Partial Differentiation

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Related lectures (28)

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Linear Properties of Gradients

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.

Partial Differentiation

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.