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MA50063: Mathematical biology 2

Follow this link for further information on academic years Academic Year: 2012/3
Follow this link for further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Follow this link for further information on credits Credits: 6
Follow this link for further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Follow this link for further information on period slots Period: Semester 2
Follow this link for further information on unit assessment Assessment: OR 25%, EX 75%
Follow this link for further information on supplementary assessment Supplementary Assessment: MA50063 Mandatory extra work (where allowed by programme regulations)
Follow this link for further information on unit rules Requisites:
Follow this link for further information on unit content 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 in-depth 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 diffusion-advection 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 diffusion-driven instability; dispersion relation and Turing space.
Tumour Growth
* Formation of necrotic core
* Tumour size.
Follow this link for further information on programme availabilityProgramme 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
Notes:
* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.