 Author:
 Igor Baryakhtar
 Subject:
 Mathematics
 Material Type:
 Full Course
 Level:
 Community College / Lower Division
 Tags:
 License:
 Creative Commons Attribution NonCommercial
 Language:
 English
 Media Formats:
 Text/HTML
l10_3
MassBay_C1_Summer21L3P3_Diff_Continuity
MB_C1_Summer21_C1_L7P1_Concavity
MB_C1_Summer21_L4_ChainRule
MB_C1_Summer21_L5_DerivInvFunc_Implicit
MB_C1_Summer21_L6P1_Related Rates
MB_C1_Summer21_L6P2_Min_Max
MB_C1_Summer21_L7_P2_Limit_at_infinity
MB_C1_Summer21_L8_P2_NewtonMethod
MB_ONLINE_C1_Su20_L3_p2_DiffRulesNOTES
MB_ONLINE_Su20_C1_L2_Limits
MB_ONLINE_Su20_C1_L2_Limits.tex
MB_ONLINE_SU20_C1_L3_p1_Derivative_intro
MB_ONLINE_Summer21_L1_p1_Func_Rev
MB_ONLINE_Summer21_L1_p1_Func_Rev.tex
Calculus I online
Overview
This is the curriculum for the asynchronous Calculus I course implemented for a tenweek semester and based on the courses, which the author taught in Summer 2020 and Summer 2021 at MassBay Community College.
Instructor Overview
This is the curriculum for the asynchronous Calculus I course implemented for a tenweek semester and based on the courses, which the author taught in Summer 2020 and Summer 2021 at MassBay Community College.
Summary of Posting
This is the curriculum for the asynchronous Calculus I course implemented for a tenweek semester and based on the courses, which the author taught in Summer 2020 and Summer 2021 at MassBay Community College.
The posting includes instructions, lecture notes, worksheets, study guides, assignments, rubrics, and other materials.
The following sources have been used in this course:
1. A.D. Myshkis, Lectures in higher mathematics: Introductory mathematics for engineers. Mir, Moscow, 1972.
2. Gilbert Strang, Calculus. WellesleyCambridge Press, 2nd ed., 1991
3. Calculus 1 by OpenStax, Senior Contributing authors: Gilbert Strang, Edwin Jed Herman, 2016
4. David Jerison, Single Variable Calculus.
https://ocw.mit.edu/courses/mathematics/1801singlevariablecalculusfall2006/videolectures/
Welcome message
WELCOME TO ONLINE MA200700 Calculus I COURSE AT MASSBAY!
My name is Igor Baryakhtar. My educational background is theoretical and mathematical physics.
Currently, in addition to teaching, I am interested in developing free open source materials for all levels of math courses and integrating math software into math courses at community colleges.
I invite you to have a new learning experience. Our focus will be on the mathematical language and how to use it to solve real problems.
Syllabus
MA 200700 ONLINE Calculus I  4 Credit Hours  Summer 2021
MA 200700 ONLINE Calculus I
Instructor Dr. Igor Baryakhtar
Virtual Office Hours via WebEx:
email: ibaryakhtar@massbay.edu
Faculty info
My name is Igor Baryakhtar. My educational background is theoretical and mathematical physics.
Currently, in addition to teaching, I am interested in developing free open materials for all levels math courses and implementing mathematical software in mathematical courses at community colleges.
Course Description
Designed to parallel firstsemester calculus courses at fouryear institutions of learning and to prepare the student for further work in calculus. Topics include a review of functions and their graphs, properties of limits, continuity, derivatives of algebraic and transcendental functions, differentials, Max  Min applications, related rates, the Fundamental Theorem of Calculus, the antiderivative, and the definite and indefinite integrals. For students in mathematics, engineering, sciences and liberal arts.
This course is designed to give students the basic knowledge of calculus, to develop students’ critical thinking skills, quantitative and symbolic reasoning skills, and to improve their mathematical literacy. Students will achieve these goals by attending video lectures, actively participating in class, studying the textbook, and working on homework assignments, quizzes and tests using electronic technologies.
This is the first course in the Calculus sequence. Students will study the fundamental concepts of calculus. The topics are divided into five units:
1. Limits and Derivatives
functions and their graphs; derivatives, slope, velocity, rate of change, limits, techniques for computing limits, the Squeeze Theorem, limits at infinity, continuity.
2. Differentiation techniques
rules of differentiation, higher order derivatives, the chain rule, implicit differentiation, derivative of logarithms, exponential, and trigonometric functions.
3. Applications of differentiation I
related rates, maximum and minimum, function sketching, optimization problems.
4. Applications of differentiation II
linear approximation, differentials, L'Hopital rule, Newton's method.
5. Integrals
antiderivatives, definite integrals, Fundamental Theorem of Calculus.
