Lectures related to Local Extremums of Functions in Multivariable Calculus

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Optimization Techniques: Local and Global Extrema

Discusses optimization techniques, focusing on local and global extrema in functions.

Extrema of Functions in Several Variables

Explains extrema of functions in several variables, stationary points, saddle points, and the role of the Hessian matrix.

Applications of Differential Calculus

Explores applications of differential calculus, including theorems, convexity, extrema, and inflection points.

Local Extremum Points Determination

Focuses on determining local extremum points of functions through various examples.

Extrema of Functions

Covers the discussion of local extrema, concavity, convexity, and inflection points in functions.

Stationary Points and Saddle Points

Explores stationary points, saddle points, symmetric matrices, and orthogonal properties in optimization.

Directional Derivatives

Explores directional derivatives in two-variable functions and extremum points.

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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.