Differential Forms

In this chapter and the next we show how to generalize line and surface integrals to more general sorts of integrals in Rⁿ . At the end, we shall give a far-reaching generalization of Green’s theorem and Stokes’ theorem. Before then, however, we need to develop a good deal of material, much of it not obviously connected with integration. This chapter then is concerned with the more formal aspects of the theory; in the next chapter we show how to give it substance. As a result, this chapter may seem rather abstract and artificial.