Is there a rigorous integral definition of the exterior derivative analogous to the way the gradient, divergence & curl in vector analysis can be defined in integral form? Furthermore can it be formulated before stating & proving Stokes theorem? Finally, a beautiful classical argument for the integral definition of the divergence intuitively existing is given in Purcell (page 78), & it leads to the quickest (one line, coordinate independent!) proof of the Divergence theorem I've ever seen. How does one make the limiting process rigorous, & will making the limiting process rigorous justify that one-line proof? Really appreciate any help with this - thanks!