CANCELLED Partial Differential Equations (PDE)

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

Education

MSc Programme in Mathematics

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

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

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

ECTS
7,5 ECTS
Type of assessment
Written examination, 4 hours under invigilation
---
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
  • Exercises
  • 16
  • Exam
  • 4
  • Preparation
  • 146
  • English
  • 206