Slope Fields

As discussed in the previous unit, differential equations relate a function of an independent variable and the functions derivatives. A slope field is a graphical representation of a differential equation on a finite set of points in the plane.

Slope fields provide information about the behavior of solutions to first-order differential equations.

Solutions to differential equations are functions or families of functions.

Essential Questions

How can slope fields be used to find solution(s) to differential equations?


  1. Estimate solutions to differential equations.

  2. Sketch a slope field of a differential equation.