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During 2021 we will continue to support students who need to study remotely due to the ongoing impacts of COVID-19 and travel restrictions. Make sure you check the location code when selecting a unit outline or choosing your units of study in Sydney Student. Find out more about what these codes mean. Both remote and on-campus locations have the same learning activities and assessments, however teaching staff may vary. More information about face-to-face teaching and assessment arrangements for each unit will be provided on Canvas.

Unit of study_

MATH3063: Nonlinear ODEs with Applications

This unit of study is an introduction to the theory of systems of ordinary differential equations. Such systems model many types of phenomena in engineering, biology and the physical sciences. The emphasis will not be on finding explicit solutions, but instead on the qualitative features of these systems, such as stability, instability and oscillatory behaviour. The aim is to develop a good geometrical intuition into the behaviour of solutions to such systems. Some background in linear algebra, and familiarity with concepts such as limits and continuity, will be assumed. The applications in this unit will be drawn from predator-prey systems, transmission of diseases, chemical reactions and other equations and systems from mathematical biology.

Code MATH3063
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites:
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12 credit points of MATH2XXX units of study
Corequisites:
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None
Prohibitions:
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MATH3963 or MATH4063
Assumed knowledge:
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MATH2061 or MATH2961 or [MATH2X21 and MATH2X22]

At the completion of this unit, you should be able to:

  • LO1. explain the principle of linear approximations to nonlinear systems and use this to analyse system behaviour close to steady states
  • LO2. synthesise graphical information from nullclines and flow to construct qualitative phase plane solutions to problems in nonlinear systems
  • LO3. demonstrate knowledge of the theory of existence and uniqueness, and the determination of stability of solutions of ordinary differential equations, including special cases such as Hamiltonian and gradient systems.
  • LO4. interpret model results and evaluate and explain the limitations of models in representing real systems
  • LO5. demonstrate a broad understanding of the role of basic bifurcations in nonlinear systems and evaluate the effect of parameter variation on observed model behaviour
  • LO6. apply mathematical theory in novel and diverse applications.

Unit outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.