# Advanced Course on Partial Differential Equations - II

- Institution: IISc Bangalore
- Department: Mathematics
- Teacher: Prof. A. K. Nandakumaran Prof. P. S. Datti
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111108412)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111108412)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lec 01 - Introduction and Outline](https://invisiblenetwork.ai/learn/nptel/111108412/fc716ec9e733) (Video)
2. [Lec 02 - Review of Sobolev spaces-1](https://invisiblenetwork.ai/learn/nptel/111108412/b3ca57a50052) (Video)
3. [Lec 03 - Review of Sobolev spaces-2](https://invisiblenetwork.ai/learn/nptel/111108412/6d8155f70086) (Video)
4. [Lec 04 - Review of Sobolev spaces-3](https://invisiblenetwork.ai/learn/nptel/111108412/5b107653cac6) (Video)
5. [Lec 05 Review of Sobolev spaces-4](https://invisiblenetwork.ai/learn/nptel/111108412/8af9ea15fce1) (Video)
6. [Lec 06 - Review of Sobolev spaces-5](https://invisiblenetwork.ai/learn/nptel/111108412/868977d2a25c) (Video)
7. [Lec 07 - Elliptic equations and weak formulation](https://invisiblenetwork.ai/learn/nptel/111108412/0ce8a7a8b2d0) (Video)
8. [Lec 08 - Abstract Formulation](https://invisiblenetwork.ai/learn/nptel/111108412/0acd69889136) (Video)
9. [Lec 09 Variational Inequality](https://invisiblenetwork.ai/learn/nptel/111108412/03671b9ef709) (Video)
10. [Lec 10 - Babuska-Brezzi Theorem](https://invisiblenetwork.ai/learn/nptel/111108412/9d2cdd6b36a9) (Video)
11. [Lec 11 Strong vs Weak Form of PDE](https://invisiblenetwork.ai/learn/nptel/111108412/0b6a1af85e93) (Video)
12. [Lec 12 General Second Order Equations](https://invisiblenetwork.ai/learn/nptel/111108412/869960e3aab4) (Video)
13. [Lec 13 Non-uniqueness of Neumann problem](https://invisiblenetwork.ai/learn/nptel/111108412/efdaa282f563) (Video)
14. [Lec 14 Biharmonic equation, Stokes system](https://invisiblenetwork.ai/learn/nptel/111108412/a71c6eda0682) (Video)
15. [Lec 15 Stokes system (continued)](https://invisiblenetwork.ai/learn/nptel/111108412/a298e55e19bc) (Video)
16. [Lec 16 Regularity of Ellptic Equations](https://invisiblenetwork.ai/learn/nptel/111108412/44d4bb473493) (Video)
17. [Lec 17 Regularity Continued](https://invisiblenetwork.ai/learn/nptel/111108412/5f02a3827769) (Video)
18. [Lec 18 Maximum and Minimum Principles for weak formulation](https://invisiblenetwork.ai/learn/nptel/111108412/de9e675ecd61) (Video)
19. [Lec 19 Spectrum of the Laplace operator](https://invisiblenetwork.ai/learn/nptel/111108412/3f71a86e6488) (Video)
20. [Lec 20 First eigenvalue of the Laplace operator and a brief discussion of a Galerkin method](https://invisiblenetwork.ai/learn/nptel/111108412/88f2975018bb) (Video)
21. [Lec 21 Introduction to semi-groups and unbounded operators](https://invisiblenetwork.ai/learn/nptel/111108412/82d3bbd4b237) (Video)
22. [Lec 22 Spectrum of an operator](https://invisiblenetwork.ai/learn/nptel/111108412/5dad4af4e2ec) (Video)
23. [Lec 23 Examples of operators and operators in a Hilbert space](https://invisiblenetwork.ai/learn/nptel/111108412/e2ffdc22e4b3) (Video)
24. [Lec 24 Perturbation of an operator, Kato theorems. Definition of a semi-group](https://invisiblenetwork.ai/learn/nptel/111108412/040bac78f326) (Video)
25. [Lec 25 Semi-group and its infinitesimal generator](https://invisiblenetwork.ai/learn/nptel/111108412/5cab9d1f5bde) (Video)
26. [Lec 26 Examples of semi-groups;spectrum and resolvent of the infinitesimal generator](https://invisiblenetwork.ai/learn/nptel/111108412/571934f3ade0) (Video)
27. [Lec 27 An application. Saturation theorem](https://invisiblenetwork.ai/learn/nptel/111108412/2451d1951118) (Video)
28. [Lec 28 Hille-Yosida Theorem](https://invisiblenetwork.ai/learn/nptel/111108412/22e91aeb8190) (Video)
29. [Lec 29 Lumer-Philips Theorem. Stone's theorem](https://invisiblenetwork.ai/learn/nptel/111108412/407d2621febe) (Video)
30. [Lec 30 Abstract Cauchy Problem](https://invisiblenetwork.ai/learn/nptel/111108412/1a17b094ab48) (Video)
31. [Lec 31 Semi-group arising from the heat equation](https://invisiblenetwork.ai/learn/nptel/111108412/8eb322ebc702) (Video)
32. [Lec 32 Geneartor of the heat semi-group](https://invisiblenetwork.ai/learn/nptel/111108412/90e9b1ed79d1) (Video)
33. [Lec 33 Semi-group arising from the wave equation](https://invisiblenetwork.ai/learn/nptel/111108412/6e509db6283a) (Video)
34. [Lec 34 Semi-group arising from the wave equation in energy space](https://invisiblenetwork.ai/learn/nptel/111108412/91ead75f4342) (Video)
35. [Lec 35 Wave equation in energy space](https://invisiblenetwork.ai/learn/nptel/111108412/5b0cf4f369e7) (Video)
36. [Lec 36 Wave equation in energy space (continued)](https://invisiblenetwork.ai/learn/nptel/111108412/0b710ceaeab4) (Video)
37. [Lec 37 Semi-group arising from the wave equation in H^1 x L^2](https://invisiblenetwork.ai/learn/nptel/111108412/f4e05f4fda7b) (Video)
38. [Lec 38 Schroedinger equation in free space](https://invisiblenetwork.ai/learn/nptel/111108412/40e66a27ae79) (Video)
39. [Lec 39 Schroedinger equation with a potential. Application of Kato's theorem](https://invisiblenetwork.ai/learn/nptel/111108412/606fc3967cf2) (Video)
40. [Lec 40 Equations in a bounded domain. Concluding remarks](https://invisiblenetwork.ai/learn/nptel/111108412/f00de618e9b0) (Video)