TMA4170 Fourieranalyse våren 2016
Kursbeskrivelse finnes i studiehåndboka.
*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 *
- Monday 10.15-12, Auditorium KJL24
- Friday 14.15-16, Auditorium KJL24
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!
- Tuesday 17.15-18, KJL24.
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).
- Peter Lindqvist: Office 1152 in SB II, email@example.com
Please write TMA4170 in the subject line on all e-mail related to the course.
- Office hours: ???day 1?:15-1?:00
This is from 2015 and will gradually be updated.
|Week 3||Exercises||Text lost now|
|week 7||Exercises||Misprint: multiply dr by r in ex. 3|
|week 9||Exercises||Some helpdistribution.pdf|
|week 10||Exercises||Laplace Eqn|
|week 11||Exercises||Ex. 2, misprint: square the norm. (use Thm for orthonorm. of translates)|
|week 12||Chapter V: 3,4,6,17,18|
|week 13||Exercises||Moved to April 10th. Obvious missprint in the range of integration of the Four.coeff.|
|week 15||See week 13|
|week 17||Extra Exercises||Compensates 27.III. Second part of 7 Solution?! In 9 misprint|
More "advanced" theory:
- 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 Distributions||Not in the text book.|
|week 9||Notes||Fourier Transform of Distributions. The Schwartz class. Haar basis||not in the text book.|
|week 10||Ch 4||Haar Basis. Wavelets.|
|week 11||Ch 5||Wavelets.|
|week 13||Ch 6||Daubechies' Wavelets. Shannon's Wavelet||Calculation 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|
- N. N.* * ???@stud.ntnu.no
- N. N. * * ???@stud.ntnu.no ?
- N. N.