Lectures related to Partial Differentiation

Explores the linear properties of gradients and the importance of understanding scalar products and Jacobian matrices.

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

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

Partial Derivatives and Matrix Hessians

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

Gradient Existence in R2

Explores the existence of the gradient in R2 and its implications on derivability and directional derivatives.

Second Order Approximations: The Hessian Matrix

Explores second order approximations for twice differentiable functions using the Hessian matrix.

Differential Calculus: Applications and Reminders

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Partial Derivatives: Matrices and Local Extrema

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

Mechanics: Introduction and Calculus

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Differentiability Analysis

Explores differentiability, partial derivatives, Schwarz's theorem, and function continuity in mathematical analysis.

Partial Derivatives and Functions

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

Derivatives and Differential Equations

Covers trigonometric functions, derivatives, differential equations, and vector properties.

Metric Tensor: Definition

Explores the definition and properties of the metric tensor, enabling control of geometric quantities and lengths.

Differentiability and Partial Derivatives

Explores differentiability in two variables and the chain rule for compositions.

Eigenvalues and Optimization: Numerical Analysis Techniques

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

Derivatives of Functions: Differentiability and Matrices

Explores differentiability, matrices, and composite functions through examples and mathematical notations.

Differentiability and Hessians

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

Derivatives and Tangent Planes

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

Partial Derivatives: Derivability

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.