TMA401/MMA400, Functional analysis/Applied functional analysis, 2017/18

Latest news

Here is the written exam given 2018-01-04 and here are the solutions.

Tuesday 21/11 there will be a "tentavisning" (review of the written exam) in MVL15 at 12.00-12.30.

Here is the written exam given 2017-10-25 and here are solutions.

Question session: Room MVL15 on Tuesday 17/10 at 10.00.

Welcome to the course! The course starts on Tuesday 2017-08-29 and the schedule for the course can be found in TimeEdit.The general setup of the course will be the same as last year. 

Course representatives: The following students are selected for TMA401

Karen Baca

Bernhard Philipp Glauber

Konrad Thorsteinsson

Hans Gunnar WesterstÃ¥hl Oliveira

David Winant


Course coordinator: Peter Kumlin  

Course literature

[DM] L.Debnath/P.Mikusinski: Hilbert Spaces with Applications, 3rd ed, Chapters 1-5

[K] material not contained in the textbook together with additional exercises. I will continuously update these notes. Here [K2016] you can find last year version of [K].



Introduction, vector spaces, completeness
DM1, K
Banach spaces, linear mappings, fixed point theory
K Fixed point theory (cont.), Lp-spaces
K, DM3 Lp-spaces (cont.), Hilbert spaces
DM4 Linear operators on Hilbert spaces
DM4, K Compact operators, spectral theory
DM5, K Applications to ODE

Question session

Recommended exercises

Week Exercises
    1 DM1: 1, 5, 13, 14, 36, 37, 40, 45
    2 K 6.2: 11, 12, 13, 17
K 6.3: 11
    3 K 6.4: 2, 6, 7, 14, 16, 17
    4 K 6.5: 1, 9, 10, 11, 12, 19, 35
    5 K 6.6: 2, 3, 4, 5, 6, 9, 14, 16, 29
    6 K 6.7: 1, 2, 16 24, 25

Computer labs

No computer labs or Mathlab exercises in this course.

Reference literature:

Learning MATLAB, Tobin A. Driscoll ISBN: 978-0-898716-83-2 (The book is published by SIAM).

Course requirements

The learning goals of the course can be found in the course plan.


During the course there will be three homework assignments. They are not mandatory but can result in up to 4 bonus points on the written exam. The expiring date for the bonus points is 2018-09-15. You can send your handins  (I want pdf-files)  by mail to

Homework assignment 1: Deadline 2017-09-14  

Homework assignment 2: Deadline 2017-09-28  

Homework assignment 3: Deadline 2017-10-12 is changed to 2017-10 -16!  Solutions to homework assignment 3.

Every homework assignment consists of 4 problems and a correct solution to a problem gives 1 point. The total number of points one can get is 12 points. This results in bonus points according to the following table:

4 bonus points if at least 11 points  

3 bonus points if at least 8 points    

2 bonus points if at least 5 points  

1 bonus point if at least 3 points


The written exam consists of 6 problems where 3 of them are of a more theoretical nature. To pass the exam you need to score 10 points (bonus points included) out of 25 points. To get the grades 4 and 5 you need to score 15 and 20 points respectively.

You should be able to state and explain all definitions and state and prove the theorems given in the course and also apply them in problem solving. More information on the written exam can be found here.

Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal.

At the exam, you should be able to show valid identification.

After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.

At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and retrieved at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

Old exams

Exam 2017-01-05  
Exam 2016-10-26  

Exam 2016-08-27
Exam 2016-01-07
Exam 2015-10-28

Exam 2015-08-29
Exam 2015-01-05
Exam 2014-10-29

Exam 2014-08-30
Exam 2014-01-18
Exam 2013-10-23

Exam 2013-08-31
Exam 2013-01-17
Exam 2012-10-24

Exam 2012-09-01
Exam 2012-01-12
Exam 2011-10-19

There will be more old exams later.