Graphing slope fields


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If you are manually graphing slope fields, here are some scalable graphics:

You can plot slope fields with a solution to the differential equation in Grapher (Mac only). If you haven't used Grapher, it lives in your Utilities folder. I launch it via the Spotlight:
LaunchGrapher
Here's the output for , :

grapherSlopeFieldAndODE

I'm a big fan of the simplicity of Grapher, and at first, I loved its slope field facilities. But it seems to strain Grapher's numerics. I sometimes encountered spurious artifacts, or the slope field was simply wrong. I suspect I could fix things by tuning the parameters or selecting a different algorithm.

Another tool is Eduardo Sontag's slope field applet. Easy-to-use and nice for exploring. Documentation is worth reading if you are going to use trig functions, etc. Not designed for creating sleek graphics for printing.

I decided to give Mathematica a shot, and downloaded a 30-day trial. This was the nicest solution. Scalable vector graphics rather than bitmaps, and more numerically stable. Here's a sample of a Mathematica slope field for the differential equation :

tickList = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5};
VectorPlot[{1, x *Exp[-y]}, {x, -5, 5}, {y, -5, 5},
VectorStyle -> {Gray, Arrowheads[0]},
LabelStyle -> Directive[16, LightGray], Axes -> True,
AxesOrigin -> {0, 0}, Frame -> False,
VectorScale -> {Tiny, Automatic, None},
Ticks -> {tickList, tickList}]

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