# Fourier Analysis and its applications

- Institution: IIT Bombay
- Department: Mathematics
- Teacher: Prof. G. K Srinivasan
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111101164)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111101164)
- 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: Genesis and a little history](https://invisiblenetwork.ai/learn/nptel/111101164/5f584bd716f7) (Video)
2. [Lecture 2: Basic convergence theorem](https://invisiblenetwork.ai/learn/nptel/111101164/81ce8578f4d0) (Video)
3. [Lecture 3: Riemann Lebesgue Lemma](https://invisiblenetwork.ai/learn/nptel/111101164/74f3b9c4f07b) (Video)
4. [Lecture 4: The ubiquitous Gaussian](https://invisiblenetwork.ai/learn/nptel/111101164/d034442c0a83) (Video)
5. [Lecture 5: Jacobi theta function identity.](https://invisiblenetwork.ai/learn/nptel/111101164/527b374bd66b) (Video)
6. [Lecture 6: The Riemann zeta function](https://invisiblenetwork.ai/learn/nptel/111101164/69c8a3063ace) (Video)
7. [Lecture 7: Bessel's functions of the first kind](https://invisiblenetwork.ai/learn/nptel/111101164/19a29f5b6daa) (Video)
8. [Lecture 8: Least square approximation](https://invisiblenetwork.ai/learn/nptel/111101164/15f26c9e70e1) (Video)
9. [Lecture 9: Parseval formula. Isoperimetric theorem](https://invisiblenetwork.ai/learn/nptel/111101164/1369cf316d52) (Video)
10. [Lecture 10: Dirichlet problem for a disc](https://invisiblenetwork.ai/learn/nptel/111101164/775fe3b9756b) (Video)
11. [Lecture 11: The Poisson kernel](https://invisiblenetwork.ai/learn/nptel/111101164/0b28cfc717c7) (Video)
12. [Lecture 12: Cesaro summability and Fejer's theorem](https://invisiblenetwork.ai/learn/nptel/111101164/60cf2212bf9d) (Video)
13. [Lecture 13: Fejer's theorem (Cond)](https://invisiblenetwork.ai/learn/nptel/111101164/dfb518002fb9) (Video)
14. [Lecture 14: Kronecker's theorem](https://invisiblenetwork.ai/learn/nptel/111101164/a8cd01c65c90) (Video)
15. [Lecture 15: Weyl's equidistribution theorem](https://invisiblenetwork.ai/learn/nptel/111101164/d69bf2638f03) (Video)
16. [Lecture 16: Borel's theorem and beyond](https://invisiblenetwork.ai/learn/nptel/111101164/c294194894f2) (Video)
17. [Lecture 17: Fourier transform and Schwartz space](https://invisiblenetwork.ai/learn/nptel/111101164/d9fcfa810b35) (Video)
18. [Lecture 18: Hermite's differential equation](https://invisiblenetwork.ai/learn/nptel/111101164/578fb948fa7b) (Video)
19. [Lecture 19: Fourier inversion theorem](https://invisiblenetwork.ai/learn/nptel/111101164/7a6c8ccbf2a3) (Video)
20. [Lecture 20: Plancherel's theorem](https://invisiblenetwork.ai/learn/nptel/111101164/0a0ac686a453) (Video)
21. [Lecture 21: Heat equation. The heat kernel](https://invisiblenetwork.ai/learn/nptel/111101164/07a017b72d6c) (Video)
22. [Lecture 22: Airy's function](https://invisiblenetwork.ai/learn/nptel/111101164/773205042689) (Video)
23. [Lecture 23: Exercises on Fourier transform](https://invisiblenetwork.ai/learn/nptel/111101164/c69cc254e601) (Video)
24. [Lecture 24: Principle of equipartitioning of energy](https://invisiblenetwork.ai/learn/nptel/111101164/bf313b7155bc) (Video)
25. [Lecture 25: Formula of Srinivasa Ramanujan](https://invisiblenetwork.ai/learn/nptel/111101164/c9ee23874b1d) (Video)
26. [Lecture 26: Sturm Liouville problems. Orthogonal systems](https://invisiblenetwork.ai/learn/nptel/111101164/6eae02fa855c) (Video)
27. [Lecture 27: Vibrations of a circular membrane](https://invisiblenetwork.ai/learn/nptel/111101164/903f88ad84c9) (Video)
28. [Lecture 28: Fourier Bessel series](https://invisiblenetwork.ai/learn/nptel/111101164/53a24865aa6f) (Video)
29. [Lecture 29: Properties of Legendre polynomials](https://invisiblenetwork.ai/learn/nptel/111101164/21e0788b4645) (Video)
30. [Lecture 30: Properties of Legendre polynomials (contd)](https://invisiblenetwork.ai/learn/nptel/111101164/319be7331012) (Video)
31. [Lecture 31: Properties of Legendre polynomials interlacing of zeros](https://invisiblenetwork.ai/learn/nptel/111101164/150433a5fe53) (Video)
32. [Lecture 32: Laplace's integrals and Rayleigh's expansion of plane waves](https://invisiblenetwork.ai/learn/nptel/111101164/e0a707cd71f8) (Video)
