Introductory course in linear algebra and differential equations (2022)

Welcome to the introductionary course in linear algebra and ordinary differential equations :-D

I have given a lot more problems than I expect you to do. Prioritise, and please do not try to do them all.

The course is voluntary with no exam.


The course will be held in August 2022, in week 32 (August 8th – 12th) and in week 33 (August 16th – 19th). Map to the rooms: EL1 and F2.

Monday 8/08 Tuesday 9/08 Wednesday 10/08 Thursday 11/08 Friday 12/08
Room EL1 EL1 EL1 EL1 EL1
09:15-10:00 Lecture Lecture Lecture Lecture Lecture
10:15-11:00 Problem session
11:15-12:00 Problem session Problem session Problem session Problem session
Monday 15/08 Tuesday 16/08 Wednesday 17/08 Thursday 18/08 Friday 19/08
Room F2 F2 F2 F2
No lecture!
(Matriculation Ceremony)
Lecture Lecture Lecture Problem session
11:15-12:00 Problem session Problem session Problem session

The web page from last year can be consulted to see the main elements. We will however not be following the exact same recipe, nor have the exact same curriculum.

Course contents

The focus in our course will be on ordinary differential equations (ODE), and mostly on linear ODE's with constant coefficients. Towards the end we will look at systems of differential equations.

Linear algebra will also be touched upon in order to study systems of differential equations, but also on its own merits. We will be covering systems of linear equations, matrices and vectors, invertability, determinants, eigenvectors, diagonalization, LU-decomposition and the matrix exponential.

Do note that we will not be covering the topics rigorously in the lectures, but for the interested student the notes should contain a bit more information and the references given at the bottom of the page can be worth checking out.


Tentative plan

Do note that this is only a tentative plan and can be changed before or during the course. If we collectively find that we can skip past some parts we may do that, or if we spend more time than planned on some part we may postpone the following parts.

Here are the notes from 2021.
Here are the notes for this year.

Day Topic Exercises Notes + Recording Notes from TMA4110/15
Only in Norwegian
Monday 8/8 Short intro to ODEs Exercises-1 + Solutions Notes-1
Rec: Lecture 1
Rec: Lecture 2
1st order ODEs
Integrating factor
Separable ODEs
Tuesday 9/8 2nd order ODEs Exercises-2 + Solutions Notes-2
Rec: Lecture 1
Rec: Lecture 2
Wedenesday 10/8 Numerical solutions Notes-3
Rec:Lecture 1
Lecture 2 used for exercises
Eulers method
Thursday 11/8 Linear algebra Exercises-4 + Solutions Notes-4
Rec:Lecture 1
Rec:Lecture 2
Systems of linear equations, Gaussian elimination Lineære likninger
Matrix operations Matriser
Matrix equations Vektorlikninger
Friday 12/8 Linear independece Exercises-5 + Solutions Notes-5
Lineær uavhengighet
Subspaces Vektorrom
The determinant Determinant
Tuesday 16/8 Eigenvectors Exercises-6 + Solutions Notes-6 Egenvektorer
Diagonalization Diagonalisering
Wednesday 17/8 System of 1st order ODEs Exercises-7 +Solutions Notes-7 Systemer av difflikninger
Andre ordens difflikninger
Matrix exponential
From nth order ODE to system
Thursday 18/8 Phase portraits No new exercises. Notes contained in above notes.
Friday 19/8 No lecture, but possibility of solving previous exercises with help.


You will not need any book to follow this course. The following resources can be used as supplementary sources, or any books you have used earlier for courses on linear algebra and differential equations. Do note that the listed books do cover a lot more than what we will be able to in our short course.

  • Erwin Kreyszig
    Advanced Engineering Mathematics
    10th edition
    ISBN 0-470-45836-4
  • Introduction to Linear Algebra, fifth edition
    Author: Gilbert Strang
    ISBN: 978-0-9802327-7-6
  • Differential Equations, Linear Algebra and its Applications, first/second edition
    Compiled by: Institutt for matematiske fag, NTNU
    ISBN: 978-1-78448-020-2
  • Matematikk i praksis
    Authors: Tor Gulliksen, Amir M. Hashemi, Arne Hole
    ISBN: 978-82-15-0208707
    Note: Only in Norwegian
2022-08-29, Endre Sørmo Rundsveen