Slope fields

Math

Definition

A visual representation of a differential equation that shows small line segments at grid points, each with the slope given by the equation dy/dx at that point. Slope fields allow you to visualize the family of solution curves without solving the equation analytically.

Examples

  • The slope field for dy/dx = x shows segments tilting right-upward for positive x and left-upward for negative x
  • Sketching a particular solution curve by following the direction of the segments from a given initial point

Related Terms

Separation of variables Antiderivatives Derivative definition

Study This Concept

Practice slope fields with free review games in these units:

AP Calculus AB Unit 7: Differential Equations