Class website of ENGR 91, Nonlinear Dynamics & Chaos @ Swarthmore Engineering, Spring 2025
Resources • Labs • Syllabus • Complete Lecture Notes
NEW: Course Evaluation
Hyperlinks to lectures and homework assignments will be posted here.
| Class | Topic | Readings | Due |
|---|---|---|---|
| 1.1 W 1/22 | Introduction & Review | ||
| 2.1 M 1/27 | Three approaches to dynamics | 2.0, 2.1, 4.0, 4.1 | |
| 2.2 W 1/29 | Potentials & Linear Stability | 2.4, 2.7 | HW 1 [solutions] |
| 3.1 M 2/03 | Bifurcations | 3.1 to 3.4 | |
| 3.2 W 2/05 [In-class exercise] |
Bifurcations | 3.4, 3.5, 3.7 | HW 2 [solutions] |
| 4.1 M 2/10 [In-class exercise] |
Linear systems | Ch. 5 | |
| 4.2 W 2/12 | Linear systems | Ch. 5.0, 5.1, 5.2 | HW 3 [solutions] |
| 5.1 M 2/17 | Nonlinear phase plane | Ch. 5.3 | |
| 5.2 W 2/19 | Linearization about fixed pts | Ch. 6.1, 6.2, 6.3 | HW 4 [solutions] |
| 6.1 M 2/24 | Hyperbolic fixed pts; popln. dyn. | Ch. 6.3, 6.4 | |
| 6.2 W 2/26 | Nonlinear phase plane; conservative systems | Ch. 6.4-6.8 | |
| 7.1 M 3/03 | Conservative systems; index | Ch. 8 | |
| 7.2 W 3/05 [In-class exercise] |
Limit Cycles | Ch. 8 | HW 5 |
| 8.1 M 3/17 [Video recording] |
Limit Cycles; Poincare-Bendixson Thm. | ||
| Midterm | |||
| 9.1 M 3/24 [In-class exercise] |
Bifurcations | ||
| 9.2 W 3/26 [In-class exercise] |
Bifurcations | ||
| 10.1 M 3/31 | Quasi-periodicity; The Lorenz Equations | ||
| 10.2 W 4/02 | The Lorenz Equations | HW 6 [solutions] |
|
| 11.1 M 4/07 [In-class exercise] |
Order and Chaos in Lorenz equations | ||
| 11.2 W 4/09 [In-class exercise] |
The Lorenz Map | HW 7 [solutions] |
|
| 12.1 M 4/14 [In-class exercise] |
Stability of maps; Logistic Map | ||
| 12.2 W 4/16 [In-class “exercise”] |
Orbit Diagram of Logistic Map | ||
| 13.1 M 4/21 | Is the orbit diagram random? | ||
| 13.2 W 4/23 | The double pendulum | HW 8 | |
| 14.1 M 4/28 | Route to chaos in damped driven pendulum | ||
| 14.2 W 4/30 | Determinism, chaos, and randomness | Course evaluation |