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Unit of study_

MATH3963: Nonlinear ODEs with Applications (Adv)

2025 unit information

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.

Unit details and rules

Managing faculty or University school:

Science

Study level Undergraduate
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) or [A mark of 65 or greater in (6 credit points of MATH2XXX) and (6 credit points of STAT2XXX)]
Corequisites:
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None
Prohibitions:
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MATH3063 or MATH4063
Assumed knowledge:
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None

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 availability

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The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.

Session MoA ?  Location Outline ? 
Semester 1 2024
Normal day Camperdown/Darlington, Sydney
Session MoA ?  Location Outline ? 
Semester 1 2025
Normal day Camperdown/Darlington, Sydney
Outline unavailable
Session MoA ?  Location Outline ? 
Semester 1 2020
Normal day Camperdown/Darlington, Sydney
Semester 1 2021
Normal day Camperdown/Darlington, Sydney
Semester 1 2021
Normal day Remote
Semester 1 2022
Normal day Camperdown/Darlington, Sydney
Semester 1 2022
Normal day Remote
Semester 1 2023
Normal day Camperdown/Darlington, Sydney

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Modes of attendance (MoA)

This refers to the Mode of attendance (MoA) for the unit as it appears when you’re selecting your units in Sydney Student. Find more information about modes of attendance on our website.