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Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Stationary Points and Saddle Points

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

Differentiable Functions and Lagrange Multipliers

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

Local Extremum Points Determination

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

Extrema of Functions in Several Variables

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

Global Extrema of Functions in R^2

Explores global extrema of functions in R^2, discussing methods to find maximum and minimum points.

Local Extremums of Functions in Multivariable Calculus

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

Local Extremum Conditions: n=2 and n=3

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

Extrema of Functions

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

Nature of Extremum Points

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

Directional Derivatives

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

Optimization Techniques: Local and Global Extrema

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

Stationary Points in Analytical Functions

Explores stationary points in analytical functions and their significance in mathematical analysis.

Stationary Points: Necessary Conditions and Examples

Covers necessary conditions for extrema and provides illustrative examples.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

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Euler-Lagrange Equations

Covers the derivation and application of Euler-Lagrange equations for optimization problems in mathematical analysis.

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.

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.