Lectures related to Continuous functions on a closed bounded interval

Limits and Continuity: Analysis 1

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

Limit of Functions: Convergence and Boundedness

Explores limits, convergence, and boundedness of functions and sequences.

Limit of a Sequence

Explores the limit of a sequence and its convergence properties, including boundedness and monotonicity.

Advanced Analysis 2: Continuity and Limits

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

Limits and Continuity

Explores limits, continuity, and elementary functions' properties, emphasizing the importance of understanding continuous functions.

Uniform Continuity: Limits, Series 8

Covers uniform continuity, one-sided limits, function behavior, and continuity conditions, with multiple-choice questions for practice.

Advanced Analysis I: Continuous Functions on Compact Sets

Explores the necessity of uniform continuity for continuous functions on compact sets.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Continuous Functions: Criteria and Equivalences

Explores criteria for continuity, convergence of sequences, and equivalence conditions for continuous functions.

Darboux Theorem: Advanced Analysis I

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

Convergence and Closed Sets

Explores convergence of sequences in closed sets and the importance of understanding convergence in relation to closedness.

Limits of Recursive Sequences

Explores limits of recursive sequences, convergence, boundedness, and algebraic operations related to limits at infinity.

Intermediate Value Theorem

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

Geometric Series: Convergence and Limit

Explores the convergence and limit of geometric series, demonstrating mathematical properties and applications.

Real Functions: Continuity Extension

Discusses extending a function uniformly and its continuity properties in real functions.

Fourier Series: Understanding Periodicity and Coefficients

Explores t-periodic functions in Fourier series, discussing intervals, propositions, and variable changes for coefficient calculation and series convergence.

Bolzano-Bastra-Sterl: Applications and Uniform Continuity

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

Definition of Limit

Explains the concept of approaching a point to define the limit of a function.

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Sequence Convergence: Definitions and Properties

Covers definitions and properties of sequence convergence, including limits, uniqueness, and the two gendarmes theorem.