Direction Field

Definition

Direction fields are graphical representations used to visualize the behavior and solutions of first-order ordinary differential equations. They indicate the direction in which solutions tend to move at different points on a plane.

Related terms

Slope Fields:

Similar to direction fields, slope fields also represent the behavior and solutions of differential equations but provide information about both direction and magnitude (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).

Initial Value Problem (IVP): An IVP involves finding the solution(s) to a differential equation that satisfy certain initial conditions. These conditions specify the value(s) of the unknown function and its derivative at a particular point.