Advanced Analysis 2: Continuity and Limits

Related lectures (31)

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Covers optimization methods without constraints, including gradient and line search in the quadratic case.

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

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

Explores the Bolzano-Bastra-Sterl theorem and uniform continuity in sequences.

Covers Newton's method conditions and convergence, extension to multiple variables, and linear models.

Explores Dirichlet series convergence properties and absolute convergence conditions, with examples and applications.

Covers projected gradient descent with a focus on quadratic penalty and optimality conditions.

Explores continuity and limits of real functions, including examples and the concept of uniform continuity.

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

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