Lectures related to Interval Analysis: Properties and Examples

The Intermediate Value Theorem

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

Supremum Theorem

Explores the Supremum Theorem, its properties, proofs, and exercises.

Introduction to Real Numbers and Their Properties

Introduces real numbers, their properties, and their significance in analysis.

Properties of Real Numbers

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

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

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

Limits and Continuity: Analysis 1

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

Q as Subset of R

Explains the concept of Q as a subset of R and their properties.

Rolle's Theorem: Applications and Examples

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

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.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Minimum and Maximum

Introduces the concepts of minimum and maximum values for continuous functions.

Derivability on an Interval: Rolle's Theorem

Covers derivability on an interval, including Rolle's Theorem and practical applications in function analysis.

Properties of Real Numbers: Bounds, Density, Absolute Value

Covers the properties of real numbers, including bounds, density, and absolute value.

Vectors and Norms: Introduction to Linear Algebra Concepts

Covers essential concepts of vectors, norms, and their properties in linear algebra.

Real Analysis: Basics and Sequences

Introduces real analysis basics, including functions, sequences, limits, and set properties in R.

Analysis I: Lecture 4 Repeated Hour 1

Explains how to find supremum and infimum of a set with examples.

Infimum and Supremum of Subsets

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

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Maximum and Minimum Values: Theorems and Continuity

Explores the theorems on maximum and minimum values of functions and their relation to continuity.