Local-existence-unicity-theorem

Related lectures (31)

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Presents a detailed proof of the uniqueness theorem for functions f and g.

Explores locally Lipschitz functions, discussing differentiability, unique solutions, and function reduction.

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

Delves into advanced analysis topics, emphasizing continuity, limits, and uniform continuity.

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

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

Covers the description of problem solutions and the concept of compactness and uniform continuity.

Discusses the Cauchy problem for ODEs with initial conditions and the importance of homeomorphism and Lipschitz continuity.

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Explores second-order linear scalar homogeneous equations in advanced analysis II.