AP Calculus AB and BC glossary

Slope field

Also called: Direction field

A slope field is a grid of short line segments, each drawn with the slope that a differential equation assigns to that point. It shows the shape of every solution curve at once without solving the equation.

To sketch a particular solution, put your pencil on the given initial condition and follow the segments, keeping the curve parallel to the nearby marks. The curve never crosses segments, it flows along them.

Matching a field to an equation is faster with structure than with arithmetic. If $\frac{dy}{dx}$ depends only on $x$ , every column of segments looks identical; if it depends only on $y$ , every row does.

Appears in: Unit 7: Differential Equations