So it seems that step 1 of my original plan is more involved than I thought. To satisfactorily derive the E- and B-field transformation equations, it would be necessary to delve into the depths of relativistic mechanics, including the transformation of equations for motion, momentum, and energy, among others. This seems like it is outside the scope of the project: indeed, Griffiths spends about 55 pages before he is able to state the field transformation equations. I thought there would be a point halfway through at which I could pick up and start the derivation, but I was incorrect, so I am going to take the transformation equations as given, and work from there.
That being said, my new timeline will be essentially the same as the old one, just starting at what used to be Step 2 with the application of the transformation equations to one or two situations.
1) 4/14-4/18: Pick one or two simple scenarios and find their E- and B- fields if they were traveling in a moving reference frame. This will be a computational step. The transformation equations are pretty straightforward, so it should take less time. This is just to have a proof of concept, so it is less important that the system has interesting behavior in a moving reference frame.
2) 4/18-4/24: Make 3D or 2D vector field models of these situations in Mathematica. This portion will be focused on figuring out how to make mathematica do what I want. The goal is to come up with an animation or interactive figure that can be used to view the vector fields when the system is moving at different speeds, starting at non-relativistic speeds and working up to the speed of light.
3) 4/24-5/2: Find and model situations that display either representative or unusual behavior when considered in a relativistic reference frame. Once the Mathematica simulation for the first situation has been figured out, the following cases should be easier to take care of. Interesting behavior might include systems that only have an electric field in one reference frame and only a magnetic frame in another. It also may be interesting to consider what happens if a reference frame is moving faster than the speed of light.
4) 5/15/14: Summarize results and write conclusions. This will consist of a final look at the systems considered earlier and suggest possible directions for future exploration.