Actually I have several related questions, not worth opening different threads:


What is the exterior derivative intuitively? What is its geometric meaning?
A possible answer I know is, that it is dual to the boundary operator of singular homology. However I would prefer a more direct interpretation.
What is a conceptually nice definition of the exterior derivative?


Many years back I wrote something about an intuitive way to look at differential forms here. In particular, figure 4 illustrates Stokes' theorem in a way that generalises to higher dimensions. Note that these are just sketches for intuition, and I've found them useful for illustrating various fields arising in physics, but they're not anything rigorous. They're also, in some sense, dual to the diagrams in Misner, Thorne and Wheeler. (There are some errors in my document, but I lost the source code many years ago...)


