# Functional Analysis

- Institution: IMSc
- Department: Mathematics
- Teacher: Prof. Kesavan
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106147)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106147)
- 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: Normed Linear Spaces](https://invisiblenetwork.ai/learn/nptel/111106147/62a7acc82bb5) (Video)
2. [1.2: Examples of Normed Linear Spaces](https://invisiblenetwork.ai/learn/nptel/111106147/d52c3d04210d) (Video)
3. [1.3: Examples, contd...](https://invisiblenetwork.ai/learn/nptel/111106147/69ea3a41863c) (Video)
4. [1.4: Continuous linear maps - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/f095be976805) (Video)
5. [1.5: Continuous linear maps - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/9971d5264298) (Video)
6. [1.6: Isomorphisms](https://invisiblenetwork.ai/learn/nptel/111106147/df966b82e8ea) (Video)
7. [2.1 - Exercises](https://invisiblenetwork.ai/learn/nptel/111106147/5d6387fc4caa) (Video)
8. [2.2 - Exercises (contd.)](https://invisiblenetwork.ai/learn/nptel/111106147/7665ca640d98) (Video)
9. [2.3 - Hahn-Banach Theorems](https://invisiblenetwork.ai/learn/nptel/111106147/c74d7e3295e1) (Video)
10. [2.4 - Reflexivity](https://invisiblenetwork.ai/learn/nptel/111106147/d63baa7f80cc) (Video)
11. [2.5 - Geometric version](https://invisiblenetwork.ai/learn/nptel/111106147/87e67d915c6f) (Video)
12. [3.1 - Geometric version (contd.)](https://invisiblenetwork.ai/learn/nptel/111106147/ef8388ea6834) (Video)
13. [3.2 - Vector valued integration](https://invisiblenetwork.ai/learn/nptel/111106147/8c68131b8690) (Video)
14. [3.3 - Exercises - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/6979292da703) (Video)
15. [3.4 - Exercises - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/df474c5a2ff4) (Video)
16. [3.5 - Baire's Theorem and Applications](https://invisiblenetwork.ai/learn/nptel/111106147/aba3c0d7dec4) (Video)
17. [4.1 - Application to Fourier series](https://invisiblenetwork.ai/learn/nptel/111106147/1882b1b20a6d) (Video)
18. [4.2 - Open mapping and closed graph theorems](https://invisiblenetwork.ai/learn/nptel/111106147/2f3651720211) (Video)
19. [4.3 - Annihilators](https://invisiblenetwork.ai/learn/nptel/111106147/03c6fd0e3b91) (Video)
20. [4.4 - Complemented subspaces](https://invisiblenetwork.ai/learn/nptel/111106147/eeca4daf9b31) (Video)
21. [4.5 - Unbounded Operators, Adjoints - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/994e56e1dc02) (Video)
22. [4.6 - Unbounded Operators, Adjoints - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/acb3a39b3c4d) (Video)
23. [5.1 - Orthogonality relations](https://invisiblenetwork.ai/learn/nptel/111106147/2eeba1982dff) (Video)
24. [5.2 - Exercises](https://invisiblenetwork.ai/learn/nptel/111106147/68f00d2b4c3f) (Video)
25. [5.3 - Exercises (contd.)](https://invisiblenetwork.ai/learn/nptel/111106147/518b26cb108e) (Video)
26. [5.4 - Weak topology - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/a7dbe942dfb9) (Video)
27. [5.5 - Weak topology - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/54c47d270e2a) (Video)
28. [5.7 - Weak topology - Part 3](https://invisiblenetwork.ai/learn/nptel/111106147/c5a12593bb1f) (Video)
29. [6.1 - Weak* topology - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/c5677873a18a) (Video)
30. [6.2 - Weak* topology - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/f768a6735899) (Video)
31. [6.3 - Reflexive Spaces](https://invisiblenetwork.ai/learn/nptel/111106147/d53a7487fc4e) (Video)
32. [6.4 - Separable Spaces - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/9931fe75e99c) (Video)
33. [6.5 - Separable Spaces - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/7323c25fd8e7) (Video)
34. [6.6 - Uniformly Convex Spaces](https://invisiblenetwork.ai/learn/nptel/111106147/f9cf87fed4da) (Video)
35. [6.7 - Applications](https://invisiblenetwork.ai/learn/nptel/111106147/0e3e6d00de6f) (Video)
36. [7.1 - Exercises](https://invisiblenetwork.ai/learn/nptel/111106147/9459e1def4e6) (Video)
