Lectures related to Mean Value Theorem (Mittelwertsatz)

Covers O-Notation, local extrema, and critical points in functions.

Discusses the Extreme Values Theorem for continuous functions on closed intervals.

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

Explores the integral change of variable formula and its applications in calculus.

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

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

Explores derivatives, O-Notation, extrema, and algorithm complexity in Analysis 1.

Covers the integration of limit expansions and continuous functions by pieces.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explains how a function reaches its maximum and minimum values.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

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

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

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

Explores applications of differential calculus, including theorems, convexity, extrema, and inflection points.

Discusses optimization techniques, focusing on local and global extrema in functions.

Covers fundamental topics in calculus of variations, including minimizers and the Euler-Lagrange equation.

Explores Lipschitz continuity in gradient descent optimization and its implications on function optimization.

Explores optimal transport in heat equations and metric spaces.

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.