====== TMA4170 Fourier analysis 2019======
===== Messages =====
* The first lecture will take place in GL-SB2 S21 on Monday, January 7. Instead of the text book, we will use the lecture notes (see below: SYLLABUS-Notes). But this is not an online course, motivation and necessary details, missing from the notes, are lectured. You are recommended to read section 4 "Appendix 1" part of notes before the lecture. \\
* The first exercise session will take place in S21, 15th January, 16:15-17:00\\
* Exercise for week 2 can be found at the end of the notes, week 3 exercise will be handed out on Thursday, 10th January.\\
* Today (17th Jan) we finished section 1.6. The next lecture will be given by Helge Holden. \\
* On Tuesday, we went through Exercise 2. Since we will not provide the solutions for the exercise. We encourage you to attend the Exercise session or hand in the exercise. Exercise for week 5 is "Exercise set 1", see section 6 of the notes. \\
* There will be no Exercise Session on 22 Jan
* There will be no Exercise Session on 29 Jan
* Week 5 exercise has two parts and can be found in the notes now, solutions for Week 3 and 4 exercises will be presented on 5th Feb, 16:15-18:00, S21. There is an error in the last exercise for Week 4, sgn(x) should be -1 when x is negative
* There will be no Exercise Session on 12 Feb
* We will need some complex analysis results form the {{ :tma4170:2019v:6.pdf |Exercise for week 6}}, please have a look if you haven't taken the complex analysis course.
* Exercise set for week 7 is online now.
* Exercise set for week 8 is online now.
* {{ :tma4170:2019v:fourier_2.pdf |Part 2 of the notes}} is online now. Next week (11-17 March) we will do central limit theorem, equidistribution theorem and random walks.
* An {{ :tma4170:2019v:errata.pdf |errata}} for part 1 of the notes (also contains a list of errors in the weekly exercises).
* The Exercise session for 26th March will by in Xu's office (942 S2), the same time.
* Complete version of {{ :tma4170:2019v:fourier_2.pdf |Part 2 of the notes}} is online now.
* The final week will be repetition based on the exercises (No Exercise Session on 9 April)
* {{ :tma4170:2019v:summary_solution.pdf |A short summary}} of the course and solutions to several exercises
===== Course Information =====
* [[https://tp.uio.no/ntnu/timeplan/timeplan.php?type=course&id%5B%5D=TMA4135&id[]=TMA4170|Time Plan]] can be found here.\\
=== LECTURES ===
* Mondays 12:15-14:00, S21 Sentralbygg 2
* Thursdays 10:15-12:00, S21 Sentralbygg 2
=== EXERCISE SESSIONS ===
* Tuesdays 16:15-17:00, S21 Sentralbygg 2
=== EXAM ===
* Exam date: May 31, 09:00-13:00
* 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 you like).
=== SYLLABUS-Notes ===
The curriculum is covered mainly by the lectures based on the following notes and everything handed out during the lectures.
1. {{ :tma4170:2019v:fourier_1.pdf |part one}}
2. {{ :tma4170:2019v:fourier_2.pdf |part two}} (renewed from time to time)
3. {{ :tma4170:2019v:errata.pdf |Errata}}
=== Recommend books ===
The Fourier analysis part of the notes is based on the following two books:
**E. M. Stein & R. Shakarchi: Fourier Analysis, An Introduction, Princeton University Press, 2003**\\
**H. Dym & H. P. McKean: Fourier Series and Integrals, Academic Press, 1972**\\
The wavelet part of the notes is based on the following book:
**A. Boggess & F. Narcowich: A first course in Wavelets with Fourier Analysis, Wiley, 2nd Edition, 2009**.
We also recommend the following standard textbook on Fourier analysis and wavelets:
** Fourier Analysis and Applications, by G. Gasquet and P. Witomski, Springer.**\\
=== LECTURER ===
* Helge Holden: Office 1156 in SB II, [[helge.holden@ntnu.no]]
* Xu Wang: Office 942 in SB II, [[xu.wang@ntnu.no]]
=== REFERENCE GROUP ===
* Paul Duffin: [[pauldu@stud.ntnu.no]]
* Dennis Fimland: [[dennishf@stud.ntnu.no]]
=== CONSULTATION BEFORE THE EXAM ===
TBA
=== FINAL EXAM ===
TBA
===== Exercises =====
Usually we will hand out the exercise, but you can also find the exercises at the end of the notes. The first five exercise sets are in page 53--59 in {{ :tma4170:2019v:fourier_1.pdf |Part 1 of the notes}}. There are some mistakes, see the {{ :tma4170:2019v:errata.pdf |Errata}} for the corrections.
