[The University of Leicester]

Department of Mathematics



Next: MA2081 Methods of Applied Mathematics II Up: ModuleGuide03-04 Previous: MA2061 Lagrangian and Hamiltonian Dynamics

MA2071 Scientific Computing

MA2071 Scientific Computing

Credits: 10 Convenor: Dr Paul Houston Semester: 2
Prerequisites: desirable: MA1151(=MC146), MA1152(=MC147), MA2101(=MC248)
Assessment: Coursework: 50% One and a half hour exam: 50%
Lectures: 18 Problem Classes: 5
Tutorials: none Private Study: 47
Labs: 5 Seminars: none
Project: none Other: none
Surgeries: none Total: 75

Subject Knowledge

Aims

By the end of this module the student should:

Learning Outcomes

Students should know the definitions of and understand the key mathematical concepts and their relationship to the general problems which motivate their consideration in each of the topics of this module.

Methods

Class sessions and laboratories together with some handouts.

Assessment

Marked problem sheets.

Subject Skills

Aims

This course will impart a basic understanding of some of the key methods of scientific computing as well as an introduction to software tools such as MATLAB. These skills are important in all areas of modern applied science and engineering and are also widely used in industry.

Learning Outcomes

Students will be able to use the techniques taught within the module to solve problems, and be able to present arguments and solutions in a coherent and logical form.

Methods

Class sessions, laboratories.

Assessment

Marked problem sheets, projects.

Explanation of Pre-requisites

Students have learned in MA1152 about the structure of linear systems of algebraic equations and something of methods for solving such problems. Here they will see how these techniques can be applied to solve problems arising in engineering and science applications. The concept of an eigenvalue (also from MA1152) will be used in the analysis of the Jacobi and Gauss-Siedel iterations. Ideas and techniques from MA1151 and MA2101 are used in error analysis for all types of problems.

Course Description

This course introduces some of the methods and ideas used in applied numerical modelling, such as one typically encounters in chemistry, physics and engineering problem-solving. The problem is usually to determine, for given input data, an approximate solution to an equation or system of equations that is accurate to some desired error tolerance. The challenge is to find ways to do this efficiently and to analyze the effects of various types of errors on the quality of the approximation.

The dimension of systems that arise in real-world applications can be quite large, and it is therefore essential to build algorithms whose complexity scales reasonably with the problem size. Sometimes a particular structure is present in the problem formulation which can improve the numerical treatment. For example, it is often possible to solve symmetric matrices more reliably and accurately than nonsymmetric ones of equivalent dimension.

Many of the most important numerical tasks have to do with approximating the solutions of differential equations. For the purposes of illustrating the process, we restrict attention to a few elementary (scalar) ordinary differential equations, and a few popular schemes for their numerical approximation. The convergence of a given method is dependent on two important properties: the magnitude of the perturbations or local error introduced at each stage of the calculation, and stability which relates to the rate of growth of perturbations through the many steps of a long computational process. We are often faced with the task of comparing two methods, in which case the order of accuracy of the method becomes important.

Besides introducing some of the theoretical issues of numerical analysis, this course will give students a taste of modern scientific computing software tools, especially the MATLAB package which facilitates interactive evaluation of numerical methods and graphical visualization of the results of simulation. As part of the course, students will complete a series of computer projects using MATLAB.

Syllabus

1. Models and Methods

2. Two-point BVPs and linear systems

3. Nonlinear Equations and Iterations

Reading list

Recommended:

D. Kincaid and W. Cheney, Numerical Analysis, Brooks/Cole. R. L. Burden and J. Douglas Faires, Numerical Analysis, PWS-Kent.

Resources

Problem sheets and laboratories.

Module Evaluation

Module questionnaires, module review, year review.

Next: MA2081 Methods of Applied Mathematics II Up: ModuleGuide03-04 Previous: MA2061 Lagrangian and Hamiltonian Dynamics

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Last updated: 2004-02-21
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