Functions of LR: Differentiability

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Derivable Functions: Partial Derivatives and Jacobian Matrix

Covers derivable functions, partial derivatives, Jacobian matrix, and rule of composition.

Functions with Multiple Variables

Covers functions with values in R^m, discussing limits, partial derivatives, and differentiability.

Functions of Class C^p

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

Differentiability of Functions in Two Variables

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

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 and Coordinate Changes

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

Differentiability Analysis

Explores differentiability, partial derivatives, Schwarz's theorem, and function continuity in mathematical analysis.

Derivatives: Definition and Properties

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Derivability and Composition

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

Directional Derivatives

Explores directional derivatives, their calculation, examples, and cases of lack of continuity.