I have one and can honestly say I think it is quite useless as a device for anything but enjoyment. Pen, paper and a ruler is going to be your best friend. At least for maths & phys where you need to draw figures and such.
For subjects where you write a lot (guessing law, econ etc.) a laptop with a good keyboard will be far superior.
The only thing I do on my iPad that can be considered productive or academic is reading and watching lectures, things that can be done just as well in a proper book or on a laptop. The short of it is; it's a product of consumption. Not creation.
My suggestion is to look into a solid and portable laptop, an ultrabook for example. It will serve you better, guaranteed.