**Class 02**:

**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.

**In class**, we'll work on examples of these ideas: (activity is available below)

**After class**, complete the homework (problems due Friday Feb 3rd)

**Video summary:**

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

Related objectives:

- 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.

activity17-01-24.pdf | 123 KB |