Lectures related to Second Order Approximations: The Hessian Matrix

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

Explores simple examples of partial differentiation, demonstrating how to calculate partial derivatives and gradients in various scenarios.

Partial Derivatives: Matrices and Local Extrema

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

Partial Derivatives and Functions

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

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Derivable Functions: Partial Derivatives and Jacobian Matrix

Covers derivable functions, partial derivatives, Jacobian matrix, and rule of composition.

Differentiability and Hessians

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

Partial Differentiation

Explores the process of partial differentiation through various examples in two dimensions, emphasizing the importance of treating each variable separately.

Objective function, Differentiability, The second order

Explores the role of first and second derivatives in function curvature and convexity.

Partial Derivatives and Gradient

Covers partial derivatives, gradient, and second partial derivatives with their applications.

Functions of Class C^p

Explores functions of class C^p, emphasizing continuity and differentiability properties.

Derivatives and Tangent Planes

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

Eigenvalues and Optimization: Numerical Analysis Techniques

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

Partial Derivatives: Generalization and Order 2

Explains partial derivatives, generalization, and second order derivatives with examples and mathematical notations.

Differentiability and Composition

Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Differential Functions: Derivability and Gradient

Explores differentiability in functions and the role of gradients in directional derivatives.

Differentiability of Functions in Two Variables

Covers differentiability of functions in two variables and the conditions for a function to be differentiable.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Gradient and Taylor Formula

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