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## Last updated:

September 23, 2023

## Duration:

Unlimited Duration

**FREE**

## This course includes:

Unlimited Duration

## Badge on Completion

## Certificate of completion

Unlimited Duration

### Description

A Basic Course in Real Analysis. Instructor: Prof. P.D. Srivastava, Department of Mathematics, IIT Kharagpur.

This is an introductory course in real analysis, covering topics: the Dedekind theory of irrational numbers; the Cantor theory of irrational numbers; bounded set and the open, closed and compact, etcetera; continuity of the function; differentiability; the Riemann integration and Riemann stieltjes integral; and the improper integral. (from **nptel.ac.in**)

### Course Curriculum

- Lecture 01 – Rational Numbers and Rational Cuts Unlimited
- Lecture 02 – Irrational Numbers, Dedekind’s Theorem Unlimited
- Lecture 03 – Continuum and Exercises Unlimited
- Lecture 04 – Continuum and Exercises (cont.) Unlimited
- Lecture 05 – Cantor’s Theory of Irrational Numbers Unlimited
- Lecture 06 – Cantor’s Theory of Irrational Numbers (cont.) Unlimited
- Lecture 07 – Equivalence of Dedekind and Cantor’s Theory Unlimited
- Lecture 08 – Finite, Infinite, Countable and Uncountable Sets of Real Numbers Unlimited
- Lecture 09 – Types of Sets with Examples, Metric Space Unlimited
- Lecture 10 – Various Properties of Open Set, Closure of a Set Unlimited
- Lecture 11 – Ordered Set, Least Upper Bound, Greatest Lower Bound of a Set Unlimited
- Lecture 12 – Compact Sets and its Properties Unlimited
- Lecture 13 – Weierstrass Theorem, Heine Borel Theorem, Connected Set Unlimited
- Lecture 14 – Tutorial II Unlimited
- Lecture 15 – Concept of Limit of a Sequence Unlimited
- Lecture 16 – Some Important Limits, Ratio Tests for Sequences of Real Numbers Unlimited
- Lecture 17 – Cauchy Theorems on Limit of Sequences with Examples Unlimited
- Lecture 18 – Fundamental Theorem on Limits, Bolzano-Weierstrass Theorem Unlimited
- Lecture 19 – Theorems on Convergent and Divergent Sequences Unlimited
- Lecture 20 – Cauchy Sequence and its Properties Unlimited
- Lecture 21 – Infinite Series of Real Numbers Unlimited
- Lecture 22 – Comparison Tests for Series, Absolutely Convergent and Conditional Convergent Series Unlimited
- Lecture 23 – Tests for Absolutely Convergent Series Unlimited
- Lecture 24 – Raabe’s Test, Limit on Functions, Cluster Point Unlimited
- Lecture 25 – Some Results on Limit of Functions Unlimited
- Lecture 26 – Limit Theorems for Functions Unlimited
- Lecture 27 – Extension of Limit Concept (One Sided Limits) Unlimited
- Lecture 28 – Continuity of Functions Unlimited
- Lecture 29 – Properties of Continuous Functions Unlimited
- Lecture 30 – Boundedness Theorem, Max-Min Theorem, and Bolzano’s Theorem Unlimited
- Lecture 31 – Uniform Continuity and Absolute Continuity Unlimited
- Lecture 32 – Types of Discontinuities, Continuity and Compactness Unlimited
- Lecture 33 – Continuity and Compactness (cont.), Connectedness Unlimited
- Lecture 34 – Differentiability of Real Valued Function, Mean Value Theorem Unlimited
- Lecture 35 – Mean Value Theorem (cont.) Unlimited
- Lecture 36 – Application of Mean Value Theorem, Darboux Theorem, L’Hospital’s Rule Unlimited
- Lecture 37 – L’Hospital’s Rule and Taylor’s Theorem Unlimited
- Lecture 38 – Tutorial III Unlimited
- Lecture 39 – Riemann/Riemann-Stieltjes Integral Unlimited
- Lecture 40 – Existence of Riemann-Stieltjes Integral Unlimited
- Lecture 41 – Properties of Riemann-Stieltjes Integral Unlimited
- Lecture 42 – Properties of Riemann-Stieltjes Integral (cont.) Unlimited
- Lecture 43 – Definite and Indefinite Integral Unlimited
- Lecture 44 – Fundamental Theorems of Integral Calculus Unlimited
- Lecture 45 – Improper Integrals Unlimited
- Lecture 46 – Convergence Test for Improper Integrals Unlimited

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