This is an approximate, provisional schedule. As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.
| Date | Class Topic | Reading (usually from Hirsch,Smale,Devaney) |
|---|---|---|
| 9/1 | Course introduction | handout |
| 9/3 | Separable equations | handout |
| 9/6 | First-order linear equations, integrating factors | handout |
| 9/8 | Applications | handout |
| 9/10 | Qualitative study of first order equations | 1.1 |
| 9/13 | Logistic population models | 1.2 |
| 9/15 | Population growth with ``harvesting'' | 1.3 |
| 9/17 | Periodic harvesting, bifurcations | 1.4 |
| 9/20 | Lab Day 1 -- Bifurcations | 1.6 |
| 9/22 | Second order equations and systems | 2.1-4 |
| 9/24 | Eigenvalues and eigenvectors | 2.5 |
| 9/27 | Linearity and Superposition | 2.6-7 |
| 9/29 | The phase portrait of a planar system | 3.1 |
| 10/1 | Midterm I | |
| 10/4 | Complex eigenvalues | 3.2 |
| 10/6 | Repeated eigenvalues, changing coordinates | 3.3 |
| 10/8 | More on changing coordinates | 3.4 |
| 10/11 | Columbus Day Break (no class) | |
| 10/13 | Classification of planar systems | 4.1 |
| 10/15 | The simple harmonic oscillator | handout |
| 10/18 | More on simple harmonic oscillator | handout |
| 10/20 | Lab Day 2 -- forced mechanical vibrations and resonance | |
| 10/22 | Higher-dimensional systems | 5.5 |
| 10/25 | More on higher-dimensional systems | 6.1, 6.3 |
| 10/27 | The existence and uniqueness theorem | 7.2 |
| 10/29 | More on the existence and uniqueness theorem | 7.2 |
| 11/1 | Continuous dependence on initial conditions | 7.3 |
| 11/3 | Equilibrium points of non-linear systems | 8.1 |
| 11/5 | Sinks, sources, saddles | 8.2-8.3 |
| 11/8 | Stability | 8.4 |
| 11/10 | Nullclines | 9.1 |
| 11/12 | More on stability | 9.2 |
| 11/15 | Lyapunov's method | 9.2 |
| 11/17 | Gradient and Hamiltonian systems | 9.3, 9.4 |
| 11/19 | Midterm II | |
| 11/22 | Lab Day 3 -- The forced pendulum | 9.5 |
| 11/24 | Thanksgiving Break (no class) | |
| 11/26 | Thanksgiving Break (no class) | |
| 11/29 | Final Application: Electrical circuits | 12.1 |
| 12/1 | Lienard and van der Pol equations | 12.2-12.3 |
| 12/3 | Lab Day 4 -- more on the van der Pol equation | |
| 12/6 | Semester wrap-up |
The final exam for this course will be given at 8:30am on Thursday, December 16.
Last modified: August 23, 2004