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
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
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.
- 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)
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Kursusinformation for indskrevne studerende