Advanced Engineering Mathematics, 7th Edition

9.1 Vector Functions

INTRODUCTION

Recall that a curve C in the xy-plane is simply a set of ordered pairs (x, y). We say that C is a parametric curve if the x- and y-coordinates of a point on the curve are defined by a pair of functions x = f(t), y = g(t) that are continuous on some interval a ≤ t ≤ b. The notion of a parametric curve extends to 3-space as well. A parametric curve in space, or space curve, is a set of ordered triples (x, y, z) where

x = f(t), y = g(t), z = h(t), (1)

are continuous on an interval defined by a ≤ t ≤ b. In this section we combine the concepts of parametric curves with vectors.

Vector-Valued Functions

It is often ...