Optimization: Extrema of Functions

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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.

Local Extrema of Functions

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.