As the Computer Science and Calculus teacher at my school, I've found it instructive to teach the students in Calculus how to write programs in TI-BASIC to investigate such algorithms as Newton's Method, Reimann Sums and Euler's Method. I also have my Computer Science students solve Calculus problems in this vein using C++ or Java.
In fact, these last few years I've done a project with Octave (much like MATLAB) after the AP with my Calculus students which the students find interesting. This project involves Vector Calculus and AP Physics C topics.
MATLAB is a great tool for dealing with vectors and marices. In fact, the base type is a matrix of doubles or ints or whatever you like. If you define a matrix with 1 row and n columns, you have a row vector. If you define a matrix with n rows and o1 column, you have a column vector. You can define a square matrix nxn or any kind of matrix nxm and have lots of built-in functions to manipulate them!
In addition, I'm hoping to start a Calculus Lab this year using Sage. Sage is much like Mathematica, but I'm not using it just for CAS, I'm using it to program numerical methods as well (Python is built into Sage).
Learning with Technology,