Type a command or search the notes. Tab cycles completions. Up and down recall history when blank. Escape dismisses, then leaves the prompt.
MATH
[1251]

Definitions from Numerical solutions

All definitions from Numerical solutions.

Back to Numerical solutions

Direction field

For

y′=f(x,y),y'=f(x,y),

the direction field assigns a short line segment of slope f(x,y)f(x,y) to each point (x,y)(x,y) on a grid. A solution curve follows these local directions and an initial condition selects the curve passing through the prescribed point.

The field gives qualitative information before any numerical calculation. It can show increasing and decreasing regions, equilibrium levels and the way nearby solution curves behave.

  1. [1]:A family of translated curves

On this page

Direction field