MAT3031

Ordinary differential equations

Coordinator: Dr Robert Griffiths

4 points
* Two 1-hour lectures per week
* First semester
* Clayton
* Prerequisites: MAT2030, MAT2040
* Prohibitions: GAS3621, MAT3026

Objectives On the completion of this subject students will be familiar with the essentials for linear systems of ordinary differential equations; and the stability theory for linear systems of ordinary differential equations, with constant or periodic coefficients; will be able to study second-order systems, using phase-plane techniques for autonomous systems, and perturbation methods to construct periodic solutions, both free and forced; will know the elements of bifurcation theory; and will learn how to combine analytical and numerical techniques for studying a dynamical system.

Synopsis Existence and uniqueness of solutions for initial-value problems, linear systems of equations, linear independence of solutions. Second-order autonomous systems, stability, phase-plane techniques and periodic solutions. Forced oscillations, resonance and perturbation methods. Introduction to bifurcation theory.

Assessment Examination (2 hours): 85%
* Assignments: 15%

Prescribed texts

Grimshaw R Nonlinear ordinary differential equations Blackwell, 1990