In this lesson, you will learn about limits and continuity for vector-valued functions, differentiation of vector-valued functions, smooth curves, and integrals of vector-valued functions.
View all of the instructional videos, read the provided readings, and practice exercises/activities. These will help you master the objectives for this lesson. Pay attention to additional comments provided. It may be helpful if you review some of the concepts, such as limit, continuity, Chain Rule, integration, from Calculus I.
Upon completion of the lesson 2.3, you will be able to:
Determine domains
Evaluate limits
Determine continuity
Find derivatives of a vector-valued function
Find tangent vectors
Recognize and apply derivative rules
Evaluate integrals
Use derivative to analyze space curves
View all of the following instructional videos. These will help you master the objectives for this module.
12.6 Calculus of Vector Valued Functions [5:44]
Source: Linda Misener from YouTube
Part 1.
Note: This video highlights most of the concepts that you need to learn from this lesson.The initial condition does not have to be the vector, r⃗ (0) .
Properties of the Derivative of a Vector-Valued Function [7:27]
Source: bullcleo1 from YouTube
Note: The video covers the "missing content" from the first video that you need to know for this lesson.
Limits of Vector Valued Functions [6:58]
Source: bullcleo1 from YouTube
Note: In example 1, you should know the value of limt→0sintt without applying the L'Hôpital's rule.
Finding the Limit of a Vector Function, Example 1 [1:46]
Source: patrickJMT from YouTube
Finding the Limit of a Vector Function, Example 2 [4:04]
Source: patrickJMT from YouTube
Note: The presenter is trying to explain to you how to evaluate the limits for each of the component functions. Please do NOT present your solution to a problem like what you see on the video, the official write up for the solution should be in a formal and organized manner.
The Derivative of a Vector Valued Function [7:01]
Source: bullcleo1 from YouTube
Determining the Unit Tangent Vector [9:51]
Source: bullcleo1 from YouTube
Unit Tangent Vector at a Given Point [4:50]
Source: patrickJMT from YouTube
Note: Make sure that you use the proper notation for each of the vectors in your solution.
Determining Where a Space Curve is Smooth from a Vector Valued Function [8:20]
Source: bullcleo1 from YouTube
Indefinite Integration of Vector Valued Functions [8:09]
Source: bullcleo1 from YouTube
Definite Integration of Vector Valued Functions [6:13]
Source: bullcleo1 from YouTube
Note: The initial condition does not have to be the vector.
The following required readings cover the content for this lesson. As you go through each reading, pay close attention to the content that will help you learn the objectives for this lesson.
This document covers materials from lessons in both Module 2 and Module 3.
Read slides 3-14 for this lesson.
Read slides 15-42 for Lesson 2.3.
Read slides 43-66 for Lesson 3.1.
Read slides 90-102 for Lesson 3.2.
Read slides 67-89, 103-127 for Lesson 3.3.
Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.
University of Canterbury 100-level Mathematics Revision Exercises
There are many problems for you to practice what you have learned in this lesson as well as for other lessons.
Before you begin, please read the instructions on how to use the applet.
Below are additional resources that help reinforce the content for this module.
2.2. Differentiation of Integration of Vector-Valued Functions
Read sections 2.2.1-2.2.3 for this lesson.
Paul's Online Math Notes
Lines and Curves in Space (video) [5:39]
Source: Linda Misener
Part 1.
Part 2.
Do Homework 2.3 on MyMathLab.
Show Your Work assignment will be given via Assignment Tool on Laulima. Please check your email for Laulima announcement.
Time to turn in your Show Your Work Assignment for this module.