# Real Analysis

- Institution: IIT Madras
- Department: Mathematics
- Teacher: Prof. S.H. Kulkarni
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106053)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106053)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Introduction](https://invisiblenetwork.ai/learn/nptel/111106053/5380d433a7db) (Video)
2. [Functions and Relations](https://invisiblenetwork.ai/learn/nptel/111106053/4f86fd816725) (Video)
3. [Finite and Infinite Sets](https://invisiblenetwork.ai/learn/nptel/111106053/cac7e063be88) (Video)
4. [Countable Sets](https://invisiblenetwork.ai/learn/nptel/111106053/1964e713be3e) (Video)
5. [Uncountable Sets, Cardinal Numbers](https://invisiblenetwork.ai/learn/nptel/111106053/44638e40eb0f) (Video)
6. [Real Number System](https://invisiblenetwork.ai/learn/nptel/111106053/9ca4f476f260) (Video)
7. [LUB Axiom](https://invisiblenetwork.ai/learn/nptel/111106053/bb6bdcdf15e9) (Video)
8. [Sequences of Real Numbers](https://invisiblenetwork.ai/learn/nptel/111106053/492340747cc0) (Video)
9. [Sequences of Real Numbers - continued](https://invisiblenetwork.ai/learn/nptel/111106053/25a3d5e049a0) (Video)
10. [Sequences of Real Numbers - continued...](https://invisiblenetwork.ai/learn/nptel/111106053/5e960056c293) (Video)
11. [Infinite Series of Real Numbers](https://invisiblenetwork.ai/learn/nptel/111106053/e614a042bc65) (Video)
12. [Series of nonnegative Real Numbers](https://invisiblenetwork.ai/learn/nptel/111106053/7e8071d354dd) (Video)
13. [Conditional Convergence](https://invisiblenetwork.ai/learn/nptel/111106053/c1593d83f326) (Video)
14. [Metric Spaces: Definition and Examples](https://invisiblenetwork.ai/learn/nptel/111106053/c031a5622f5e) (Video)
15. [Metric Spaces: Examples and Elementary Concepts](https://invisiblenetwork.ai/learn/nptel/111106053/8ef8854f3637) (Video)
16. [Balls and Spheres](https://invisiblenetwork.ai/learn/nptel/111106053/7b2dc8bf3c1c) (Video)
17. [Open Sets](https://invisiblenetwork.ai/learn/nptel/111106053/5f844bc5617a) (Video)
18. [Closure Points, Limit Points and isolated Points](https://invisiblenetwork.ai/learn/nptel/111106053/b963c945817a) (Video)
19. [Closed sets](https://invisiblenetwork.ai/learn/nptel/111106053/4bcba45d0cbb) (Video)
20. [Sequences in Metric Spaces](https://invisiblenetwork.ai/learn/nptel/111106053/3f8e4f53f0c6) (Video)
21. [Completeness](https://invisiblenetwork.ai/learn/nptel/111106053/1bc528b9467e) (Video)
22. [Baire Category Theorem](https://invisiblenetwork.ai/learn/nptel/111106053/b16d1c34b345) (Video)
23. [Limit and Continuity of a Function defined on a Metric space](https://invisiblenetwork.ai/learn/nptel/111106053/a882c1df5b0d) (Video)
24. [Continuous Functions on a Metric Space](https://invisiblenetwork.ai/learn/nptel/111106053/f5e6eec1b71f) (Video)
25. [Uniform Continuity](https://invisiblenetwork.ai/learn/nptel/111106053/96318ab8b759) (Video)
26. [Connectedness](https://invisiblenetwork.ai/learn/nptel/111106053/5804f9092dd5) (Video)
27. [Connected Sets](https://invisiblenetwork.ai/learn/nptel/111106053/a25b51e6472a) (Video)
28. [Compactness](https://invisiblenetwork.ai/learn/nptel/111106053/43c5ccb8ff6d) (Video)
29. [Compactness - Continued](https://invisiblenetwork.ai/learn/nptel/111106053/ed5cc3765f73) (Video)
30. [Characterizations of Compact Sets](https://invisiblenetwork.ai/learn/nptel/111106053/63f5c034fdbf) (Video)
31. [Continuous Functions on Compact Sets](https://invisiblenetwork.ai/learn/nptel/111106053/f9c2c2517ca9) (Video)
32. [Types of Discontinuity](https://invisiblenetwork.ai/learn/nptel/111106053/3aa904d3e6f2) (Video)
33. [Differentiation](https://invisiblenetwork.ai/learn/nptel/111106053/b06e4848e074) (Video)
34. [Mean Value Theorems](https://invisiblenetwork.ai/learn/nptel/111106053/d83729af26b7) (Video)
35. [Mean Value Theorems - Continued](https://invisiblenetwork.ai/learn/nptel/111106053/45f18e743bbb) (Video)
36. [Taylor's Theorem](https://invisiblenetwork.ai/learn/nptel/111106053/b8e8ecb0253a) (Video)
37. [Differentiation of Vector Valued Functions](https://invisiblenetwork.ai/learn/nptel/111106053/995bdcbfa108) (Video)
38. [Integration](https://invisiblenetwork.ai/learn/nptel/111106053/d86b58a4e896) (Video)
39. [Integrability](https://invisiblenetwork.ai/learn/nptel/111106053/56ac0355435f) (Video)
40. [Integrable Functions](https://invisiblenetwork.ai/learn/nptel/111106053/173850ee09db) (Video)
41. [Integrable Functions - Continued](https://invisiblenetwork.ai/learn/nptel/111106053/dbac44dd1636) (Video)
42. [Integration as a Limit of Sum](https://invisiblenetwork.ai/learn/nptel/111106053/ca5dac0269ab) (Video)
43. [Integration and Differentiation](https://invisiblenetwork.ai/learn/nptel/111106053/9b4d151a7cc1) (Video)
44. [Integration of Vector Valued Functions](https://invisiblenetwork.ai/learn/nptel/111106053/2d208fc61fad) (Video)
45. [More Theorems on Integrals](https://invisiblenetwork.ai/learn/nptel/111106053/6d9b888d6963) (Video)
46. [Sequences and Series of Functions](https://invisiblenetwork.ai/learn/nptel/111106053/98e7b642e6f5) (Video)
47. [Uniform Convergence](https://invisiblenetwork.ai/learn/nptel/111106053/ab410244f93c) (Video)
48. [Uniform Convergence and Integration](https://invisiblenetwork.ai/learn/nptel/111106053/9d144519a602) (Video)
49. [Uniform Convergence and Differentiation](https://invisiblenetwork.ai/learn/nptel/111106053/cbaf917712dd) (Video)
50. [Construction of Everywhere Continuous Nowhere Differentiable Function](https://invisiblenetwork.ai/learn/nptel/111106053/6013066d183e) (Video)
51. [Approximation of a Continuous Function by Polynomials: Weierstrass Theorem](https://invisiblenetwork.ai/learn/nptel/111106053/4e70764815b6) (Video)
52. [Equicontinuous family of Functions: Arzela - Ascoli Theorem](https://invisiblenetwork.ai/learn/nptel/111106053/3f8ecbd0a334) (Video)