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Department of Mathematical Sciences, Unit Catalogue 2011/12

MA50063: Mathematical biology 2

Click here for further information Credits: 6
Click here for further information Level: Masters UG & PG (FHEQ level 7)
Click here for further information Period: Semester 2
Click here for further information Assessment: CW 25%, EX 75%
Click here for further information Supplementary Assessment: Like-for-like reassessment (where allowed by programme regulations)
Click here for further information Requisites:
Click here for further information Description: Aims & Learning Objectives:
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. They should be able to demonstrate an in-depth understanding of the subject.

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.
Click here for further informationProgramme availability:

MA50063 is Optional on the following programmes:

Department of Biology & Biochemistry
  • RSBB-AFM07 : Integrated PhD Postgenomic Biosciences (Biosciences Route) (Full-time)
  • TSBB-AFM03 : MRes Biosciences (Full-time)
Department of Mathematical Sciences
NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.