Do yourself a favor, and bring a pen and paper to class.
You won't be doing anything other than surfing the internet if you bring your computer to class. Engineering lectures aren't like English lectures. You'll spend all day drawing diagrams, and writing out equations. Two things not exactly conducive to a laptop. If you have a laptop, your professors will know that you aren't paying attention. Period.
As for programs, the only one you'll need and be able to afford is Matlab. Everything else is going to cost you a fortune, and get you arrested if you are stupid enough to pirate it. The university won't require you to have anything, all programs will be available in one of the 24hr labs on campus.
The other programs you'll need, things like Labview, will only really be needed in lab classes... and you'll be there anyway. 3D modeling programs are going to require you to use the school lab, not much way around that.
So, what it boils down to, is that you'll be using the computer for playing games and surfing the net, occasionally doing Matlab homework, and writing papers and using Excel.
For all of that, the 13" is more than sufficient.
