Mathematics

ECMM712 - Computation and Numerical Analysis (2015)

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MODULE TITLEComputation and Numerical Analysis CREDIT VALUE15
MODULE CODEECMM712 MODULE CONVENERDr Tim Jupp (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
Number of Students Taking Module (anticipated) 33
DESCRIPTION - summary of the module content

On this module, you will get the chance to use the popular and sophisticated computer package Matlab and other relevant software. We will use topics including linear algebra, differential equations, statistical modelling, optimisation and dynamical systems to demonstrate the versatility and capabilities of such packages in the application of modern numerical modelling techniques. The background and skills you obtain in this module will underpin project work. The topics discussed have wide-ranging applications in industrial and research contexts, and will give you hands-on experience of numerical modelling, together with an understanding of the mathematics underlying each method.

AIMS - intentions of the module

This module aims to give you an understanding of modern methods of numerical approximation and modelling. Using Matlab and other relevant software, you will develop practical skills in the use of computers in mathematical modelling.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

 

Module Specific Skills and Knowledge:
1 demonstrate expertise in the use of Matlab and other relevant popular computer packages widely used both inside and outside the academic community;
2 use this expertise to model challenging mathematical problems.
Discipline Specific Skills and Knowledge:
3 tackle a wide range of mathematical problems using modern numerical methods;
4 model realistic situations and also understand the principles underlying the techniques and when they are applicable.
Personal and Key Transferable/ Employment Skills and  Knowledge:
5 show enhanced modelling, problem-solving and computing skills;
6 display knowledge of tools that are widely used in scientific research and modelling.

SYLLABUS PLAN - summary of the structure and academic content of the module

- introduction to Matlab system and interface: matrix data objects; mathematical operations and functions;
- I/O control;
- programming;
- graphical tools;
- plotting and data representation;
- approximation techniques: curve fitting and related methods;
- numerical matrix algebra: review;
- numerical calculation of eigenvalues, eigenvectors, determinants and inversion;
- decompositions;
- special topics in numerical modelling: condition number; matrix nearness;
- Matlab numerical linear algebra tools;
- practical, numerical modelling using Matlab;
- computational ODEs, PDEs and dynamical systems: series, transforms, splines and interpolation;
- finite differences, shooting methods and convergence;
- Matlab DE tools;
- practical use of Matlab;
- statistical modelling: introduction to statistical models, parametric versus non-parametric models;
- likelihood, Bayesian and resampling inferential approaches;
- Markov Chain Monte Carlo, (MCMC methods. Examples of parametric models - Linear and Generalised Linear Models;
- examples of computer-intensive non parametric modelling;
- use of relevant software in practical data modelling;
- further topics and applications in computational ODEs and PDEs.

 

 

 

 

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 45.00 Guided Independent Study 117.00 Placement / Study Abroad
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 36 Lectures
Scheduled learning and teaching activities 9 Practicals
Guided independent study 117 Lecture and assessment preparation; private study

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework – problem sheet 1: introduction to Matlab   All Written
       
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 50 Written Exams 50 Practical Exams
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 50   All None
Coursework – problem sheet 2: approximation tools 8   All Written
Coursework – problem sheet 3: numerical matrix algebra 10   All Written
Coursework – problem sheet 4: computational ODEs and PDEs 10   All Written
Coursework – problem sheet 5: statistical modelling 12   All Written
Coursework – problem sheet 6: further computational ODEs and PDEs 10   All Written

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Written exam (100%) All August Ref/Def period
       
       

 

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.


If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE: http://vle.exeter.ac.uk

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Martinez W.L. & Martinez A.R. Computational statistics handbook with MATLAB Chapman & Hall 2001 000-1-584-88229-8 [Library]
Set Maindonald J. & Braun J. Data Analysis & Graphics using R 2nd edition Cambridge University Press 2007 9780521861168 [Library]
Set Kharab A. & Guenther R.B. An Introduction To Numerical Methods: a MATLAB Approach Chapman & Hall 2012 978-1439868997 [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) 7 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Friday 09 January 2015 LAST REVISION DATE Friday 09 January 2015
KEY WORDS SEARCH Matlab; linear algebra; differential equations; statistical modelling; optimisation and dynamical systems.