Lectures related to Classes and Functions

Differentiable Functions and Lagrange Multipliers

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

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Optimization Techniques: Local and Global Extrema

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

Local Inversion Theorem

Explores the Local Inversion Theorem and extremum points in functions.

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Implicit Functions Theorem

Explores the Implicit Functions Theorem and properties of hypersurfaces and matrices.

Local Extremum Points Determination

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

Implicit Curves: Analysis & Regular Points

Covers implicit curves, regular and critical points, convexity, concavity, and inflection points.

Derivatives and Reciprocal Functions

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

Taylor Approximation: Extrema in Multivariable Functions

Covers Taylor approximation and extrema in multivariable functions with examples.

Extrema and Implicit Functions

Explores conditions for local extrema in two and three variables, along with implicit functions and finding absolute minima and maxima.

Application of Taylor's approximation formula

Covers the application of Taylor's formula, including composition of functions and detecting local extrema.

Local Extremums of Functions in Multivariable Calculus

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

Implicit Functions: Extrema and Lagrange Multipliers

Explores extrema under constraints using Lagrange multipliers for optimization problems.

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.

Extrema of Functions

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

Directional Derivatives

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

Optimization of Functions: Maximum and Minimum

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

Extrema of Functions in Several Variables

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

Local Extremum Conditions: n=2 and n=3

Explains local extremum conditions for n=2 and n=3, critical points, and stationary points.