Modulus of continuity

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Related lectures (31)

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Martingales and Brownian Motion

Explores the concept of martingales and their relation to Brownian motion through symmetric simple random walks and discusses the potential positive outcomes from the current crisis.

Local Lipschitz Functions

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

Projected Gradient Descent: Quadratic Penalty

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

Continuous Functions and Continuity Extension

Covers the concept of continuous functions and their extension to the closure of the domain.

Multiple Integration: Fubini Theorem

Explores multiple integration in R², focusing on double integrals over closed rectangles and the Fubini theorem.

Partial Derivatives: Part 1

Explores partial derivatives, continuity of functions, mean value theorem, and uniform continuity.

Optimization Methods

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

Limits and Continuity: Analysis 1

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

Cauchy Problem: Initial Conditions

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

Continuous Functions: Definitions and Criteria

Covers the definition and criteria for continuous functions and explores the intermediate value theorem.