The University of Southampton
Courses

# MATH1002 Mathematical Modelling

## Module Overview

The models will be drawn from applied mathematics, statistics and operational research and will illustrate important basic mathematical concepts and techniques such as population dynamics in applied mathematics, Markov chains in statistics and game theory in operational research. The diversity of application will be also illustrated, with examples drawn from various fields. The teaching will involve lectures and problem classes. A group project that will involve a more extensive study, and will develop comprehension, teamwork, time management, IT skills and communication skills.

### Aims and Objectives

#### Module Aims

To introduce mathematical modelling and apply the mathematics encountered in some of the core and compulsory modules to introduce mathematical modelling

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• The concept of mathematical modelling
• The mathematical descriptions of some real systems
• Correct methodology when developing mathematical models
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Appreciate the benefits of using group work skills
• Write a short project report on a mathematical topic

### Syllabus

• Introduction to modelling: Fundamentals of building a mathematical model; units and dimensions/ Newton’s laws in one dimension; Newton’s laws in two dimensions; energy conservation. • Motion in a central field: Kepler’s Laws of planetary motion; the effective potential; classification of solutions; derivation of Kepler’s laws. • Markov chains: transition matrix and transition graph; steady state probabilities; partitioning states into communicating classes; transient and recurrent states and classes; case study on Google pagerank algorithm. • Game theory: payoff matrix; dominated and dominating strategies; best response, Nash equilibria, mixed strategies.

#### Special Features

THe module has a group project.

### Learning and Teaching

#### Teaching and learning methods

Lectures, tutorials, group project work

TypeHours
Independent Study90
Teaching60
Total study time150

ROSEN K H (1988). Elementary Number Theory and its Applications.

TUNG K.K.. Topics in Mathematical Modeling.

SMITH P.A. and SMITH R.C.. Mechanics.

EDWARDS D. and HAMSON M. Guide to Mathematical Modelling.

### Assessment

#### Summative

MethodPercentage contribution
Project 20%
Project Sheets 10%

#### Referral

MethodPercentage contribution
Exam  (2 hours) 70%

#### Repeat Information

Repeat type: External

Pre-requisites: MATH1056 Calculus 2016-17, MATH1048 Linear Algebra I 2016-17

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.