Lectures related to Partial Derivatives: Extrema and Hessians

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.

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Convergence Criteria: Necessary Conditions

Explains necessary conditions for convergence in optimization problems.

Mathematical Methods for Materials Science: Integrals, Exact Differentials

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

Taylor's Formula: Developments and Extrema

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Directional Derivatives

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

Differentiability and Hessians

Explores functions of class C^p, Hessian matrices, and methods to verify differentiability at a point.

Derivatives and Convexity

Explores derivatives, local extrema, and convexity in functions, including Taylor's formula and function compositions.

Partial Derivatives and Matrix Hessians

Covers partial derivatives, Hessian matrices, and their importance for functions with multiple variables.

Derivatives and Tangent Planes

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Derivatives and Continuity in Mathematics

Covers derivatives, continuity, Rolle's Theorem, function examples, and extrema.