# Functional Analysis and its Applications

- Institution: IIT-ISM Dhanbad
- Department: Mathematics
- Teacher: Prof. Akhilesh Prasad
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105610)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105610)
- 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: An Overview and Metric Spaces with Examples](https://invisiblenetwork.ai/learn/nptel/111105610/7a9fc4855fd0) (Video)
2. [Lecture 2: Basic Inequalities and their Applications](https://invisiblenetwork.ai/learn/nptel/111105610/41e056f17701) (Video)
3. [Lecture 3: Complete Metric Spaces with Examples](https://invisiblenetwork.ai/learn/nptel/111105610/02e486789075) (Video)
4. [Lecture 4: Vector Spaces and Subspaces with Examples](https://invisiblenetwork.ai/learn/nptel/111105610/51c5f92750d3) (Video)
5. [Lecture 5: Linear Transformation with Examples](https://invisiblenetwork.ai/learn/nptel/111105610/0f7d27483a24) (Video)
6. [Lecture 6: Normed Linear Space and Pseudo-Normed Linear Space with Examples](https://invisiblenetwork.ai/learn/nptel/111105610/21d44e9d2fc4) (Video)
7. [Lecture 7: Convergence, Cauchy Sequence in Normed Linear Spaces and Banach Spaces with Examples](https://invisiblenetwork.ai/learn/nptel/111105610/57446eefffa4) (Video)
8. [Lecture 8: Further examples of Banach Spaces](https://invisiblenetwork.ai/learn/nptel/111105610/afa7ee2e115b) (Video)
9. [Lecture 9: The Linear Space C\[a, b\] as Normed Linear Space but not Banachspace](https://invisiblenetwork.ai/learn/nptel/111105610/9db51267271c) (Video)
10. [Lecture 10: The Linear Spaces ?p and ?? as Banach Spaces](https://invisiblenetwork.ai/learn/nptel/111105610/1e222a0a5ad3) (Video)
11. [Lecture 11: The Quotient Space as Banach Space](https://invisiblenetwork.ai/learn/nptel/111105610/92f3081522eb) (Video)
12. [Lecture 12: The Lp spaces as Banach Spaces](https://invisiblenetwork.ai/learn/nptel/111105610/a9da8057ce2d) (Video)
13. [Lecture 13: Bounded Linear Transformations and Equivalent Norms with Examples](https://invisiblenetwork.ai/learn/nptel/111105610/534c919315ec) (Video)
14. [Lecture 14: Norm of Bounded (Continuous) LinearTransformations and Some Related Theorems](https://invisiblenetwork.ai/learn/nptel/111105610/0e9a093724f7) (Video)
15. [Lecture 15: Continuity of Functions in Normed Linear Spaces and some related Theorems](https://invisiblenetwork.ai/learn/nptel/111105610/5209c18ff8db) (Video)
16. [Lecture 16: The set of all Bounded Linear Transformations of Normed Linear Space N into N? as a...](https://invisiblenetwork.ai/learn/nptel/111105610/a83f84a582cb) (Video)
17. [Lecture 17: Further Theorems on Bounded Linear Transformations](https://invisiblenetwork.ai/learn/nptel/111105610/8b6f4fbe6eac) (Video)
18. [Lecture 18: Linear Functionals, Dual Vector Space and Dual Basis](https://invisiblenetwork.ai/learn/nptel/111105610/7208a7229298) (Video)
19. [Lecture 19: Continuous (Bounded) Linear Functionals on Normed linear spaces](https://invisiblenetwork.ai/learn/nptel/111105610/2277f61d548e) (Video)
20. [Lecture 20: Consequences of Equivalent Norms with Examples and on a Finite-Dimensional space,....](https://invisiblenetwork.ai/learn/nptel/111105610/e297d0317b69) (Video)
21. [Lecture 21: Further Theorems on Finite-Dimensional Normed Linear Spaces](https://invisiblenetwork.ai/learn/nptel/111105610/35e0303f591c) (Video)
22. [Lecture 22: Dual Space of ?p^n, ?1^n and ??^n](https://invisiblenetwork.ai/learn/nptel/111105610/c0957f1ebd08) (Video)
23. [Lecture 23: Dual Space of ?p is ?q](https://invisiblenetwork.ai/learn/nptel/111105610/0a4909903333) (Video)
24. [Lecture 24: Dual Space of ?1 is ??](https://invisiblenetwork.ai/learn/nptel/111105610/3dd7222a2d93) (Video)
25. [Lecture 25: Dual Space of ????0 is ?1](https://invisiblenetwork.ai/learn/nptel/111105610/8dfb84219e98) (Video)
26. [Lecture 26: Dual Space of c is ?1](https://invisiblenetwork.ai/learn/nptel/111105610/83b3a83a6d1a) (Video)
27. [Lecture 27: Inner Product Space with Examples](https://invisiblenetwork.ai/learn/nptel/111105610/ce09075ff894) (Video)
28. [Lecture 28: Further Example of Inner Product Space and Schwartz’s Inequality](https://invisiblenetwork.ai/learn/nptel/111105610/5c14ba31bf1e) (Video)
29. [Lecture 29: Continuity of Inner Product, Parallelogram Law and Polarization Identity](https://invisiblenetwork.ai/learn/nptel/111105610/6e3332840d67) (Video)
