You have finally arrived. This is where you need to be. Scroll down below to view my math notes. If you're the kind of person that would rather do anything but math, first of all, lame, but second of all, click here.
Most treatments of differential forms out there are completely undecipherable, and even when bits and pieces do make sense, they still leave you wondering what ever happened to dx and dy just being tiny nudges. My hope with these notes is to remedy this sort of thing.
These notes couldn't be possible without Michael Penn's excellent playlist on differential forms on YouTube, as it is the only resource I could find which makes any sense whatsoever. With the exception of Chapter I, these notes are basically just a reinterpretation of his approach.
My understanding of differential forms is still incomplete. This is effectively an open notebook at this time. If you see any mistakes, let me know! Also, I'm not even going to attempt to touch manifolds because they scare me.
