# Real Analysis I

- Institution: IIT Palakkad
- Department: Mathematics
- Teacher: Prof. Jaikrishnan J
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106142)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106142)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [1.1 WEEK 1 INTRODUCTION](https://invisiblenetwork.ai/learn/nptel/111106142/5042b028c4f1) (Video)
2. [1.2 Why study Real Analysis](https://invisiblenetwork.ai/learn/nptel/111106142/ce7aef1fd21f) (Video)
3. [1.3 Square root of 2](https://invisiblenetwork.ai/learn/nptel/111106142/a35c95ab8245) (Video)
4. [1.4 Wason's selection task](https://invisiblenetwork.ai/learn/nptel/111106142/439b114dbfd6) (Video)
5. [1.5 Zeno's Paradox](https://invisiblenetwork.ai/learn/nptel/111106142/93e22bb2ffdd) (Video)
6. [2.1 Basic set theory](https://invisiblenetwork.ai/learn/nptel/111106142/64d7c25307f1) (Video)
7. [2.2 Basic logic](https://invisiblenetwork.ai/learn/nptel/111106142/2bbeb6744720) (Video)
8. [2.3 Quantifiers](https://invisiblenetwork.ai/learn/nptel/111106142/21627c4d9b1a) (Video)
9. [2.4 Proofs](https://invisiblenetwork.ai/learn/nptel/111106142/24334b8226e0) (Video)
10. [2.5 Functions and relations](https://invisiblenetwork.ai/learn/nptel/111106142/c5d5005939fb) (Video)
11. [3.1 Axioms of Set Theory](https://invisiblenetwork.ai/learn/nptel/111106142/dece7ff34ecf) (Video)
12. [3.2 Equivalence relations](https://invisiblenetwork.ai/learn/nptel/111106142/38e607f04449) (Video)
13. [3.3 What are the rationals](https://invisiblenetwork.ai/learn/nptel/111106142/f7d3edf70ddc) (Video)
14. [3.4 Cardinality](https://invisiblenetwork.ai/learn/nptel/111106142/869b1e3775af) (Video)
15. [WEEK 2 INTRODUCTION](https://invisiblenetwork.ai/learn/nptel/111106142/0f4bd44e70ac) (Video)
16. [4.1 Field axioms](https://invisiblenetwork.ai/learn/nptel/111106142/108b7e78158b) (Video)
17. [4.2 Order axioms](https://invisiblenetwork.ai/learn/nptel/111106142/fb8b69b71354) (Video)
18. [4.3 Absolute value](https://invisiblenetwork.ai/learn/nptel/111106142/2831bf3eccc6) (Video)
19. [5.1 The completeness axiom](https://invisiblenetwork.ai/learn/nptel/111106142/95270f38b8d2) (Video)
20. [5.2 Nested intervals property](https://invisiblenetwork.ai/learn/nptel/111106142/796f0434a58c) (Video)
21. [6.1 NIP+AP⇒ Completeness](https://invisiblenetwork.ai/learn/nptel/111106142/1a566fd0d563) (Video)
22. [6.2 Existence of square roots](https://invisiblenetwork.ai/learn/nptel/111106142/034915041994) (Video)
23. [6.3 Uncountability of the real numbers](https://invisiblenetwork.ai/learn/nptel/111106142/4dc3426c91f6) (Video)
24. [6.4 Density of rationals and irrationals](https://invisiblenetwork.ai/learn/nptel/111106142/a8a9e4aa4bcb) (Video)
25. [WEEK 3 INTRODUCTION](https://invisiblenetwork.ai/learn/nptel/111106142/97fee9c7c92d) (Video)
26. [7.1 Motivation for infinite sums](https://invisiblenetwork.ai/learn/nptel/111106142/abb34b27d0da) (Video)
27. [7.2 Definition of sequence and examples](https://invisiblenetwork.ai/learn/nptel/111106142/c6ccf5c090dd) (Video)
28. [7.3 Definition of convergence](https://invisiblenetwork.ai/learn/nptel/111106142/b5eca328d7e0) (Video)
29. [7.4 Uniqueness of limits](https://invisiblenetwork.ai/learn/nptel/111106142/5813803f1f03) (Video)
30. [7.5 Achilles and the tortoise](https://invisiblenetwork.ai/learn/nptel/111106142/869a6b8babe0) (Video)
31. [8.1 Deep dive into the definition of convergence](https://invisiblenetwork.ai/learn/nptel/111106142/0d61633f5f72) (Video)