{{ :tma4170:2019v:6.pdf |Week 6 Exercise}}
{{ :tma4170:2019v:7.pdf |Week 7 Exercise}}
{{ :tma4170:2019v:8.pdf |Week 8 Exercise}}
{{ :tma4170:2019v:9.pdf |Week 9 Exercise}}
{{ :tma4170:2019v:10_11.pdf |Week 10-11 Exercise}}
Wavelet Exercise (Week 12-14): from Boggess--Narcowich
Ch.4: 1, 3, 4, 5
Ch.5: 5, 6, 10, 12
Ch.5: 8, 17, 18
Solutions can be found in the 2018 TMA4170 course page.
=== Previous exams: ===
**NOTE:** The exams from 2014 and older are written with a slightly different curriculum in mind and as such may contain exercises not covered by the current curriculum!
| 2017 | {{ :tma4170:2017v:tma4170_exam_2017.pdf | Exam}} | {{ :tma4170:2017v:tma4170_exam_2017_solution.pdf | Solution}} |
| 2016 | {{:tma4170:2017v:exam2016fou.pdf|Exam}} Misprint in ex. 2: Should be 1/abs(x)² not 1/abs(x) | {{:tma4170:2017v:solutionsfou2016.pdf|Solution}} |
| 2015 | {{:tma4170:2017v:exam2015fou.pdf|Exam}} | {{:tma4170:2017v:examfou2015solutions.pdf|Solution}} |
| 2014 | {{ :tma4170:2017v:2014.pdf |Exam}} | {{ :tma4170:2017v:2014lf.pdf |Solution}} |
| 2013 continuation | {{ :tma4170:2017v:contexam13.pdf |Exam}} | {{ :tma4170:2017v:losncont13.pdf |Solution}} |
| 2013 | {{ :tma4170:2017v:exam13.pdf |Exam}} | {{ :tma4170:2017v:losnex13.pdf |Solution}} |
| 2012 | {{ :tma4170:2017v:exam2012.pdf | Exam}} | {{ :tma4170:2017v:losn2012.pdf |Solution}} |
| 2006 | {{ :tma4170:2017v:exam2006.pdf |Exam}} | {{ :tma4170:2017v:soln2006.pdf |Solution}} |
| 2004 | {{ :tma4170:2017v:exam2004.pdf |Exam}} | {{ :tma4170:2017v:soln2004.pdf |Solution}} |
===== Tentative Lecture Plan (according to the notes) =====
| Week 2 | 1.1-1.5 | |
| Week 3 | 1.5, Appendix 2 | |
| Week 4 | 1.6-1.7 | |
| Week 5 | 1.7-1.8 | |
| Week 6 | 2.1-2.3 | |
| Week 7 | 2.4 | |
| Week 8 | 2.5-2.6 | |
| Week 9 | 2.7-2.8 | |
| Week 10 | B&N Ch.4 | |
| Week 11 | B&N Ch.5 | |
| Week 12 | B&N Ch.6 | |
| Week 13 | B&N Ch.7 | |
| Week 14 | Repetition | |
| Week 15 | Repetition | |
===== Actual Lecture Plan =====
| Week 2 | Fourier series, Pointwise and Mean square convergence | Xu |
| Week 3 | Lebesgue integral, elementary solution of D+s | Xu |
| Week 4 | Sec 1.7.1, 1.7.2 Sec 1.8.1 | Helge |
| Week 5 | Sec 2.1-2.3 | Helge(Monday), Ho Cheung Pang(Thursday) |
| Week 6 | 2.4.1-2.4.2 | Helge(Monday), Xu(Thursday) |
| Week 7 | 2.4.3-2.4.5 | Xu |
| Week 8 | Exercise set 6 on complex analysis | Xu |
| Week 9 | 2.5 | Xu |
| Week 10 | 2.6-2.7 | Xu |
| Week 11 | 2.8, 1.7.3, 1.8.2 | Xu |
| Week 12 | Mon: Ch 4 in BN, Thu: Se 5.1 | Xu(Monday), Ho Cheung Pang(Thursday) |
| Week 13 | Mon: Sec 5.2 (p. 204-214) in Boggess & Narcowich. Thu: Sec. 5.3 (up to p. 222) | Helge |
| Week 14 | Mon: The remaining part of Ch. 5, and Ch. 6 up to and incl. p. 237 , Thu: wavelet transform | Helge(Monday), Xu(Thursday) |
| Week 15 | Repetition based on exercises | Xu |