Lectures related to Functions and Derivatives

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

Covers differentiability, derivatives, continuity, and matrices in functions from R^n to R^m.

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

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

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

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Explores differentiability, matrices, Jacobian matrix, and derivatives calculation.

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

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

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

Explores derivability and continuity of functions, showcasing examples of functions with differentiability properties.

Explores the conditions for continuity and differentiability of functions on a closed interval.

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Explores lateral derivatives, limits of derivatives, and function differentiability at specific points.

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

Explores bijective functions, coordinate transformations, and graphical representations in two dimensions.

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

Covers the concept of functions being n+1 times differentiable and the Taylor formula.

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

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.