MATH3201 is a Mathematics Level III course. See the course overview below.

Units of credit: 6

Prerequisites: 12 units of credit in Level II Mathematics courses including MATH2120 or MATH2130, and MATH2501 or MATH2601.

Cycle of offering: yearly in Semester 1

Graduate attributes: the course will enhance your research, inquiry and analytical thinking abilities.

More information: this recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus. (This pdf will usually be updated by the end of the first week of the semester.)

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH3201, you can log into the My eLearning Vista instance of this course.

Many nonlinear ODEs do not have explicit solutions. The dynamical systems approach shifts the focus from finding explicit solutions to discovering geometric properties of solutions. It also recognises that even a small amount of nonlinearity in a physical system can be responsible for very complicated chaotic behaviour.
In this course you will learn the fundamentals of dynamical systems in (continuous time) nonlinear ODEs and in (discrete time) nonlinear maps, allowing you to analyse the local and global behaviour of nonlinear systems. You will also learn how to analyse time series data using nonlinear tools and build appropriate predictive models. Applications and computations play a significant role in this course and MATLAB will be used frequently.

Nonlinear maps: The building blocks of dynamics

fixed points, periodic points, invariant sets, recurrence, nonwandering sets, symbolic dynamics, conjugacy, sensitive dependence on initial conditions, Lyapunov exponents, fractals, Stable Manifold Theorem, chaotic attractors, Smale's Horseshoe, ergodic theory

Nonlinear ODEs: A geometric, qualitative approach to ODEs

phase portraits, fixed points, periodic and chaotic trajectories, sources, sinks, and saddles, stable and unstable subspaces, robustness, hyperbolicity, stability, conjugacy, stable and unstable manifolds, bifurcations

Nonlinear time series analysis: What to do with real data?

stationarity, linear or nonlinear, embedding and delay reconstruction, invariants, modelling and forecasting