Lectures related to Extremes of Functions: Desirability and Decorability

Extrema of Functions in Several Variables

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

Limits Recapitulation

Covers the definition of limits and continuous functions with examples and exercises.

Continuity: Examples and Definitions

Covers the concept of continuity, providing examples and definitions of continuous functions.

Optimization: Local Extrema

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

Functions and Periodicity

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

Local Extremum Points Determination

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

Differentiable Functions and Lagrange Multipliers

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

Real Functions: Definitions and Properties

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

Optimization of Functions: Maximum and Minimum

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

Solving Mathematical Equations

Covers the resolution of mathematical equations and series convergence.

Generalized Fine Increments: Applications and Examples

Discusses generalized fine increments, function evaluation, theorems, and derivative applications.

Convex Functions

Covers the properties and operations of convex functions.

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Functions on R^n: Limits and Partial Differentiation

Delves into functions on R^n, covering limits and partial differentiation.

Extrema of Functions in Several Variables

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

Limits and Continuity

Covers limits, continuity, and the intermediate value theorem in functions.

Optimization: Lagrange Multipliers

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

Definitions and Notations

Covers the definitions and notations related to functions.

Level Sets of Functions

Covers the concept of level sets of functions and their graphical representation.