Mathematics

MTH1003 - Mathematical Modelling (2019)

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MODULE TITLEMathematical Modelling CREDIT VALUE30
MODULE CODEMTH1003 MODULE CONVENERProf John Thuburn (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 11 0
Number of Students Taking Module (anticipated) 181
DESCRIPTION - summary of the module content

This module will introduce you to the theory and tools for analysing real physical systems, including pendulums, planetary motion and predator-prey models. As part of a team, you will explore this theory with computer-generated models, developing your programming skills, and writing up your findings and conclusions of your investigations of the models you develop.

This module will also introduce you to the process of mathematical research and help you to understand the nature of the mathematical research community that you will be joining at the University of Exeter. An expert tutor will guide you through three short investigations as you develop a range of independent and group research skills across a variety of engaging topics.  With an emphasis on teamwork and community building, this module provides you with a great opportunity to meet your colleagues and lecturers on your mathematics degree programme.

AIMS - intentions of the module

The module aims to introduce you to Newtonian dynamics and its applications; to show you the use of calculus and vectors in the modelling of physical systems; to introduce you to applied mathematics as a tool for investigating natural phenomena. As examples, you will explore the consequences of physical laws, as well as the behaviour of physical systems from projectiles and rockets to planetary motion.

The module aims also to develop your abilities to: use computer packages such as Matlab to develop computer models for independent exploration; programme in order to solve mathematical problems; undertake open-ended investigations using mathematical material, and in doing so engage you in active learning; collaborate in small teams under the guidance of a member of staff and provide reinforcing material for other core stage one material in mathematics.

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 recall and apply basic techniques in classical mechanics to model simple mechanical and dynamical systems;

2 work on your own and as part of a small team to formulate and solve both well defined and more open-ended problems in mathematics;

3 use a high-level programming language for basic numerical analysis, simulation and data visualisation.

Discipline Specific Skills and Knowledge:

4 formulate models of the physical world, applying mathematical machinery such as vectors and calculus to develop and analyse these models.

5 present your findings in a logical and coherent manner;

6 use mathematical computing software (such as Matlab) to assist problem solving.

Personal and Key Transferable/ Employment Skills and  Knowledge:

7 formulate and solve problems;

8 work effectively as part of a small team;

9 communicate orally with team members and via written presentation;

10 undertake research using a variety of sources.

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

- basic concepts: modelling; point particles, space, time, velocity, acceleration; Newton's laws;


- projectiles: gravity; trajectories; envelope of trajectories;


- simple harmonic motion: elasticity, Hooke's law; strings and springs; equilibria and oscillations;


- energy: kinetic energy and gravitational potential energy; elastic potential energy; motion under general potentials, equilibria, stability and small oscillations;


- oscillations: damping, forcing and resonance; coupled oscillations; normal coordinates;


- nonlinear systems: first order systems; phase plane; classification of equilibria in linear systems; linearisation about equilibria in nonlinear systems; examples of predator-prey models;


- planetary motion: motion in plane polar coordinates; velocity and acceleration; central forces and angular momentum;


- numerical methods for solving equations using a computer: root finding; finite differences; order of accuracy, stabilty, and convergence; implementation in a typical high-level programming language.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 77.00 Guided Independent Study 223.00 Placement / Study Abroad 0.00
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 55 3 or 2 x 1 hour lecture per week.
Scheduled learning and teaching activities 11 1 hour practical in a computer lab per fortnight.
Scheduled learning and teaching activities 11 1 hour tutorial per fortnight.
Guided independent study 223 Reading lecture notes; independent research for assessments; development of LaTeX and other computing skills; preparation and revision for examination.
     

 

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
Exercise sheets 10 x 5 hours All Peer and tutor
Draft submissions Once for each project (as project outputs) All Peer and tutor
Programming assignment 10 hours 3 Tutor

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 40 Written Exams 60 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework – Group Project 1 10 Poster presentation All Feedback sheet
Coursework – Individual Project 10 Computer code All Feedback sheet
Coursework - Group Project 2 20 5,000 words or equivalent All Feedback sheet
Written Exam 60 2 hours All Via SRS
 
 

 

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 Examination (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 Collinson C.D. and Roper T. Particle Mechanics Arnold 1995 000-0-340-61046-8 [Library]
Set Lunn M. A first course in Mechanics Oxford University Press 1991 978-0198534334 [Library]
Set Dyke P. & Whitworth R. Guide to Mechanics Macmillan 1992 000-0-333-51072-0 [Library]
Set Smith P. & Smith R.C. Mechanics 2nd Wiley 1990 000-0-471-92737-6 [Library]
Set Hahn, Brian D Essential MATLAB for Engineers and Scientists 4th Academic Press 2010 9780123748836 012 [Library]
CREDIT VALUE 30 ECTS VALUE 15
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) 4 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Wednesday 11 January 2017 LAST REVISION DATE Thursday 27 June 2019
KEY WORDS SEARCH Dynamics; projectiles; oscillations; coupled oscillators; stability theory; planetary motion; mathematical research; Computer; programming; algorithms; problem solving; Matlab.