Calculus III
Overview
This is the curriculum for a asynhronous Calculus III course implemented for an eightweek semester and based on courses, which the author taught in 20162021 at Middlesex Community College and MassBay Community College.
Summary of Posting
This is the curriculum for an asynchronous Calculus III course implemented for an eightweek semester and based on the courses, which the author taught in 20162021 at Middlesex Community College and MassBay Community College.
This posting includes the syllabus, course schedule, instructions, worksheets, study guides, assignments, rubrics, and other materials.
The following sources have been used in this posting:
1.Ya. B. Zeldovich, A. D. Myskis, Elements Of Applied Mathematics, Mir,1976
2. Gilbert Strang, Calculus, WellesleyCambridge Press, 2nd ed., 1991
3. Calculus 3 by OpenStax, Senior Contributing authors: Gilbert Strang, Edwin Jed Herman, 2020
4. Denis Auroux, Multivariable Calculus, MIT, 2007.
https://ocw.mit.edu/courses/mathematics/1802multivariablecalculusfall2007/videolectures/
Syllabus
Middlesex Community College
MAT 29230: Calculus III for Science 4 Credit Hours Summer 2021
Instructor Dr. Igor Baryakhtar
Office hours: via ZOOM
email: baryakhtari@middlesex.mass.edu
Course Goals
This asynchronous course is designed to give students a basic knowledge of multivariable calculus, to develop students’ critical thinking skills, quantitative and symbolic reasoning skills, and to improve their mathematical literacy. The course is focused on students’ ability to solve scientific and engineering problems using multivariable calculus concepts. Students will achieve these goals by studying the textbook, attending online video lectures, and doing assignments using traditional and electronic technologies.
Course Description
Topics include vectorvalued functions, dot and cross products, motion, curvature and arc length in 3space, partial derivatives and Chain Rule, directional derivatives and gradients, max/min and Lagrange Multipliers. Also: double and triple integrals, polar coordinates, and parametric surfaces, and Green's Theorem with applications in work and potential energy in the study of electricity and magnetism.
This is the third course in the Calculus sequence. Students will study the fundamental concepts of differential calculus. The topics are divided into four units:
1. Introduction. Cartesian, Cylindrical and Spherical Coordinates; Conic Sections.
(parametric equations, polar coordinates, converting between cartesian and polar coordinates, converting between cartesian and cylindrical and spherical coordinates, calculus in polar coordinates, conic sections)
2. Vectors and Vector Values Functions
(vectors in three dimensions, dot and cross product, curves in space, calculus of vector valued function, arc length, curvature and normal vector)
3. Functions of Several Variables
(surfaces, functions of two and more than two variable, visualization of functions of two variables, limit and continuity of a function of two variable, partial derivatives, the chain rule, directional derivatives and gradient, tangent planes, linear approximation, max min problems, Lagrange multipliers)
4. Multiple Integration & Vector Calculus
(double integrals in Cartesian and polar coordinates, triple integrals in Cartesian and cylindrical and spherical coordinates, vector fields, conservative vector fields, Green’s theorem, Stoke’s theorem, Divergence theorem)
Prerequisite MAT 291 Calculus II
Technical Requirements
To succeed in this online course you must be familiar with electronic technologies.
Ability to use the Internet in an effective and efficient manner, including: installation and management of browser plugins and addons, download, upload and print files, send/reply emails with attachments.
Basic knowledge about the operation of a computer, file management, and software installation.
Learning management systems
Calculus III course at Middlesex Community college will use the following electronic learning management systems.
Blackboard (main platform): for announcements, discussion boards, lectures notes and other learning materials, test, grades, and information about MCC Learning Resources and Support Services.
ZOOM: office hours, Q&A sessions (upon request), proctored exams
MyOpenMath: for online homework assignments and quizzes
Software
Mathematical software will be used to demonstrate calculus concepts and to visualize calculations.
MATLAB (optional), MAXIMA CAS (optional).
Free Open Educational Resources are required for this course
Textbook
Calculus Volume 3
Senior Contributing Authors:
Gilbert Strang, Massachusetts Institute of Technology
Edwin “Jed” Herman, University of WisconsinStevens Point
Publish Date Mar 30, 2016
Print ISBN10: 1938168070 Digital ISBN10: 1947172166
ISBN13: 9781938168079 ISBN13: 9781947172166
Additional textbook (optional)
Calculus for Scientists & Engineers. Multivariable.
by Briggs, Cochran, & Gillett, with assistance of Eric Schulz.
