Lecture Description
This video lecture, part of the series Real Analysis with Prof. S.H. Kulkarni by Prof. , does not currently have a detailed description and video lecture title. If you have watched this lecture and know what it is about, particularly what Mathematics topics are discussed, please help us by commenting on this video with your suggested description and title. Many thanks from,
- The CosmoLearning Team
- The CosmoLearning Team
Course Index
- Introduction to Real Analysis
- Functions and Relations
- Finite and Infinite Sets
- Countable Sets
- Uncountable Sets, Cardinal Numbers
- Real Number System
- LUB Axiom
- Sequences of Real Numbers
- Sequences of Real Numbers - continued
- Sequences of Real Numbers - continued...
- Infinite Series of Real Numbers
- Series of nonnegative Real Numbers
- Conditional Convergence
- Metric Spaces: Definition and Examples
- Metric Spaces: Examples and Elementary Concepts
- Balls and Spheres
- Open Sets
- Closure Points, Limit Points and isolated Points
- Closed sets
- Sequences in Metric Spaces
- Completeness
- Baire Category Theorem
- Limit and Continuity of a Function defined on a Metric space
- Continuous Functions on a Metric Space
- Uniform Continuity
- Connectedness
- Connected Sets
- Compactness
- Compactness - Continued
- Characterizations of Compact Sets
- Continuous Functions on Compact Sets
- Types of Discontinuity
- Differentiation
- Mean Value Theorems
- Mean Value Theorems - Continued
- Taylor's Theorem
- Differentiation of Vector Valued Functions
- Integration
- Integrability
- Integrable Functions
- Integrable Functions - Continued
- Integration as a Limit of Sum
- Integration and Differentiation
- Integration of Vector Valued Functions
- More Theorems on Integrals
- Sequences and Series of Functions
- Uniform Convergence
- Uniform Convergence and Integration
- Uniform Convergence and Differentiation
- Construction of Everywhere Continuous Nowhere Differentiable Function
- Approximation of a Continuous Function by Polynomials: Weierstrass Theorem
- Equicontinuous family of Functions: Arzela - Ascoli Theorem
Course Description
Real number system and its order completeness, sequences and series of real numbers. Metric spaces: Basic concepts, continuous functions, completeness, contraction mapping theorem, connectedness, Intermediate Value Theorem, Compactness, Heine-Borel Theorem. Differentiation, Taylor's theorem, Riemann Integral, Improper integrals Sequences and series of functions, Uniform convergence, power series, Weierstrass approximation theorem, equicontinuity, Arzela-Ascoli theorem.
Comments
There are no comments.
Be the first to post one.
Posting Comment...