Learn · Fourier Analysis and its applications

Lecture 22 of 65week-05

Lecture 22: Airy's function

Prof. G. K Srinivasan · IIT Bombay

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Fourier Analysis and its applications, IIT Bombay (at NPTEL)
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All the lectures

  1. Lecture 1: Genesis and a little history Video
  2. Lecture 2: Basic convergence theorem Video
  3. Lecture 3: Riemann Lebesgue Lemma Video
  4. Lecture 4: The ubiquitous Gaussian Video
  5. Lecture 5: Jacobi theta function identity. Video
  6. Lecture 6: The Riemann zeta function Video
  7. Lecture 7: Bessel's functions of the first kind Video
  8. Lecture 8: Least square approximation Video
  9. Lecture 9: Parseval formula. Isoperimetric theorem Video
  10. Lecture 10: Dirichlet problem for a disc Video
  11. Lecture 11: The Poisson kernel Video
  12. Lecture 12: Cesaro summability and Fejer's theorem Video
  13. Lecture 13: Fejer's theorem (Cond) Video
  14. Lecture 14: Kronecker's theorem Video
  15. Lecture 15: Weyl's equidistribution theorem Video
  16. Lecture 16: Borel's theorem and beyond Video
  17. Lecture 17: Fourier transform and Schwartz space Video
  18. Lecture 18: Hermite's differential equation Video
  19. Lecture 19: Fourier inversion theorem Video
  20. Lecture 20: Plancherel's theorem Video
  21. Lecture 21: Heat equation. The heat kernel Video
  22. Lecture 22: Airy's function Video
  23. Lecture 23: Exercises on Fourier transform Video
  24. Lecture 24: Principle of equipartitioning of energy Video
  25. Lecture 25: Formula of Srinivasa Ramanujan Video
  26. Lecture 26: Sturm Liouville problems. Orthogonal systems Video
  27. Lecture 27: Vibrations of a circular membrane Video
  28. Lecture 28: Fourier Bessel series Video
  29. Lecture 29: Properties of Legendre polynomials Video
  30. Lecture 30: Properties of Legendre polynomials (contd) Video
  31. Lecture 31: Properties of Legendre polynomials interlacing of zeros Video
  32. Lecture 32: Laplace's integrals and Rayleigh's expansion of plane waves Video
  33. Lecture 33: Regular SturmLiouville problems Video
  34. Lecture 34: Variational properties of eigenvalues Video
  35. Lecture 35: The Dirichlet principle Video
  36. Lecture 36: Regular SturmLiouville problems Existence of eigenvalues Video
  37. Lecture 37: The Bergman space Video
  38. Lecture 38: The BanachSteinhaus' theorem Video
  39. Lecture 39: Hilbert space basics Video
  40. Lecture 40: Completeness of Hermite functions Video
  41. Lecture 41 : Laugerre polynomials Video
  42. Lecture 42: Orthonormal bases in Hilbert spaces Video
  43. Lecture 43: Nonseparable Hilbertspaces. Almost periodic functions Video
  44. Lecture 44: HilbertSchmidt operators and Green's functions Video
  45. Lecture 45: Spectrum of a bounded linear operator Video
  46. Lecture 46: Weak (sequential) compactness of the closed unit ball Video
  47. Lecture 47: Compact selfadjoint operators. Existence of eigen values Video
  48. Lecture 48: Compact selfadjoint operators. Existence of eigen values continued Video
  49. Lecture 49: Celestial Mechanics Video
  50. Lecture 50: Inverting the Kepler equation using Fourier series Video
  51. Lecture 51: Odds and Ends Video
  52. Lecture 52: Dirichlet's theorem on Fouier series Video
  53. Lecture 53: Dirichlet's theorem on Fouier series continued Video
  54. Lecture 54: Topology on the Schwartz space Video
  55. Lecture 55: Examples of tempered distributions Video
  56. Lecture 56: Operations on distributions Video
  57. Lecture 57: Fourier Transform of tempered distribution Video
  58. Lecture 58: Support of a distribution. Distributions with point support Video
  59. Lecture 59: Distributional solutions of ODEs. Continuity of the Fourier transform and differentiation Video
  60. Lecture 60: The Poisson summation formula Video
  61. Live Session 13-03-2024 Video
  62. Live Session 22-03-2024 Video
  63. Live Session 12-04-2024 Video
  64. Live Session 07-03-2025 Video
  65. Live Session 27-03-2025 Video