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Department of Mathematical Sciences, Unit Catalogue 2008/09

MA30063 Mathematical biology 2

Credits: 6
Level: Honours
Semester: 2
Assessment: EX 100%
Before taking this unit you must take MA20010 and take MA20013

Aims & Learning Objectives:
Aims: The aim of the course is to introduce students to applications of partial differential equations to model problems arising in biology. The course will complement Mathematical Biology I where the emphasis was on ODEs and Difference Equations.
Objectives: Students should be able to derive and interpret mathematical models of problems arising in biology using PDEs. They should be able to perform a linearised stability analysis of a reaction-diffusion system and determine criteria for diffusion-driven instability. They should be able to interpret the results in terms of the original biological problem.
Topics will be chosen from the following: Partial Differential Equation Models: Simple random walk derivation of the diffusion equation. Solutions of the diffusion equation. Density-dependent diffusion. Conservation equation. Reaction-diffusion equations. Chemotaxis. Examples for insect dispersal and cell aggregation. Spatial Pattern Formation: Turing mechanisms. Linear stability analysis. Conditions for diffusion-driven instability. Dispersion relation and Turing space. Scale and geometry effects. Mode selection and dispersion relation. Applications: Animal coat markings. "How the leopard got its spots". Butterfly wing patterns.