Lectures related to Extrema of Functions in Several Variables

Extrema of Functions in Several Variables

Explores the conditions for local extrema of functions in several variables, including critical points and the Hessian matrix.

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.

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Local Extremum Points Determination

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

Optimization Techniques: Local and Global Extrema

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

Differentiable Functions and Lagrange Multipliers

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

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.

Gradient and Taylor Formula

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Taylor Polynomial in Two Variables

Covers the Taylor polynomial in two variables and the concept of extrema in functions of several variables.

Taylor's Formula: Developments and Extrema

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Optimization: Lagrange Multipliers

Covers the method of Lagrange multipliers to find extrema subject to constraints.

Local Extrema of Functions

Discusses local extrema of functions in two variables around the point (0,0).

Extrema of Functions

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

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Optimization: Local Extrema

Explains how to find local extrema of functions using derivatives and critical points.

Characterization of Sequences

Explores the convergence criteria and the importance of continuity in sequences near a point xo.

Local Extremums of Functions

Explains local and absolute extremums of functions and the classification of critical points.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Partial Derivatives: Taylor Formula

Explores partial derivatives, Taylor formula, examples, and extrema of functions.