Fourier Analysis and its applications AMJDKYQZN8

URI	`m2://res/AMJDKYQZN8`
Kind	course
Creators	G. K Srinivasan (instructor)
Date	2023-01-05
Scope	in
Ids	course 02qyf5152:111101164

Expressions

e1: edition

Language	en
Date	2023-01-05

m1: page, IIT Bombay (record). nptel 111101164
m2: page, 2023-01-05 (record). nptel 111101164

Contents

part 1: week-01
session 1: Lecture 1: Genesis and a little history
session 2: Lecture 2: Basic convergence theorem
session 3: Lecture 3: Riemann Lebesgue Lemma
session 4: Lecture 4: The ubiquitous Gaussian
session 5: Lecture 5: Jacobi theta function identity.
part 2: week-02
session 6: Lecture 6: The Riemann zeta function
session 7: Lecture 7: Bessel's functions of the first kind
session 8: Lecture 8: Least square approximation
session 9: Lecture 9: Parseval formula. Isoperimetric theorem
session 10: Lecture 10: Dirichlet problem for a disc
part 3: week-03
session 11: Lecture 11: The Poisson kernel
session 12: Lecture 12: Cesaro summability and Fejer's theorem
session 13: Lecture 13: Fejer's theorem (Cond)
session 14: Lecture 14: Kronecker's theorem
session 15: Lecture 15: Weyl's equidistribution theorem
part 4: week-04
session 16: Lecture 16: Borel's theorem and beyond
session 17: Lecture 17: Fourier transform and Schwartz space
session 18: Lecture 18: Hermite's differential equation
session 19: Lecture 19: Fourier inversion theorem
session 20: Lecture 20: Plancherel's theorem
part 5: week-05
session 21: Lecture 21: Heat equation. The heat kernel
session 22: Lecture 22: Airy's function
session 23: Lecture 23: Exercises on Fourier transform
session 24: Lecture 24: Principle of equipartitioning of energy
session 25: Lecture 25: Formula of Srinivasa Ramanujan
part 6: week-06
session 26: Lecture 26: Sturm Liouville problems. Orthogonal systems
session 27: Lecture 27: Vibrations of a circular membrane
session 28: Lecture 28: Fourier Bessel series
session 29: Lecture 29: Properties of Legendre polynomials
session 30: Lecture 30: Properties of Legendre polynomials (contd)
part 7: week-07
session 31: Lecture 31: Properties of Legendre polynomials interlacing of zeros
session 32: Lecture 32: Laplace's integrals and Rayleigh's expansion of plane waves
session 33: Lecture 33: Regular SturmLiouville problems
session 34: Lecture 34: Variational properties of eigenvalues
session 35: Lecture 35: The Dirichlet principle
part 8: week-08
session 36: Lecture 36: Regular SturmLiouville problems Existence of eigenvalues
session 37: Lecture 37: The Bergman space
session 38: Lecture 38: The BanachSteinhaus' theorem
session 39: Lecture 39: Hilbert space basics
session 40: Lecture 40: Completeness of Hermite functions
part 9: week-09
session 41: Lecture 41 : Laugerre polynomials
session 42: Lecture 42: Orthonormal bases in Hilbert spaces
session 43: Lecture 43: Nonseparable Hilbertspaces. Almost periodic functions
session 44: Lecture 44: HilbertSchmidt operators and Green's functions
session 45: Lecture 45: Spectrum of a bounded linear operator
part 10: week-10
session 46: Lecture 46: Weak (sequential) compactness of the closed unit ball
session 47: Lecture 47: Compact selfadjoint operators. Existence of eigen values
session 48: Lecture 48: Compact selfadjoint operators. Existence of eigen values continued
session 49: Lecture 49: Celestial Mechanics
session 50: Lecture 50: Inverting the Kepler equation using Fourier series
part 11: week-11
session 51: Lecture 51: Odds and Ends
session 52: Lecture 52: Dirichlet's theorem on Fouier series
session 53: Lecture 53: Dirichlet's theorem on Fouier series continued
session 54: Lecture 54: Topology on the Schwartz space
session 55: Lecture 55: Examples of tempered distributions
part 12: week-12
session 56: Lecture 56: Operations on distributions
session 57: Lecture 57: Fourier Transform of tempered distribution
session 58: Lecture 58: Support of a distribution. Distributions with point support
session 59: Lecture 59: Distributional solutions of ODEs. Continuity of the Fourier transform and differentiation
session 60: Lecture 60: The Poisson summation formula
part 13: Live Session
session 61: Live Session 13-03-2024
session 62: Live Session 22-03-2024
session 63: Live Session 12-04-2024
session 64: Live Session 07-03-2025
session 65: Live Session 27-03-2025

Catalogue records

nptel: 111101164 (manifestation)
nptel_video: 111101164 (manifestation)