Taylor's Formula: Developments and Extrema

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Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Explores partial derivatives, Taylor formula, examples, and extrema of functions.

Presents the solution to finding the second-order Taylor polynomial of a function.

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

Covers the concepts of limits and continuity, focusing on the demonstration of various theorems.

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

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

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Introduces Taylor series, covering their basics and applications in approximating functions and calculating limits.