| Module Name | Download | Description | Download Size |
|---|---|---|---|
| Rational Numbers and Rational Cuts | Self Evaluation | Please see all the questions attached with the last module. | 25 |
| Convergence Test for Improper Integrals | Self Evaluation | This is questionnaire that covers all the modules and could be attempted after listening to the full course. | 66 |
| Sl.No | Chapter Name | English |
|---|---|---|
| 1 | Rational Numbers and Rational Cuts | Download Verified |
| 2 | Irrational numbers, Dedekind's Theorem | Download Verified |
| 3 | Continuum and Exercises | Download Verified |
| 4 | Continuum and Exercises (Contd.) | Download Verified |
| 5 | Cantor's Theory of Irrational Numbers | Download Verified |
| 6 | Cantor's Theory of Irrational Numbers (Contd.) | Download Verified |
| 7 | Equivalence of Dedekind and Cantor's Theory | Download Verified |
| 8 | Finite, Infinite, Countable and Uncountable Sets of Real Numbers | Download Verified |
| 9 | Types of Sets with Examples, Metric Space | Download Verified |
| 10 | Various properties of open set, closure of a set | Download Verified |
| 11 | Ordered set, Least upper bound, greatest lower bound of a set | Download Verified |
| 12 | Compact Sets and its properties | Download Verified |
| 13 | Weiersstrass Theorem, Heine Borel Theorem, Connected set | Download Verified |
| 14 | Tutorial - II | Download Verified |
| 15 | Concept of limit of a sequence | Download Verified |
| 16 | Some Important limits, Ratio tests for sequences of Real Numbers | Download Verified |
| 17 | Cauchy theorems on limit of sequences with examples | Download Verified |
| 18 | Fundamental theorems on limits, Bolzano-Weiersstrass Theorem | Download Verified |
| 19 | Theorems on Convergent and divergent sequences | Download Verified |
| 20 | Cauchy sequence and its properties | Download Verified |
| 21 | Infinite series of real numbers | Download Verified |
| 22 | Comparison tests for series, Absolutely convergent and Conditional convergent series | Download Verified |
| 23 | Tests for absolutely convergent series | Download Verified |
| 24 | Raabe's test, limit of functions, Cluster point | Download Verified |
| 25 | Some results on limit of functions | Download Verified |
| 26 | Limit Theorems for functions | Download Verified |
| 27 | Extension of limit concept (one sided limits) | Download Verified |
| 28 | Continuity of Functions | Download Verified |
| 29 | Properties of Continuous Functions | Download Verified |
| 30 | Boundedness Theorem, Max-Min Theorem and Bolzano's theorem | Download Verified |
| 31 | Uniform Continuity and Absolute Continuity | Download Verified |
| 32 | Types of Discontinuities, Continuity and Compactness | Download Verified |
| 33 | Continuity and Compactness (Contd.), Connectedness | Download Verified |
| 34 | Differentiability of real valued function, Mean Value Theorem | Download Verified |
| 35 | Mean Value Theorem (Contd.) | Download Verified |
| 36 | Application of MVT , Darboux Theorem, L Hospital Rule | Download Verified |
| 37 | L'Hospital Rule and Taylor's Theorem | Download Verified |
| 38 | Tutorial - III | Download Verified |
| 39 | Riemann/Riemann Stieltjes Integral | Download Verified |
| 40 | Existence of Reimann Stieltjes Integral | Download Verified |
| 41 | Properties of Reimann Stieltjes Integral | Download Verified |
| 42 | Properties of Reimann Stieltjes Integral (Contd.) | Download Verified |
| 43 | Definite and Indefinite Integral | Download Verified |
| 44 | Fundamental Theorems of Integral Calculus | Download Verified |
| 45 | Improper Integrals | Download Verified |
| 46 | Convergence Test for Improper Integrals | Download Verified |
| Sl.No | Language | Book link |
|---|---|---|
| 1 | English | Not Available |
| 2 | Bengali | Not Available |
| 3 | Gujarati | Not Available |
| 4 | Hindi | Not Available |
| 5 | Kannada | Not Available |
| 6 | Malayalam | Not Available |
| 7 | Marathi | Not Available |
| 8 | Tamil | Not Available |
| 9 | Telugu | Not Available |