TMA4170 Fourier Analysis - Spring 2026
Kont/Retake exam 2026
The exam will be a standard oral exam, where you answer questions for about 40 min. Paper and whiteboard will be available.
Date: Thursday August 13.
Place: Room 1148, SB2 (Espen's office).
Important: You can take the exam only if you have been assigned a time slot!
- Time slots will (only) be assigned in a physical meeting at the exam location on August 13 at 9:00.
- Make sure to be there at 9:00.
| Tentative exam schedule (room 1148 SB2) | ||
|---|---|---|
| Thursday 13.08. | 09:00-09:15 | Meeting to assign time slots |
| 09:15-09:55 | Candidate 1 | |
| 10:00-10:40 | Candidate 2 | |
| 10:45-11:25 | Candidate 3 | |
| 11:30-12:10 | Candidate 4 | |
PS: I will not answer emails during my vacation.
Welcome to TMA4170 Fourier Analysis!
Messages
| Date | Title | Message |
|---|---|---|
| 08.7. | Exam 2026 | Updated constant in inequality in Problem 1b, see Problems and solutions. |
| 15.6. | Exam 2026 | Updated solutions to problem 4c, see solutions. Grading completed, results will be available in Studweb soon. Grading document/retteveiledning available in Blackboard. |
| 5.6. | Exam 2026 | Problems and solutions I hope you did well all of you, have a nice summer! |
| 2.6. | Exam hints | There will be problems involving PDEs on the exam. The problems I did the last week of teaching are relevant. |
| Last office hours | Wednesday June 3, 14:15-16:00 in F3. \\ \\ | |
| Mistake | Exam 2025, problem 4 ii: \(\quad C_m\subset L^1\cap L^2\quad\) so \(\quad\mathcal F[C_m]\subset C_0\cap L^2\). Hence \(L^2\) is also correct here. |
|
| Exam | Friday 5.6. 9:00-13:00 See 'Course info' in the menu for important info about the exam. NTNU rule: You need to use a black or blue permanent marker or pen when filling out the question code, exam information, and answers to questions. Pencil or red ink are not allowed. School exam with hand drawings - for students - Kunnskapsbasen - NTNU Aids: Approved simple calculator and one handwritten sheet of A4 paper is allowed on the exam. You can write on both sides, but no printing or copying is allowed. Language: English only. OBS: * 9 problems in total (counting 1a, 1b etc.), all of which will be given equal weight when the grade is computed. * 8 problems to be answered on paper sheets (use correct codes), 1 problem in Inspera. * Some exam problems will be taken from the Exercise problems, or problems very close to exercise problems. Good luck! |
|
| 23.4. | Exercise 10 | Solutions posted in Blackboard. Thanks to group 2! |
| 22.4. | Reference group | Meeting 3: short summary posted, see 'reference groups' in the menu. If your concerns have not been addressed, contact the lecturer directly. |
| Lectures notes | I have posted all my handwritten notes for the lectures below (one pdf per week) - under 'lectures' below (this page). | |
| Exercise 11 | Solutions posted in Blackboard. Thanks to group 3! | |
| Exercise 12 | Solutions posted in Blackboard. Thanks to group 4! | |
| 16.4. | Last lecture | Friday 17.4. (tomorrow) |
| Todays lecture | Some repetition and solution of exam relevant problems from the exercises: Monotone and regular functions, decay of Fourier coefficients, convergence of Fourier series (\(L^2\), pt.wise, uniform). Problems: SS 2.7:1, 3.3:17, Exercise 5 P1. | |
| Old exams | Exam May 2025 problems and solutions. 2025 is very relevant, but rather simple. Only parts of older exams are relevant because the curriculum or emphasis of the course has been different. See 'Relevant problems from previous exams (tentative)' under 'Course info' in the menu for more details. | |
| Exam | Friday 5.6. 9.00-13:00, see 'Course info' in the menu for important info about the exam. NTNU rule: You need to use a black or blue permanent marker or pen when filling out the question code, exam information, and answers to questions. Pencil or red ink are not allowed. School exam with hand drawings - for students - Kunnskapsbasen - NTNU Aids: Approved simple calculator and one handwritten sheet of A4 paper is allowed on the exam. You can write on both sides, but no printing or copying is allowed. Language: English only. OBS: Some exam problems will be taken from the Exercise problems, or problems very close to exercise problems. |
|
| Office hours | … before the exam: Tuesday 02.06. 10:15-12:00 in F3. Wednesday 03.06. 14:15-16:00 in F3. |
|
| Final curriculum | Available under 'Course info' in the menu. Note that all Exercise problems are relevant for the exam, and some exam problems will be close some of the exercise problems. |
|
| 10.4. | Next week | Last week of lectures. I will do relevant exam and exercise problems. There will be exercise class on Wednesday (Exercise 12). |
| Todays lecture | I discussed FFT and the carefully did problem 3.3:15 from the book (SS). This problem is relevant for the exam. |
|
| 25.3. | Exercise 9 | Solutions posted in Blackboard. Thanks to group 1! |
| Friday 27.3. | No lecture because of imminent Easter holidays. | |
| 19.3. | Next week | No lecture Friday before Easter (27.3.). Lecture on Thursday 26.3. and exercise class on Wednesday 25.3. as usual. |
| This week | The discussion on the central limit theorem is only given in the handwritten notes. It follows Dym and McKean chp. 2.7.7. | |
| Reference group | Meeting 2: short summary posted, see 'reference groups' in the menu. If your concerns have not been addressed, contact the reference groups. |
