Lectures related to Implicit Functions: Unique Solutions and Class C Functions

Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Covers examples of direct and indirect proofs in mathematics.

Covers weak derivatives, their properties, and applications in functional analysis.

Covers the extension and periodicity of Fourier series and the interpretation of coefficients.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Explores optimal transport in heat equations and metric spaces.

Explores Fourier series coefficients, periodicity, and series relations.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.