Differential Equations

First Order Autonomous Differential Equations

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Session Overview

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:

• First Order Autonomous Differential Equations: Introduction (PDF)

Watch the lecture video clips:

• First Order Autonomous Equations
• Bank Account

Read the course notes:

• Logistic Model: Qualitative Analysis (PDF)

Watch the lecture video clip:

• Example: Logistic Model

Read the course notes:

• Phase Lines (PDF)

Learn from the Mathlet materials:

• Watch the video Exploration of the Phase Lines Applet
• Work with the Phase Lines Applet

Check Yourself

Take the quiz:

• Stability of Equilibria (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Watch the lecture video clip:

• Example: Logistic Model with Harvesting

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

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)

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