Remember that this particular calculation is one that has a significant computational load. So don't judge Mathematica based on it if this is your beginning experience. I will set the computation running later on when I don't need to see how long it takes. Also, since there are dynamic interactive elements to that CDF, avoid scrolling down to them (they only attempt to format and evaluate when on the screen) while this particular computation is running since it is so very CPU-intensive.

8 Gb should be enough for you to do significant work with Mathematica in general. You'd only need to optimize more if you are going to be solving things like 30000 simultaneous equations ... ;-)

I am guessing that your Kernel crashed when computing the "sol" expression. (you can tell if this is what happened by looking at then in the In[n] value for the Line Integral-Plot cell that generated your empty plot)

I tried doing the calculation on my machine (16 Gb I7). I executed up to the "sol" expression and went to make lunch and came back 10 or 15 minutes later with it still running at 400% CPU. So I killed the computation so I could go about other business. As the blog poster noted, he's solving 30,000 simultaneous equations, but I don't know what to expect in terms of how long it should take and he doesn't comment on this.

But to answer your first question, no, this does not need the loading of an external package as far as I can see.