Department of Mathematical Sciences, Unit Catalogue 2011/12 

Credits:  6 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 2 
Assessment:  CW 25%, EX 75% 
Supplementary Assessment:  Likeforlike reassessment (where allowed by programme regulations) 
Requisites:  
Description:  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 reactiondiffusion system and determine criteria for diffusiondriven instability. They should be able to interpret the results in terms of the original biological problem. They should be able to demonstrate an indepth understanding of the subject. Content: Topics will be chosen from the following: Partial Differential Equation Models: Simple random walk derivation of the diffusion equation. Solutions of the diffusion equation. Densitydependent diffusion. Conservation equation. Reactiondiffusion equations. Chemotaxis. Examples for insect dispersal and cell aggregation. Spatial Pattern Formation: Turing mechanisms. Linear stability analysis. Conditions for diffusiondriven 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. 
Programme availability: 
MA50063 is Optional on the following programmes:Department of Biology & Biochemistry
