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