Before class, watch the lecture material linked below
Post at least one question or comment on Piazza (access via Canvas or directly). See "Check Yourself" Q1 for details.
Check yourself via the Class 02 Check Yourself on Canvas (Due by 11:59pm on Tues Jan 24)
In class, we'll work on examples of these ideas: (activity is available below)
After class, complete the homework (problems due Friday Feb 3rd)
Watch L1 by Steve from 1:10:11 to the end (16 min),
Watch the definitions and example extension video (10 min),
Watch L2 by Steve from the beginning to 32:20 (32 min).
Corresponding text: sections 2.1-2.6
Total: 58 minutes of lecture
Note: For videos, by clicking on the gear symbol you can change the speed of the video replay (and can turn on closed captions).
Video clips broken down by topic:
V01 | Youtube (Steve Strogatz) | Geometric (qualitative) methods (L1 1:00:11 to 1:11:45) | 12 minutes
V02 | Youtube (St) | Logistic example (L1 1:11:45 to 1:16:30) | 4 min
V03 | Youtube (Sarah Iams) | Definitions and example extension (All) | 10 min
Optional video | Youtube (St) | Brief summary (L2 00:29 to 3:26) | 3 min
V04 | Youtube (St) | Linearizing (L2 3:35 to 13:30) | 10 min
V05 | Youtube (St) | No linear term (L2 13:35 to 19:27) | 6 min
V06 | Youtube (St) | Linearization in logistic (L2 19:29 to 22:25) | 3 min
V07 | Youtube (St) | Existence, Uniqueness, Oscillations | (L2 23:14 to 32:20) | 9 min
- Interpret differential equations as a way of encoding information about the time evolution of a system.
- Use geometric methods to identify the long term behavior of a solution function to a differential equation.
- Distinguish between analytic methods for finding a solution to a differential equation and qualitative methods that provide only an estimate or approximation of the solution function.
- Identify critical points of a differential equation.
- Use the method of linearization to assess the stability of critical points.
- Use a phase portrait to identify possible long term behaviors of solutions to a differential equation.