Numerical Differential Equations (U03663)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : MAT-2-NuD

This 2nd year course is an introduction to numerical methods, taught from the perspective of qualitative treatment of differential equations. Convergence of numerical methods for ordinary differential equations (especially Euler's methods) is considered, as are issues such as stability and integral preservation under discretisation. The course focuses on planar models and the Kepler problem.

? Keywords :

Entry Requirements

? Pre-requisites : (MAT-1-PCa, MAT-1-SEq, MAT-1-GCo and MAT-1-GTh) or (MAT-1-am1, MAT-1-mm1, MAT-1-am2 and MAT-1-mm2) or (MAT-1-mi1 and MAT-1-mi2)

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Year 2), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 2nd year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
22/09/2008	10:00	10:50	Lecture Room 3317, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	10:00	10:50	KB
Lecture	Thursday	10:00	10:50	KB

Summary of Intended Learning Outcomes

1. Knowledge ofbasic concepts of qualitative theory of ODEs, specifically : stability, phase portraits, 1st integrals, area preserving flows and maps, time-reveral symmetry are all discussed.

2. Understand numerical methods for solving ODEs, including the concept of convergence of a numerical method, and to see how numerical methods can be studied in terms of qualitative properties.

3. Knowledge of simple physical models such as the pendulum and Kepler's problem, and example-based introduction to integrability (or lack thereof).

4. Familiarity with MATLAB and its use for graphical investigation of models and solutions.