Lectures related to Derivative and Function Variation

Covers the Mean Value Theorem, l'Hopital rule, Taylor's approximation, and more.

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

Covers the theorem of finite increments in derivative functions.

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers continuous differentiability, the Bernoulli-l'Hôpital rule, and finding extrema using derivatives.

Covers the theory of finite differences and the mean value theorem.

Explores the connection between limit existence and function continuity, emphasizing derivative properties and function graphs.