Education Technology

Slope Fields Introduction

Published on 08/31/2011

Activity Overview

Explore the concept of slope field to the first order differential equation.

Objectives

  • Describe the idea behind slope fields in terms of visualization of the family of solutions to a differential equation
  • Describe the slope of a tangent line at a point on the graph of a solution to a differential equation
  • Describe the general nature of a solution to a differential equation as suggested by a slope field
  • Use the TI-Nspire built-in function deSolve to find the general family of solutions to a differential equation
  • Match a differential equation with its corresponding slope field

Vocabulary

  • slope field
  • first order differential equation
  • family of solutions
  • particular solution

About the Lesson

This lesson involves the concept of a slope field, a graphical representation of the family of solutions to the first order differential equation, y'=g(x,y). As a result, students will:

  • Understand that a slope field is a visualization of the family of solutions to a differential equation.
  • Use characteristics in a slope field to describe the general nature of a solution to a differential equation.
  • Be able to match a differential equation with the appropriate slope field and find the family of solutions using the TI-Nspire.