Slope Fields

Definition

Slope fields are graphical representations of differential equations that show the slope at various points on a plane. They help visualize the behavior and solutions of differential equations.

Related terms

Direction Field:

Similar to slope fields, direction fields also represent the behavior of solutions to differential equations but focus on indicating the direction rather than the exact slope at each point.

dy/dx = f(x,y):

This notation represents a general form of a first-order ordinary differential equation, where y is dependent on x and its derivative dy/dx is equal to some function f(x,y).

Differential Equation:

A mathematical equation that relates an unknown function with its derivatives. It describes rates of change and helps model various phenomena in science and engineering.