# 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

Skills:

• Solve classical PDEs
• Establish existence, uniqueness and regularity of solutions to certain PDEs

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

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)
- 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.

After taking this course, "PDE", in Block 1, note that one may naturally continue with the next course in the string, "PDE2", which is offered in the subsequent Block 2.

Written
Individual
Collective
Continuous feedback during the course of the semester
ECTS
7,5 ECTS
Type of assessment
On-site written exam, 4 hours under invigilation
Aid
All aids allowed
Marking scale
Censorship form
No external censorship
One internal examiner
Re-exam

Same 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 limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Studyboard
Study Board of Mathematics and Computer Science
##### Contracting department
• Department of Mathematical Sciences
##### Contracting faculty
• Faculty of Science
##### Course Coordinators
• Niels Martin Møller   (7-504f716e6e6774426f63766a306d7730666d)
• Artemis Aikaterini Vogiatzi   (3-636378426f63766a306d7730666d)
• Léo Morin   (4-6f736770437064776b316e7831676e)
Saved on the 22-08-2024

### Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students