Lectures related to Local Extremum Conditions: n=2 and n=3

Stationary Points and Saddle Points

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

Local Extremum Points Determination

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

Local Extremums of Functions in Multivariable Calculus

Revisits local and absolute extremums of multivariable functions, emphasizing critical points and their classification.

Optimization Techniques: Local and Global Extrema

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

Extrema of Functions

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

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.

Untitled

Applications of Differential Calculus

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

Directional Derivatives

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

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.

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.

Local Inversion Theorem

Explores the Local Inversion Theorem and extremum points in functions.

Analyse II: Stationary Points Classification

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

Derivatives and Reciprocal Functions

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

Nature of Extremum Points

Covers the nature of extremum points and their classification as stationary or saddle points.