Credits:
 6 
Level:
 Honours (FHEQ level 6) 
Period: 
Semester 2

Assessment:
 EX 100% 
Supplementary Assessment:  MA30063 Mandatory Extra Work (where allowed by programme regulations) 
Requisites:
 Before taking this unit you must take MA20223 and take MA30047 
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.
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:

MA30063 is Optional on the following programmes:
Department of Biology & Biochemistry
 RSBBAFM07 : Integrated PhD Postgenomic Biosciences (Biosciences Route) (Fulltime)  Year 1
 TSBBAFM03 : MRes Biosciences (Fulltime)  Year 1
Programmes in Natural Sciences
 UXXXAFB01 : BSc (hons) Natural Sciences (Fulltime)  Year 3
 UXXXAKB02 : BSc (hons) Natural Sciences with Industrial Placement (Fulltime with Thick Sandwich Placement)  Year 4
 UXXXAAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 UXXXAFM01 : MSci (hons) Natural Sciences (Fulltime)  Year 3
 UXXXAKM02 : MSci (hons) Natural Sciences with Professional Placement (Fulltime with Thick Sandwich Placement)  Year 4
 UXXXAAM02 : MSci (hons) Natural Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
Department of Mathematical Sciences
 USMAAFB15 : BSc (hons) Mathematical Sciences (Fulltime)  Year 3
 USMAAKB16 : BSc (hons) Mathematical Sciences (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB13 : BSc (hons) Mathematics (Fulltime)  Year 3
 USMAAKB14 : BSc (hons) Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAFB01 : BSc (hons) Mathematics and Statistics (Fulltime)  Year 3
 USMAAKB02 : BSc (hons) Mathematics and Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAAB14 : BSc (hons) Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB05 : BSc (hons) Statistics (Fulltime)  Year 3
 USMAAKB06 : BSc (hons) Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB06 : BSc (hons) Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 3
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 4
 USMAAAM15 : MMath Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 TSMAAFM09 : MSc Mathematical Sciences (Fulltime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 2
 TSMAAFM08 : MSc Modern Applications of Mathematics (Fulltime)  Year 1
 TSMAAFL02 : PG Dip Modern Applications of Mathematics (Fulltime)  Year 1
