Skip to content


Linear Algebra and Differential Equations 7.5 credits

Linjär algebra och differentialekvationer
First cycle, M0049M
Course syllabus valid: Autumn 2021 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Education level
First cycle
Grade scale
G U 3 4 5
Subject group (SCB)

Entry requirements

In order to meet the general entry requirements for first cycle studies you must have successfully completed upper secondary education and documented skills in English language and the course Linear Algebra and Calculus (M0048M) or equivalent.

More information about English language requirements


The selection is based on 1-165 credits.

Course Aim
After completed course, the students should be able to:
  • use central concepts and techniques for complex numbers, algebraic equations and the complex exponential function.
  • use vector spaces, subspaces and bases.
  • use eigenvectors and eigenvalues for diagonalization.
  • perform orthogonal diagonalization for symmetric matrices.
  • solve basic differential equations as first order separable equation, linear equation of order one and higher.
  • use computers programs to do calculations within the course (MATLAB).
  • identify and solve problems within the course. 

This course treats basic principles and techniques concerning complex numbers, algebraic equations and differential equation and a continuation of linear algebra. The linear algebra part deal with vector spaces, subspaces and bases, eigenvalues and eigenvectors, diagonalization, orthogonal projection, method of least square and quadratic forms. Several concepts are investigated with computer aid (MATLAB).

Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website.
The teaching consists of lectures and tutorials. The main learning is achieved by home studies, mainly problem solving.

If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.
The course aims are examined by a written individual exam and compulsory computer tasks. Grading according to the scale G U 3 4 5.

Transition terms
The course replaces M0031M

Stefan Ericsson

Literature. Valid from Autumn 2021 Sp 1 (May change until 10 weeks before course start)
Lay D: Linear algebra and its applications. Addison-Wesley, senaste upplagan.
Dunkels m fl: Derivator, integraler och sånt ... Studentlitteratur, senaste upplagan.
Jönsson, Per: MATLAB – beräkningar inom teknik och naturvetenskap. Studentlitteratur, latest edition. (Note: voluntary)

Course offered by
Department of Engineering Sciences and Mathematics

CodeDescriptionGrade scaleHPStatusFrom periodTitle
0002LaborationU G#1.00MandatoryA19
0003Written examG U 3 4 56.50MandatoryA21

Study guidance
Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.

Syllabus established
by Niklas Lehto 15 Feb 2019

Last revised
by Head Faculty Programme Director Niklas Lehto 17 Feb 2021