are there any programs out there that draw vector fields for you?

You mean like Matlab?

 

edit:

Comparing 2D Vector Field Visualization Methods: A User Study

http://vis.cs.brown.edu/docs/pdf/Laidlaw-2005-CVF.pdf

Mathematica has a package that will draw vector fields for you. Not used it much myself, but I am sure it is good.

speaking of matlab, mathmatica, and maple.

 

are they all roughly equivalent or is one superior?

I find Mathematica vastly superior to Matlab/Maple, but the latter are probably better for programming. Mainly I use Mathematica for calculations so programming isn't a major concern.

Mathematica is generally considered to be superior. I have never used Maple or Mathlab.

 

If you have access to Mathematica you will need to load the following packages;

 

Graphics`PlotField3D`

or

Graphics`PlotField`

 

If you want to calculate div and grad etc. you can use the package

 

Calculus`VectorAnalysis`

 

All 3 are part of the standard add-ons included with Mathematica.