Academic Year:  2017/8 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Honours (FHEQ level 6) 
Period: 
 Semester 2

Assessment Summary:  EX 100% 
Assessment Detail:  
Supplementary Assessment: 
 Likeforlike reassessment (where allowed by programme regulations)

Requisites: 
Before taking this module you must ( take MA20223 OR take PH20020 ) 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:
Department of Mathematical Sciences
 TSMAAFM08 : MSc Modern Applications of Mathematics
 TSMAAWM14 : MSc Modern Applications of Mathematics
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 3)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
 USMAAFB13 : BSc(Hons) Mathematics (Year 3)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
 USMAAFM14 : MMath(Hons) Mathematics (Year 3)
 USMAAFM14 : MMath(Hons) Mathematics (Year 4)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
 USMAAFB05 : BSc(Hons) Statistics (Year 3)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
Programmes in Natural Sciences
 UXXXAFM01 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Professional Placement (Year 4)
 UXXXAFM01 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Professional Placement (Year 4)
 UXXXAFM01 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) with Professional Placement (Year 4)
 UXXXAFM01 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) with Professional Placement (Year 4)
 UXXXAFM01 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Professional Placement (Year 4)
 UXXXAFM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) (Year 3)
 UXXXAAM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
 UXXXAKM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Professional Placement (Year 4)
