Lectures related to Optimization: Extrema of Functions

Optimization Techniques: Local and Global Extrema

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

Optimization of Functions: Maximum and Minimum

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

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

Limits of Multivariable Functions: Techniques and Theorems

Discusses limits of multivariable functions, focusing on definitions, examples, and techniques for calculating limits effectively.

Compact Sets and Extreme Values

Explores compact sets, extreme values, and function theorems on bounded sets.

Maximum and Minimum of Functions

Explores limits, minimum and maximum values of functions, and continuity criteria in a compact set.

Optimization Methods: Lagrange Multipliers

Covers advanced optimization methods using Lagrange multipliers to find extrema of functions subject to constraints.

Minimization of functions

Explores techniques for minimizing functions and finding critical points.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

Morse Theory: Critical Points and Non-Degeneracy

Covers Morse theory, focusing on critical points and non-degeneracy.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Construction of Measures: Separation and Partition

Covers the construction of measures in RN, focusing on separation and partition of compact sets.

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Taylor's Formula: Developments and Extrema

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

Limits of Functions in Several Variables

Explores limits of functions in several real variables, including the two gendarmes theorem and the minimum and maximum theorem on compact sets.

Mathematics: Functions and Series

Explores functions, series, and critical points in mathematics, including maximum, minimum, supremum, and infimum concepts.

Convex Functions

Covers the properties and operations of convex functions.

Limits and Continuity: Analysis 1

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Differentiable Functions and Lagrange Multipliers

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

Bernoulli's Hospital Rule

Covers the statement of the Bernoulli's Hospital Rule and its application.