MA3NATNU-Numerical Analysis II

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:6
Terms in which taught: Autumn / Spring term module
Pre-requisites: MA0MANU Mathematical Analysis MA1RA1NU Real Analysis 1 and MA1RA2NU Real Analysis II
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2021/2

Module Convenor: Dr 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.

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The module lead at NUIST is to be confirmed.

Aims:

To motivate, develop and analyse a range of algorithms for the approximate solution of problems 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 analyse a 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.

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:	Ìý	Ìý	Ìý
Ìý Ìý Exam revision/preparation	20	20
Ìý Ìý Completion of formative assessment tasks	15	15
Ìý Ìý Reflection	40	42
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:

3 hours.

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:
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 40% 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):

Last updated: 8 June 2021