Lectures related to Continuous Functions: Theory and Applications

Continuous Functions: Definitions and Criteria

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

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

Functions Composition: Continuity & Elements

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

Limits and Continuity: Analysis 1

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

Advanced Analysis: Differential Equations Overview

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

Separation of Variables: Solving Differential Equations

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

Rolle's Theorem: Applications and Examples

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

Continuous Functions: Definitions and Continuity Criteria

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

Intermediate Value Theorem

Covers the Intermediate Value Theorem and its applications in finding solutions of equations and understanding the properties of continuous functions.

Intermediate Value Theorem

Explores the Intermediate Value Theorem, continuous functions, and the verification of their continuity in various examples.

Advanced Analysis: Differential Equations Overview

Provides an overview of differential equations, their properties, and methods for finding solutions through various examples and graphical representations.

Analysis II: Abstract Integration

Explores the extension of functions and the conditions for continuity.

Advanced Analysis II: Solving Separable Differential Equations

Covers the theory and methods for solving separable differential equations, focusing on existence, uniqueness, and the construction of solutions through integration.

Fourier Series: Convergence and Dirichlet Theorem

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

Functions Extension and Taylor Expansion

Covers functions extension and Taylor expansion, exploring mathematical concepts in depth.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Cauchy Problem: Existence and Uniqueness of Solutions

Covers the Cauchy problem, focusing on the existence and uniqueness of solutions to differential equations.

Advanced Analysis II: Differential Equations and Timers

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

Intermediate value theorem

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

Semi-groups of Contractions

Explores semi-groups of contractions, discussing uniqueness theorems, maximum principles, and the infinitesimal generator.