Course syllabus

Numerical Methods for Differential Equations, 7.5 credits

Course code: MA128G Credits: 7.5
Main field of study: Mathematics Progression: G2F
    Last revised: 13/03/2020
Education cycle: First cycle Approved by: Head of school
Established: 02/12/2019 Reading list approved: 13/03/2020
Valid from: Autumn semester 2020 Revision: 1

Aims and objectives

General aims for first cycle education

First-cycle courses and study programmes shall develop:

  • the ability of students to make independent and critical assessments
  • the ability of students to identify, formulate and solve problems autonomously, and
  • the preparedness of students to deal with changes in working life.

In addition to knowledge and skills in their field of study, students shall develop the ability to:

  • gather and interpret information at a scholarly level
  • stay abreast of the development of knowledge, and
  • communicate their knowledge to others, including those who lack specialist knowledge in the field.

(Higher Education Act, Chapter 1, Section 8)

Course objectives

Knowledge and understanding
After completed studies, the student shall have

  • account for and use the most important numerical methods for ordinary and partial differential, and
  • determine suitable methods for a given problem.

Competence and Skills
After completed studies, the student shall be able to

  • classify differential equations,
  • define and use the concepts consistence, stability and convergence,
  • use and analyze the most important numerical methods for ordinary differential equations, ordinary boundary value problems, and the simplest partial differential equations,
  • for a given problem identify the type and suggest a solution method, and
  • use suitable software for simulation and visualization of the solution to differential equations in some relevant applications.

Main content of the course

Eulers forward and backward. Runge-Kutta methods. Multistep methods. Consistence, stability and convergence for ODE. Difference methods for boundary value problems (BVP). Finite element methods for BVP. Numerical solution of parabolic PDE with method of lines. Finite difference and finite element metods for elliptic equations. Finite difference methods for hyperbolic equations. Convergence analysis. Programming in Matlab. Overview of commercial software.

Teaching methods

Lectures and exercises in computer lab.

The teaching methods may be altered, should only a few students take the course.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

Examination methods

Theory, 3.5 credits (Code: A001)
Written exam.
The re-exam will take place within eleven weeks after the regular exam.

Computer Assignments, 4 credits (Code: A002)
Assignments presented written individually and orally in a group.


For students with a documented disability, the university may approve applications for adapted or other forms of examinations.

For further information, see the university's local examination regulations (in Swedish).

Grades

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may prescribe which grading system shall apply. The grade is to be determined by a teacher specifically appointed by the university (an examiner).

In accordance with university regulations regarding grading systems for first and second-cycle courses (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades shall be used: Fail (U), Pass (G) or Pass with Distinction (VG). For courses that are included in an international Master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the grading scale of A-F shall be used. The vice-chancellor, or a person appointed by the vice-chancellor, may decide on exceptions from this provision for a specific course, if there are special grounds.

Grades used on course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Theory
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Computer Assignments
Grades used are Fail (U) or Pass (G).

For further information, see the university's local examination regulations (in Swedish).

Comments on grades

The grade from the course as a whole is given the grade from the examination part A001.

Specific entry requirements

Linear Analysis, 7.5 Credits, Complex Analysis, 7.5 Credits.

For further information, see the university's admission regulations (in Swedish).

Transfer of credits for previous studies

Students who have previously completed higher education or other activities are, in accordance with the Higher Education Ordinance, entitled to have these credited towards the current programme, providing that the previous studies or activities meet certain criteria.

For further information, see the university's local credit transfer regulations (in Swedish).

Other provisions

All or part of the course may be given in English.

Reading list and other teaching materials

Required Reading

Sauer, Timothy (latest edition)
Numerical Analysis
Pearson

Materials provided by the Mathematics Unit.