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

Learning outcome

Knowledge:
The properties of the PDEs covered in the course

Competencies:

  • 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


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 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.

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
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The course has been selected for ITX exam
Aid
All aids allowed

 

The University will make computers available to students taking on-site exams at ITX. Students are therefore not permitted to bring their own computers, tablets or mobile phones. If textbooks and/or notes are permitted, according to the course description, these must be in paper format or uploaded through Digital Exam.

Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.
Criteria for exam assessment

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

Single subject courses (day)

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