32. [8.2 A descriptive language for convergence](https://invisiblenetwork.ai/learn/nptel/111106142/9605062171c1) (Video)
33. [8.3 Limit laws](https://invisiblenetwork.ai/learn/nptel/111106142/e99a64579138) (Video)
34. [9.1 Subsequences](https://invisiblenetwork.ai/learn/nptel/111106142/e45d868a6fe2) (Video)
35. [9.2 Examples of convergent and divergent sequences](https://invisiblenetwork.ai/learn/nptel/111106142/1d0c4dd31877) (Video)
36. [9.3 Some special sequences-CORRECT](https://invisiblenetwork.ai/learn/nptel/111106142/f5c96a1a5aea) (Video)
37. [10.1 Monotone sequences](https://invisiblenetwork.ai/learn/nptel/111106142/361b90876dac) (Video)
38. [10.2 Bolzano-Weierstrass theorem](https://invisiblenetwork.ai/learn/nptel/111106142/7a5c2e5d6e06) (Video)
39. [10.3 The Cauchy Criterion](https://invisiblenetwork.ai/learn/nptel/111106142/ccd73eb51c7f) (Video)
40. [10.4 MCT implies completeness](https://invisiblenetwork.ai/learn/nptel/111106142/9f739a2bc178) (Video)
41. [11.1 Definition and examples of infinite series](https://invisiblenetwork.ai/learn/nptel/111106142/58280c3fa57e) (Video)
42. [11.2 Cauchy tests-Corrected](https://invisiblenetwork.ai/learn/nptel/111106142/40e7ea2add9b) (Video)
43. [11.3 Tests for convergence](https://invisiblenetwork.ai/learn/nptel/111106142/6c539ffba122) (Video)
44. [11.4 Erdos_s proof on divergence of reciprocals of primes](https://invisiblenetwork.ai/learn/nptel/111106142/814da7a5538f) (Video)
45. [11.5 Resolving Zeno_s paradox](https://invisiblenetwork.ai/learn/nptel/111106142/a4621a81e4e5) (Video)
46. [12.1 Absolute and conditional convergence](https://invisiblenetwork.ai/learn/nptel/111106142/94d9195fd6bc) (Video)
47. [12.2 Absolute convergence continued](https://invisiblenetwork.ai/learn/nptel/111106142/e8ed08eba0da) (Video)
48. [12.3 The number e](https://invisiblenetwork.ai/learn/nptel/111106142/2ffd536fd36e) (Video)
49. [12.4 Grouping terms of an infinite series](https://invisiblenetwork.ai/learn/nptel/111106142/b35259e016be) (Video)
50. [12.5 The Cauchy product](https://invisiblenetwork.ai/learn/nptel/111106142/fbd244df2efd) (Video)
51. [WEEK 5 - INTRODUCTION](https://invisiblenetwork.ai/learn/nptel/111106142/90db8fe8add5) (Video)
52. [13.1 The role of topology in real analysis](https://invisiblenetwork.ai/learn/nptel/111106142/748ee94456c9) (Video)
53. [13.2 Open and closed sets](https://invisiblenetwork.ai/learn/nptel/111106142/3ad759dbfc3f) (Video)
54. [13.3 Basic properties of adherent and limit points](https://invisiblenetwork.ai/learn/nptel/111106142/387530f000d1) (Video)
55. [13.4 Basic properties of open and closed sets](https://invisiblenetwork.ai/learn/nptel/111106142/11c7174f01ad) (Video)
56. [14.1 Definition of continuity](https://invisiblenetwork.ai/learn/nptel/111106142/0607d28280c3) (Video)
57. [14.2 Deep dive into epsilon-delta](https://invisiblenetwork.ai/learn/nptel/111106142/30351af09dde) (Video)
58. [14.3 Negating continuity](https://invisiblenetwork.ai/learn/nptel/111106142/c096bdaf31c0) (Video)
59. [15.1 The functions x and x2](https://invisiblenetwork.ai/learn/nptel/111106142/ab50eb912b79) (Video)
60. [15.2 Limit laws](https://invisiblenetwork.ai/learn/nptel/111106142/a1d80f58c1a1) (Video)
61. [15.3 Limit of sin x_x](https://invisiblenetwork.ai/learn/nptel/111106142/17137b945816) (Video)
62. [15.4 Relationship between limits and continuity](https://invisiblenetwork.ai/learn/nptel/111106142/627489790057) (Video)
