This is a one semester introduction to ordinary differential equations. In the first half of the course we will cover the theory of first and second order scalar equations, including the Laplace transform and numerical methods. The second half will be devoted to first order systems, both linear and nonlinear.
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 26 |
| Midterm II | Tuesday, April 16 |
| Final | Monday, May 13, 1:30-4:30 |
We will have several computer lab sessions to try out software for solving and visualizing differential equations.
| Week | Topics | Sections |
| 1/23-1/25 | ODEs and PDEs. Separable ODEs. | 2.1-2.3 |
| 1/28-2/1 | First order tricks and examples, Lab I | 2.4-2.5 |
| 2/4-2/8 | Existence theory, phase line, stability | 2.7-2.9 |
| 2/11-2/15 | Second-order linear ODEs. Oscillators | 4.1-4.4 |
| 2/18-2/22 | Forcing and resonance. | 4.5-4.7 |
| 2/25-3/1 | Midterm I. Laplace transform | 5.1-5.3 |
| 3/4-3/8 | More Laplace. d-functions | 5.4-5.7 |
| 3/11-3/15 | Numerical Methods, Lab II | Ch. 6 |
| 3/18-3/22 | Spring Break. | |
| 3/25-3/29 | Linear systems, eigenvalues, eigenvectors | 9.1-9.3 |
| 4/1-4/5 | More linear systems, matrix exponential | 9.4-9.5 |
| 4/8-4/12 | Linear flows, variation of parameters | 9.6-9.8 |
| 4/15-4/19 | Midterm II, Linearization of nonlinear ODEs | 10.1-10.2 |
| 4/22-4/26 | Phase portraits, periodic orbits | 10.3-10.4 |
| 4/29-5/3 | Nonlinear mechanics | 10.5-10.6 |
| 5/6-5/10 | More nonlinear systems, Lab III | 10.7-10.8 |