Study information

Mathematical Modelling - 2024 entry

MODULE TITLEMathematical Modelling CREDIT VALUE30
MODULE CODEMTH1003 MODULE CONVENERDr Jemma Shipton (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 11 0
Number of Students Taking Module (anticipated) 200
DESCRIPTION - summary of the module content
This module will introduce you to the theory and tools for analysing real physical systems, such as pendulums, planetary motion, and predator-prey models. You will also develop programming and coding skills using a language such as Python, and learn how mathematical theory and computer-based modelling can complement each other to help us understand and predict the world around us.
 
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. You will work individually or as part of a team to carry out three short projects that will develop a range of individual and group research and communication skills. The ideas and skills in the module are developed further in MTH2005 Modelling: Theory and Practise.
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 and natural systems from projectiles to predator-prey systems and planetary motion.
 
The module aims also to develop your abilities to: express mathematical problems in a form suitable for solution by computer; use computer languages such as Python to develop computer models for independent exploration; programme in order to solve mathematical problems; collaborate in small teams to tackle mathematical projects. The module will provide reinforcing material for other core stage one modules 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 Python) 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, stability, 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 88 Guided Independent Study 212 Placement / Study Abroad 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 66 3 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 212 Reading lecture notes; formative coursework; 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 1-10 Peer and tutor
Programming assignment 10 x 1 hour 3, 6 Feedback from staff in computer lab classes / solutions uploaded to ELE

 

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 – Individual Project 10 Computer code 3, 6 Feedback sheet
Coursework - Group Project 1 15 Poster presentation 1-10 Feedback sheet
Coursework - Group Project 2 15 5,000 words or equivalent 1-10 Feedback sheet
Written Exam 60 2 hours 1-10 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
Coursework - individual Project Coursework Individual Project 3,6 Referral/Deferral period
Coursework - Group Project 1 Coursework - Individual Poster 1-10 Referral/Deferral period
Coursework - Group Project 2 Coursework - Individual Report 1-10 Referral/Deferral period
Written Exam Written Exam   1-10 Referral/Deferral period

 

RE-ASSESSMENT NOTES

Deferrals: Reassassment will be by coursework and/or exam in the deferred element only.  For deferred candidates, the module mark will be uncapped.

Referrals: Reassessment will be by a single written exam worth 100% of the module only.  As it is a referral, the mark will be capped at 40%.   

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

Reading list for this module:

Type Author Title Edition Publisher Year ISBN
Set Collinson C.D. and Roper T. Particle Mechanics Arnold 1995 000-0-340-61046-8
Set Lunn M. A First Course in Mechanics Oxford University Press 1991 978-0198534334
Set Dyke P. & Whitworth R. Guide to Mechanics Macmillan 1992 000-0-333-51072-0
Set Smith P. & Smith R.C. Mechanics 2nd Wiley 1990 000-0-471-92737-6
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 11th January 2017 LAST REVISION DATE Tuesday 5th March 2024
KEY WORDS SEARCH Dynamics; projectiles; oscillations; coupled oscillators; stability theory; planetary motion; mathematical research; Computer; programming; algorithms; problem solving; Python

Please note that all modules are subject to change, please get in touch if you have any questions about this module.