Lectures related to Continuous Functions: Definitions and Continuity Criteria

Limits and Continuity: Analysis 1

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

Continuous Functions on Closed Interval

Explores continuous functions on closed intervals, emphasizing the importance of understanding definitions for continuity.

Continuous Functions: Theory and Applications

Explores continuous functions, Cauchy criterion, and function extension by continuity.

Darboux Theorem: Advanced Analysis I

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

Continuous Functions: Definitions and Criteria

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

Analysis II: Abstract Integration

Explores the extension of functions and the conditions for continuity.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Limit and Function Composition

Covers the concept of limit at a point and function composition in the context of continuous functions.

The Intermediate Value Theorem

Explains the Intermediate Value Theorem for continuous functions on closed intervals.

Continuous Functions: Integrability and Examples

Explores continuous functions and integrability through practical examples.

Rolle's Theorem: Applications and Examples

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

Taylor Expansion and Convex Functions

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

Advanced Analysis II: Integrals on Continuous Functions

Explores integrals on continuous functions and their properties, including uniform continuity.

Continuous Functions: Definition

Explains the definition of continuous functions and isolated points.

Integral Techniques: Integration by Parts

Explores the integration by parts technique through examples, showcasing its step-by-step application to functions like cos(x) and sin(x.

Fourier Series: Convergence and Dirichlet Theorem

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

Advanced Analysis: Differential Equations Overview

Covers the fundamentals of differential equations, their properties, and methods for finding solutions through various examples.

Intermediate value theorem

Explores uniform continuity, Lipschitz functions, and the intermediate value theorem with examples and proofs.

Finite Element Interpolation: Clément Operator

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

Uniform Continuity: Proof and Theorem

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