2013 Ed., Pearson Education, Inc., ISBN13: 9780321785510
COURSE OBJECTIVES
By the end of the course students should be able to:
Answer conceptual questions about calculus of vectorvalued functions, calculus of a function of several variables, calculus of vector fields.
Demonstrate basic knowledge of equations of curves and surfaces in 3D space, properties of dot and cross products of vectors, limit and continuity of a function of two or more variables, chain rule with several independent variables, implicit differentiation rule with three variables,
directional derivatives, maximum/minimum problems, Lagrange multipliers, double integrals in cartesian and polar coordinates, triple integrals in cartesian, cylindrical and spherical coordinates,
Green’s theorem, Stoke’s theorem, Divergence theorem.
Solve problems involving polar, cylindrical and spherical coordinates, 2D and 3D motion problems, find equation of a plane through the given points or for given vectors, sketch level curves and traces of surfaces, evaluate dot and cross products of vectors, compute arc length, curvature and torsion of a curve, tangential and normal components of an acceleration, calculate derivatives of a function of two or more variables using chain rule and implicit differentiation, calculate directional derivatives and gradients, solve maxima/minima problems, solve maxima/minima problems with a constraint using Lagrange multipliers method, calculate double integrals using cartesian and polar coordinates, calculate triple integrals using cartesian, cylindrical and spherical coordinates, solve word problems using multivariable calculus.
Credit Hour Policy
Students are expected to spend a minimum of 45 hours of work for each credit.
Course Grades
Participation 10%
Homework (on MyOpenMath) 20%
Quizzes (on MyOpenMath) 20%
Project 10%
One Test (remotely proctored test) 20%
Final Exam (remotely proctored exam) 20%
Class format
Class is a combination of different elearning activities:
 eLearning Assessments
 reading assignments with realworld examples
 video watching assignments
 online homework assignments on MyOpenMath
 online quizzes on MyOpenMath
 Online Discussions of selected topics on the Blackboard discussion board and wikis
 Synchronous online Q&A sessions via ZOOM (upon request)
 Individual work.
Attendance
Attending an online course includes but is not limited to
Submission of an academic assignment by a student
Taking the online quiz by a student
Student submission of an exam
Student's posting to a discussion forum
An email from a student showing that the student has initiated contact with the instructor
Attendance is mandatory in this course. Stop attending a course does not constitute a withdrawal. If you can no longer participate in this class, you must formally withdraw because unfinished coursework may result in a failing "F" grade.
Students are expected to submit work weekly and complete all assignments on time. Students who miss two or more weeks of classes may be withdrawn from the course.
ASSESSMENT
Attendance and participation
10% of the Grade
Students are expected to participate in all scheduled assignments on a daily basis.
Discussion Board
Students will be asked to reflect and respond to Discussion Board questions and post your responses. Responses should be clear, accurate and complete sentences.
Online homework
Reading a textbook is a very important part of the learning process. First, read the assigned section. Make sure that all notations are understood. Use lecture notes and recommended multimedia resources to clarify concepts. Try examples in the textbook. Do optional problems from the textbook.
Instructor will assign online homework and/or handwritten assignments every week.
20% of the Grade.
Two late online home works accepted.
One late paper and pencil homework accepted.
Quizzes
There will be six online quizzes on MyOpenMath.
20% of the Grade
One make up quiz for a missed quiz will be allowed. Lowest quiz grade is dropped.
Project
The purpose of an individual project is to boost the deeper understanding of calculus. Students may work on the Project with their classmates and receive help from Math Center or use any other recourses, but every student must submit his/her individual work
10% of the Grade
Late submission. 10% of the grade is deducted per day after the assignment's due date.
Test
Test will be remotely proctored and handwritten on paper. It will be posted on Blackboard.
20% of the Grade
No make up for the missed Test will be provided.
Final Exam
The Final Exam will be remotely proctored and handwritten on paper. It will be posted on Blackboard.
The Final Exam will require the student to demonstrate mastery of the techniques of differentiation and integration and their uses in realworld applications. Students should review all quizzes, practice problems, test & handouts.
Final Exam: 20% of the Grade
No make up for the missed Final Exam will be provided.
