NMAK16022U  Partial Differential Equations (PDE)

Volume 2017/2018
Education

MSc Programme in Mathematics

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

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

See Absalon for a list of course literature

A knowledge of complex analysis, Banach and Hilbert Spaces, the Fourier transform, and distribution theory corresponding to KomAn An2 and DifFun.
5 hours of lectures and 2 hours of exercises each week for 8 weeks
Credit
7,5 ECTS
Type of assessment
Written examination, 4 hours under invigilation
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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 min. oral exam with 30 min preparation. 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.

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