Exterior Calculus: Theory and Cases

Vector Algebra on R2 and R3

Author(s): Carlos Polanco *

Pp: 1-13 (13)

DOI: 10.2174/9789814998789121010007

* (Excluding Mailing and Handling)


In this chapter, we introduce the main operators of Heaviside-Gibbs algebra: addition, subtraction, norm of vectors, as well as inner and cross product. From the point of view of Vector Calculus, we introduce the line and surface integrals, and the Green’s, Stokes’, and Gauss’ Theorems. The last section discusses the extension of this algebra in n-dimensional space. The examples are in plane and space.

Keywords: cross product: v×w, divergence of vector function, Gauss’ Theorem, Green’s Theorem, inner product: v ·w, limitations, line integral, norm: ||v||, normed vector space, rotational of vector function, scalar multiplication: av, Stokes’ Theorem, surface integral, vector addition: v + w, vector Subtraction: v−w

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