Session Overview
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In this session we take a break from linear equations to study autonomous equations. Many systems, e.g. populations, are modeled by autonomous DE's. We will look at the critical points and stability and learn how to predict the long term behavior of these systems without actually solving them. |
Session Activities
Read the course notes:
Watch the lecture video clips:
- First Order Autonomous Equations (00:13:51)
- Bank Account (00:08:19)
Read the course notes:
Watch the lecture video clip:
- Example: Logistic Model (00:13:53)
Read the course notes:
Learn from the Mathlet materials:
- Watch the video Exploration of the Phase Lines Applet (00:08:54)
- Work with the Phase Lines Applet
Check Yourself
Take the quiz:
Session Activities
Watch the lecture video clip:
-
Example: Logistic Model with Harvesting (00:09:44)
Example: Logistic Model with Harvesting
> Download from iTunes U (MP4 - 87MB)
> Download from Internet Archive (MP4 - 87MB)
Check Yourself
Take the quizzes:
- Can Solutions have a Local Maximum? (PDF)
- Choices (PDF)
- Answer (PDF)
- Inflection Points (PDF)
- Choices (PDF)
- Answer (PDF)
Session Activities
Watch the problem solving video:
- Autonomous Equations and Phase Lines (00:11:44)
Check Yourself
Complete the problem sets:
- Problem Set Part I Problems (PDF)
- Problem Set Part I Solutions (PDF)
- Problem Set Part II Problems (PDF)
- Problem Set Part II Solutions (PDF)