Local-existence-unicity-theorem

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

Uniform Continuity: Proof and Theorem

Covers the concept of uniform continuity and a theorem on continuous functions.

Advanced Analysis I: Continuous Functions on Compact Sets

Explores the necessity of uniform continuity for continuous functions on compact sets.

Existence of Solutions for Poisson-Dirichlet Problem

Covers the existence of solutions for the Poisson-Dirichlet problem, focusing on showing that certain conditions hold for locally bounded and Hölder continuous functions.

Advanced Analysis II: Hessians and Directional Derivatives

Explores Hessians, directional derivatives, and function continuity in advanced analysis.

Intermediate Value Theorem

Covers the Intermediate Value Theorem, uniform continuity, Lipschitz functions, and the properties of continuous functions.

Separation of Variables: Solving Differential Equations

Covers the method of separation of variables for solving differential equations, focusing on the construction and uniqueness of solutions.

Real Functions: Continuity Extension

Discusses extending a function uniformly and its continuity properties in real functions.

Limits and Continuity: Analysis 1

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Cantor-Heine Theorem

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.