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## MTH1003 - Mathematical Modelling (2019)

MODULE TITLE | Mathematical Modelling | CREDIT VALUE | 30 |
---|---|---|---|

MODULE CODE | MTH1003 | MODULE CONVENER | Prof John Thuburn (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
---|---|---|---|

DURATION: WEEKS | 11 | 11 | 0 |

Number of Students Taking Module (anticipated) | 181 |
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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.

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.

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.

- 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.

Scheduled Learning & Teaching Activities | 77.00 | Guided Independent Study | 223.00 | Placement / Study Abroad | 0.00 |
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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. |

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 |

Coursework | 40 | Written Exams | 60 | Practical Exams | 0 |
---|

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 |

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 |

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.

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 |
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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. |
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