Concept

Semi-differentiability

Related lectures (32)

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

Differentiable Functions: Definitions and Interpretation

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

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

Linear Approximation and Derivative Parametric

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

Derivability and Limits in Analysis I

Explores derivability, limits computation, and properties of functions in Analysis I.

Taylor Series: Expansion and Properties

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

Differentiability Theorems

Explores differentiability theorems, including partial derivatives, existence of derivatives, and Schwartz's theorem reciprocals.

Osculating Planes and Parameterized Curves

Covers the concept of osculating planes and parameterized curves, discussing the speed of points and linear independence.

Continuous Functions: Derivability and Global Properties

Covers continuous functions, derivability, and global properties in differential calculus.

Counter-example: Continuity and Differentiability MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Explores a counter-example of a function that is continuous and differentiable on an interval, challenging students to understand limits geometrically.

Polynomial, Exponential, Logarithmic Functions

Covers polynomial, exponential, and logarithmic functions, differentiability, compositions, and limits.

Differentiability Theorems

Covers differentiability theorems and methods to check for differentiability in functions.

Differential Calculus: Definition and Derivability Log in to Mediaspace to watch this video

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

Differentiable Functions: Definitions and Properties Log in to Mediaspace to watch this video

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

Computing Derivatives: Derivatives and Algebraic Operations Log in to Mediaspace to watch this video

Covers the computation of derivatives and the properties of differentiable functions.

Differentiability in Analysis Log in to Mediaspace to watch this video

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

Differentiability and Tangent Lines Log in to Mediaspace to watch this video

Explores differentiability, tangent lines, and graph interpretation.

Differentiability of Functions in Two Variables Log in to Mediaspace to watch this video

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

Differentiability and Partial Derivatives Log in to Mediaspace to watch this video

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

Differentiability and Composition Log in to Mediaspace to watch this video

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