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Differential Equations and Transform Theory 7.5 credits

Differentialekvationer och transformteori
First cycle, M0052M
Course syllabus valid: Spring 2022 Sp 3 - 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 Integrals, Vectors and Matrices (M0051M), or equivalent.

More information about English language requirements


The selection is based on 1-165 credits.

Course Aim
After completing the course, the student will

  • have knowledge of calculations using complex numbers, first and second order differential equations, power series, and transform theory
  • know how to solve differential equations using standard methods, including simple numerical methods, power series and Laplace transform.
  • have basic insight into mathematical modeling with differential equations.
  • be able to use mathematical software for the problem areas of the course
  • be able to validate the plausibility of the results
  • have insight into interpreting and validating the results from applied problems

Complex numbers.
Differential equations: Ordinary differential equations, systems of differential equations. Applications. Improper integrals.
Series. Transform Theory and Applications.
Use of computer tools.

Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website.
Lectures and tutorials where theory and example problems are reviewed, with som degree of personal practice.

Mandatory marking conferences for grading of the course assignments.

The assignments may be marked using other methods.

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 is graded with a written exam, and mandatory assignments. To pass the course, both parts need to be passed. The final grade of the course is set by the grade of the written exam.

Transition terms
The course replaces M0039M.

Ove Edlund

Literature. Valid from Spring 2022 Sp 3 (May change until 10 weeks before course start)
Forsling/Neymark: Matematisk analys - En variabel, upplaga 2. Liber, ISBN 978-91-47-10023-1, for course in Swedish.
Lundberg: En bok om Laplacetransformen. Studentlitteratur, ISBN 978-91-44-15445-9, for course in Swedish.

Adams Robert A: Calculus, A Complete Course. Addison-Wesley, latest edition, for course in English.

Course offered by
Department of Engineering Sciences and Mathematics

CodeDescriptionGrade scaleCrStatusFrom periodTitle
0002Assignment reportU G#1.50MandatoryA19
0003Written examG U 3 4 56.00MandatoryA21

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 Niklas Lehto Head Faculty Programme Director 04 Nov 2021