Official course website
Spring 2025 • E91 • Swarthmore College
Welcome to the website for E91: Nonlinear Dynamics & Chaos! Lecture notes and homework assignments will be posted here.
| Class | Date | Topic | Readings | HW |
|---|---|---|---|---|
| 1.1 | Wed, Jan 22 | Introduction & Review of Differential Equations | Ch. 1 | |
| 1.2 | Wed, Jan 22 | 1-d dynamics on R^1: equilibrium, stability & potentials | Ch. 2.0, 2.1, 2.2, 2.4, 2.7 | |
| 2.1 | Mon, Jan 27 | Bifurcations 1 | ||
| 2.2 | Wed, Jan 29 | Bifurcations 2 | HW 1 | |
| 3.1 | Mon, Feb 3 | Linear systems n = 2 | ||
| 3.2 | Wed, Feb 5 | Phase plane 1 | HW 2 | |
| 4.1 | Mon, Feb 10 | Phase plane 2 | ||
| 4.2 | Wed, Feb 12 | Phase plane 3 | HW 3 | |
| 5.1 | Mon, Feb 17 | Limit Cycles 1 | ||
| 5.2 | Wed, Feb 19 | Limit Cycles 2 | HW 4 | |
| 6.1 | Mon, Feb 24 | Limit Cycles 3 | ||
| 6.2 | Wed, Feb 26 | Bifurcations 1 | HW 5 | |
| 7.1 | Mon, Mar 3 | Bifurcations 2 | ||
| 7.2 | Wed, Mar 5 | Bifurcations 3 | HW 6 | |
| 8.1 | Mon, Mar 17 | The Lorenz system | ||
| 8.2 | Wed, Mar 19 | Chaotic waterwheel | ||
| 9.1 | Mon, Mar 24 | |||
| 9.2 | Wed, Mar 26 | |||
| 10.1 | Mon, Mar 31 | |||
| 10.2 | Wed, Apr 2 | |||
| 11.1 | Mon, Apr 7 | |||
| 11.2 | Wed, Apr 9 | |||
| 12.1 | Mon, Apr 14 | |||
| 12.2 | Wed, Apr 16 | |||
| 13.1 | Mon, Apr 21 | |||
| 13.2 | Wed, Apr 23 | |||
| 14.1 | Mon, Apr 28 | |||
| 14.2 | Wed, Apr 30 |
This course will follow the classic textbook by Strogatz. It is available in two equally acceptable editions:
The Swarthmore textbook store stocks copies of this book; meanwhile, Cornell library holds copies in reserve. You can also find electronic copies on the internet. However, you must have a physical copy of your own for the duration of the semester.
The labs for this class will be self-scheduled. This means that you should expect to spend the same amount of time doing ‘lab work’ that you would in any other ENGR class at Swarthmore, but you this may happen in a less structured way than you’re used to.
More details to follow…
This course will be conducted in the form of (in-person) lectures during the regularly scheduled meeting times (i.e., Mondays and Wednesdays at 11:45 AM for 75 minutes per class meeting). Students are expected to attend every class meeting and take notes. The instructor will make available the lecture notes developed in class, but these do not replace the need for students to actively engage with the material, ideally by taking their own notes. Please be respectful of everyone else’s time by being punctual. You must not use cell phones or laptop computers during class, but you are permitted to take notes on a tablet or tablet-like device. Note that you need explicit permission of the instructor to take notes on your laptop, and such permission will be granted only in exceptional circumstances. If you must use your cell phone during class, you may excuse yourself from the classroom.
There will be one midterm exam and one final exam for this course. You should expect the midterm to be held around spring break, and you should expect the final to be a take-home exam which you can complete over a 24-hour period of your choosing during finals week. The final exam will be cumulative.
Homework assignments are an integral part of this course. You should expect to turn in approximately 12 homework assignments over the course of the semester. These assignments will collectively serve as a written document testifying to your ability to solve problems in nonlinear dynamics. As such, you should strive to turn in your best work.
Due dates are strict on the timescale of days (e.g., you can’t normally submit a homework assignment a day or two late) but flexible on the time scale of an hour (i.e., you can typically submit a homework assignment up to an hour after the deadline and still ‘have it count’ as if it was submitted on time. A penalty of 10% per day will be applied for late homework assignments, and they will not be accepted more than seven days after the deadline. The purpose of the 10% penalty is two-fold: it eliminates the need for negotiations about exactly what happens when you miss a deadline, and it encourages you to stick to the deadlines to stay on track.
Working together with others on homework assignments is acceptable and even encouraged. However, what you submit must either be entirely your own work, or clearly name your collaborators. If you worked closely enough with a fellow student that you suspect your solutions will be substantially similar, you should attribute each other on your homework on the front page with a statement like “I worked together with X on problem 2”. You are also encouraged to attribute online resources if you use them.
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Your grade will consist of the following components:
| Component | Weight |
|---|---|
| Homework | 25% |
| Midterm | 25% |
| Final | 35% |
| Lab | 15% |
The thresholds for this class will be as follows:
| Letter grade | Min. score |
|---|---|
| A- | 80 |
| B- | 70 |
| C- | 60 |
| D- | 50 |