Matlab is one of the most widely used and powerful numerical packages available. I have used Matlab to solve for the energy levels of rare earth ions in different coordinations using the Steven's Operator Equivalent method and also to determine the principal g-values of a g-tensor in electron paramagnetic resonance (ESR/EPR).
An excellent introduction to the uses of Matlab can be found in the book by Garcia Numerical methods for Physics. All of the programs in this book can be downloaded from this site.
There are also some good Matlab tutorial sites available
A good tutorial
A link to other tutorials.