37. [7.2 - L-p Spaces - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/7d9a34d5df4f) (Video)
38. [7.3 - L-p Spaces - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/9319bfba4469) (Video)
39. [7.4 - Completeness](https://invisiblenetwork.ai/learn/nptel/111106147/4bd9993b2a57) (Video)
40. [7.5 -Duality](https://invisiblenetwork.ai/learn/nptel/111106147/2a3d2160ceec) (Video)
41. [7.6 - L-p Spaces in Euclidean spaces - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/077b1cd962f8) (Video)
42. [7.7 - L-p Spaces in Euclidean spaces - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/691774b012dd) (Video)
43. [8.1 - Dual of L-1](https://invisiblenetwork.ai/learn/nptel/111106147/a1de9639e678) (Video)
44. [8.2 - The space L-1 (contd.)](https://invisiblenetwork.ai/learn/nptel/111106147/2d6ccf1b24cc) (Video)
45. [8.3 - Exercises - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/5aa6e1fa666a) (Video)
46. [8.4 - Exercises - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/343a226b8c6e) (Video)
47. [8.5 - Exercises - Part 3](https://invisiblenetwork.ai/learn/nptel/111106147/bdba7ad0791d) (Video)
48. [8.6 - Exercises - Part 4](https://invisiblenetwork.ai/learn/nptel/111106147/8ec4f923e12a) (Video)
49. [9.1 - Hilbert spaces - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/2faa48eed9f2) (Video)
50. [9.2 - Hilbert spaces - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/dbd5f646a377) (Video)
51. [9.3 - Duality](https://invisiblenetwork.ai/learn/nptel/111106147/eeb9e8b6ddd2) (Video)
52. [9.4 - Adjoints](https://invisiblenetwork.ai/learn/nptel/111106147/5a3d6e8c70ab) (Video)
53. [9.5 - Applications](https://invisiblenetwork.ai/learn/nptel/111106147/2c926e862c2b) (Video)
54. [9.6 - Orthonormal sets](https://invisiblenetwork.ai/learn/nptel/111106147/f3af884c0591) (Video)
55. [10.1 - Orthonormal bases - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/c7a3d8a021a5) (Video)
56. [10.2 - Orthonormal bases - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/81ffe366087c) (Video)
57. [10.3 -Fourier series](https://invisiblenetwork.ai/learn/nptel/111106147/3023bb53a221) (Video)
58. [10.4 - Spectrum of an operator - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/88531fc29d41) (Video)
59. [10.5 - Spectrum of an operator - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/65685726a0bf) (Video)
60. [10.6 - Exercises - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/edf497f5a505) (Video)
61. [11.1 - Exercises - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/56b96715e275) (Video)
62. [11.2 - Exercises - Part 3](https://invisiblenetwork.ai/learn/nptel/111106147/6ab7d5f30c54) (Video)
63. [11.3 - Compact operators - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/41ff31033be6) (Video)
64. [11.4 - Compact operators - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/cf59bdc4cedc) (Video)
65. [11.5 - Riesz-Fredholm theory - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/98a4f6c06f86) (Video)
66. [11.6 -Riesz-Fredholm theory - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/4304e6a5388e) (Video)
67. [12.1 - Riesz-Fredholm theory](https://invisiblenetwork.ai/learn/nptel/111106147/6cca41b79ca9) (Video)
68. [12.2 - Spectrum of a compact operator](https://invisiblenetwork.ai/learn/nptel/111106147/0b28621776de) (Video)
69. [12.3 - Spectrum of a compact self-adjoint operator](https://invisiblenetwork.ai/learn/nptel/111106147/eccdadfd0f97) (Video)
70. [12.4 - Eigenvalues of a compact self-adjoint operator](https://invisiblenetwork.ai/learn/nptel/111106147/ebb4c9950d85) (Video)
71. [12.5 - Exercises - Part 1](https://invisiblenetwork.ai/learn/nptel/111106147/0574cf160ebd) (Video)
72. [12.6 - Exercises - Part 2](https://invisiblenetwork.ai/learn/nptel/111106147/aa20eb79d5b3) (Video)
73. [12.7 - Exercises - Part 3](https://invisiblenetwork.ai/learn/nptel/111106147/2c81202df021) (Video)
74. [12.8 - Exercises - Part 4](https://invisiblenetwork.ai/learn/nptel/111106147/772eb0b7c507) (Video)