Department of Mathematical Sciences, Unit Catalogue 2009/10
MA20202: Modelling the dynamics of life 2
|Assessment:||CW 50%, EX 50%|
|Supplementary Assessment:||Like-for-like reassessment (where allowed by programme regulations)|
|Requisites:||Before taking this unit you must take MA20201|
To develop students' mathematical techniques so that they can model a range of biological systems and interpret the outcomes of the modelling.
At the end of this unit, students should be able to:
* write down and analyse a range of classical mathematical models used to describe biological processes;
* carry out a range of techniques in matrix algebra and understand its role in analysing biological models;
* work competently with complex numbers.
Calculus and matrix algebra (T, A); modelling (T, F, A).
First-order non-linear difference equations: cobweb diagrams, steady states, stability; biological applications, e.g. density-dependent population growth, selection in a bacterial population.
Matrices and determinants: eigenvalues and eigenvectors, complex numbers; Leslie matrices, age-structured populations, host-parasitoid systems.
Second-order linear ordinary differential equations.
Second-order non-linear ordinary differential equations: steady states, Jacobian, phase plane analysis; prey-predator systems, competition systems.