module specification

This module enables the student to further develop and apply numerical techniques to a range of problems including the solution of ordinary differential equations related to both physical and financial/economic models. 

To enable students to apply approximation techniques to problems of both theoretical and practical importance and understand the cause of and interpret the degree of error involved;

To prepare students with the tools necessary for solving a range of problems in situations suitably described by ordinary differential equations and by difference equations;

To understand modelling with linear and nonlinear dynamical systems and iterative methods of solution;

To enable students to understand and manipulate coded programmes for software packages such as Maple for solving larger problems.

To develop students’ knowledge, confidence and problem solving skills leading to further academic progression and future employability in this area.

Iterative methods for approximating solutions of systems of linear equations; 
Initial Value Problems - Euler and Trapezium methods;
Linear Multistep Methods with Maple;
Predictor-Corrector Methods;
Numerical approximations to Two-point Boundary Value problems;
Discrete Dynamical Systems and Difference Equations.
 

This module will be delivered through a mixture of lectures, tutorials and laboratory workshops.
Students will be expected to spend some time on unsupervised work, for example, private study of problem sheets and on the preparation of coursework, test and examination.

Lecture notes and links to useful resources will be available on the module website (WebLearn) and can be accessed at any time. The module website will also be used as an additional medium of communication between the module teaching team and the students.

On successful completion of this module, students should be able to:

LO1.     Understand and implement numerical methods to approximate the solutions of initial value problems and implement simple predictor-corrector methods.

LO2.     Obtain numerical approximations to the solutions to certain boundary value problems.

LO3.     Understand discrete dynamical systems and their application in modelling problems in natural sciences, engineering and finance.

LO4.     Appreciate the limitations of the methods and be able to evaluate the feasibility of solutions, use appropriate software, analyse and interpret the results. 

LO5.     Critically evaluate and reflect on their learning, development and achievements within the Context of computational mathematics.

The assessment consists of a coursework assignment, a class test and an end of year examination. The coursework assignment allows the individual to demonstrate the ability to work independently on some investigative topics. A degree of creativity will be required in the presentation of results and the written report and an essential ingredient in marking will be the assessment of how the student’s perception of the errors encountered is demonstrated. [LO1-5].

The class test and the end of year examination will require students to demonstrate their understanding of the techniques by performing a range of numerical tasks under time constraint. [LO1-3]

Core text:
Burden, R.L. and J. Douglas Faires, Thomson (latest ed.) Numerical Analysis,

Other resoucres:
Sandefur, J. ( 1990),Discrete Dynamical Systems Theory and Applications, T, Oxford.

Maple 13- Introductory Programming Guide, Maplesoft, 2009.

on-line sources :
http://helm.lboro.ac.uk/pages/helm_workbooks.html
http://www.maplesoft.com/