# Functional Analysis

- Institution: IIT Kharagpur
- Department: Mathematics
- Teacher: Prof. P.D. Srivastava
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105037)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105037)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Metric Spaces with Examples](https://invisiblenetwork.ai/learn/nptel/111105037/bddddbdefd98) (Video)
2. [Holder Inequality and Minkowski Inequality](https://invisiblenetwork.ai/learn/nptel/111105037/7f415bf9f003) (Video)
3. [Various Concepts in a Metric Space](https://invisiblenetwork.ai/learn/nptel/111105037/64070c60dc8e) (Video)
4. [Separable Metrics Spaces with Examples](https://invisiblenetwork.ai/learn/nptel/111105037/c73b82ea467d) (Video)
5. [Convergence, Cauchy Sequence, Completeness](https://invisiblenetwork.ai/learn/nptel/111105037/dc07d95e1576) (Video)
6. [Examples of Complete and Incomplete Metric Spaces](https://invisiblenetwork.ai/learn/nptel/111105037/2a79011a34ec) (Video)
7. [Completion of Metric Spaces + Tutorial](https://invisiblenetwork.ai/learn/nptel/111105037/957ffa738bc3) (Video)
8. [Vector Spaces with Examples](https://invisiblenetwork.ai/learn/nptel/111105037/2afaf4ed13c2) (Video)
9. [Normed Spaces with Examples](https://invisiblenetwork.ai/learn/nptel/111105037/cfb94ede6232) (Video)
10. [Banach Spaces and Schauder Basic](https://invisiblenetwork.ai/learn/nptel/111105037/35f40b939d49) (Video)
11. [Finite Dimensional Normed Spaces and Subspaces](https://invisiblenetwork.ai/learn/nptel/111105037/d4b8d264801a) (Video)
12. [Compactness of Metric/Normed Spaces](https://invisiblenetwork.ai/learn/nptel/111105037/7a174227c810) (Video)
13. [Linear Operators-definition and Examples](https://invisiblenetwork.ai/learn/nptel/111105037/3360d7e76a10) (Video)
14. [Bounded Linear Operators in a Normed Space](https://invisiblenetwork.ai/learn/nptel/111105037/a85e6e29d8b8) (Video)
15. [Bounded Linear Functionals in a Normed Space](https://invisiblenetwork.ai/learn/nptel/111105037/46b9a5d65e37) (Video)
16. [Concept of Algebraic Dual and Reflexive Space](https://invisiblenetwork.ai/learn/nptel/111105037/11f549d790d7) (Video)
17. [Dual Basis & Algebraic Reflexive Space](https://invisiblenetwork.ai/learn/nptel/111105037/b3e82a5591af) (Video)
18. [Dual Spaces with Examples](https://invisiblenetwork.ai/learn/nptel/111105037/d0ca2d53a53b) (Video)
19. [Tutorial - I](https://invisiblenetwork.ai/learn/nptel/111105037/96bb76cfef11) (Video)
20. [Tutorial - II](https://invisiblenetwork.ai/learn/nptel/111105037/67c59fcd9c11) (Video)
21. [Inner Product & Hilbert Space](https://invisiblenetwork.ai/learn/nptel/111105037/57dbd67f5355) (Video)
22. [Further Properties of Inner Product Spaces](https://invisiblenetwork.ai/learn/nptel/111105037/8e18aad57a5c) (Video)
23. [Projection Theorem, Orthonormal Sets and Sequences](https://invisiblenetwork.ai/learn/nptel/111105037/b234b6bb15d0) (Video)
24. [Representation of Functionals on a Hilbert Spaces](https://invisiblenetwork.ai/learn/nptel/111105037/09824178e6f9) (Video)
25. [Hilbert Adjoint Operator](https://invisiblenetwork.ai/learn/nptel/111105037/5b712480e3c1) (Video)
26. [Self Adjoint, Unitary & Normal Operators](https://invisiblenetwork.ai/learn/nptel/111105037/9e974744594c) (Video)
27. [Tutorial - III](https://invisiblenetwork.ai/learn/nptel/111105037/5ad02485eb9e) (Video)
28. [Annihilator in an IPS](https://invisiblenetwork.ai/learn/nptel/111105037/6c8a644a8a2f) (Video)
29. [Total Orthonormal Sets And Sequences](https://invisiblenetwork.ai/learn/nptel/111105037/ac018c4cb016) (Video)
30. [Partially Ordered Set and Zorns Lemma](https://invisiblenetwork.ai/learn/nptel/111105037/d8719dcc117b) (Video)
31. [Hahn Banach Theorem for Real Vector Spaces](https://invisiblenetwork.ai/learn/nptel/111105037/5d32fb886a4b) (Video)
32. [Hahn Banach Theorem for Complex V.S. & Normed Spaces](https://invisiblenetwork.ai/learn/nptel/111105037/97055f692bcf) (Video)
33. [Baires Category & Uniform Boundedness Theorems](https://invisiblenetwork.ai/learn/nptel/111105037/a5c77bdca8fc) (Video)
34. [Open Mapping Theorem](https://invisiblenetwork.ai/learn/nptel/111105037/74230438d65b) (Video)
35. [Closed Graph Theorem](https://invisiblenetwork.ai/learn/nptel/111105037/ff7715030a28) (Video)
36. [Adjoint Operator](https://invisiblenetwork.ai/learn/nptel/111105037/ba9519aebcfd) (Video)
37. [Strong and Weak Convergence](https://invisiblenetwork.ai/learn/nptel/111105037/0ac3f6007d46) (Video)
38. [Convergence of Sequence of Operators and Functionals](https://invisiblenetwork.ai/learn/nptel/111105037/0b53109c6561) (Video)
39. [LP - Space](https://invisiblenetwork.ai/learn/nptel/111105037/f789744e32fb) (Video)
40. [LP - Space (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105037/d2fa373c8700) (Video)