Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

CANCELLED Partial Differential Equations (PDE)

Practical information
Study year 2016/2017
Time
Block 1
Programme level Full Degree Master
ECTS 7,5 ECTS
Course responsibles
  • Jesper Lützen (6-7f88878d7881538074877b417e8841777e)
  • Jan Philip Solovej (7-75716e7178676c426f63766a306d7730666d)
  • Department of Mathematical Sciences
Course number: NMAK16022U

Course content

A selection form the following list of subjects:

The classical PDE:

                             -Laplace's equation

                             -The Heat equation

                             -The Wave equation

 

Second order linear elliptic equations

                             -Existence of weak solutions

                             -Regularity

                             -Maximum principles

 

Second order linear parabolic equations

                             -Existence of weak solutions

                             -Regularity

                             -Maximum principles

 

Second order linear hyperbolic equations

                             -Existence of weak solutions

                             -Regularity

                             -Propgation of singularities

 

Non-linear PDE

                             -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

Competences:

  • Understand the characteristics of the different types of PDE
  • Understand concepts such as existence uniqueness and regularity of solutions to differential equations.
  • Determine when a certain solution method applies

Skills:

  • Solve classical partial differential equations
  • Establish existence, uniqueness and regularity of solutions to certain differential equations

Recommended prerequisites

A knowledge of complex analysis, Banach and Hilbert Spaces, Fourier transform and distribution theory corresponding to KomAn An2 and DifFun.

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Education

MSc Programme in Mathematics

Studyboard

Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)

Duration

1 block

Schedulegroup

C
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Teaching and learning methods

5 hours of lectures and 2 hours of exercises each week for 8 weeks

Capacity

No restrictions/ no limitation

Language

English

Workload

Category Hours
Lectures 40
Exercises 16
Exam 4
Preparation 146
English 206

Exam

Type of assessment

Written examination, 4 hours under invigilation
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Aid

All aids allowed

Marking scale

7-point grading scale

Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

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.

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