Every student must follow the Middlesex Community College Honor Code
Academic Integrity Policy
Middlesex Community College does not tolerate academic dishonesty. As outlined in more detail in Middlesex Community College Code of Conduct, academic dishonesty can include, but is not limited to the following
Use of any unauthorized assistance in taking quizzes, tests, or examinations;
Dependence upon the aid of sources beyond those authorized by the instructor in writing papers, preparing reports, solving problems, or carrying out other assignments;
The acquisition, without permission, of tests or other academic material belonging to a member of the College faculty or staff; or
Plagiarism, which is defined as the use, by paraphrase or direct quotation, of the published or unpublished work of another person without full and clear acknowledgment. It also includes the unacknowledged use of materials prepared by another person or agency engaged in the selling of term papers or other academic materials. Taking credit for work done by another person or doing work for which another person will receive credit. Copying or purchasing other’s work or arranging for others to do work under a false name.
MyOpenMath
MyOpenMath is a free online educational platform.
MyOpenMath provides
a set of overview videos
online homework assignments, most with videos
online quizzes
Students should have convenient and reliable access to a personal computer and internet.
_________________________________________________________________________________
Sign Up in MyOpenMath https://www.myopenmath.com
The course ID: xxxxx
The enrollment key: xxxxxxxx
________________________________________________________________________________
Free Support Services
Students are encouraged to use the tutoring service  Math Center
https://www.middlesex.mass.edu/ace/math.aspx
Disability Support Services
The Disability Support Services offices are offering remote services at this time
https://www.middlesex.mass.edu/disabilityservices/
Personal Counseling is available
https://www.middlesex.mass.edu/personalcounseling/
Inform Your Instructor of Any Accommodations Needed
This work is licensed under a Creative Common Attribution 4.0 International license
2021 Igor Baryakhtar
Course Schedule
COURSE SCHEDULE
Online weekly quizzes are scheduled on __ at __. You will have __ hours to complete.
The Test and the Final Exam are handwritten on paper, you will have __ hours to complete.
week  MyOpenMath  Textbook 
1  Calculus I Review Calculus II Review Homework #1. Parametric curves. Polar Coordinates  1.1 Parametric Equations 1.2 Calculus of Parametric curves (optional) 1.3 Polar Coordinates 

 WELCOME QUIZ 
2  Homework #2. Vectors
 2.12.4 Vectors

2 
 QUIZ # 1 
3  Homework #3. Straight Line in 3D. Planes and Surfaces Homework #3. Straight Line in 3D. Planes and Surfaces Homework #4.Spherical and Cylindrical Coord.  2.5 Lines and Planes in Space 2.6 Quadric Surfaces 2.7 Cylindrical and Spherical Coordinates 
3 
 QUIZ # 2 
4  Homework #5. Calculus of VectorValued Functions Homework #6. Arc Length. Curvature and Normal Vectors  3.1 VectorValued Functions and Space Curves 3.2 Calculus of VectorValued Functions 3.3 Arclength and Curvature 3.4 Motion in Space 
4 
 QUIZ # 3 
5  Homework #7. Limit of a Function of Two Variables Homework #8. Partial Derivatives Homework #9. Tangent Planes and Linear Approx. Homework #10. PartialDerivatives. Chain Rule  4.1 Functions of Several Variables 4.2 Limits and Continuity 4.3 Partial Derivatives 4.4 Tangent Planes and Linear Approximation 4.5 Chain Rule 
5 
 TEST: 
week  MyOpenMath  Textbook 
6  Homework #11. Partial Derivatives. Directional Derivatives and Gradient Homework #12. Maxima/Minima Problem  4.6 Directional Derivatives and Gradient 4.7 Maxima/Minima Problems 4.8 Lagrange Multipliers 
6 
 Quiz #4 
7  Homework #13. Integrals. Part 1 Homework #14. Integrals. Part 2 Homework #15. Integrals. Part 3 Homework #16. Integrals. Part 4
 5.1 Double integrals over rectangular regions 5.2 Double Integrals over general regions 5.3 Double Integrals in Polar Coord. 5.4 Triple Integrals 5.5 Triple Integrals in Cylindrical and Spherical Coordinates 
7 
 Quiz #5 
7 
 Project due 
8  Homework #17. Vector Fields (Extra credit)
 5.7 Change of Variables in Multiple Integrals 6. Vector Calculus FINAL REVIEW 

 FINAL EXAM 
ORIENTATION
Welcome to the Middlesex Community College online course!
