
Academic Year:  2014/5 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 2 
Assessment Summary:  CW 25%, EX 75% 
Assessment Detail: 

Supplementary Assessment: 
MA50063 Mandatory extra work (where allowed by programme regulations) 
Requisites:  
Description:  Aims: To introduce students to applications of partial differential equations to model problems arising in biology. Both mathematical modelling and mathematical analysis will be covered, and at all times the interplay between the mathematics and the underlying biological concepts will be emphasised. Learning Outcomes: At the end of this unit, students should be able to: * Derive and interpret mathematical models of problems arising in biology using partial differential equations * Analyse models written in terms of partial differential equations * Give a qualitative and quantitative account of their solution, and * Interpret the results in terms of the original biological problem * Discuss the ideas presented in this unit orally to demonstrate indepth understanding of the material. Skills: Mathematical modelling in biology T/F A Problem solving T/F A Written communication F A Content: Biological Motion * Derivation of general conservation equation (macroscopic approach) * Properties of a conservation equation * Boundary conditions * Derivation of the diffusionadvection equation (microscopic approach) * Components of flux  diffusion, advection, chemotaxis * Solution of the advection equation using method of characteristics * Age structured problems * Solutions of the diffusion equation using the fundamental solution * Steady state distributions; transit times Biological Invasions * Wavefront and wavespeed calculations for exponentially growing populations * Planar travelling waves; minimum wavespeed Spatial Pattern Formation * Critical domain size; scale and geometry effects * Turing mechanisms * Linear stability analysis; conditions for diffusiondriven instability; dispersion relation and Turing space. Tumour Growth * Formation of necrotic core * Tumour size. 
Programme availability: 
MA50063 is Optional on the following programmes:Department of Biology & Biochemistry
