|| MA34810 |
|| MATHEMATICAL MODELS OF BIOLOGICAL SYSTEMS |
|| 2007/2008 |
|| Dr Simon J Cox |
|| Semester 2 |
|| Dr Simon J Cox |
|| MA25110 |
| Course delivery
|| Lecture || 14 Hours. (14 x one-hour lectures) |
|| Seminars / Tutorials || 6 Hours. (6 x one-hour exercise classes) |
|| Practical || 4 Hours. (2 two-hour computer classes) |
|Assessment Type||Assessment Length/Details||Proportion|
|Semester Exam||2 Hours (written examination) ||80%|
|Semester Assessment|| coursework (4 assignments) ||20%|
|Supplementary Assessment||2 Hours (written examination) ||100%|
Learning outcomesOn successful completion of this module students should be able to:
1. Identify key parameters in a complex system upon which to base a model.
2. Demonstrate an understanding of the stability of the solutions to a mathematical model.
3. Apply a range of criteria to show that a system may behave chaotically.
4. Demonstrate an ability to solve differential and difference equations, including those representing population balances.
5. Explain the use of computers as a tool to explore complex dynamics.
Mathematical Biology is an area of interest that is growing rapidly in popularity; with a little knowledge of biology, mathematicians are now able to develop appropriate models of biological phenomena which are also of mathematical interest in their own right. Mathematicians who are familiar with rigorous biological modelling have extremely attractive employment prospects in this and related areas such as medicine.
This course aims to develop students' ability to identify the key parameters in a complex system and create and solve a comparatively simple model, the results of which can then be related back to the original system. Examples will include chaotic population models and waves in reaction-diffusion systems.
Continuous and Discrete Single Species Population Models; Logistic Map; Limit Cycles and Fixed points; Linear Stability Analysis; Transition to Chaos.
Two species population models; Lotka Volterra; Predator Prey.
Spread of Epidemics; Cellular Automata; Game of Life.
Reaction Diffusion Equations; Propagating Wave Solutions; Travelling Fronts; Spatial Pattern Formation; Animal Coat Patterns.
|| In addition to problem classes, further exercises will be set and marked. These will involve the identification and derivation of appropiate solutions. |
|| Computer classes will allow students to explore the parameter space of a dynamical system, and draw conclusions about determining solutions relevant to the physical system. |
|| Written answers to exercises must be clear and well-structured. Good listening skills are essential to successful progress in this course. |
|Improving own Learning and Performance
|| Students will be expected to develop their own approach to time-management in their attitude to the completion of work on time, and in doing the necessary preparation between lectures. |
|| Students will be set exercises involving the use of computer and library facilities. |
|Application of Number
|| Necessary throughout. |
|Personal Development and Career planning
|| Completion of tasks (problem sheets) to set deadlines will aid personal development. The course will give clear indications of the range of possible employment opportunities available to students who successfully complete it. |
** Recommended Text
Murray, J. D. (1997) Mathematical Biology
Murray, J. D. (1989) Mathematical biology
Springer Verlag 3540194606
** Supplementary Text
Crichton, M (1991.) Jurassic park
Jones, D S and Sleeman, B D (2003) Differential Equations and Mathematical Biology
CRC Press 1584882964
Jones, D S and Sleeman, B D (1983.) Differential equations and mathematical biology
Allen & Unwin
This module is at CQFW Level 6