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Course: Calculus III
Topic: Vector-Valued Functions
Subtopic: Introduction to VV Functions

Overview

A vector-valued function (a.k.a. vector function) is a vector whose components are functions. For example the vector vecr(t)=<<t,1>> whose graph contains the points (1,1), (3,1), (pi,1), (-5.2,1), etc. in other words it is a way of expressing in vector form the line y=1. Using parametric equations for each of the components, we can control the vector over time, e.g. vecv(t)=<<cos(t), sin(t), ln(t)>>.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 14.1.1 Understand what a vector-valued function is and where it might be used in the real world
• 14.1.2 Understand and use vector-valued function definition, terminology, and formulae
• 14.1.3 Determine the curve formed by a vector-valued function
• 14.1.4 Graph a vector-valued function electronically
• 14.1.5 Find the domain of a vector-valued function

Terminology

Define: vector-valued function, parametric equation

Supplemental Resources (optional)

Dale Hoffman's Contemporary Calculus III: Introduction to Vector-Valued Functions and Vector-Valued Functions and Curves in Space

Paul's OL Notes - Calc III: Vector Functions

More tutorial videos if you need them are listed at James Sousa's MathIsPower4U - Calc II. Scroll down right column to "Vector Valued Functions". There are several related titles in the first half of that list.