Education Technology

Slope Fields and Euler's Method for AP Calculus

Published on 07/30/2005

Activity Overview

In this activity students use Computer Algebra System (CAS) to solve differential equations using Euler's method, Runge Kutta method, and other built-in methods.

Before the Activity

  • Install TI Connect™ using the TI connectivity cable
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 9 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Understand the concept of a first order differential equation
  • Understand that the general solution for a first order differential equation is usually a family of functions
  • Compute the tangent line for the member of the family passing through a point without knowing the solution


  • Learn to sketch an approximate solution, given only the slope field
  • Program slope fields on the TI-83 calculator


  • Use Euler's method to solve a differential equation numerically
  • Explore various methods to solve differential equations
  • After the Activity

    Students' answer questions on the Activity sheet.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary