Exterior Calculus: Theory and Cases

Fundamental Theorem of Calculus

Author(s): Carlos Polanco *

Pp: 82-89 (8)

DOI: 10.2174/9789814998789121010013

* (Excluding Mailing and Handling)


This chapter reviews The Green’s, Stokes’, and Gauss’ Theorems as a direct result of the differentiation and integration operations set out in previous chapters. All the exercises are solved using the Grassmann algebra. The Fundamental theorem of calculus is introduced at the end of this chapter, as an extension of the theorems studied here.

Keywords: dw1 form, dw2 form, w1 form, w2 form, divergence, Field associated, Fundamental Theorem of Calculus, Gauss’ theorem, Grassmann algebra, Green`s theorem, Heaviside-Gibbs algebra, rotational, Stokes` theorem

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