This course syllabus is discontinued or replaced by a new course syllabus. |
|
Course Syllabus |
Numerical Methods for Differential Equations, 7.5 Credits |
Course Code: | MA115G | Subject Area: | Field of Science |
---|---|---|---|
Main Field of Study: | Mathematics | Credits: | 7.5 |
Subject Group (SCB): | Mathematics | ||
Education Cycle: | First Cycle | Progression: | G2F |
Established: | 2014-12-09 | Last Approved: | 2015-09-30 |
Valid from: | Spring semester 2016 | Approved by: | Head of School |
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)
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.
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.
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.
For further information, see the university's local examination regulations (in Swedish).
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).
According to regulations on grading systems for first- and second-cycle education (vice-chancellor's decision 2010-10-19, reg. no. CF 12-540/2010), one of the following grades is to be used: fail, pass, or pass with distinction. 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 reasons.
Grades used on course are Fail (U), Pass (G) or Pass with Distinction (VG).
For further information, see the university's local examination regulations (in Swedish).
Linear Analysis, 7,5 Credits, Complex Analysis, 7,5 Credits.
For further information, see the university's admission regulations (in Swedish).
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).
All or part of the course may be given in English.
Transitional Provisions
When a course has been discontinued or been the subject of major changes there are specific rules regarding examination /completion of compulsory components.
Required Reading
Material som tillhandahålls av enheten för matematik.