30. [Lecture 30: Hilbert Space with Examples](https://invisiblenetwork.ai/learn/nptel/111105610/8e33f9684cdb) (Video)
31. [Lecture 31: Application of Polarization Identity](https://invisiblenetwork.ai/learn/nptel/111105610/9c2932693522) (Video)
32. [Lecture 32: Applications of the Parallelogram Law](https://invisiblenetwork.ai/learn/nptel/111105610/462c8fb6eaae) (Video)
33. [Lecture 33: Weak Convergence and Strong Convergence](https://invisiblenetwork.ai/learn/nptel/111105610/d2924b5a06da) (Video)
34. [Lecture 34: Orthogonality of Vectors](https://invisiblenetwork.ai/learn/nptel/111105610/4b2a25487125) (Video)
35. [Lecture 35: Orthogonal Complement of an Orthogonal Complement](https://invisiblenetwork.ai/learn/nptel/111105610/a8a210b64960) (Video)
36. [Lecture 36: The Orthogonal Decomposition (Projection) Theorem](https://invisiblenetwork.ai/learn/nptel/111105610/ff3ab3e3e411) (Video)
37. [Lecture 37: Orthonormal Sets in Hilbert Spaces and Bessel’s Inequality](https://invisiblenetwork.ai/learn/nptel/111105610/8fd2b5767a3b) (Video)
38. [Lecture 38: Complete Orthonormal Sets](https://invisiblenetwork.ai/learn/nptel/111105610/312adbe9d534) (Video)
39. [Lecture 39: Further Theorems on Complete Orthonormal Sets and Riesz-Fischer Theorem](https://invisiblenetwork.ai/learn/nptel/111105610/9b6564425fb4) (Video)
40. [Lecture 40: Gram-Schmidt Orthogonalization Process](https://invisiblenetwork.ai/learn/nptel/111105610/6bd21a6797e9) (Video)
41. [Lecture 41: The Conjugate Space H* and The Riesz Representation Theorem](https://invisiblenetwork.ai/learn/nptel/111105610/6c0529b0edfd) (Video)
42. [Lecture 42: Further Theorems on Conjugate Space H*](https://invisiblenetwork.ai/learn/nptel/111105610/655be26da163) (Video)
43. [Lecture 43: The Conjugate of an Operator](https://invisiblenetwork.ai/learn/nptel/111105610/5b9b994bd4ee) (Video)
44. [Lecture 44: The Adjoint of an Operator on a Hilbert Space](https://invisiblenetwork.ai/learn/nptel/111105610/5e25dc53a546) (Video)
45. [Lecture 45: Properties of Adjoint Operators on Hilbert Spaces](https://invisiblenetwork.ai/learn/nptel/111105610/b1184f649358) (Video)
46. [Lecture 46: Self Adjoint Operators](https://invisiblenetwork.ai/learn/nptel/111105610/43c4ffe7a6e1) (Video)
47. [Lecture 47: Partially Ordered Set and Positive Operators](https://invisiblenetwork.ai/learn/nptel/111105610/1cfce5e31877) (Video)
48. [Lecture 48: Normal Operators](https://invisiblenetwork.ai/learn/nptel/111105610/ab27adb9af2b) (Video)
49. [Lecture 49: Further Theorems of Normal Operators](https://invisiblenetwork.ai/learn/nptel/111105610/5e14aad898ca) (Video)
50. [Lecture 50: Unitary Operators](https://invisiblenetwork.ai/learn/nptel/111105610/81520dc4ea3f) (Video)
51. [Lecture 51: Partial Order Relations, Total Order, Maximaland Minimal Elements, Zorn’s Lemma](https://invisiblenetwork.ai/learn/nptel/111105610/cf22dbed85cf) (Video)
52. [Lecture 52: Hahn-Banach Theorem (Part-I)](https://invisiblenetwork.ai/learn/nptel/111105610/fc6097118fba) (Video)
53. [Lecture 53: Hahn-Banach Theorem (Part-II) and Proofof the Main Theorem](https://invisiblenetwork.ai/learn/nptel/111105610/cd0e670cce36) (Video)
54. [Lecture 54: Sublinear Functional and GeneralizedHahn-Banach Theorem](https://invisiblenetwork.ai/learn/nptel/111105610/f2db24e18021) (Video)
55. [Lecture 55: Uniform Boundedness Principle](https://invisiblenetwork.ai/learn/nptel/111105610/ea4ef370065c) (Video)
56. [Lecture 56: Application of the Uniform BoundednessPrinciple and Uniform Boundedness Principle.....](https://invisiblenetwork.ai/learn/nptel/111105610/2cbdb12de95e) (Video)
57. [Lecture 57: Applications of Uniform Boundedness Principle for Continuous Linear Functionals](https://invisiblenetwork.ai/learn/nptel/111105610/2a7deaba00f2) (Video)
58. [Lecture 58: Open Mapping Theorem](https://invisiblenetwork.ai/learn/nptel/111105610/31916e4280ec) (Video)
59. [Lecture 59: Applications of Open Mapping Theorem](https://invisiblenetwork.ai/learn/nptel/111105610/78d911d9b0e5) (Video)
60. [Lecture 60: The Closed Graph Theorem](https://invisiblenetwork.ai/learn/nptel/111105610/252affce9a63) (Video)
61. [Live Session 25-02-2025](https://invisiblenetwork.ai/learn/nptel/111105610/7a9fc4855fd0-2) (Video)
62. [Live Session 18-03-2025](https://invisiblenetwork.ai/learn/nptel/111105610/41e056f17701-2) (Video)
63. [Live Session 11-04-2025](https://invisiblenetwork.ai/learn/nptel/111105610/02e486789075-2) (Video)