# NUMERICAL AND COMPUTATIONAL METHODS - 2019/0

Module code: MAT2001

## Module Overview

When an analytical approach is not known or practical for solving a mathematical problem, the numerical approach can be useful in finding approximate solutions as close as possible to the exact one. This module introduces a selection of numerical methods for the solution of linear and nonlinear algebraic equations, and differential equations, for finding a function that interpolates a set of data, and for finding numerical values of derivatives and integrals.

For each numerical method, we will consider the error that results from using approximations and introduce some theories of quantifying the error, which then indicates the accuracy of a numerical solution. We also consider the efficiency of a numerical method, which tells how much computational resource is required for achieving a given accuracy. Students will learn and practice implementing some of the methods in MatLab codes.

### Module provider

Mathematics

TURNER Matthew (Maths)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 112

Lecture Hours: 33

Laboratory Hours: 5

Semester 2

## Prerequisites / Co-requisites

MAT1035 or basic knowledge of Matlab coding, MAT1030, MAT1034

## Module content

The module will consider the following:

• Numerical solution of systems of linear equations

• Numerical solution of systems of nonlinear equations

• Polynomial interpolation

• Numerical methods for differentiation and integration

• Numerical methods for solving ordinary differential equation

## Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test IN-SEMESTER TEST (50 MINS) 20
Examination EXAMINATION (2 HOURS) 80

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Understanding of and ability to derive, devise and analyse numerical methods.

• Subject knowledge through the recall of key definitions, theorems and their proofs.

• Analytical ability through the solution of unseen problems in the test and exam.

• Practical skills of implementing numerical methods in MATLAB code, and ability to understand and interpret given code.

Thus, the summative assessment for this module consists of:

• One two hour examination (three of four best answers contribute to exam mark) at the end of the Semester; worth 80% module mark.

• One in-semester test; worth 20% module mark

Formative assessment and feedback

Students receive written feedback via a number of marked coursework assignments which include computation projects over an 11 week period.  In addition, verbal feedback is provided by lecturer/teaching assistant at lab sessions.

## Module aims

• The aim of this module is to introduce students to a selection of numerical methods in terms of their derivation, their accuracy and efficiency and their implementation.

## Learning outcomes

 Attributes Developed 1 Demonstrate knowledge and literacy of the taught numerical methods; K 2 For basic numerical methods, prove their convergence and error bounds, and demonstrate understanding of their efficiency; KC 3 Derive and devise numerical schemes with specific details for a range of mathematical problems; KCT 4 Apply the above knowledge to determine the most suitable numerical method(s) for a practical problem; CPT 5 Implement some numerical Linear Algebra methods in Matlab code, and gain proficiency in basic programming structures and methodology that can be used for general coding purposes. KPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• A detailed introduction to the derivation of numerical methods and the concepts of accuracy and efficiency

• Experience (through demonstration) of the methods used to find approximate solutions of basic mathematical problems

The learning and teaching methods include:

• 3 x 1 hour lectures per week x 11 weeks with examples to supplement the module lecture notes and questions & answer opportunities for students.

• 1 x 1 hour lab drop-in session every 2 weeks (weeks 2, 4, 6, 8, 10) to provide hands-on learning experience of implementing numerical methods in MATLAB codes. Students are given lab sheets and template codes in order to solve practical problems. Instructor and teaching assistant(s) provide real time guidance, and students can also discuss with peers.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: MAT2001

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics and Physics BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Computer Science BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2019/0 academic year.