Prerequisite MA 102 & MA 103T, or MA 104 or permission of instructor.
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.
 Student must use MassBay Community College email account
Learning management systems
Calculus 1 course at MassBay Community college will use the following electronic learning management systems.
Blackboard: for announcements, discussion boards and wikis, grades, and information about MassBay Learning Resources and Support Services.
WebEx: for office hours, review lessons and proctored Exams
MyOpenMath: for online homework assignments with minivideolectures and quizzes
Computer Algebra System (CAS)
Mathematical software will be used to demonstrate calculus concepts and to visualize calculations.
MATLAB (optional), MAXIMA CAS (optional).
Textbook
Calculus Volume 1
Senior Contributing Authors
Edwin “Jed” Herman, University of WisconsinStevens Point
Gilbert Strang, Massachusetts Institute of Technology
Publish Date Mar 30, 2016
Print ISBN10: 193816802X Digital ISBN10: 1947172131
ISBN13: 9781938168024 ISBN13: 9781947172135
Additional textbook
Calculus for scientists and engineers: early transcendentals / William L. Briggs et al.
© 2013 Pearson Education, Inc.
ISBN 0321785509  9780321785503
Suggested websites
Khan Academy. Calculus 1
https://www.khanacademy.org/math/calculus1
Wolfram MathWorld
https://mathworld.wolfram.com/
Encyclopedia Brittanica
David Jerison, MIT OpenCourseware, Single Variable Calculus
https://ocw.mit.edu/courses/mathematics/1801singlevariablecalculusfall2006/videolectures/
COURSE OBJECTIVES
By the end of the course students should be able to:
Answer conceptual questions about limits, continuity, derivatives, rates of change, implicit differentiation, differentials, linear approximations, related rates, antiderivatives, definite integrals.
Demonstrate basic knowledge of limit laws, the Squeeze Theorem, rules of differentiation, L'Hopital rule, Fundamental Theorem of Calculus.
Solve problems involving evaluation of limits of functions, compute derivatives using limit techniques, differentiate functions applying product, quotient and chain rules; compute higher derivatives, use implicit differentiation to calculate derivatives of functions; compute antiderivatives and basic definite integrals.
Calculate maxima, minima, and inflection points of functions and sketch the graph of a function using derivative techniques, sketch the graph of the derivative for a given graph of a function.
Solve application problems involving position, displacement, velocity, acceleration, related rates; optimization; use derivatives to estimate the value of a function and the error of an approximation, use integrals to compute areas and distances.
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 (proctored exam) 20%
Every student must follow the MassBay Community College Code of Conduct.
Official Course Grade
Your final grade will be based on the following point/letter grade breakdown:
A: 94100 A: 9093
B+: 8789 B: 8386 B: 8082
C+: 7779 C: 7376 C: 7072
D+: 6769 D: 6366 F: 062
Class format
Class is a combination of different elearning activities:
 eLearning Assessments
 reading assignments, including lecture notes and study guides with realworld examples
 video watching assignments
 online homework assignments on MyOpenMath
 online quizzes on MyOpenMath
 Project
individual realworld project
 Online Discussions
discussions of selected topics on the Blackboard discussion board and and Blackboard wikis
 Q&A Sessions
online synchronous 60 min review lessons using WebEx (optional)
 Individual work.
Lecture slides and other materials, paper and pencil homework assignments, quizzes and Test will be posted on the Blackboard.
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 and to wikis
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 weekly basis.
Discussion Board
Students will participate in discussions on several topics on the Discussion Board. Your contribution must be clear, accurate, and complete. This activity requires you to read the answers posted by your classmates and comment on them.
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 every week.
20% MyOpenMath
Two late online homework assignments accepted.
Quizzes
There will be eight online quizzes on MyOpenMath.
20% of the Grade
One make up quiz for a missed quiz will be allowed. Lowest quiz grade is dropped.
Test
There will be a handwritten test. Instructor will announce the test two weeks ahead.
20% of the Grade
The Test will be remotely proctored and handwritten on paper. It will be posted on Blackboard.
No make up for the missed Test will be provided.
Project
The purpose of an individual project is to boost the deeper understanding of calculus. Students will create and edit wiki posts using Blackboard’s wikis tool.
10% of the Grade
Late submission. 10% of the Project’s grade is deducted per day after the assignment's due date.
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, tests & handouts.
Final Exam: 20% of the Grade
No make up for the missed Final Exam will be provided.
Academic Integrity Policy
MassBay Community College does not tolerate academic dishonesty. As outlined in more detail in The Student Handbook, academic dishonesty can include, but is not limited to, cheating on an exam or quiz and submitting work that is not your own (plagiarism):
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 acknowledgement. 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.
Penalties can include a failing grade on an assignment, a failing grade in the course, suspension, or expulsion from the college.
