Vector Analysis and Vector Fields

Abstract

A vector function of a scalar variable is a vector $\vec a$ whose components are real functions of t:

$$ \vec a = \vec a(t) = a_x (t)\vec e_x + a_y (t)\vec e_y + a_z (t)\vec e_z . $$

((13.1))

The notions of limit, continuity, differentiability are defined componentwise for the vector $\vec a(t)$.