MA4NAT-Numerical Analysis II

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:7
Terms in which taught: Autumn / Spring term module
Pre-requisites: MA1LA Linear Algebra and MA2NAN Numerical Analysis or MT24C Numerical Methods for Environmental Science and MA1RA1 Real Analysis I or MA2RA1 Real Analysis I
Non-modular pre-requisites: Some knowledge of Matlab programming
Co-requisites:
Modules excluded: MA3NAT Numerical Analysis II
Current from: 2023/4

Module Convenor: Prof Amos Lawless
Email: a.s.lawless@reading.ac.uk

Type of module:

Summary module description:

This course introduces and analyses a range of techniques in numerical approximation, numerical integration, and numerical linear algebra, with connections being made between these areas. One half of the module will consider the design and analysis of algorithms for the approximate solution of problems of continuous mathematics, with a particular focus on topics such as interpolation, polynomial approximation, and integration. The other half of the module will introduce and analyse a range of techniques in numerical linear algebra for solving very large systems of linear equations.

Aims:

To motivate, develop and analyse a range of algorithms for the approximate solution of continuous mathematics and of techniques in numerical linear algebra.

Assessable learning outcomes:

By the end of the module students are expected to be able to:

• Apply and analyseÌýa range of techniques in approximation theory for appropriate problems;


• Devise, analyse and apply a range of numerical integration techniques;


• Apply and analyse a range of methods in numerical linear algebra including direct and iterative methods;


• Implement a range of numerical methods on a computer.

This module will be assessed to a greater depth than the excluded module MA3NAT.

Additional outcomes:

Outline content:

In one half of the module we consider the design and analysis of algorithms for the approximate solution of problems of continuous mathematics, with a particular focus on topics such as interpolation, polynomial approximation, and integration. The other half of the module will cover stability of linear systems, direct and iterative methods for solving such systems and linear least squares problems.

Brief description of teaching and learning methods:
Lectures supported by problem sheets and tutorials/practicals.

Contact hours:

Ìý	Autumn	Spring	Summer
Lectures	20	20
Practicals classes and workshops	5	3
Guided independent study:	75	77
Ìý	Ìý	Ìý	Ìý
Total hours by term	100	100	0
Ìý	Ìý	Ìý	Ìý
Total hours for module	200

Summative Assessment Methods:

Method	Percentage
Written exam	80
Set exercise	20

Summative assessment- Examinations:

3Ìýhours.

The examination for this module will require a narrowly defined time window and is likely to be held in a dedicated exam venue.

Summative assessment- Coursework and in-class tests:

A number of assignments and one examination.

Formative assessment methods:
Problem sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

The University policy statement on penalties for late submission can be found at: /cqsd/-/media/project/functions/cqsd/documents/cqsd-old-site-documents/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:
A mark of 50% overall

Reassessment arrangements:

One examination paper of 3 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus coursework marks (80% exam, 20% coursework).

Additional Costs (specified where applicable):

1) Required text books:Ìý

2) Specialist equipment or materials:Ìý

3) Specialist clothing, footwear or headgear:Ìý

4) Printing and binding:Ìý

5) Computers and devices with a particular specification:Ìý

6) Travel, accommodation and subsistence:Ìý

Last updated: 30 March 2023