Here are some resources to get you started with numerical computations. Since everyone has different backgrounds, I have included various options:
Matlab is the computing language of choice for APPM 2360, so many of you will already have some experience with it. Here is a link to some examples of Matlab applications to dynamical systems:
Mathematica is very powerful once you get used to its commands. Here is a link to a tutorial from Purdue University
Once you get used to the conventions and the way to output and plot data, C++ gives you speed and control over what the simulation is doing. Here is some sample code that you can modify to get you started. To run these programs in Mac or Unix/Linux, go to the directory where you saved them in a terminal, type "make filename.cpp" and then "./filename", where "filename" is the name of the program. You will then have a text file with the data on two columns. You can plot this using gnuplot or importing it to Matlab or Mathematica.
Here is a C++ tutorial and resource site.
Using a spreadsheet like Excel you can quickly iterate one dimensional maps, implement Euler's method to solve differential equations, etc. Although it is simple to start with, it becomes limited for more complicated simulations. Here are some links to examples: