Continuous Functions and Continuity Extension

Related lectures (30)

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Explores the continuity of elementary functions and the properties of continuous functions on closed intervals.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explores finite element interpolation using the Clément operator for non-continuous functions and discusses error estimation.

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

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

Covers the concept of uniform convergence of continuous functions towards a limit function.

Explores convergence and approximation in L² space, emphasizing the limitations of continuous functions and the importance of closed sets.

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

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

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