Igor Baryakhtar
Material Type:
Full Course
Community College / Lower Division
  • Calculus
  • Mass CC Mathematics
  • Open Washington
  • OpenWA
  • WA 100
  • Washington 100
  • mass-cc-mathematics
  • open-washington
  • openwa
  • wa-100
  • washington-100
    Creative Commons Attribution
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    Calculus III


    This is the curriculum for a asynhronous Calculus III course implemented for an eight-week semester and based on courses, which the author taught in 2016-2021 at Middlesex Community College and MassBay Community College.


    Summary of Posting

    This is the curriculum for an asynchronous Calculus III course implemented for an eight-week semester and based on the courses, which the author taught in 2016-2021 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, Wellesley-Cambridge 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.



    Middlesex Community College

    MAT 292-30: Calculus III for Science 4 Credit Hours Summer 2021

    Instructor  Dr. Igor Baryakhtar       
    Office hours: via ZOOM 

    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 vector-valued functions, dot and cross products, motion, curvature and arc length in 3-space, 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 plug-ins and add-ons, 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


    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


    Calculus Volume 3
    Senior Contributing Authors:
    Gilbert Strang, Massachusetts Institute of Technology
    Edwin “Jed” Herman, University of Wisconsin-Stevens Point

    Publish Date Mar 30, 2016
    Print ISBN-10: 1-938168-07-0                       Digital  ISBN-10: 1-947172-16-6
             ISBN-13: 978-1-938168-07-9                             ISBN-13: 978-1-947172-16-6

    Additional textbook (optional)
    Calculus for Scientists & Engineers. Multivariable.
    by  Briggs, Cochran, & Gillett, with assistance of Eric Schulz.
    2013  Ed., Pearson Education, Inc.,  ISBN-13: 978-0-321-78551-0


    By the end of the course students should be able to:
    Answer conceptual questions about calculus of vector-valued 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 real-world 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.


    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.


    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.


    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.


    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 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 real-world 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 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
    The course ID: xxxxx
    The enrollment key: xxxxxxxx

    Free Support Services

    Students are encouraged to use the tutoring service - Math Center

    Disability Support Services

    The Disability Support Services offices are offering remote services at this time

    Personal Counseling is available


    Inform Your Instructor of Any Accommodations Needed













    This work is licensed under a Creative Common Attribution 4.0 International license

    CC-BY 4.0   2021 Igor Baryakhtar

    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.





    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





    Homework #2. Vectors


    2.1-2.4  Vectors




    QUIZ # 1 


    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 



    QUIZ # 2


    Homework #5. Calculus of Vector-Valued Functions

    Homework #6. Arc Length. Curvature and Normal Vectors

    3.1 Vector-Valued Functions and Space Curves 

    3.2 Calculus of Vector-Valued Functions

    3.3 Arclength and Curvature

    3.4 Motion in Space



    QUIZ # 3


    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








    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 



    Quiz #4


    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



    Quiz #5



    Project due


    Homework #17. Vector Fields

    (Extra credit)


    5.7 Change of Variables in Multiple Integrals

    6. Vector Calculus 






    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


    The course menu is the panel on the left side of the interface that contains links to all course areas.

    Toggle buttons

    navigate 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 mini-lectures, 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 one-time online orientation to MyOpenMath, free Learning Management System.
    This small self-paced 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 292-31

    1. Go to
    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










    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 292-30 Calculus III.  Discussion Board RUBRIC







    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


    guide 2

    Study Guide #3. Equations of Lines and Planes in Space

    Equations of Lines and Planes in Space

    guide 3

    Study Guide #4. Calculus of Vector-Valued Functions

    Calculus of Vector-Valued Functions

    guide 4

    Study guide #5. Arc Length. Curvature. Normal and tangential components of acceleration

    Arc Length. Curvature. Normal and tangential components of acceleration.

    guide 5

    Study guide #6. Partial derivatives

    Partial derivatives

    guide 6

    Study Guide #7. Gradient. Directional derivative. Extrema

    Gradient. Directional derivative. Extrema

    guide 7

    Study Guide #8. Double Integrals

     Double Integrals

    guide 8

    Study Guide #9. Triple Integrals

    Triple Integrals

    study 9_1

    study 9_2

    study 9_3