|
| 18.3. | Exercise 8 | Solutions posted in Blackboard. Thanks to group 4! |
| 16.3. | Exercise 7 | Solutions posted in Blackboard. Thanks to group 3! |
| 11.3. | Friday lecture | … this week is at the usual time: 14:15-16:00. |
| Exercise class | … this week is Thursday 08:15-08:50 in F3. | |
| Mistake in class today | Correct Poisson formula is: \[\sum_{n\in\mathbb Z}f(x+n)=\sum_{n\in\mathbb Z}\hat f(n) e^{2\pi i nx}.\] This is what we proved in class. See updated notes for Week 11 below. | |
| Reference group | Meeting 2 Wednesday 18.3. (tentatively). Contact the referance group if you have feedback on the course, see 'reference groups' in the menu. |
|
| Exercise 6 | Solutions posted in Blackboard. Thanks to group 2! | |
| 5.3. | Next week | … week 11: Lectures: - Wednesday 11.3. 16:15-18:00, - Friday 13.3. 14:15-16:00 (the usual time) Exercise class: - Thursday 12.3. 8:15-8:50 (Espen in meeting on Thursday) |
| This week | … curriculum: Fourier inversion 2 and 3, examples, "Riemann-Lebesgue", and everything on Fourier transform in \(L^2\) are not covered by the SS book. See class and handwritten notes. | |
| Exercises 7 and 8 | Posted under 'Exercises' in the menu. Responsible: Groups 3 and 4. |
|
| 27.2. | Next week | … week 10: -Lectures: Wednesday 4.3. 16:15-18:00, Thursday 5.3. 08:15-10:00 -No exercise class (Espen travelling on Friday) |
| Exercise 5 | Solutions posted in Blackboard. Thanks to group 1! | |
| 18.2. | Exercise 4 | Solutions posted in Blackboard. Thanks to group 4! |
| March 2026 Week 10: Week 11: | Lectures: … Wednesday 4.3. 16:15-18:00 … and … Thursday 5.3. 08:15-10:00 No exercise class (Espen travelling on Friday) Lectures: … Wednesday 11.3. 16:15-18:00 … and … Friday 13.3. 14:15-16:00 Exercise class: Thursday 8:15-8:50 (Espen in faculty board meeting the rest of the day) |
|
| 12.2. | Exercise 3 | Solutions posted in Blackboard. Thanks to group 3! |
| Exercise 6 | Posted under 'Exercises' in the menu. Responsible: Group 2. |
|
| 5.2. | Lectures… | …this week: Materiel on pointwise convergence and decay vs. regularity not in SS book, see 'Plan of Lectures' for more details. |
| Exercise 5 | Posted under 'Exercises' in the menu. Responsible: Group 1. |
|
| Exercise 2 | Solutions posted in Blackboard. Thanks to group 2! | |
| 30.1. | Reference group | Meeting 1. Short summary posted, see 'reference groups' in the menu. If your concerns have not been addressed, contact the reference groups. |
| Exercise 4 | Posted under 'Exercises' in the menu. Responsible: Group 4. |
|
| 26.1. | Reference group | Meeting 1 wednesday 28.1. (confirmed). Contact the referance group if you have feedback on the course, see 'reference groups' in the menu. |
| OBS Exercise Groups | I have merged group 2 and 5 to make a new group 2 with five students. We have 4 groups now, which will be responsible for exercises in turns. See info under 'Exercises' in the menu for detailed instructions and expectations. |
|
| Exercise 3 | Posted under 'Exercises' in the menu. Responsible: Group 3. |
|
| Exercise 1 | Solutions posted in Blackboard. Thanks to group 1! | |
| 16.1. | Exercise Groups | Still some people have not signed up, please do so here. Note again that how much your group does is up to you, and everything you do will help also the other students. |
| Reference group | Now appointed, many thanks to Andrzej and Magnus for volunteering! See 'Reference group' in the menu for more info. | |
| Exercise 2 | Posted under 'Exercises' in the menu. Responsible: Group 2. |
|
| 09.01. | Exercise Groups | Please sign up for exercise groups here by next Wednesday (14.01.) |
| Reference group | I am looking for 2 volunteers - send me an email/tell me in class if you are interested. Light workload: 3 meetings (< 45 mins) and one (< 1 page) final report. |
|
| Notes | I will post my handwritten notes (on Fridays after the lectures) - at least when I deviate much from the book. See below under 'lectures'. This week's discussion on uniform convergence and continuity ++ can be found there. |
|
| Slides | I will also post any slides I use at the same place. | |
| Exercise 1 | Posted under 'Exercises' in the menu. Responsible: Group 1. |
|
| 05.01. | First lecture | Thursday 08.01.2026 at 8:15 in F3 |
| First exercise class | Wednesday 14.01.2025 at 16:15 in F3 | |
| Homework: | Read chapter 1 and the appendix in SS. Review basic complex analysis as in Exercise 1-5 in section 1. |
|
| Mathematics 4 or MA2106 | Definitions for Fourier series and transforms, examples, and applications to PDEs are known from TMA4120 Mathematics 4K or MA2106 Complex Function Theory and Differential Equations. This includes separation of variables and transform methods for solving wave, heat, and Laplace equation equations. |
|
| Tentative plan | … of lectures can be found in the menu under 'Plan of Lectures' (updated weekly) | |
| Exercises and Groups | There are supervised exercises in this course. These are part of the curriculum and relevant for the exam. Solutions will be provided by the exercise groups. Go 'Exercises' in the menu and read carefully. Please sign up for exercise groups here by next Wednesday (14.01.) |
Lecturer:
- Office hours: During exercise classes
Lectures:
Exercises:
- Wednesday 16:15-18:00, F3
Espen present from 16:15-17:00.