Integration of Differential Forms

Abstract

This chapter covers the integration of differential forms over surfaces, culminating in the general fundamental theorem of integral calculus. The general fundamental theorem is often called Stokes’s theorem, but along with generalizing the classical Stokes’s theorem, it also subsumes the divergence theorem (or Gauss’s theorem), Green’s theorem, and the one-variable fundamental theorem. Much of the chapter’s work is algebraic, in particular the result that differential forms innately pass through changes of variable.