Existence and Uniqueness Theorem

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Distribution Interpolation Spaces

Covers the proof of UE Lipschitz constant and distribution interpolation spaces.

Gradient Descent: Lipschitz Continuity

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

Real Functions: Continuity Theorem

Covers the Continuity Theorem for functions dependent on a parameter, proving the continuity of a function g.

Intermediate Value Theorem

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

Advanced Analysis II: Solving Separable Differential Equations

Covers the theory and methods for solving separable differential equations, focusing on existence, uniqueness, and the construction of solutions through integration.

Distribution to Spaces: Interpolation and Continuity

Covers weak derivatives, interpolation spaces, and continuity in function spaces.

Intermediate value theorem

Explores uniform continuity, Lipschitz functions, and the intermediate value theorem with examples and proofs.

Cauchy-Lipschitz Theorem

Explores the Cauchy-Lipschitz theorem for ODE solutions and linear transformations.

Accelerated Algorithms for Monotone Inclusions

By Quoc Tran-Dinh explores accelerated algorithms for monotone inclusions, covering optimization models, challenges, and new algorithms.

Taylor Expansion and Convex Functions

Explores Taylor expansion, convex functions, and Lipschitz continuity with illustrative examples.