Academic Year:
 2013/4 
Owning Department/School:
 Department of Mathematical Sciences 
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: 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.
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: 
MA30063 is Optional on the following programmes:
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)
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)
 TSMAAFM08 : MSc Modern Applications of Mathematics (Fulltime)
 TSMAAWM14 : MSc Modern Applications of Mathematics (Fulltime incorporating placement)
 TSMAAFL02 : PG Dip Modern Applications of Mathematics (Fulltime)
