4.4 Introduction to Direction Fields (also called Slope Fields)

In this lesson, you will learn about direction (slope) fields.

Lesson Objectives

  • 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.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

  1. YouTube video: Direction Fields|MIT 18.03SC Differential Equations
  2. YouTube video: Vector Fields – Sketching
  3. YouTube video: Slope Fields and Differential Equations: Soup to Nuts
  4. YouTube video: Slope Fields

Lesson Readings

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.

  1. Direction Fields
  2. 1.2 Direction Fields
  3. Direction Fields, by Bernd Schroder

Lesson Practice Exercises/Activities

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.

  1. 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.
  2. Tools for Enriching Calculus  – Direction Fields and Euleris Method Note: Click on Browse Homework Hints and then choose Direction Fields and Euleris Method.


Additional Resources

Below are additional resources that help reinforce the content for this module.

  1. Direction Fields; Euler’s Method
  2. 1.4 Direction Fields
  3. A Theoretical Introduction to Slope Fields
  4. 6.1 The Differential Equation – direction fields
  5. Direction Fields and Euler’s Method (App)