TMA4170 Fourieranalyse våren 2016

Kursbeskrivelse finnes i studiehåndboka.

Beskjeder

*NO EXERCISE SESSION TUESDAY 12.I.*

No lectures on week 1
* THE FIRST LECTURE WILL TAKE PLACE ON MONDAY THE 11th of January
* THE FIRST EXERCISE ON TUESDAY the 19th *

Kursinformasjon

LECTURES

  • Monday 10.15-12, Auditorium KJL24
  • Friday 14.15-16, Auditorium KJL24

EXAM.

  • Exam date: Friday, June 16th.
  • PERMITTED AIDS: One A-4 sized sheet of yellow paper stamped by the Department of Math. Sciences (on it you may in advance write whatever pleases you).
  • 16.V.2015 Text
  • 16.V.2015 Solutions

SYLLABUS

From the book by Boggess& Narcowich

  • Chapter 1
  • Chapter 2
  • Section 3.1
  • Chapter 4
  • Chapter 5
  • Chapter 6
  • Section 7.4

Moreover, the syllabus contains:

  • the Fourier Transform of Distributions
  • all the EXERCISES!

___

EXERCISES

  • Tuesday 17.15-18, KJL24.

TEXT BOOK

Most of the material will be found in
A. Boggess & F. Narcowich: A first course in Wavelets with Fourier Analysis.
The Fourier Series and Transforms have to be complemented with other sources.(The book is too weak when it comes to some proofs).

Teacher

  • Peter Lindqvist: Office 1152 in SB II, lqvist@math.ntnu.no
    Please write TMA4170 in the subject line on all e-mail related to the course.
  • Office hours: ???day 1?:15-1?:00

EXERCISES

This is from 2015 and will gradually be updated.

Week 3 Exercises Text lost now
Week 4 Exercises
week 5 Exercises
week 6 Exercises
week 7 ExercisesMisprint: multiply dr by r in ex. 3
week 8 Exercises
week 9 ExercisesSome helpdistribution.pdf
week 10Exercises Laplace Eqn
week 11ExercisesEx. 2, misprint: square the norm. (use Thm for orthonorm. of translates)
week 12Chapter V: 3,4,6,17,18
week 13ExercisesMoved to April 10th. Obvious missprint in the range of integration of the Four.coeff.
week 15See week 13
week 16Exercises
week 17Extra ExercisesCompensates 27.III. Second part of 7 Solution?! In 9 misprint

Notes

More "advanced" theory:

Additional Literature

  • E. Stein, R. Shakarchi: "Fourier Analysis", Princeton.
  • "A Guide to Distribution Theory and Fourier Transforms" by R. Strichartz, World Scientific.–Easy to read. Useful information.
  • "Wavelets -A Primer" by Ch. Blatter
  • "Fourier Series and Orthogonal Functions" by H. Davis, Dover. Clear examples and good proofs. (No wavelets.)

Tentative lecture plan

===usually according to Boggess & Narcowich===

Week 2 Ch. 0 The Hilbert Space. Orthonormal bases. Fourier Coefficients. The Trigonometric System.
Week 3 Ch 1 Convergence. Dirichlet's Kernel, Fejer's Kernel. Gibb's Phenomenon
week 4 Ch 2 (Parseval's formula Ch 1), The Fourier Transform
week 5 Ch 2 Fourier transform in L2, Plancherel's formula, convolutions. Sampling Theorem.
week 6 Ch 2 Oversampling. Heisenberg's Principle. Poisson's summation formula.
——–7 Ch 3 Discrete Fourier Transform.
week 8 Ch 3 Fast Fourier Transform. Theory of DistributionsNot in the text book.
week 9 Notes Fourier Transform of Distributions. The Schwartz class. Haar basisnot in the text book.
week 10 Ch 4 Haar Basis. Wavelets.
week 11 Ch 5 Wavelets.
week 13 Ch 6 Daubechies' Wavelets. Shannon's WaveletCalculation of 2nd moment Last 5 lines irrelevant. One 1/2 missing inside Q(w)
week 14 Ch 6 Continuous Wavelet Transform. Battle-Lemarie wavelet
week 15…Equidistributed numbers, various things, Repetition
week 16 …Repetition
week 17..???

Referansegruppe

  • N. N.* * ???@stud.ntnu.no
  • N. N. * * ???@stud.ntnu.no ?
  • N. N.
2015-12-30, Lars Peter Lindqvist