In this lesson, you will learn about direction (slope) fields.
Recognize how a direction (slope) field is created.
Interpret a given direction (slope) field.
Recognize the direction field for a common differential equation.
Given a direction field, draw the graph of a particular solution to the associated differential equation.
View all of the following instructional videos. These will help you master the objectives for this module.
YouTube video: Direction Fields|MIT 18.03SC Differential Equations
YouTube video: Vector Fields - Sketching
YouTube video: Slope Fields and Differential Equations: Soup to Nuts
YouTube video: Slope Fields
The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.
Direction Fields, by Bernd Schroder
Slope Fields, by Dr. Marcel B. Finan
A Quick Guide to Sketching Direction Fields - definition of nullcline, how to use the nullcline, definition of isoclines, how to use the method of isoclines
Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.
Download and install the CDF player and go through the example functions. Pay careful attention to the slope fields for (natural logarithm), (hyperbola centered at the origin), (circle centered at the origin), and (sine function). Compare the slope fields to the properties of these familiar functions.
Tools for Enriching Calculus - Direction Fields and Euleris Method Note: Click on Browse Homework Hints and then choose Direction Fields and Euleris Method.
Below are additional resources that help reinforce the content for this module.