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(continued fromÌýlast page...)

Hopefully you successfully managed to get a reasonable picture of a slope field during your little trip over toÌýMathematica. The slope field you got should have been very much like the following:

The fact that we got a slope field at all, without having to do huge numbers of calculations by hand, is somewhat encouraging, but there are a couple of things about this plot that could use some improvement. First, theÌýVectorPlotÌýcommand seems to default to drawing little arrow heads on each vector that it renders. While this is useful when studying vectors in their own right, in the context of slope fields, these are less necessary, (though they do have their uses,) and to some extent they clutter the image. Second, it looks likeÌýVectorPlotÌýdefaults to leaving theÌýx- andÌýy-axes off of the graph. Let's deal with these complaints by adding some options to theÌýVectorPlotÌýcommand we used on the last page, as follows:

VectorPlot[{1, x^2}, {x, -2, 2}, {y, -2, 2},
VectorStyle -> Arrowheads[0], Axes -> True]

The two options we've added are self-explanatory. The first says that the arrow heads should be left off, and the second asks for the axes to be included.

Switch back toÌýMathematicaÌýand enter the above command, looking carefully at the resulting graph, then return here.

Let's nowÌýgo and seeÌýwhat you should have gotten this time.