Author:
Igor Baryakhtar
Subject:
Mathematics
Material Type:
Full Course
Level:
Community College / Lower Division
Tags:
  • Calculus
  • Calculus 1
  • OpenStax
  • License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    Text/HTML

    Calculus I online

    Overview

    This is the curriculum for the asynchronous Calculus I course implemented for a ten-week 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 ten-week 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 ten-week 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. Wellesley-Cambridge 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/18-01-single-variable-calculus-fall-2006/video-lectures/

    Welcome message

    WELCOME TO ONLINE MA200-700 Calculus I COURSE AT MASSBAY!

     

    derivative gif

     

    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.

    Igor Baryakhtar  CC

     

     

     

    Syllabus

    MassBay logo      MA 200-700 ONLINE Calculus I                |    4 Credit Hours    |                           Summer 2021

     

    MA 200-700 ONLINE Calculus I 

    Instructor  Dr. Igor Baryakhtar      

    Virtual Office Hours via WebEx: 

    e-mail: 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 first-semester calculus courses at four-year 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 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. 
    • 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 mini-video-lectures 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 Wisconsin-Stevens Point

    Gilbert Strang, Massachusetts Institute of Technology

    Publish Date   Mar 30, 2016

    Print       ISBN-10: 1-938168-02-X                                    Digital    ISBN-10: 1-947172-13-1

                   ISBN-13: 978-1-938168-02-4                                           ISBN-13: 978-1-947172-13-5

    Additional textbook

    Calculus for scientists and engineers: early transcendentals / William L. Briggs et al. 

    © 2013 Pearson Education, Inc. 

    ISBN 0-321-78550-9 | 978-0-321-78550-3

    Suggested websites

    Khan Academy. Calculus 1

    https://www.khanacademy.org/math/calculus-1

    Wolfram MathWorld

    https://mathworld.wolfram.com/ 

    Encyclopedia  Brittanica

    https://www.britannica.com/

    David Jerison, MIT OpenCourseware, Single Variable Calculus 

    https://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/

    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: 94-100 A-: 90-93 

    B+: 87-89 B: 83-86 B-: 80-82 

    C+: 77-79 C: 73-76 C-: 70-72 

    D+: 67-69 D: 63-66 F: 0-62 

    Class format 

    Class is a combination of different elearning activities: 

    • eLearning Assessments

    - reading assignments, including lecture notes and study guides with real-world examples 

    - video watching assignments

    - online homework assignments on MyOpenMath

    - online quizzes on MyOpenMath

    • Project 

    individual real-world 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 real-world 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: 781-239-2632 (Wellesley Hills) or 508-270-4213 (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 781-239-2234 (Wellesley Hills) or 508-270-4267 (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
    1.1-1.5
    Review of Functions and Graphs 
    
    WELCOME QUIZ
    1
    2.1, 3.1
    A Preview of Calculus. The Limit of a Function.Derivative.
    2
    2.1-2.5
    The Limit of a Function.The Limit Laws. Continuity. The Precise Definition of a Limit (optional)
    2
    2.1- 2.5
    QUIZ 1
    3
    3.1-3.4
    Defining the Derivative. The  Derivative as  a Function. Differentiation Rules. Derivative as rate of Change.
    3
    3.1-3.4
    QUIZ 2
    4
    3.5, 3.6 
    Derivatives of Trigonometric Functions. Change Rule. 
    4
    3.5,3.6
    QUIZ 3 
    5
    3.3-3.9
    Derivatives of Inverse Functions. Implicit Differentiation. Derivatives of Exponential and Logarithmic Functions. 
    5
     
    TEST: 6/23/2021
    6
    4.1-4.3
    Related rates. Linear Approximations and Differentials. Maxima and Minima.
    6
    4.1-4.3
    QUIZ 4
    7
    4.4-4.6
    The Mean Value Theorem. Derivatives and the Shape of a Graph. 
    
    Limits at Infinity and Asymptotes. 
    7
    4.4-4.6
    QUIZ 5
    8
    4.7-4.9
    Applied Optimization Problems. L’Hopital’s Rule. Newton’ Method.
    8
    4.6-4.9
    QUIZ 6
    9
    4.10, 5.1-5.3
    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 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  MA 200-700:  

    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 function-even, 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

     

    Igor Baryaktar CC

    Rubrics

    MA 200-700 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 200-700 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