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MATH2051: NUMERICAL ANALYSIS II

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Type	Open
Level	2
Credits	20
Availability	Available in 2023/24
Module Cap
Location	Durham
Department	Mathematical Sciences

Prerequisites

Calculus I (Maths Hons) (MATH1081) or Calculus I (MATH1061) and Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra I (MATH1071) and Analysis I (MATH1051) and (Programming I (MATH1587) and Dynamics I (MATH1607) or Discovery Skills in Physics (PHYS1101) or Introduction to Programming (COMP1011) or Computational Thinking (COMP1051)); Analysis I (MATH1051) may be taken as a co-requisite.

Corequisites

Analysis I (MATH1051) unless taken before.

Excluded Combinations of Modules

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

Aims

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

Content

Introduction: The need for numericalmethods.
Statement of some problems which can be solved bytechniques described in this module.
What is Numerical Analysis? Non-linearequations.
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 arange of predictable and unpredictable problems in NumberAnalysis.
have an awareness of the abstract concepts of theoreticalmathematics in the field of Numerical Analysis.
have a knowledge and understanding of fundamental theories ofthese subjects demonstrated through one or more of the following topicareas: 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 anddefend the use of alternative mathematical skills in the followingareas 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 theapplication of the theory to practical examples.
Weekly homework problems provide formative assessment to guidestudents in the correct development of their knowledge and skills.
Tutorials provide active engagement and feedback to thelearning process.
The end-of-year examination assesses the knowledge acquiredand the ability to solve predictable and unpredictableproblems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total	Monitored
Lectures	42	2 per week for 21 weeks	1 Hour	42
Tutorials	10	Fortnightly for 21 weeks	1 Hour	10	Yes
Problems Classes	9	Fortnightly for 20 weeks	1 Hour	9
Computer Practicals	20	Weekly for 20 weeks	1 Hour	20	Yes
Preparation and Reading				119
Total				200

Summative Assessment

Component: Examination		Component Weighting: 90%
Element	Length / Duration	Element Weighting	Resit Opportunity
Written examination	3 hours	100	yes

Component: Continuous assessment		Component Weighting: 10%
Element	Length / Duration	Element Weighting	Resit Opportunity
A computer based 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.

More information

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