Lectures related to Differentiability and Tangent Planes

Tangent to Graph of a Function

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

Functions and Coordinate Changes

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

Differentiability and Tangent Lines

Explores differentiability, tangent lines, and graph interpretation.

Differentiable Functions: Definitions and Interpretation

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

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Differentiability and Derivatives

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

Differentiability of Functions in Two Variables

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

Differentiability and Tangent Planes in Multivariable Functions

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Derivatives: Definition and Properties

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

Derivability and Continuity

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

Differential Forms on Manifolds

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

Functions of Class C^p

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

Differentiability and Composition

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

Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Derivatives and Functions: Definitions and Interpretations

Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.

Differentiability of Functions: Properties and Methods

Explores the properties and methods of differentiable functions, including strong recurrence and demonstration techniques.

Functions and Derivatives

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

Differentiability and Matrices

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

Theorem of Generalized Mean Value: Study of Functions

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