# Basic Real Analysis

- Institution: IIT Bombay
- Department: Mathematics
- Teacher: Prof. I. K. Rana
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111101134)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111101134)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 1 : Real Numbers and Sequences - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/489e47ba6763) (Video)
2. [Lecture 2 : Real Numbers and Sequences - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/3a5237f7a7ad) (Video)
3. [Lecture 3 : Real Numbers and Sequences - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/05b7dfa227f4) (Video)
4. [Lecture 4 : Convergence of Sequences - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/55cd45296315) (Video)
5. [Lecture 5 : Convergence of Sequences - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/3b6d7b775356) (Video)
6. [Lecture 6 : Convergence of Sequences - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/8636a85b477a) (Video)
7. [Lecture 7 : The LUB Property and Consequences - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/3901bb9ea18f) (Video)
8. [Lecture 8 : The LUB Property and Consequences - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/b950ea752797) (Video)
9. [Lecture 9 : The LUB Property and Consequences - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/83871d1f9156) (Video)
10. [Lecture 10 : Topology of Real Numbers: Closed Sets - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/8ba49ce971fa) (Video)
11. [Lecture 11 : Topology of Real Numbers: Closed Sets - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/d4756603da67) (Video)
12. [Lecture 12 : Topology of Real Numbers: Closed Sets - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/e7023d2133d3) (Video)
13. [Lecture 13 : Topology of Real Numbers: Limit Points, Interior Points, Open Sets and Compact Sets - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/c1af74719d48) (Video)
14. [Lecture 14 : Topology of Real Numbers: Limit Points, Interior Points, Open Sets and Compact Sets - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/8e0c21a0c22d) (Video)
15. [Lecture 15 : Topology of Real Numbers: Limit Points, Interior Points, Open Sets and Compact Sets - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/1dbb1f2f9550) (Video)
16. [Lecture 16 : Topology of Real Numbers: Compact Sets and Connected Sets - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/72eae66c0c95) (Video)
17. [Lecture 17 : Topology of Real Numbers: Compact Sets and Connected Sets - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/5bad11ff00cf) (Video)
18. [Lecture 18 : Topology of Real Numbers: Compact Sets and Connected Sets - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/c3802c2648b0) (Video)
19. [Lecture 19 : Topology of Real Numbers: Connected Sets; Limits and Continuity - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/7891f9fdc6ff) (Video)
20. [Lecture 20 : Topology of Real Numbers: Connected Sets; Limits and Continuity - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/072d91e20a9d) (Video)
21. [Lecture 21 : Topology of Real Numbers: Connected Sets; Limits and Continuity - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/03cf2dd38b13) (Video)
22. [Lecture 22 : Continuity and Uniform continuity - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/40e0191e7adc) (Video)
23. [Lecture 23 : Continuity and Uniform continuity - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/4a4f7e30e644) (Video)
24. [Lecture 24 : Continuity and Uniform continuity - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/52019a8a5897) (Video)
25. [Lecture 25 : Uniform continuity and connected sets - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/ef7f19640598) (Video)
26. [Lecture 26 : Uniform continuity and connected sets - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/a49b7205e216) (Video)
27. [Lecture 27 : Uniform continuity and connected sets - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/b336c3adfe48) (Video)
28. [Lecture 28 : Connected sets and continuity - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/b68f25ebd991) (Video)
29. [Lecture 29 : Connected sets and continuity - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/62e92087aae9) (Video)
30. [Lecture 30 : Connected sets and continuity - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/83b0627e7bbc) (Video)
31. [Lecture 31 : Differentiability - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/68617ee3c46c) (Video)
32. [Lecture 32 : Differentiability - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/0c33dfb88f07) (Video)
33. [Lecture 33 : Differentiability - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/dd9f3eeed101) (Video)
