions in Multivariable Calculus

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Local Extremum Conditions: n=2 and n=3

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

Taylor Approximation: Extrema in Multivariable Functions

Covers Taylor approximation and extrema in multivariable functions with examples.

Analyse II: Stationary Points Classification

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

Local Inversion Theorem

Explores the Local Inversion Theorem and extremum points in functions.

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.

Euler-Lagrange Equations

Covers the derivation and application of Euler-Lagrange equations for optimization problems in mathematical analysis.

Stationary Points: Necessary Conditions and Examples

Covers necessary conditions for extrema and provides illustrative examples.

Optimization of Functions: Maximum and Minimum

Covers the optimization of functions, focusing on finding the maximum and minimum values over a given domain.

General Case

Explores determining local maximums, minimums, and inflection points of functions.

Stationary Points Analysis

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