We will be interested in the careful construction of objects and the rigorous proof of results which are for most of them already known to students with background in ordinary differential equations (ODE). We will consider results from the general theory of ODE. We will then study linear systems, emphasizing their role in the study of nonlinear systems (which we will not cover). If time permit, other topics will be chosen from closely related subjects (delay differential equations, linear control theory, differential equations in a more general setting, etc.).

Ordinary Differential Equations, P. Hartman, SIAM (2004) |

Principles of Differential Equations, N.G. Markley, Wiley (2004) |

Basic Theory of Ordinary Differential Equations, P.-F. Hsieh and Y. Sibuya, Springer (1999) |

General theory of ODEs | 3 weeks | Existence and uniqueness of solutions |

Continuation of solutions | ||

Continuous dependence on initial values, on parameters | ||

Nonuniqueness. | ||

Homogeneous linear systems | 2 weeks | Asymptotic behavior of solutions |

Linearization | 2 weeks | Hartman-Grobman theorem |

General linear systems | 4 weeks | Floquet theory |

Fredholm alternative | ||

Exponential dichotomy | 2 weeks | Exponential dichotomy |

First approximate theory (a.k.a. Hartman-Grobman for nonautonomous systems) |

Lecture notes (posted 7 February 2007): whole file.

Assignments and final examination for a somewhat similar course taught at McMaster in 2003: I will post solutions to these once we have done the corresponding assignments (which will not be like these, but in the same "philosophy").

Last modified: Wed Feb 7 16:31:07 CST 2007