I know this is a bit of a late response, but you may try taking a look at [1]. I believe Kelley and Peterson discuss casoratian in their text. Even still, this is a very nice text to reference when talking about difference equations. They do a very nice job presenting the material.
It is important to note, as Qiaochu Yuan has, that differential equations and difference equations parallel one another to an extent. They have the same goals, just on a different domain. If you have not heard of time scale calculus, I would recommend you take a look at that as well. It is the natural next step after seeing the connection between difference calculus and differential calculus. [2] is a good resource for time scale.
Let me know if I can be of any help to you!
[1] Kelley, W. & Peterson, A. (2001). Difference Equations: An Introduction with Applications (2nd Ed.). San Diego, CA: Academic Press.
[2] Bohner, M. & Peterson, A. (2001). Dynamic Equations on Time Scales: An Introduction with Applicaitons. Boston, MA: Birkhäuser.