33. [Lecture 33: Regular SturmLiouville problems](https://invisiblenetwork.ai/learn/nptel/111101164/a36d4c6357aa) (Video)
34. [Lecture 34: Variational properties of eigenvalues](https://invisiblenetwork.ai/learn/nptel/111101164/4bc7a7ea8c37) (Video)
35. [Lecture 35: The Dirichlet principle](https://invisiblenetwork.ai/learn/nptel/111101164/4dac909d0518) (Video)
36. [Lecture 36: Regular SturmLiouville problems Existence of eigenvalues](https://invisiblenetwork.ai/learn/nptel/111101164/6262eb37aced) (Video)
37. [Lecture 37: The Bergman space](https://invisiblenetwork.ai/learn/nptel/111101164/db7dae8c74dc) (Video)
38. [Lecture 38: The BanachSteinhaus' theorem](https://invisiblenetwork.ai/learn/nptel/111101164/c4018f99de3b) (Video)
39. [Lecture 39: Hilbert space basics](https://invisiblenetwork.ai/learn/nptel/111101164/c2f224b3141e) (Video)
40. [Lecture 40: Completeness of Hermite functions](https://invisiblenetwork.ai/learn/nptel/111101164/5eb97ef08cb9) (Video)
41. [Lecture 41 : Laugerre polynomials](https://invisiblenetwork.ai/learn/nptel/111101164/9689ef76cd43) (Video)
42. [Lecture 42: Orthonormal bases in Hilbert spaces](https://invisiblenetwork.ai/learn/nptel/111101164/8828eb033193) (Video)
43. [Lecture 43: Nonseparable Hilbertspaces. Almost periodic functions](https://invisiblenetwork.ai/learn/nptel/111101164/48f8895ad812) (Video)
44. [Lecture 44: HilbertSchmidt operators and Green's functions](https://invisiblenetwork.ai/learn/nptel/111101164/e1ba8bf66d13) (Video)
45. [Lecture 45: Spectrum of a bounded linear operator](https://invisiblenetwork.ai/learn/nptel/111101164/3ffc6c28bc36) (Video)
46. [Lecture 46: Weak (sequential) compactness of the closed unit ball](https://invisiblenetwork.ai/learn/nptel/111101164/c2f1906c9050) (Video)
47. [Lecture 47: Compact selfadjoint operators. Existence of eigen values](https://invisiblenetwork.ai/learn/nptel/111101164/e900d363e5f4) (Video)
48. [Lecture 48: Compact selfadjoint operators. Existence of eigen values continued](https://invisiblenetwork.ai/learn/nptel/111101164/c0e4a9b09f56) (Video)
49. [Lecture 49: Celestial Mechanics](https://invisiblenetwork.ai/learn/nptel/111101164/63f563eb1c9f) (Video)
50. [Lecture 50: Inverting the Kepler equation using Fourier series](https://invisiblenetwork.ai/learn/nptel/111101164/7720ae30c528) (Video)
51. [Lecture 51: Odds and Ends](https://invisiblenetwork.ai/learn/nptel/111101164/421b3f31d3de) (Video)
52. [Lecture 52: Dirichlet's theorem on Fouier series](https://invisiblenetwork.ai/learn/nptel/111101164/c91b1a3dfd34) (Video)
53. [Lecture 53: Dirichlet's theorem on Fouier series continued](https://invisiblenetwork.ai/learn/nptel/111101164/1391c59a85b7) (Video)
54. [Lecture 54: Topology on the Schwartz space](https://invisiblenetwork.ai/learn/nptel/111101164/b0f70a060aaf) (Video)
55. [Lecture 55: Examples of tempered distributions](https://invisiblenetwork.ai/learn/nptel/111101164/20b74d24deab) (Video)
56. [Lecture 56: Operations on distributions](https://invisiblenetwork.ai/learn/nptel/111101164/b8829d3ff635) (Video)
57. [Lecture 57: Fourier Transform of tempered distribution](https://invisiblenetwork.ai/learn/nptel/111101164/1c504456d0f8) (Video)
58. [Lecture 58: Support of a distribution. Distributions with point support](https://invisiblenetwork.ai/learn/nptel/111101164/b315383fd015) (Video)
59. [Lecture 59: Distributional solutions of ODEs. Continuity of the Fourier transform and differentiation](https://invisiblenetwork.ai/learn/nptel/111101164/1d7ce6578874) (Video)
60. [Lecture 60: The Poisson summation formula](https://invisiblenetwork.ai/learn/nptel/111101164/32755c1ee0fc) (Video)
61. [Live Session 13-03-2024](https://invisiblenetwork.ai/learn/nptel/111101164/5f584bd716f7-2) (Video)
62. [Live Session 22-03-2024](https://invisiblenetwork.ai/learn/nptel/111101164/81ce8578f4d0-2) (Video)
63. [Live Session 12-04-2024](https://invisiblenetwork.ai/learn/nptel/111101164/74f3b9c4f07b-2) (Video)
64. [Live Session 07-03-2025](https://invisiblenetwork.ai/learn/nptel/111101164/d034442c0a83-2) (Video)
65. [Live Session 27-03-2025](https://invisiblenetwork.ai/learn/nptel/111101164/527b374bd66b-2) (Video)