63. [15.5 Global continuity and open sets](https://invisiblenetwork.ai/learn/nptel/111106142/194b86a04119) (Video)
64. [15.6 Continuity of square root](https://invisiblenetwork.ai/learn/nptel/111106142/b6b46a3bc7f9) (Video)
65. [15.7 Operations on continuous functions](https://invisiblenetwork.ai/learn/nptel/111106142/da504e568927) (Video)
66. [16.1 Language for limits](https://invisiblenetwork.ai/learn/nptel/111106142/1f8f07161988) (Video)
67. [16.2 Infinite limits](https://invisiblenetwork.ai/learn/nptel/111106142/cceb92e873d9) (Video)
68. [16.3 One sided limits](https://invisiblenetwork.ai/learn/nptel/111106142/9938b6f2bc1f) (Video)
69. [16.4 Limits of polynomials](https://invisiblenetwork.ai/learn/nptel/111106142/be7f2f3fe03f) (Video)
70. [17.1 Compactness](https://invisiblenetwork.ai/learn/nptel/111106142/94eb66b95bd0) (Video)
71. [17.2 The Heine-Borel theorem](https://invisiblenetwork.ai/learn/nptel/111106142/1f95c833c0b1) (Video)
72. [17.3 Open covers and compactness](https://invisiblenetwork.ai/learn/nptel/111106142/31b581f0eb48) (Video)
73. [17.4 Equivalent notions of compactness](https://invisiblenetwork.ai/learn/nptel/111106142/856fe124560d) (Video)
74. [18.1 The extreme value theorem](https://invisiblenetwork.ai/learn/nptel/111106142/7e56948edf5f) (Video)
75. [18.2 Uniform continuity](https://invisiblenetwork.ai/learn/nptel/111106142/562e8c6f52ea) (Video)
76. [19.1 Connectedness](https://invisiblenetwork.ai/learn/nptel/111106142/63e3e90a9774) (Video)
77. [19.2 Intermediate Value Theorem](https://invisiblenetwork.ai/learn/nptel/111106142/0534181076af) (Video)
78. [19.3 Darboux continuity and monotone functions](https://invisiblenetwork.ai/learn/nptel/111106142/80307452eb4b) (Video)
79. [20.1 Perfect sets and the Cantor set](https://invisiblenetwork.ai/learn/nptel/111106142/6ccb4e216766) (Video)
80. [20.2 The structure of open sets](https://invisiblenetwork.ai/learn/nptel/111106142/f875671d961e) (Video)
81. [20.3 The Baire Category theorem](https://invisiblenetwork.ai/learn/nptel/111106142/0869927541ab) (Video)
82. [21.1 Discontinuities](https://invisiblenetwork.ai/learn/nptel/111106142/04636ea36dee) (Video)
83. [21.2 Classification of discontinuities and monotone functions](https://invisiblenetwork.ai/learn/nptel/111106142/616191ad6954) (Video)
84. [21.3 Structure of set of discontinuities](https://invisiblenetwork.ai/learn/nptel/111106142/972550e4cdb6) (Video)
85. [WEEK 8 & 9 - INTRODUCTION](https://invisiblenetwork.ai/learn/nptel/111106142/72f810f2b9da) (Video)
86. [22.1 Definition and interpretation of the derivative](https://invisiblenetwork.ai/learn/nptel/111106142/eb3810b7662e) (Video)
87. [22.2 Basic properties of the derivative](https://invisiblenetwork.ai/learn/nptel/111106142/97f3f4d73099) (Video)
88. [22.3 Examples of differentiation](https://invisiblenetwork.ai/learn/nptel/111106142/e46ba4e011a1) (Video)
89. [23.1 Darboux_s theorem](https://invisiblenetwork.ai/learn/nptel/111106142/604dd513e05e) (Video)
90. [23.2 The mean value theorem](https://invisiblenetwork.ai/learn/nptel/111106142/9175a8e8baaa) (Video)
91. [23.3 Applications of the mean value theorem](https://invisiblenetwork.ai/learn/nptel/111106142/3b07d9c5f996) (Video)
92. [24.1 Taylor's theorem NEW](https://invisiblenetwork.ai/learn/nptel/111106142/5c9e5cccbbac) (Video)
93. [24.2 The ratio mean value theorem and L_Hospital_s rule](https://invisiblenetwork.ai/learn/nptel/111106142/3ba131addad2) (Video)