Free Support Services
Students are encouraged to use the tutoring service  Math & Science Center
Wellesley Hills: Room 214 Framingham: Inside Library, Room 308, phone: 7812392632 (Wellesley Hills) or 5082704213 (Framingham) or email aac@massbay.edu.
https://www.massbay.edu/academics/aac
Inform Your Instructor of Any Accommodations Needed
Disability Resources
Wellesley Hills: Room 216 or
Framingham: Room 306
For more information, call 7812392234 (Wellesley Hills) or 5082704267 (Framingham) or email aac@massbay.edu
https://www.massbay.edu/facilities/accessibility
Personal Counseling is available
http://www.massbay.edu/counseling/
The instructor may change this syllabus and related materials if necessary for this course.
Course Schedule
Week  Sections  Reading 
1  1.11.5  Review of Functions and Graphs
WELCOME QUIZ 
1  2.1, 3.1  A Preview of Calculus. The Limit of a Function.Derivative. 
2  2.12.5  The Limit of a Function.The Limit Laws. Continuity. The Precise Definition of a Limit (optional) 
2  2.1 2.5  QUIZ 1 
3  3.13.4  Defining the Derivative. The Derivative as a Function. Differentiation Rules. Derivative as rate of Change. 
3  3.13.4  QUIZ 2 
4  3.5, 3.6  Derivatives of Trigonometric Functions. Change Rule. 
4  3.5,3.6  QUIZ 3 
5  3.33.9  Derivatives of Inverse Functions. Implicit Differentiation. Derivatives of Exponential and Logarithmic Functions. 
5  TEST: 6/23/2021  
6  4.14.3  Related rates. Linear Approximations and Differentials. Maxima and Minima. 
6  4.14.3  QUIZ 4 
7  4.44.6  The Mean Value Theorem. Derivatives and the Shape of a Graph.
Limits at Infinity and Asymptotes. 
7  4.44.6  QUIZ 5 
8  4.74.9  Applied Optimization Problems. L’Hopital’s Rule. Newton’ Method. 
8  4.64.9  QUIZ 6 
9  4.10, 5.15.3  Antiderivatives. Approximating Ares. The Definite Integral.
The Fundamental Theorem of calculus. 
9  QUIZ 7  
10  All Sections  FINAL EXAM: 7/28/2021 
The instructor may change this schedule if necessary for this course.
Online Student Orientation to the MyOpenMath
Online Student Orientation to the MyOpenMath
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 MA 200700:
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: xxxxxxxxxxx
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
Skills Needed for Success in Calculus 1
Calculus is considered by many students as a very difficult subject. In fact many students who are not successful in Calculus because of gaps in their algebra and trigonometry skills.
I highly recommend to review the following.
 The equation of line  slope of a straight line tangent to a curve at a point is the derivative!
 Polynomial function  any continuous function can be approximated by a polynomial
 Rational functions  good way to learn asymptotes
 exponential function  the most famous function in calculus, especially theses days: exponential growth!
 logarithmic function  logarithmic scale is commonly use in logarithmic scale is commonly use when analyzing a huge range of quantities: pH, for solutions’ acidity, decibels for sound intensity, Richter scale to measure of the strength of earthquakes.
 trigonometric functions  model periodic phenomenon, such as oscillations and waves.
 the concept of a function you should know the definition of elementary functions, their domain, range basic properties and graphs.
 symmetry of a functioneven, odd, translational
 composite function definition, how to use
 inverse function, definition, how to use
It is necessary to have some basic technical skills to succeed in calculus 1 and in math in general.
You need to be able
 factor expressions,
 simplify expressions, combine like terms, add/subtract/multiply/divide fraction, use properties of exponents and logarithms,
 solve equations in letters
 evaluate expressions with radicals and fractional exponents
 find the value of an expression for given value(s) of variable(s).
 angles measures,
 right triangle trigonometry
 unit circle and the values of the trigonometric functions in the different quadrants
 basic trigonometric identities.
 how to solve basic trigonometric equations.
I highly recommend to complete the mandatory assignments “Precalculus Review” and “Trigonometry Review” within one week. Additional help is available through MassBay Math Center.
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
Rubrics
MA 200700 Calculus I. 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 






MA 200700 Calculus I. Discussions 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. 






Lecture 1 part 1. Functions
Lecture notes. Functions
Lecture 1 Part 2. How to Solve It
Lecture 2. Limits
Lecture notes. Limits
Lecture 3. Intro to Derivative. Derivatives Rules. Continuity
Lecture 4. Chain Rule
Lecture notes.
Lecture 5. Derivative of Inverse Functions, Derivative of Inverse Trig Functions, Implicit Differentiation
Lecture 6.
Lecture 7. Concavity. Limits at infinity
Lecture 8. Optimization
Lecture 9. Antiderivatives and Integrals
Lecture Notes