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.

Linked modules

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

Aims and Objectives

Learning Outcomes

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.

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

Knowledge and Understanding

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

Identify the basic sorts of differential and algebraic equations that are commonly encountered during mathematical modelling of physical processes
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.
Understand a wide range of models that have been used in practical situations and be able to relate them to other situations.

Learning and Teaching

Teaching and learning methods

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

Study time
Type	Hours
Independent Study	114
Teaching	36
Total study time	150

Resources & Reading list

Textbooks

S HOWISON (2005). Practical applied mathematics. Cambridge University Press.

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

Assessment

Summative

This is how we’ll formally assess what you have learned in this module.

Breakdown
Method	Percentage contribution
Coursework	100%

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Breakdown
Method	Percentage contribution
Written assessment	100%

Repeat Information

Repeat type: Internal & External