Lectures related to Properties of Continuous Functions: Maximum and Minimum

Covers the properties of continuous functions and explores inverse and injective functions with examples.

Continuous Functions: Definitions and Criteria

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

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

Vector Functions: Parameterization of Curves

Explains vector functions and the parameterization of curves with examples.

The Intermediate Value Theorem

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

Global Properties of Continuous Functions

Explores the global properties of continuous functions, including behavior, limits, and interval characteristics.

Max Local Exercise

Covers finding unique local maxima and functions oscillating infinitely.

Advanced Analysis II: Integrals on Continuous Functions

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

Derivability and Maximum Values

Covers the theorem of intermediate values and finding maximum and minimum values of 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.

Fundamental Theorem of Analysis: Integral (Part 2)

Explores the integral part of the Fundamental Theorem of Analysis with examples like y = cos(x).

Integral Change of Variable Formula

Explores the integral change of variable formula and its applications in calculus.

Intermediate Values Theorem

Explores the Intermediate Values Theorem for continuous functions on closed intervals.

Continuous Functions: Theory and Applications

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

Rolle's Theorem: Applications and Examples

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

Advanced Analysis: Differential Equations Overview

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

Functions of Class Ck: Terminology and Definitions

Covers the terminology and definitions of functions of class Ck on real number intervals.

Advanced Analysis I: March 14

Covers advanced topics in analysis, focusing on continuity and differentiability of functions.

Intermediate Value Theorem

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

Cauchy Problem: Existence and Uniqueness of Solutions

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