Description:
| Aims: To develop students' mathematical techniques so that they can model a range of biological systems and interpret the outcomes of the modelling.
Learning Outcomes: 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;
* make use of a computer package to simulate biological processes.
Skills: Calculus and matrix algebra (T, A); use of a computer package (T, A); modelling (T, F, A).
Content: 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.
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