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Direction Fields and Flow Fields

We use some nomenclature that is not standard. By direction field, we mean a plot of example vectors from the vector field for a differential equation. A direction field plot differs from a direct plot of vectors from the vector field in that magnitudes of vectors are not shown, nor are arrows indicating the initial and terminal points of the vectors. Think of each little segment drawn as an indicator of the tangent line to a solution at that point. In contrast, we talk about the flow field when example orbits are shown. It is possible to draw only the direction field or only the flow field, or both together.

To create a direction field in a display rectangle, check the 'Direction Field' box at the bottom of the display dialog box. The Direction Field dialog box will appear.

1. Set the number of points in each direction for the grid. The grid is always square. The number you specify in the text box at the top will govern the number of points in both the horizontal and vertical directions. The more points you choose, the shorter the segments indicating direction will be. 2. If you want to have arrows clarifying the direction in which the segments point, check the 'Arrows' box.

If you later decide that you do not want the direction field to appear in this box, go to the display dialog box and remove the check mark.

Kevin Cooper
Wed Sep 30 15:21:52 PDT 1998