94. [25.1 Axiomatic characterisation of area and the Riemann integral](https://invisiblenetwork.ai/learn/nptel/111106142/e830c754b7bd) (Video)
95. [25.2 Proof of axiomatic characterization](https://invisiblenetwork.ai/learn/nptel/111106142/d3d8ae899259) (Video)
96. [26.1 The definition of the Riemann integral](https://invisiblenetwork.ai/learn/nptel/111106142/daa2484f783e) (Video)
97. [26.2 Criteria for Riemann integrability](https://invisiblenetwork.ai/learn/nptel/111106142/b2981219a704) (Video)
98. [26.3 Linearity of integral](https://invisiblenetwork.ai/learn/nptel/111106142/bdb86d133209) (Video)
99. [27.1 Sets of measure zero](https://invisiblenetwork.ai/learn/nptel/111106142/d5f36616b097) (Video)
100. [27.2 The Riemann-Lebesgue theorem](https://invisiblenetwork.ai/learn/nptel/111106142/ab94a016c865) (Video)
101. [27.3 Consequences of the Riemann-Lebesgue theorem](https://invisiblenetwork.ai/learn/nptel/111106142/89a6a6dd702e) (Video)
102. [WEEK 10 & 11 - INTRODUCTION](https://invisiblenetwork.ai/learn/nptel/111106142/c3cf9f8dfb98) (Video)
103. [28.1 The fundamental theorem of calculus](https://invisiblenetwork.ai/learn/nptel/111106142/199bf2553341) (Video)
104. [28.2 Taylor's theorem-Integral form of remainder](https://invisiblenetwork.ai/learn/nptel/111106142/56895629b055) (Video)
105. [28.3 Notation for Taylor polynomials](https://invisiblenetwork.ai/learn/nptel/111106142/8247d3923e47) (Video)
106. [28.4 Smooth functions and Taylor series](https://invisiblenetwork.ai/learn/nptel/111106142/b312e812a28c) (Video)
107. [29.1 Power series](https://invisiblenetwork.ai/learn/nptel/111106142/7c53cf866066) (Video)
108. [29.2 Definition of uniform convergence](https://invisiblenetwork.ai/learn/nptel/111106142/1232a49b3456) (Video)
109. [31.1 The exponential function](https://invisiblenetwork.ai/learn/nptel/111106142/42e1df39b009) (Video)
110. [31.2 The inverse function theorem](https://invisiblenetwork.ai/learn/nptel/111106142/01b200654193) (Video)
111. [31.3 The Logarithm](https://invisiblenetwork.ai/learn/nptel/111106142/a7cd0625573b) (Video)
112. [32.1 Trigonometric functions](https://invisiblenetwork.ai/learn/nptel/111106142/71e385ed486b) (Video)
113. [32.2 The number Pi](https://invisiblenetwork.ai/learn/nptel/111106142/010ac6ce3a94) (Video)
114. [32.3 The graphs of sin and cos](https://invisiblenetwork.ai/learn/nptel/111106142/8a52fd9e692a) (Video)
115. [33.1 The Basel problem](https://invisiblenetwork.ai/learn/nptel/111106142/92990b2134e7) (Video)
116. [34.1 Improper integrals](https://invisiblenetwork.ai/learn/nptel/111106142/cb749bd7dad5) (Video)
117. [34.2 The Integral test](https://invisiblenetwork.ai/learn/nptel/111106142/2a59fb48e09f) (Video)
118. [35.1 Weierstrass approximation theorem](https://invisiblenetwork.ai/learn/nptel/111106142/6f5530253f0a) (Video)
119. [35.2 Bernstein Polynomials](https://invisiblenetwork.ai/learn/nptel/111106142/8296ae956a76) (Video)
120. [35.3 Properties of Bernstein polynomials](https://invisiblenetwork.ai/learn/nptel/111106142/bf746bbd1a52) (Video)
121. [35.4 Proof of Weierstrass approximation theorem](https://invisiblenetwork.ai/learn/nptel/111106142/503b8a590981) (Video)
122. [Live Session 04-10-2020](https://invisiblenetwork.ai/learn/nptel/111106142/5042b028c4f1-2) (Video)
123. [Live Session 10-11-2020](https://invisiblenetwork.ai/learn/nptel/111106142/ce7aef1fd21f-2) (Video)