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.
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 Coordinator
- Niels Martin Møller (7-504f716e6e6774426f63766a306d7730666d)
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Courseinformation of students