Partial Differential Equations (PDE)

Course content

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

Education

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject

Learning outcome

Knowledge:
The properties of the PDEs covered in the course

Competencies:

  • Understand the characteristic properties 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


Skills:

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

5 hours of lectures and 2 hours of exercises each week for 8 weeks

See Absalon for a list of course literature

A knowledge of real analysis, Lebesgue measure theory, L^p spaces and basic theory of Banach/Hilbert spaces, corresponding to at least the contents of the following courses:

- Analyse 0 (An0), and
- Analyse 1 (An1), and
- Lebesgueintegralet og målteori (LIM), or alternatively Analyse 2 (An2) from previous years.
- Advanced Vector Spaces (AdVec), which may be taken simultaneously with (PDEs), or alternatively Functional Analysis (FunkAn).

Having academic qualifications equivalent to a BSc degree is recommended.

Written
Individual
Collective
Continuous feedback during the course of the semester
Feedback by final exam (In addition to the grade)
ECTS
7,5 ECTS
Type of assessment
Written examination, 4 hours under invigilation
Type of assessment details
---
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.
Re-exam

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 assessment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 40
  • Preparation
  • 146
  • Exercises
  • 16
  • Exam
  • 4
  • English
  • 206

Kursusinformation

Language
English
Course number
NMAK16022U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Placement
Block 1
Schedulegroup
B
Capacity
No limit
The number of seats may be reduced in the late registration period
Studyboard
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinators
  • Niels Martin Møller   (7-53527471716a77457266796d33707a336970)
  • Alex Mramor   (4-636e6f74426f63766a306d7730666d)
Saved on the 24-08-2023

Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students