Mathematical Biology III
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The application of mathematics to problems arising in the life sciences is a rapidly growing area yielding quantitative understanding of questions about such things as the spread of infectious diseases, population growth and interaction, organ (e.g. heart) function, cell signalling, nutrient supply, and more. This course will introduce students to the fascinating world of modelling biological systems. A variety of biological problems will be considered, in the context of which students will be exposed to a variety of mathematical techniques. No previous exposure to biology is necessary.
Topics covered are: Scalar, discrete-time models, analysed using the mathematical tools of cobwebbing and linear stability analysis of fixed points; Linear stability analysis of systems of discrete-time equations; The theory of dynamical systems for models comprised of linear and nonlinear scalar and coupled ordinary differential equations, including vector fields, phase-plane analysis and elementary bifurcation theory; Reaction-advection-diffusion models, including equation derivation from the law of mass conservation and Fick's law. The 1D Fisher equation is examined in particular, a Hamiltonian function is introduced for analysis of the steady equation, while travelling wave solutions of the unsteady equation are obtained.
This course is not recorded as prequisite for other courses.