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 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
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.
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

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)
  • John Ma   (2-6f72457266796d33707a336970)
Teacher

John Ma

Saved on the 18-07-2022

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