TMA401/MMA400, Functional analysis/Applied functional analysis, 2018/19

Latest news

Welcome to the course! The schedule for the course can be found in TimeEdit.

The setup is the same as last year.

Course representatives: The following students are selected for TMA401:

Anton Björk              

Jakub Joska             

Niklas Moszczynski 

Selma Tabakovic     

Adam Östberg         

There will be question session on the 25 of October at 13.15  in MVF:31

"Tentagranskning" (handout of the examination papers) will be held in room MVL14 on 22 of November at 12.00-12.30.

Here is the written exam from 2018-10-31 with solutions.

Here is the written exam from 2019-01-08 with solutions.


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. Notes from last year can be found here.  

English-Swedish mathematical dictionary



 Week  Chapter  Contents
   1   DM1  Introduction, vector spaces, completeness
   2   DM1, K  Banach spaces, linear mappings, fixed point theory
   3   K  Fixed point theory (cont.), Lp-spaces
   4   K, DM3  Lp-spaces (cont.), Hilbert spaces
   5   DM4  Linear operators on Hilbert spaces
   6   DM4, K  Compact operators, spectral theory
   7   DM5, K  Applications to ODE
 Question session

Recommended exercises

 Week  Exercises
   1  DM1: 1, 5, 13, 14, 36, 37, 40, 45
   2  K7.2: 11, 12, 13, 17
 K7.3: 11
   3  K7.4: 2, 6, 7, 14, 16, 17
   4  K7.5: 1, 9, 10, 11, 12, 19, 37
   5  K7.6: 2, 3, 4, 5, 6, 9
   6  K7.6: 14, 16, 29
   7  K7.7: 1, 2, 16, 24, 25

Exercises green-marked have been treated in class.

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 are 2019-09-15. You can send your solutions to the handins (I want pdf-files) by mail to

  Homework assignment 1: Deadline 2018-09-18 changed to 2018-09-21  Solutions

 Homework assignment 2: Deadline 2018-10-02 changed to 2018-10-05  Solutions

 Homework assignment 3:  Deadline 2018-10-18 changed to 2018-10-21

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 course is examined by a written exam. This 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 apply them in problem solving. More information on the written exam is given 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 can do this from 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 2018-09-01  Exam 2018-01-04  Exam 2017-10-25

Exam 2017-08-26  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

Solutions to some old exams will be given later.

Here are some solutions

Solution 2018-09-01  Solution 2018-01-04  Solution 2017-10-25

Solution 2017-08-26  Solution 2017-01-05  Solution 2016-10-26                                                                 

                                                                      Solution 2015-10-28

                                   Solution 2015-01-05  Solution 2014-10-29

Solution 2014-08-30                                     Solution 2013-10-23