Differential Forms, 2nd Edition

Chapter 7

The Generalized Stokes’s Theorem

Abstract

In this chapter we arrive at our main goal, the Generalized Stokes’s Theorem (GST). We begin by stating this theorem and deriving some of its consequences. We first see how, in the -dimensional case, it generalizes the Fundamental Theorem of Calculus (FTC), and we apply the GST to line integrals. We next develop the notion of cap independence, a higher-dimensional analog to path-independence. We then see how in the -dimensional case the GST generalizes the classical Green’s and Stokes’s theorems, ...