Three popular choices for software in this class are Excel, Octave and Matlab.
Excel you have paid for with your student fees.
GNU Octave is a free version of Matlab but does not perform symbolic calculations.
Matlab is used widely in industry. Octave uses the same notation as Matlab.
This Matlab Basics comes from the VT math department and is a great primer on working with Matlab and Octave.
Using Matlab to generate Direction Fields