Undergraduate Programme and Module Handbook 2013-2014 (archived)

Module MATH2051: NUMERICAL ANALYSIS II

Department: Mathematical Sciences

MATH2051: NUMERICAL ANALYSIS II

Type	Open	Level	2	Credits	20	Availability	Available in 2013/14	Module Cap	None.	Location	Durham

Prerequisites

Calculus and Probability 1 (MATH1061) and Linear Algebra 1 (MATH1071) and Analysis 1 (MATH1051)[the latter may be a co-requisite].

Corequisites

Analysis 1 (MATH1051) unless taken before.

Excluded Combination of Modules

Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), SIngle Mathematics B (MATH1571), Foundation Mathematics (MATH1641)

Aims

Numerical analysis has the twin aims of producing efficient algorithms for approximation, and the analysis of the accuracy of these algorithms.
The purpose of this module is to introduce the basic framework of the subject, enabling the student to solve a variety of problems and laying the foundation for further investigation of particular areas in the Levels 3 and 4.

Content

Introduction: The need for numerical methods.
Statement of some problems which can be solved by techniques described in this module.
What is Numerical Analysis? Non-linear equations.
Errors.
Polynomial interpolation.
Least squares approximation.
Numerical differentiation.
Numerical integration.
Linear equations.
Practical sessions.

Learning Outcomes

Subject-specific Knowledge:

By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Number Analysis.
have an awareness of the abstract concepts of theoretical mathematics in the field of Numerical Analysis.
have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas: Non-linear equations.
Errors.
Polynomial interpolation.
Least squares approximation.
Numerical differentiation and integration.
Matrix equations.

Subject-specific Skills:

In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Modelling, Computation.

Key Skills:

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
Tutorials provide active engagement and feedback to the learning process.
The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems..

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total/Hours
Lectures	42	2 per week for 21 weeks	1 Hour	42
Tutorials	10	Fortnightly for 20 weeks	1 Hour	10	■
Problems Classes	10	Fortnightly for 20 weeks	1 Hour	10
Practicals	19	Weekly for 19 weeks	1 Hour	19	■
Preparation and Reading				119
Total				200

Summative Assessment

Component: Examination		Component Weighting: 80%
Element	Length / duration	Element Weighting	Resit Opportunity
end of year written examination	3 hours	100%	yes
Component: Continuous assessment		Component Weighting: 20%
Element	Length / duration	Element Weighting	Resit Opportunity
an assessment every three weeks	one week	100%	yes

Formative Assessment:

One written assignment to be handed in every third lecture in the first 2 terms. Normally each will consist of solving problems from a Problems Sheet and typically will be about 2 pages long. Students will have about one week to complete each assignment.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University