Ordinary differential equations
4 points * First semester * Clayton * Prerequisites: MAA2011, MAA2032 and MAT2010 * Prohibitions: GAS3621
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 and Green's functions. Linear equations with periodic coefficients. Second order autonomous systems, stability, phase plane techniques and periodic solutions. Forced oscillations, resonance and perturbation methods. Introduction to bifurcation theory.
Assessment Examinations (1.5 hours): 85% * Assignments: 15%
Prescribed texts
Grimshaw R Nonlinear ordinary differential equations Blackwell, 1990
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