Lectures related to Partial Derivatives: Functions and Definitions

Partial Derivatives and Functions

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

Functions of Class C^p

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

Partial Derivatives and Functions

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

Partial Derivatives: Definitions and Examples

Covers the concept of partial derivatives and their applications in mathematical analysis.

Derivatives and Continuity in Multivariable Functions

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

Limits and Derivatives in Multivariable Functions

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

Gradient and Taylor Formula

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

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.

Differentiability of Functions of Several Variables

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

Taylor Polynomial: Order 2

Presents the solution to finding the second-order Taylor polynomial of a function.

Analysis IV: Convolution and Partial Derivatives

Covers the properties of functions in Rn and the computation of partial derivatives by induction.

Partial Derivatives of Order 3

Covers the calculation of partial derivatives of order 3 and the concept of differentiability in functions.

Differentiability Theorems

Covers differentiability theorems and methods to check for differentiability in functions.

Differentiability and Tangent Planes in Multivariable Functions

Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.

Differentiability and Tangent Planes in Multivariable Functions

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Differentiability and Composition

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

Laplacian in Polar and Spherical Coordinates: Derivatives

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

Partial Derivatives and Gradient

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