Lectures related to Partial Derivatives: Gradient and Theorem of Mean Value

Partial Derivatives and Functions

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

Optimization Basics

Introduces optimization basics, covering logistic regression, derivatives, convex functions, gradient descent, and second-order methods.

Differentiability: Theorem and Mean Value Theorem

Explores differentiability, gradients, and the Mean Value Theorem in open sets.

Differential Functions: Derivability and Gradient

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

Differentiability of Functions of Several Variables

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

Derivatives and Tangent Planes

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

Differentiability: Theorem and Mean Value Theorem

Explores differentiability, gradients, and the Mean Value Theorem for functions.

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Recurrence Method: Generalization and Differential Calculus

Explores the fundamental principle of the recurrence method and differential calculus of functions of several variables.

Gradient and Taylor Formula

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

Partial Derivatives: Derivability

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

Limits and Derivatives in Multivariable Functions

Covers limits and derivatives in multivariable functions, focusing on continuity, partial derivatives, and the gradient.

Methods of Demonstrations: Recurrence and Differential Calculus

Covers methods of demonstrations and differential calculus of functions of several variables.

Partial Derivatives: Definitions and Applications

Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.

Partial Derivatives: Derivative of an Integral with Parameter-dependent Bounds

Covers the derivative of an integral with parameter-dependent bounds and the gradient.

Partial Derivatives and Gradient

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

Partial Derivatives and Functions

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Differentiability and Partial Derivatives

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

Derivatives and Continuity in Multivariable Functions

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

Differentiability Theorems

Explores differentiability theorems, including partial derivatives, existence of derivatives, and Schwartz's theorem reciprocals.