Overview

MATH5295 is a Special Topic course in Applied Mathematics for Honours and Postgraduate Coursework students. The current topic is Fractional Calculus.

Units of credit: 6

Prerequisites:  Nil

Cycle of offering: Term 2 2023

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

More information: The Course outline is linked within the course offering table for the term applicable.  NB: Outlines will be made available closer to the start of term.

The course outline 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.