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Unit of study_

MATH3963: Nonlinear ODEs with Applications (Adv)

The theory of ordinary differential equations is a classical topic going back to Newton and Leibniz. It comprises a vast number of ideas and methods of different nature. The theory has many applications and stimulates new developments in almost all areas of mathematics. The emphasis is on qualitative analysis including phase-plane methods, bifurcation theory and the study of limit cycles. The more theoretical part includes existence and uniqueness theorems, linearisation, and analysis of asymptotic behaviour. The applications in this unit will be drawn from predator-prey systems, population models, chemical reactions, and other equations and systems from mathematical biology.

Code MATH3963
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites:
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A mark of 65 or greater in 12 credit points of MATH2XXX units of study
Corequisites:
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None
Prohibitions:
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MATH3063 or MATH4063
Assumed knowledge:
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Linear ODEs (for example, MATH2921), eigenvalues and eigenvectors of a matrix, determinant and inverse of a matrix and linear coordinate transformations (for example, MATH2922), Cauchy sequence, completeness and uniform convergence (for example, MATH2923)

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 of solutions of ordinary differential equations
  • LO4. interpret model results and evaluate and explain the limitations of models in representing real systems
  • LO5. understanding the role of basic bifurcations in nonlinear systems by synthesising graphical, symbolic and computational information 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 1 week before the first day of teaching for the relevant session.