Taylor Approximation: Extrema in Multivariable Functions

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Extrema of Functions in Several Variables

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

Directional Derivatives

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

Advanced analysis II

Delves into eigenvectors, eigenvalues, extrema conditions, and saddle points in functions.

Optimization Techniques: Local and Global Extrema

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

Partial Derivatives: Matrices and Local Extrema

Covers hessian matrices, positive definite matrices, and local extrema of functions.

Local Extremums of Functions in Multivariable Calculus

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

Implicit Function Theorem

Explores the Implicit Function Theorem, supporting hyperplanes, local extrema, and higher-order derivatives, concluding with the classification of stationary points.

Integration: Taylor Approximation & Convex Functions

Covers Taylor approximation, convex functions, and integrable properties.

Mathematical Methods for Materials Science: Integrals, Exact Differentials

Explores limits, derivation rules, integrals, and exact differentials for practical applications.

Local Extrema of Multivariable Functions

Revisits local and absolute extrema of multivariable functions, discussing their properties and identification conditions.