Intended Learning Outcomes
Once you've successfully completed this module you should be able to:
- Interpret differential equation models for populations, relating the expressions appearing in the model to processes
that affect the population.
- Formulate and analyse ordinary differential equation (ODE) models for the population of a single species, finding
equilibrium populations and determining how their stability depends on parameters.
- Analyse delay-differential equation (DDE) models for the population of a single species and use linear stability
analysis to determine which values of the parameters induce oscillatory instabilities.
- Analyse ODE models for the populations of two interacting species, finding equilibria and using information about their
linear stability to characterise the long-term behaviour of the system.
- Define a conserved quantity for a system of ODEs and, where possible, use such quantities to determine the
long-term behaviour of both two-species ODE models and single-species models population models that include diffusion.
- Construct the ODEs associated with a system of chemical reactions subject to mass-action kinetics and analyse them to
discover conserved quantities.
- Construct the Markov process associated with a system of chemical reactions and, for small numbers of reactions,
analyse it to determine the long-term behaviour of the system.
- Analyse two key models, Wolpert's Frech flag model and Turing's reaction-diffusion model, relating the
solutions of the associated PDEs to the processes of pattern-formation in developing organisms.
The first half of the course will cover classical topics in mathematical biology, following sections of Jim Murray's famous text,
Mathematical Biology I: An Introduction. This book is available online
from within the University's network. For off-campus access, you can install software that will allow you to use all the Library's services via the
University's Virtual Private Network (VPN).
The notes below outline topics discussed in more depth in lectures.
to the top
Opportunities for feedback
The main channel for formal, written feedback in this module is the coursework. It will be a problem set similar to the ones provided on this page, but devoted to a specific application that uses the ideas from the course. Written solutions will be marked and scripts returned, providing both written comments and a mark. In addition, the weekly examples classes provide further opportunities for verbal feedback and, for students who bring written solutions to the exercises, on-the-spot marking and written feedback as well.
Problem Sets & Solutions
to the top
The coursework will be due at 3:00 PM on Friday, 22 March 2019. Please hand it in at Reception. The coursework contributes 20% to your final mark for the module and will be marked out of 20. Scripts and marks will be returned by Friday 12 April.
Week 3 Questionnaires
Watch here for a brief summary of and response to the Week 3 questionnaires
Coursework & Exams
to the top
to the top
▲ Up to the top