Lectures related to Limits and Continuity: Concepts and Examples

Covers a recap of Analysis I and delves into the concept of open sets in R^n, emphasizing their importance in mathematical analysis.

Explains continuous functions, criteria for continuity, and continuity concepts at points and intervals.

Covers the convergence of sequences in multivariable analysis, including definitions, properties, and examples in higher dimensions.

Explores the change of variables theorem in the plane, emphasizing boundedness and continuity of functions.

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Introduces measurable sets, functions, and the Cantor set properties, including ternary development of numbers.

Explores the construction of the Lebesgue function on the Cantor set and its unique properties.

Explores the extension of functions and the conditions for continuity.