Slope Field

Definition

A slope field, also known as a direction field, is a graphical representation of solutions to a differential equation. It consists of small line segments or arrows that indicate the slope (rate of change) at different points on a coordinate plane.

Related terms

Differential Equation:

A differential equation is an equation that relates a function with its derivatives. It involves rates of change and can be used to model various real-world phenomena.

Solution Curve:

A solution curve represents the graph of a particular solution to a differential equation. It follows the directions indicated by the slope field, connecting points with consistent slopes.

Euler's Method:

Euler's method is an iterative numerical technique used to approximate solutions to ordinary differential equations. It uses small steps based on information from the slope field to estimate values along solution curves.