Lectures related to Derivability and Composition

Differentiability and Composition

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

Derivability and Composition

Covers derivability, linear applications, composition of functions, and the gradient vector.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Derivability and Continuity

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

Differentiability and Derivatives

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

Continuity and Limits

Covers continuity, limits, and different approaches to approaching points in various coordinate systems.

Differentiability and Tangent Lines

Explores differentiability, tangent lines, and graph interpretation.

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Limits of Functions: Calculus Methods

Explores the concept of limits of functions of several variables and methods for calculation, including criteria based on convergent sequences and the 'two gendarmes' theorem.

Functions and Coordinate Changes

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

Differentiability and Matrices

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

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

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.

Functions: Differentials, Taylor Expansions, Integrals

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

Functions: Limits, Continuity, Differentiability

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Gradient and Taylor Formula

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

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Differentiability of Functions in Two Variables

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

Laplacian in Polar and Spherical Coordinates: Derivatives

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

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.