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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
MVE580 - Linear algebra and differential equations  
Linjär algebra och differentialekvationer
Syllabus adopted 2020-02-19 by Head of Programme (or corresponding)
Owner: TIMEL
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Major subject: Mathematics

Students admitted to the program before 2019/20 should contact their UBS before being registered on the course.
Teaching language: Swedish
Application code: 67114
Open for exchange students: No
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0119 Examination 7,5c Grading: TH   7,5c   14 Jan 2021 pm L   07 Apr 2021 pm L,  16 Aug 2021 pm L

In programs



Timo Vilkas

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General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

The course LMA401 Calculus, or equivalent knowledge.


The aim of the course is to, in a logically coherent way, give basic knowledge of differential equations and linear algebra. The course will also give necessary prerequisites for mathematical treatment of technical problems in future profession and supply a good base for further studies.

Learning outcomes (after completion of the course the student should be able to)

  • define basic concepts in matrix and vector algebra and formulate, and in some cases prove, fundamental concepts in these areas.
  • solve systems of linear equation.
  • determine if a matrix is invertible and, if so, determine the inverse.
  • calculate determinants.
  • calculate scalar and vector product.
  • apply vectors within space geometry.
  • use the least squares method.
  • calculate with complex numbers on both rectangular and polar form.
  • set up and solve simple differential equations.


  • Linear equation systems: row equivalents for matrices, the elimination method on matrix form.
  • Matrix algebra: addition, subtraction, multiplication, inverse matrix.
  • The least squares method.
  • Linear combination, linearly independent / dependent.
  • Determinants: conditions for invertability, laws of calculation, Cramers rule.
  • Geometric vectors: addition, subtraction, scalar and vectorial product, applications in space geometry.
  • Complex numbers: rectangular coordinates,  laws of calculation, algebraic equations, polar coordinates, de Moivre's formula, Euler's formulas, binomial equations.


The course includes lectures, tutorials, quizzes and homework.


Course literature is announced on the course web page before start.

Examination including compulsory elements

Examination consists of a written exam. Quizzes giving bonus points may be offered. Grades TH.

Page manager Published: Thu 04 Feb 2021.