LESSON NOTES MENU
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
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 r(t)=<t,1> whose graph contains the points (1,1), (3,1), (π,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. v(t)=<cos(t), sin(t), ln(t)>.

Objectives

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

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.