# NMAK16022U Partial Differential Equations (PDE)

Volume 2024/2025
Education

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

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
Learning Outcome

Knowledge:
The properties of the PDEs covered in the course

Skills:

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

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

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)
- 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.
5 hours of lectures and 2 hours of exercises each week for 8 weeks
After taking this course, "PDE", in Block 1, note that one may naturally continue with the next course in the string, "PDE2", which is offered in the subsequent Block 2.
• Category
• Hours
• Lectures
• 40
• Preparation
• 146
• Exercises
• 16
• Exam
• 4
• Total
• 206
Written
Individual
Collective
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
On-site written exam, 4 hours under invigilation
Aid
All aids allowed
Marking scale