MATH5295 Special Topics (Applied)

MATH5295 is a Special Topic in Applied Mathematics course for Honours and Postgraduate Coursework students. The current topic is Dynamical Systems & Chaos (co-taught with MATH3201). See the course overview below.

Units of credit: 6

Prerequisites:  Nil

Cycle of offering: Term 3 2022.

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.

If you are currently enrolled in MATH5295, you can log into UNSW Moodle for this course.

Course Overview

A dynamical system is any system whose state changes as a function of time. This course studies the regular and irregular behaviour of nonlinear dynamical systems, concentrating on ordinary differential equations (ODEs) and their solutions. Topics from the theory of ODEs include: existence and uniqueness theorems; linear ODEs with constant and periodic coefficients and Floquet theory; linearization and stability analysis; perturbation methods; bifurcation theory; phase plane analysis for autonomous systems.

The theory is illustrated with applications to physical, biological and ecological systems. In addition, a selection from the dynamical concepts: Hamiltonian dynamics, resonant oscillations, chaotic systems, Lyapunov exponents, Poincare maps, homoclinic tangles.