# A Basic Course in Real Analysis

- Institution: IIT Kharagpur
- Department: Mathematics
- Teacher: Prof. P.D. Srivastava
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105069)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105069)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Rational Numbers and Rational Cuts](https://invisiblenetwork.ai/learn/nptel/111105069/c139635dc816) (Video)
2. [Irrational numbers, Dedekind's Theorem](https://invisiblenetwork.ai/learn/nptel/111105069/02f4fdfbb76a) (Video)
3. [Continuum and Exercises](https://invisiblenetwork.ai/learn/nptel/111105069/afa263032e25) (Video)
4. [Continuum and Exercises (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105069/1a10897eeab4) (Video)
5. [Cantor's Theory of Irrational Numbers](https://invisiblenetwork.ai/learn/nptel/111105069/a44eed89cc0f) (Video)
6. [Cantor's Theory of Irrational Numbers (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105069/7be7a0ad40f3) (Video)
7. [Equivalence of Dedekind and Cantor's Theory](https://invisiblenetwork.ai/learn/nptel/111105069/2183bd39d975) (Video)
8. [Finite, Infinite, Countable and Uncountable Sets of Real Numbers](https://invisiblenetwork.ai/learn/nptel/111105069/e49caa970e82) (Video)
9. [Types of Sets with Examples, Metric Space](https://invisiblenetwork.ai/learn/nptel/111105069/fe639e704603) (Video)
10. [Various properties of open set, closure of a set](https://invisiblenetwork.ai/learn/nptel/111105069/e9cc27b6d197) (Video)
11. [Ordered set, Least upper bound, greatest lower bound of a set](https://invisiblenetwork.ai/learn/nptel/111105069/d0eb16fda08e) (Video)
12. [Compact Sets and its properties](https://invisiblenetwork.ai/learn/nptel/111105069/a809f28fc830) (Video)
13. [Weiersstrass Theorem, Heine Borel Theorem, Connected set](https://invisiblenetwork.ai/learn/nptel/111105069/5aa575f25f51) (Video)
14. [Tutorial - II](https://invisiblenetwork.ai/learn/nptel/111105069/47a798631218) (Video)
15. [Concept of limit of a sequence](https://invisiblenetwork.ai/learn/nptel/111105069/c5ce3f5eba07) (Video)
16. [Some Important limits, Ratio tests for sequences of Real Numbers](https://invisiblenetwork.ai/learn/nptel/111105069/8fb7de40c591) (Video)
17. [Cauchy theorems on limit of sequences with examples](https://invisiblenetwork.ai/learn/nptel/111105069/e7e7004af85d) (Video)
18. [Fundamental theorems on limits, Bolzano-Weiersstrass Theorem](https://invisiblenetwork.ai/learn/nptel/111105069/e022efa94534) (Video)
19. [Theorems on Convergent and divergent sequences](https://invisiblenetwork.ai/learn/nptel/111105069/30010794c2a7) (Video)
20. [Cauchy sequence and its properties](https://invisiblenetwork.ai/learn/nptel/111105069/633a20219856) (Video)
21. [Infinite series of real numbers](https://invisiblenetwork.ai/learn/nptel/111105069/a28447351878) (Video)
22. [Comparison tests for series, Absolutely convergent and Conditional convergent series](https://invisiblenetwork.ai/learn/nptel/111105069/f2bd673e2079) (Video)
23. [Tests for absolutely convergent series](https://invisiblenetwork.ai/learn/nptel/111105069/5c727c47ae0a) (Video)
24. [Raabe's test, limit of functions, Cluster point](https://invisiblenetwork.ai/learn/nptel/111105069/46e76944f5b2) (Video)
25. [Some results on limit of functions](https://invisiblenetwork.ai/learn/nptel/111105069/430bd5a42095) (Video)
26. [Limit Theorems for functions](https://invisiblenetwork.ai/learn/nptel/111105069/4602cbe3d89c) (Video)
27. [Extension of limit concept (one sided limits)](https://invisiblenetwork.ai/learn/nptel/111105069/49dae2bce5fc) (Video)
28. [Continuity of Functions](https://invisiblenetwork.ai/learn/nptel/111105069/0a56eacf7c41) (Video)
29. [Properties of Continuous Functions](https://invisiblenetwork.ai/learn/nptel/111105069/9a77bff45030) (Video)
30. [Boundedness Theorem, Max-Min Theorem and Bolzano's theorem](https://invisiblenetwork.ai/learn/nptel/111105069/126a1cdd2ded) (Video)
31. [Uniform Continuity and Absolute Continuity](https://invisiblenetwork.ai/learn/nptel/111105069/0d0c30e93927) (Video)
32. [Types of Discontinuities, Continuity and Compactness](https://invisiblenetwork.ai/learn/nptel/111105069/929c13e9123b) (Video)
33. [Continuity and Compactness (Contd.), Connectedness](https://invisiblenetwork.ai/learn/nptel/111105069/1aab01eeb529) (Video)
34. [Differentiability of real valued function, Mean Value Theorem](https://invisiblenetwork.ai/learn/nptel/111105069/ccae990476dd) (Video)
35. [Mean Value Theorem (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105069/a0fd6a36c565) (Video)
36. [Application of MVT , Darboux Theorem, L Hospital Rule](https://invisiblenetwork.ai/learn/nptel/111105069/0d7d2c400abf) (Video)
37. [L'Hospital Rule and Taylor's Theorem](https://invisiblenetwork.ai/learn/nptel/111105069/361dc68b6372) (Video)
38. [Tutorial - III](https://invisiblenetwork.ai/learn/nptel/111105069/7df598d4a935) (Video)
39. [Riemann/Riemann Stieltjes Integral](https://invisiblenetwork.ai/learn/nptel/111105069/64dd1f8ebe82) (Video)
40. [Existence of Reimann Stieltjes Integral](https://invisiblenetwork.ai/learn/nptel/111105069/11d17a8c7ec2) (Video)
41. [Properties of Reimann Stieltjes Integral](https://invisiblenetwork.ai/learn/nptel/111105069/cc1749d34faa) (Video)
42. [Properties of Reimann Stieltjes Integral (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105069/c693689a153f) (Video)
43. [Definite and Indefinite Integral](https://invisiblenetwork.ai/learn/nptel/111105069/79cdce803218) (Video)
44. [Fundamental Theorems of Integral Calculus](https://invisiblenetwork.ai/learn/nptel/111105069/643825b0f486) (Video)
45. [Improper Integrals](https://invisiblenetwork.ai/learn/nptel/111105069/dc25cbc5ffd7) (Video)
46. [Convergence Test for Improper Integrals](https://invisiblenetwork.ai/learn/nptel/111105069/5f5a59de3bdc) (Video)