Lectures related to Gradient and Taylor Formula

Laplacian in Polar and Spherical Coordinates: Derivatives

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

Limits and Derivatives in Multivariable Functions

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

Taylor Polynomial: Order 2

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

Partial Derivatives: Taylor Formula

Explores partial derivatives, Taylor formula, examples, and extrema of functions.

Taylor's Formula: Developments and Extrema

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Partial Derivatives and Functions

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

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Differentiability and Composition

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

Functions of Class C^p

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

Partial Derivatives: Definitions and Examples

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

Functions and Derivatives

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Differentiability of Functions in Two Variables

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

Differential Functions: Derivability and Gradient

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

Taylor Polynomial in Two Variables

Covers the Taylor polynomial in two variables and the concept of extrema in functions of several variables.

Derivatives and Continuity in Multivariable Functions

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

Differentiability of Functions of Several Variables

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

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Taylor's Formula in Two Variables

Explores Taylor's formula in two variables, emphasizing its application and importance for functions of a single variable.