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MC320 Modelling Biological Systems
| Credits: 20 |
Convenor: Dr. M. Walmsley |
Semester: 1 |
| Prerequisites: |
essential: MC120, MC121, MC144, MC145, MC146, MC147, MC248 |
desirable: MC122 |
| Assessment: |
Coursework: 10% |
Three hour exam: 90% |
| Lectures: |
36 |
Classes: |
12 |
| Tutorials: |
12 |
Private Study: |
102 |
| Labs: |
none |
Seminars: |
none |
| Project: |
none |
Other: |
none |
| Total: |
150 |
|
|
Explanation of Pre-requisites
The module requires a general mathematical background, with some knowledge
of the use of Maple. It is not necessary for the first year module MC122 to
have been taken.
Course Description
This module uses differential equations of various kinds to describe certain
problems in the biological sciences. There are particular applications to
population models (including interaction between species) and epidemic
models. Some new techniques concerned with coupled differential equations
and partial differential equations are introduced.
Aims
The module will investigate a range of biological problems using modern
mathematical tools. The aim is to indicate the applicability of mathematics
to recent work in the life sciences.
Objectives
It is hoped that at the end of the module the student can use a variety of
techniques to describe various problems in the biological and life sciences.
Transferable Skills
Mathematical modelling and problem solving skills, including the use of
differential equations routines in Maple.
Syllabus
- 1.
- Single species population models -- deterministic (and possibly
stochastic) models.
- 2.
- Phase-plane methods and qualitative solutions of systems of ordinary differential
equations, with applications to predator-prey models, the Lotka-Volterra equations, the
population biology of infectious diseases. Maple provides suitable tools for the investigation
of problems arising in this area.
- 3.
- Introduction to the diffusion equation and its solutions with applications
to particular problems.
Reading list
Background:
M.Braun,
Differential Equations and Their Applications,
???.
E. Renshaw,
Modelling Biological Populations in Space
and Time,
???.
J. D. Murray,
Mathematical Biology,
???
There is no single textbook for the course and
students will be referred to the above
relevant texts where appropriate; for example, Braun
discusses Phase-plane methods, and
Renshaw includes items of interest. Murray
is an advanced
textbook, small parts of which are relevant to the course.
All books are available in the library.
Next: MC322 Modelling physical systems
Up: Year 3
Previous: MC316 Parallel and Distributed
Roy L. Crole
10/22/1998