34. [Lecture 34 : Differentiability - Part IV](https://invisiblenetwork.ai/learn/nptel/111101134/04d7c2368402) (Video)
35. [Lecture 35 : Differentiability - Part V](https://invisiblenetwork.ai/learn/nptel/111101134/a929d9b5aa8a) (Video)
36. [Lecture 36 : Differentiability - Part VI](https://invisiblenetwork.ai/learn/nptel/111101134/d74799c85e15) (Video)
37. [Lecture 37 : Riemann Integration - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/dca82f992269) (Video)
38. [Lecture 38 : Riemann Integration - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/b0dd33203821) (Video)
39. [Lecture 39 : Riemann Integration - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/941171aef4dc) (Video)
40. [Lecture 40 : Riemann Integration - Part IV](https://invisiblenetwork.ai/learn/nptel/111101134/80fdc2c1f5ed) (Video)
41. [Lecture 41 : Riemann Integration - Part V](https://invisiblenetwork.ai/learn/nptel/111101134/e119460be7b8) (Video)
42. [Lecture 42 : Riemann Integration - Part VI](https://invisiblenetwork.ai/learn/nptel/111101134/e718633ab7c1) (Video)
43. [Lecture 43 : Riemann Sum and Riemann Integrals - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/07a310627e97) (Video)
44. [Lecture 44 : Riemann Sum and Riemann Integrals - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/063aad3e8b31) (Video)
45. [Lecture 45 : Riemann Sum and Riemann Integrals - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/33251b1978bd) (Video)
46. [Lecture 46 : Optimization in several variables - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/193e1cd348c6) (Video)
47. [Lecture 47 : Optimization in several variables - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/bb68050c2ec7) (Video)
48. [Lecture 48 : Optimization in several variables - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/5a64b9792434) (Video)
49. [Lecture 49 : Integration in several variables - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/ab022ffed1ee) (Video)
50. [Lecture 50 : Integration in several variables - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/e56412e17464) (Video)
51. [Lecture 51 : Integration in several variables - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/024d553c1cd5) (Video)
52. [Lecture 52 : Change of variables - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/785d5e54e346) (Video)
53. [Lecture 53 : Change of variables - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/5bb545284a6f) (Video)
54. [Lecture 54 : Change of variables - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/a732bcd1a727) (Video)
55. [Lecture 55 : Change of variables - Part IV](https://invisiblenetwork.ai/learn/nptel/111101134/30bc2a9ed318) (Video)
56. [Lecture 56 : Metric Spaces - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/9f9356d209d1) (Video)
57. [Lecture 57 : Metric Spaces - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/6b2c0b8aecce) (Video)
58. [Lecture 58 : Metric Spaces - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/62739855d064) (Video)
59. [Lecture 59 : L^p Metrics - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/45d8968d3591) (Video)
60. [Lecture 60 : L^p Metrics - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/4b422e15bd00) (Video)
61. [Lecture 61 : L^p Metrics - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/baefb1df149b) (Video)
62. [Lecture 62 : Pointwise and Uniform convergence - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/adb3497288f9) (Video)
63. [Lecture 63 : Pointwise and Uniform convergence - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/ff5141d437e4) (Video)
64. [Lecture 64 : Pointwise and Uniform convergence - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/57fbf5e774a9) (Video)
65. [Lecture 65 : Pointwise and Uniform convergence - Part IV](https://invisiblenetwork.ai/learn/nptel/111101134/dbee9b7fb952) (Video)
66. [Lecture 66 : Series of Numbers - Part I](https://invisiblenetwork.ai/learn/nptel/111101134/39beb0ea5bc9) (Video)
67. [Lecture 67 : Series of Numbers - Part II](https://invisiblenetwork.ai/learn/nptel/111101134/bf565d99e0a7) (Video)
68. [Lecture 68 : Series of Numbers - Part III](https://invisiblenetwork.ai/learn/nptel/111101134/336141450597) (Video)
69. [Lecture 69 : Alternating Series and Power Series](https://invisiblenetwork.ai/learn/nptel/111101134/884e66eacae4) (Video)
70. [Live Session 23-02-2021](https://invisiblenetwork.ai/learn/nptel/111101134/489e47ba6763-2) (Video)
71. [Live Session 26-03-2021](https://invisiblenetwork.ai/learn/nptel/111101134/3a5237f7a7ad-2) (Video)
72. [Live Session 06-03-2020](https://invisiblenetwork.ai/learn/nptel/111101134/05b7dfa227f4-2) (Video)