NMAK16022U Partial Differential Equations (PDE)

Volume 2021/2022

MSc Programme in Mathematics


A selection from the following list of subjects:

The classical PDEs:

                             - Laplace's equation

                             - The heat equation

                             - The wave equation


Second order linear elliptic PDEs:

                             - Existence of weak solutions

                             - Regularity

                             - Maximum principles


Second order linear parabolic PDEs:

                             - Existence of weak solutions

                             - Regularity

                             - Maximum principles


Second order linear hyperbolic PDEs:

                             - Existence of weak solutions

                             - Regularity

                             - Propagation of singularities


Nonlinear PDEs:

                             - The Calculus of Variations

                             - Fixed point methods

                             - Method of sub-/supersolutions

                             - Non-existence of solutions

Learning Outcome

The properties of the PDEs covered in the course


  • Understand the characteristics of the different types of PDEs
  • Understand concepts such as existence, uniqueness and regularity of solutions to PDEs
  • Determine when a certain solution method applies


  • Solve classical PDEs
  • Establish existence, uniqueness and regularity of solutions to certain PDEs

See Absalon for a list of course literature

A knowledge of Lebesgue measure theory and Banach/Hilbert spaces, corresponding to at least the contents of the following courses:

Analyse 0 (An0),
Analyse 1 (An2) and
Lebesgueintegralet og målteori (LIM) - alternatively Analyse 2 (An2) from previous years.

Additionally, it might be helpful to have had some exposure to the material from a more advanced Analysis course, f.ex. one of either FunkAn or DifFun.

Academic qualifications equivalent to a BSc degree is recommended.
5 hours of lectures and 2 hours of exercises each week for 8 weeks
  • Category
  • Hours
  • Lectures
  • 40
  • Preparation
  • 146
  • Exercises
  • 16
  • Exam
  • 4
  • Total
  • 206
Continuous feedback during the course of the semester
Feedback by final exam (In addition to the grade)
7,5 ECTS
Type of assessment
Written examination, 4 hours under invigilation
All aids allowed



Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.

As ordinary exam.

If ten or fewer students have signed up for re-exam, the type of assessment will be changed to a 30 minutes oral exam with 30 minutes preparation time. All aids allowed during preparation time, none for the examination. Several internal examiners.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.