I am currently a Mechanical Engineering major and would like to start taking some math notes/engineering notes on my iPad...however I need something that I can write very small on and fit a lot of writing on a single page (I have an Adonit Jot Pro stylus). I won't be doing any typed notes (at least not much) so I am really focused on trying to find something that is great for hand writing.

Also do you guys have any recommendations for a good "white board" app that I can easily do problems on and then erase (keep in mind I need to be able to write small as most my homework problems are quite lengthy).

Did you consider Notes Plus? It has several paper types that you can further customize (width, height, margins, space between lines) and the close-up box can be resized so that you can make it as small as you'd like.

I will give that one a shot, I am sure I will end up trying each one and seeing which one works best. Thanks!