U Of U Mathematical Biology
The work carried out by the Mathematical Biology group includes high-high quality interdisciplinary links across the University, and the group continuously attracts main analysis grants. Consideration will probably be given to the physiological problems of life on land (reproductive freedom from water, breathing air especially during the mid- Devonian drop in global oxygen ranges, water conservation and the emergence of the mammal -like reptiles).
It will cowl major climatic themes that have formed trendy life together with sea stage change and glaciation; evolutionary growth of birds and mammals; the evolution of endothermy; the biogeographic distributions of biota; and the adaptive radiation/evolution of the mammals.
This module is obligatory for college kids taking the BSc or MMath in Mathematics or the BSc or MSci in Mathematical Biology, and may optionally be taken in combination with other modules by students on any of the opposite Mathematics mixed levels.
Background, Examples of essential Physical and Organic Processes described by Ordinary Differential Equations (ODEs), Existence and uniqueness of solutions of ODEs, Linearised Stability Analysis, Two-dimensional Methods: Hamiltonian and Gradient techniques, Periodic solutions: Floquet concept, Poincare Map and Stability of Periodic Orbits, Bifurcation and Chaos.
Transformation of an nth order equation to a system of n first order equations, Homogeneous linear techniques with constant coefficients, Basic sets of solutions and fundamental matrices, the Wronskian and Abel′s system, The exponential of a matrix, Nonhomogeneous linear systems, Variation of parameters, Homogeneous linear techniques of two first order equations with fixed coefficients, Stability and the section airplane.