 In this unit you will learn how to navigate in the course shell.
 What do you need to succeed in Calculus III.
 Become familiar with MyOpenMath  free online learning management system.
 Become familiar with the discussion board and post you first thread.
 Become familiar with netiquette in online education
 Obtain help
COURSE MENU
The course menu is the panel on the left side of the interface that contains links to all course areas.
Toggle buttons
Announcements The course announcements your instructor have posted.
Getting Started Welcome message
Orientation, and Getting Help Contact the Instructor How to contact your instructor.
Syllabus Syllabus of the course and tentative schedule
Course Textbook Link to the course textbook
WEEKLY CONTENT The folder for weekly moduli: for reading assignments, handouts, lectures notes, weblink to minilectures, information about online assignments and other materials for the week A.
MyOpenMath Link to the MyOpenMath website. Online homework assignment will be posted on this website.
Discussion Board Discussion Board. You will use the discussion board to explore interesting questions with your classmates.
Maxima Online Link to the wxmaxima webpage  free and convenient online mathematical tool based on MAXIMA CAS. May be used for symbolic calculations and for graphing.
Tools Blackboard’s Tools
Netiquette Guide
It is important to understand that the online class is actually a class, and certain behavior is expected when communicating with your peers and the instructor.
 Be polite and respectful, honesty and integrity are expected from all
 Be professional, follow the rules, including how and when submit your work: format and due date
 Make sure identification is clear in all communications, include your first and last name and the course number
 Be careful with humor and sarcasm, be aware of strong language  use proper language, grammar, and spelling
MyOpenMath Orientation
All students enrolled in courses using MyOpenMath are required to complete a onetime online orientation to MyOpenMath, free Learning Management System.
This small selfpaced orientation is available on MyOpenMath should be completed during first two days of classes. On average the orientation should take approximately 30 min.
How to enroll into MyOpenMath
MyOpenMath is a free online learning management system.
To register for CALCULUS III MAT 29231
1. Go to www.myopenmath.com
2. Under Login, select Register as a new student
3. Complete the required fields
4. Enter your instructor’s
Course ID: XXXXXX
Enrollment Key: xxxxxxxx
5. Click Sign Up
You can now return to the login page and login with your new username and password.
Once you log in you will see in the center of a webpage the folder “ORIENTATION”.
Inside the folder you will find
Intro to MyOpenMath, an assignment how to enter formulas in MyOpenMath
Course Home Page video
Course Content video
Rubrics
MAT 29230 Calculus III. HANDWRITTEN EXAM RUBRIC
GRADE  EXCELLENT  GOOD  FAIR  POOR  FAILURE 
Understanding of Concept  Student knows the concept and can use it to solve challenging problems  Student knows the concept and can use it to solve basic problems  Student knows the concept but does not know how to use it properly.  Student has some knowledge about the concept but does not know how to use it.  Student does not understand the concept 






Calculation skills  All calculations are correct  Student made minor mistakes in calculations  Student made big mistakes in calculations  Student made many big mistakes in calculations  Student cannot perform necessary calculations 






MAT 29230 Calculus III. Discussion Board RUBRIC
GRADE  EXCELLENT  GOOD  FAIR  POOR  FAILURE 
Postings on Discussion Board will be graded based upon the following  Posting related to the topic, respectful to other postings. Post helps others to understand material.  Posting related to the topic, respectful to other postings.  Posting does not related to the topic or posting is too obvious.  Posting is too short, like “Agree/Disagree” or “Great point”.  No post. 






Study Guide #1. Parametric Equations
Parametric Equations
Study Guide #2. Vectors
Vectors
Study Guide #3. Equations of Lines and Planes in Space
Equations of Lines and Planes in Space
Study Guide #4. Calculus of VectorValued Functions
Calculus of VectorValued Functions
Study guide #5. Arc Length. Curvature. Normal and tangential components of acceleration
Arc Length. Curvature. Normal and tangential components of acceleration.
Study guide #6. Partial derivatives
Partial derivatives
Study Guide #7. Gradient. Directional derivative. Extrema
Gradient. Directional derivative. Extrema
Study Guide #8. Double Integrals
Double Integrals
Study Guide #9. Triple Integrals
Triple Integrals