Differential Equations

Numerical Methods

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Session Overview

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:

• Numerical Methods: Introduction (PDF)

Watch the lecture video clip:

• Euler’s Method

Read the course notes:

• Motivation and Implementation of Euler’s Method (PDF)

Watch the lecture video clip:

• Example of Euler’s Method

Complete the practice problem:

• An Example of Euler’s Method (PDF)
• Exercise Solution (PDF)

Session Activities

Learn from the Mathlet materials:

• Watch the video Exploration of the Euler’s Method Applet
• Read about how to work with the Euler’s Method Applet (PDF)
• Work with the Euler’s Method Applet

Read the course notes:

• Errors in Euler’s Method (PDF)

Watch the lecture video clip:

• Better Methods

Read the course notes:

• Further Numerical Methods (PDF)

Watch the lecture video clip:

• Pitfalls

Watch the problem solving video:

• Euler’s Method

Complete the practice problems:

• Practice Problems 3 (PDF)
• Practice Problems 3 Solutions (PDF)

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)

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