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MA50063: Mathematical biology 2

Follow this link for further information on academic years Academic Year: 2019/0
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period:
Semester 2
Further information on unit assessment Assessment Summary: CW 25%, EX-TH 75%*
Further information on unit assessment Assessment Detail:
  • Coursework* (CW 25%)
  • Open Book Examination with a Duration of 24 hours* (EX-TH 75%)

*Assessment updated due to Covid-19 disruptions
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites:
Further information on descriptions 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.

Mathematical modelling in biology T/F A
Problem solving T/F A
Written communication F A

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.
Further information on programme availabilityProgramme availability:

MA50063 is Optional on the following programmes:

Department of Mathematical Sciences