Existence, uniqueness, continuous-dependence, and differentiable dependence of solutions. Fixed points, periodic orbits, and their stability. Phase plane analysis, the Poincaré-Bendixson Theorem, homoclinic and heteroclinic orbits. Stable manifold theorem, Hartman-Grobman Theorem. Centre manifold Theorem and codimension-one bifurcations. Three term hours; lectures. (3.0 credit units)
Existence, uniqueness, continuous-dependence, and differentiable dependence of solutions. Fixed points, periodic orbits, and their stability. Phase plane analysis, the Poincaré-Bendixson Theorem, homoclinic and heteroclinic orbits. Stable manifold theorem, Hartman-Grobman Theorem. Centre manifold Theorem and codimension-one bifurcations. Three term hours; lectures. (3.0 credit units)
