This is a one semester introduction to ordinary differential equations. In the first part of the course we will cover the theory of first and second order scalar equations. The second part will be devoted to first order linear systems. Finally, we will have a look at some nonlinear systems.

Differential Equations, by Polking, Boggess and Arnold. This book comes packaged with another book about using Matlab to solve differential equations (at no additional charge!). Occasionally I will cover topics which are not in the text or present a different approach to some topic.

Homework / Quizzes | 20 % |

Midterm Exams (20 % each) | 40 % |

Final Exam | 40 % |

Midterm I | Tuesday, February 25 |

Midterm II | Tuesday, April 7 |

Final | Monday, May 12, 1:30-4:30 |

Below is a link for a Mathematica notebook which you can download and go through on your own in one of the campus computer labs.

You can also use the Java ODE solver at
http://math.rice.edu/~dfield/dfpp.html

Week |
Topics |
Sections |

1/21-1/24 | ODEs and PDEs. Separable ODEs. | 2.1-2.3 |

1/27-1/31 | First order tricks and examples, Lab I | 2.4-2.5 |

2/3-2/7 | Existence theory, phase line, stability | 2.7-2.9 |

2/10-2/14 | Second-order linear ODEs | 4.1-4.4 |

2/17-2/21 | Forcing and resonance. | 4.5-4.7 |

2/24-2/28 | Midterm I, Numerical methods | Ch. 6 |

3/3-3/7 | First-order systems, linear systems | Ch.8, 9.1 |

3/10-3/14 | Eigenvalues, eigenvectors | 9.2-9.3 |

3/17-3/21 | Spring Break ! | |

3/24-3/28 | More linear systems, matrix exp. | 9.4-9.5 |

3/31-4/4 | Fund. matrices, var. of parameters | 9.6,9.8 |

4/7-4/11 | Midterm II, Linearization of nonlinear ODEs | 10.1-10.2 |

4/14-4/18 | Phase portraits, periodic orbits | 10.3-10.4 |

4/21-4/25 | Nonlinear mechanics | 10.5-10.6 |

4/28-5/2 | More nonlinear systems | 10.7-10.8 |

5/5-5/9 | Special topics | 10.7-10.8 |