Partial Derivatives: Extrema and Hessians

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Partial Derivatives: Taylor Formula

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

Partial Derivatives: Matrices and Local Extrema

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

Partial Derivatives and Differential Equations

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Optimization Techniques: Local and Global Extrema

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

Supporting Hyperplanes

Illustrates finding supporting hyperplanes for surfaces and determining stationary point nature.

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Implicit Function Theorem

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

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Derivatives and Reciprocal Functions

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

Gradient and Taylor Formula

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