Lectures related to Implicit Functions: Lagrange Multipliers

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

Differentiable Functions: Definitions and Properties

Covers the definition and properties of differentiable functions, focusing on differentiability, limits, continuity, and partial derivatives.

Derivability of Reciprocal Function

Covers the derivative of the reciprocal function and its properties.

Functions and Coordinate Changes

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

Differentiability and Tangent Planes in Multivariable Functions

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

Vector spaces and norms

Covers vector spaces, differentiable functions, scalar product, and norms in depth.

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Implicit functions theorem

Explores the implicit functions theorem, showcasing examples of implicit differentiation and function definition.

Implicit Differentiation

Explores implicit differentiation and the Implicit Function Theorem for finding unique local functions.

Derivable Functions: Partial Derivatives and Jacobian Matrix

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

Differentiable Functions: Definitions and Interpretation

Covers the definitions of differentiable and derivable functions and their geometric interpretation.

Taylor Series: Derivatives and Integrals

Explores Taylor series expansions for derivatives and integrals, including practical applications.

Algebraic Operations on Limited Developments

Explores algebraic operations on limited developments and their consequences on differentiable functions, illustrated through examples.

Implicit Functions: Theory and Examples

Explores the theory of implicit functions, their properties, and illustrative examples.

Definition of Differentiable Functions

Covers the definition of differentiable functions and explores the representation of the remainder in derivatives.

Differential Functions and Tangent Plan

Covers differentiable functions, derivatives, and tangent planes in mathematics.

Derivation Term by Term

Introduces the study of functions defined by power series and emphasizes the importance of separately considering boundary points.

Differentiable Functions in R²

Explores differentiable functions in R², including vector fields and coordinate transformations.

Chain Rules

Explores the extension of the chain rule to higher dimensions and compositions of functions.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.