Aims & Learning Objectives:
Aims: To provide an accessible but rigorous treatment of initial-value problems for nonlinear systems of ordinary differential equations. Foundations will be laid for advanced studies in dynamical systems and control. The material is also useful in mathematical biology and numerical analysis.
Objectives:
Conversance with existence theory for the initial-value problem, locally Lipschitz righthand sides and uniqueness, flow, continuous dependence on initial conditions and parameters, limit sets.
Content:
Topics will be chosen from the following:
Motivating examples from diverse areas. Existence of solutions for the initial-value problem. Uniqueness. Maximal intervals of existence. Dependence on initial conditions and parameters. Flow. Global existence and dynamical systems. Limit sets and attractors.
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