Session Overview
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Many differential equations cannot be solved exactly. For these DE's we can use numerical methods to get approximate solutions. In the previous session the computer used numerical methods to draw the integral curves. We will start with Euler's method. This is the simplest numerical method, akin to approximating integrals using rectangles, but it contains the basic idea common to all the numerical methods we will look at. We will also discuss more sophisticated methods that give better approximations. |
Session Activities
Read the course notes:
Watch the lecture video clip:
- Euler's Method (00:09:20)
Read the course notes:
Watch the lecture video clip:
- Example of Euler's Method (00:16:55)
Complete the practice problem:
Session Activities
Learn from the Mathlet materials:
- Watch the video
Exploration of the Euler's Method Applet (00:06:37)
Exploration of the Euler's Method Applet
> Download from iTunes U (MP4 - 10MB)
> Download from Internet Archive (MP4 - 10MB)
- Read about how to work with the Euler's Method Applet (PDF)
- Work with the Euler's Method Applet
Read the course notes:
Watch the lecture video clip:
- Better Methods (00:20:41)
Read the course notes:
Watch the lecture video clip:
- Pitfalls (00:03:51)
Watch the problem solving video:
- Euler's Method (00:10:16)
Complete the practice problems:
Check Yourself
Take the quiz:
- Problem Set Part I Problems (PDF)
- Problem Set Part I Solutions (PDF)
- Problem Set Part II Problems (PDF)
- Problem Set Part II Solutions (PDF)