Lectures related to Derivatives and Continuity

Differentiability and Partial Derivatives

Explores differentiability in two variables and the chain rule for compositions.

Chain Rules

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

Differentiability and Composition

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

Differentiability and Derivatives

Covers differentiability, derivatives, composite functions, linear approximation, and partial derivatives.

Derivability and Chain Rule

Covers the demonstration of the chain rule and the theorem of Rolle.

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Derivatives Rules: Notation, Extrema

Covers the rules of derivatives, O-notation, and extrema in the context of theorem 6.5 and examples.

Derivative Chain Rule

Covers the derivative of the composition of two functions and the chain rule theorem.

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.

Linear Applications and Matrix Derivatives

Explores linear applications, derivatives, Jacobian matrix, composition of functions, and matrix products.

Demonstration of Rolle's Theorem

Demonstrates how to use a specific function to prove Rolle's Theorem.

Differentiability in Analysis

Explores differentiability in analysis, discussing conditions for functions to be differentiable and continuous.

Generalized Finite Increments

Explores generalized finite increments, derivatives, reciprocals, and Bernoulli-L'Hospital rule.

Derivatives and Local Extrema

Explores derivatives, local extrema, and function variation in mathematical analysis.

Taylor Series: Expansion and Properties

Explores Taylor series expansion, derivatives, uniqueness, and applications in function approximation.

Derivative of an Integral with Parameter

Covers deriving integrals with parameters and their derivatives, including special cases and proofs.

Functions and Derivatives

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

Derivatives: Definition and Properties

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

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.