You CAN Ace Differential Equations
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Differential Equations Alpha List
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Here is a great wikibooks page explaining slope fields in more detail: WikiBooks - Slope Fields
Alternate Name For Slope Fields - Direction Fields
Slope Fields are two dimensional representations of the slope of a differential equation. Here is an example of what a slope field looks like. The little lines all over the graph are what we call the slope field lines and they indicate the slope at those points. The three graphs are three possible solutions to the differential equation that was used to produce the slope field.
As you can probably tell from the graph, slope fields are best drawn by a computer. There are many online graphing sites out there. You can also use winplot to plot slope fields.
Here are couple of videos explaining slope fields and how to graph them. The first video is much better and more accurate than the second. So if you have time for only one, the first one is best to watch.
This first video is an indepth introduction to slope fields and a few other introductory topics. He does not actually solve any differential equations using regular techniques in this video. He spends time explaining the concept of differential equations, which is important to understand.
MIT OCW - slope fields
Here is another video that shows how to plot a slope field by hand. It is not the best video in the world but it has some good techniques. Make sure you read the comments we've written about the video before accepting everything that he does in this video. That said, this video is included to give you another perspective.