The University of Southampton
Courses

# MATH6149 Modelling with Differential Equations

## Module Overview

The emphasis of this module is on the methods required to develop mathematical models using differential equations to understand physical problems. The module involves both conventional lectures as well as discussion lectures. The discussion lectures comprise structured group work in which small groups of students develop mathematical models to solve practical problems in partnership with one another and under the guidance of the lecturer (attendance at these discussion lectures is an essential part of the module). After an introduction to the module there are four blocks, in which the opening lectures will introduce the students to a physical problem and subsequent discussion lectures will allow possible modelling methods to be explored. Some lectures on relevant mathematical theory will also be presented. After each block students will write a report describing their investigations.

### Aims and Objectives

#### Module Aims

• To give students a good understanding of how mathematical modelling is used to solve real world problems. • To introduce students to a wide variety of practical situations where the theoretical aspects of differential equations can give physical insight • To give students an understanding of the successful use of mathematics to solve a problem through experiment, numerical methods and analytical approximation. • To give students experience of working in small research groups.

#### Learning Outcomes

##### Knowledge and Understanding

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

• Distil the major elements of a physical problem into a mathematical model that is simple enough to allow some intelligent predictions to be made and valuable conclusions to be drawn.
• Identify the basic sorts of differential and algebraic equations that are commonly encountered during mathematical modelling of physical processes
• Understand a wide range of models that have been used in practical situations and be able to relate them to other situations.
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Present, either in written or verbal form, or a combination of both, results from models that have been derived during the course
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Learn how to work closely with other group members making use of varying expertise within the group.

### Syllabus

• Mathematical modelling methodology. • Modelling using ODEs, both single and coupled. • Modelling using PDEs, both single and coupled. • Approximation and perturbation techniques. • Use of computer packages (e.g. Matlab) in solving problems and presenting their solutions.

### Learning and Teaching

#### Teaching and learning methods

Student led small group discussions, lectures, private study and research.

TypeHours
Independent Study114
Teaching36
Total study time150

#### Resources & Reading list

A B TAYLER (1986). Mathematical Models in Applied Mechanics.

S HOWISON (2005). Practical applied mathematics.

### Assessment

#### Summative

MethodPercentage contribution
Group Projects 100%

#### Referral

MethodPercentage contribution
Coursework assignment(s) 100%

#### Repeat Information

Repeat type: Internal & External

### Linked modules

Prerequisites: MATH2038 AND (MATH1057 OR MATH2008) AND (MATH3018 OR MATH3052 OR MATH3072).

### 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.

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