TMA4215 Numerical Mathematics, Autumn 2016


09.12 The projects have been graded, and the result sent by email to the one who submitted it. So if you have not heard anything, ask your colleague.
09.12 The exam with solutions.
01.12 Meeting hours before the exam and some advices can be found under Preparations.
01.12 I can not promise to finish the grading of the projects before the exam (but I will do my best).
28.11 Note: There is no exercise session today (supervision ended last week), but the solution of Problem set 10 is available.
21.11 For the exam preparation, there is also now an Problem set 10 on splines and Bezier-curves on the exercise page.
21.11 Some old exam papers are now available, se the menu to the left.
7.11 The project description is given at the project page.
NB! There will be no supervision in the exercise hours today. A timetable for when we will be available for supervision is given at project page.
6.11 A list of the project groups can be found here.
3.11 Project groups signup: students can form groups of up to 2 members, but you will possibly be 3 in total. Please read the instructions and answer the following form before Friday Nov 4 at 16:00.
3.11 There will be no regular exercise session on Monday November 7 at 16:15–18:00.
26.10 Minutes (in Norwegian) from the meeting with the reference group.
Point 2 (all notes at one place) has already been carried out, see Notes in the menu to the left.
17.10 I messed up the figures in the lecture today. On the lecture plan, there is a note on the QR-factorization, including the Householder reflections, (which are reflections relative to the space orthogonal to \(v\), not to \(v\) itself). I hope the figures are correct now.
Thank you to the student pointing out my mistake, you were absolutely right.
07.10 There will be no new exercise available this week. If you have question from the curriculum or old exercises, Fredrik will be available during the exercise sessions on Monday as usual.
29.9 We will now start on a new main topic, Numerical solution of linear and nonlinear systems of equations. The book by Sauer do not cover this topic well, although there are plenty of examples there which you may find helpful. The main material will be taken from the book by Quarteroni which can be downloaded for free. (see Teaching material). For those of you who have the book by Süli and Mayers, most of the curriculum can be found in the section 2.1-2.6, 3.1-3.3, 4 and 5.1-5.7. However, iterative methods for linear systems are not covered there.
13.9 It seems like some of you did not find the note on numerical ODEs on the lecture plan page, so to be sure, here it is:
Note on numerical ODEs (NODE).
The note will be extended ( additional sections posted on the lecture plan page), corrected and recompiled at the end of the course. So I would be grateful if you give me feedback on the note, and point out potential errors and mistakes.
12.9 A clarification: Our definition of local truncation error (LTE) \(d_{n+1}\) (or \(\tau_{n+1}\)) is the algorithmic error after one step when starting at the exact solution \((t_n, y(t_n)) \), while the the error after one step when starting at the approximate solution \((t_n, y_n)\) is called the local error. If anyone reads the book by Sauer, note that he uses our definition of local error as LTE, while Süli and Mayers defines LTE as \(d_{n+1}/h\).
8.9 The next two Mondays there will be lectures in EL2 17:15-18:00 on the following topics, which was at least partly covered in TMA4320:
12.09: Error estimation and stepsize selection (section 4.2 in the NODE-note)
19.09: Interpolation (Sauer, 3.1-2)
5.9 There has been a question about the alternative textbooks, in particular Süli and Mayers, and if we could also include text from this book on the lecture plan. The answer is no. Although reading other textbooks can be encouraged, you are responsible for finding the relevant parts yourself.
2.9 I did a mistake today, when computing the Lipschitz constant of the increment function for a second order RK method. This is corrected here.
31.8 The name of the members of the reference group is listed on the end of this page. Thank you to Rasmus, Julie and Jan Birger!
30.8 We encourage you to ask about anything you need help with during the exercise sessions: all the current problem sets, how to structure proof arguments, programming advice and theory in/outside the course (but you may experience large output error!).
30.8 Update: The denominator in exercise 6 in Problem set 1 should have been \(t+5\).
26.8 Problem set 1 is now available and will be supervised the following two Mondays since it arrived late.
26.8 Those of you who signed up after Tuesday's lecture or sent an e-mail should now have access to Nullrommet and other relevant doors.
23.8 Please see the Exercises-page for how to find and get access to the computer room (Nullrommet) for the exercise sessions. Those of you who signed up after today's lecture will probably get access this week.
16.8 First lecture is 23.08 in K5. Welcome! Exercises start 29.08.


  • Tuesday 10:15-12:00, K5
  • Friday 08:15–10:00, KJL2


  • Monday 17:15-18:00, EL2
  • Monday 16:15-18:00, Nullrommet (Room 380A in floor 3 of Sentralbygg II ).

Regular exercises will be in Nullrommet. Activities in EL2 will be announced.

Please see the Exercises-page for how to find and get access to Nullrommet.


NB! Please use TMA4215 in the subject heading in your emails.

Teaching Assistant

NB! Please use TMA4215 in the subject heading in your emails.

Teaching material

I assume that you all have Numerical Analysis by Timothy Sauer, 2nd edition (for example ISBN 9781292023588 (likely the cheapest)) available. Some topics will be covered by additional lecture notes.

There are several alternative textbooks, e.g.

  • Süli and Mayers, An Introduction to Numerical Analysis (ISBN 9780521007948).
  • Hämmerlin and Hoffman, Numerical Mathematics (free e-book (PDF) with NTNU network access).
  • Quarteroni, Sacco and Saleri, Numerical Mathematics (free e-book (PDF) with NTNU network access).

The exercises are included in the curriculum. 1-2 questions from the exercises will be given at the exam.

Information about the exam

  • December 9, 2016, kl. 09:00-13:00
  • Permitted aids: Code C
    • Approved simple pocket calculator is allowed.
    • Rottman is allowed.
    • One yellow, stamped A5 sheet with own handwritten formulas and notes (on both sides). You get this sheet from the department office of the department of Mathematical Sciences in the 7th floor in Sentralbygg II.

NB! This has been changed from last year!

  • The project counts 30/100 of the final grade and it has to be done this semester. It is not mandatory, but you will loose these 30 points if it is not done.
  • In order to pass the course the exam must be passed separately. The combination of exam and work/project must be passed as well.


Meeting hours before the exam (may be changed)

  • Tuesday 06.12: 14:15-16:00
  • Wednesday 07.12: 14:15-16:00
  • Thursday 08.12: 13:45-16:00

in 1348, SBII.

Some advices:

  • Get a good understanding of all concepts listed in the Lecture Plan.
  • Do all the exercises (or the parts of them) which only require pen, paper and a simple calculator.
  • Bring all the permitted aids, and use the yellow A5-sheet wisely.

Reference group

2016-12-09, Anne Kværnø