Introduction to Fourier Analysis 5ARMFGD7YV

URI	`m2://res/5ARMFGD7YV`
Kind	course
Creators	Parasar Mohanty (instructor)
Date	2024-07-18
Scope	in
Ids	course 05pjsgx75:111104519

Expressions

e1: edition

Language	en
Date	2024-07-18

m1: page, IIT Kanpur (record). nptel 111104519
m2: page, 2024-07-18 (record). nptel 111104519

Contents

part 1: Week 1
session 1: Lecture 01: Origin of Fourier series
session 2: Lecture 02: Convergence of a series and Riemann integration
session 3: Lecture 03: Riemann integration and periodic functions
session 4: Lecture 04: Fourier coefficients and series
session 5: Lecture 05: Complex Fourier series
part 2: Week 2
session 6: Lecture 06: Riemann Lebesgue lemma and Dirichlet kernel
session 7: Lecture 07: Convolution of two Riemann integrable functions
session 8: Lecture 08: Properties of convolution
session 9: Lecture 09: Cesaro summability and summation by parts
session 10: Lecture 10: Fejer kernel
part 3: Week 3
session 11: Lecture 11: Fejer theorem and applications
session 12: Lecture 12: Good kernels and Poisson kernel
session 13: Lecture 13: Abel summability
session 14: Lecture 14: Dirichlet problem
session 15: Lecture 15: Convergence at jump discontinuity
part 4: Week 4
session 16: Lecture 16: Orthonormal families
session 17: Lecture 17: Pythagoras theorem and Parseval identity
session 18: Lecture 18: Pointwise convergence
session 19: Lecture 19: Parseval identity applications
session 20: Lecture 20: Divergent Fourier series
part 5: Week 5
session 21: Lecture 21: Pointwise convergence of S_N(f)
session 22: Lecture 22: Isoperimetric problem
session 23: Lecture 23: Weyl's equidistribution theorem
session 24: Lecture 24: on Equidistributed sequences
session 25: Lecture 25: Proof of Weyl's criterion
part 6: Week 6
session 26: Lecture 26: Fourier analysis on finite groups
session 27: Lecture 27: Fourier transform on Z(N)
session 28: Lecture 28: Inversion theorem and Parseval identity
session 29: Lecture 29: Results on Fourier coefficients of two functions
session 30: Lecture 30: Fast Fourier transform
part 7: Week 7
session 31: Lecture 31: Fourier analysis on finite abelian group
session 32: Lecture 32: Fourier analysis on finite abelian groups
session 33: Lecture 33: Simultaneously diagonalizable operators and characters
session 34: Lecture 34: Results of Fourier series on finite abelian group
session 35: Lecture 35: Applications in Number theory
part 8: Week 8
session 36: Lecture 36: Fourier transform on R
session 37: Lecture 37: Properties of Fourier transform
session 38: Lecture 38: Inversion formula and convolution
session 39: Lecture 39: Fejer kernel on R
session 40: Lecture 40: Schwartz space
part 9: Week 9
session 41: Lecture 41: Convolution and Good kernel in Schwartz space
session 42: Lecture 42: Multiplication formula and Fourier inversion theorem
session 43: Lecture 43: Plancherel formula and Poisson summation formula
session 44: Lecture 44: Application of Poisson summation formula
session 45: Lecture 45: Weierstrass theorem and Heisenberg uncertainty principle
part 10: Week 10
session 46: Lecture 46: Hermite operator
session 47: Lecture 47: Solution of ODE by using Fourier transform
session 48: Lecture 48: Laplacian equation
session 49: Lecture 49: Poisson kermal and mean value theorem for harmonic functions
session 50: Lecture 50: Wave equation
part 11: Week 11
session 51: Lecture 51: Eigenvalues of Fourier transform
session 52: Lecture 52: Fourier transform on R^n
session 53: Lecture 53: Properties of Fourier transform on R^n
session 54: Lecture 54: Inversion theorem and Plancherel theorem
session 55: Lecture 55: Wave equation, heat equation and Poisson kernel
part 12: Week 12
session 56: Lecture 56: Fourier series in higher dimension
session 57: Lecture 57: Poission summation formula
session 58: Lecture 58: Application of Poission summation formula
session 59: Lecture 59: Radon transform
session 60: Lecture 60: Reconstruction formula

Catalogue records

nptel: 111104519 (manifestation)
nptel_video: 111104519 (manifestation)