Lectures related to Minimum and Maximum

Global Properties of Continuous Functions

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

Rolle's Theorem: Applications and Examples

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

Properties of Continuous Functions

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

Properties of Real Numbers

Explains the properties of subsets of real numbers, including Supremum, Infimum, intervals, open sets, and closed sets.

Limits and Continuity: Analysis 1

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

Derivability and Maximum Values

Covers the theorem of intermediate values and finding maximum and minimum values of functions on closed intervals.

The Intermediate Value Theorem

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

Extreme Values Theorem

Discusses the Extreme Values Theorem for continuous functions on closed intervals.

Infimum and Supremum of Subsets

Covers the concepts of infimum and supremum of subsets in real numbers.

Interval Analysis: Properties and Examples

Explores infimum, supremum, and absolute value concepts with examples and proofs.

Properties of Continuous Functions

Explores the continuity of elementary functions and the properties of continuous functions on closed intervals.

Differential Calculus: Theorem of Finite Increments

Explains how a function reaches its maximum and minimum values.

Surjectivity of Derivative Application

Covers the surjectivity of the derivative application for continuous functions on closed intervals.

Math-101(en) / Min/Max, Inf/Sup

Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.

Integration by Change of Variables

Covers integration by change of variables and the derivation in chain rule.

Real Numbers: Order and Completeness

Covers the properties of real numbers, focusing on the total order and completeness, including the Archimedean property and the concepts of supremum and infimum.

Fundamental Theorem of Calculus Example

Demonstrates the practical importance of the fundamental theorem of calculus through a detailed example.

Functions: Continuity and Derivability

Explores continuous and derivable functions on closed intervals.

Limits and Continuity

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

Bisection Method: Proposition and Demonstration

Covers the bisection method proposition and its demonstration for finding roots.