Undergraduate Course: Numerical Ordinary Differential Equations and Applications (MATH10060)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 10 (Year 3 Undergraduate)
||Availability||Available to all students
|Summary||Most ordinary differential equations (ODEs) lack solutions that can be given in explicit analytical formulas. Numerical methods for ordinary differential equations allow for the computation of approximate solutions and are essential for quantitative study. In some cases, a numerical method can facilitate qualitative analysis as well, such as probing the long term solution behaviour. Modern applications of ODEs (e.g. in biology) will be discussed as well as particularities for their numerical approximation.
See 'Course Description' above.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| Student MUST NOT have taken MATH08036 Numerical Differential Equations in a previous session.
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2015/16, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Supervised Practical/Workshop/Studio Hours 10,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 30%, Examination 70%
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Numerical Ordinary Differential Equations and Applications (MATH10060) ||2:00|
| 1. Understanding of the differences between types of ordinary differential equations in terms of order, dimension, autonomous/non-autonomous character, linearity/nonlinearity.
2. Understanding of the convergence of numerical methods.
3. Familiarity with popular classes of methods: Linear Multistep Methods and Runge-Kutta Methods.
4. Ability to derive methods in item 3 based upon local truncation error (consistency).
5. Ability to calculate stability regions for methods in item 3; classes of stability.
6. Understanding that consistency plus stability implies convergence.
7. Understanding of the concept of 'stiffness' in ordinary differential equations.
8. Perception of some applications of ordinary differential equations, particularly in biological models.
|An electronic textbook/course notes set will be provided. Students may find the following useful: Numerical Methods for Ordinary Differential Equations: Initial Value Problems (ISBN 978-0857291479, Springer, 2010) Additional potentially useful references included:|
1. Numerical Methods for Ordinary Differential Equations by Butcher.
2. Numerical Methods for Ordinary Differential Systems: The Initial Value Problem, by Lambert.
3. A First Course in the Numerical Analysis of Differential Equations by Iserles.
|Graduate Attributes and Skills
|Course organiser||Prof Benedict Leimkuhler
|Course secretary||Mr Thomas Robinson
Tel: (0131 6)50 4885
© Copyright 2015 The University of Edinburgh - 18 January 2016 4:24 am