Math 131 2020 Fall Course Web



High school algebra I and II, Trigonometry, Plane geometry and Pre-calculus (Analytic geometry).


Math131 is the first in a three course Calculus sequence Math131–132–233 which covers basic concepts, methods, and applications suitable for majors in engineering, natural sciences, computer science, mathematics, etc. The emphasis is on problem-solving instead of on proving theorems. Math 131 mainly studies derivatives of single-variable functions, covering these topics: limits, continuity, derivatives, implicit differentiation, related rates, maxima and minima, and an introduction to definite integrals with applications to area. 


1.You may purchase James Stewart, Calculus: Early Transcendentals , Loose-leaf, 8th Edition, Cengage Learning, 2016. Paperback printed book + eBook + WebAssign multi-term from Cengage ($134.15). See

 2.You may purchase WebAssign Instant Access (Webassign access code+ebook) for Stewart’s Calculus: Early Transcendentals; Multi-Term; 8th Edition, multi-term ($114.40). See

3.You may purchase WebAssign Instant Access (Webassign access code+ebook) for Stewart’s Calculus: Early Transcendentals; single-Term; 8th Edition, single-term ($78.00). See

 4. You purchase Enhanced WebAssign directly from the WebAssign website as opposed to the above linked microsite, you will get the same stand-alone Instant Access Code to Enhanced WebAssign (with ebook) but at a higher price.

Please note that you do *not* need to buy any other materials for the course.



Introduction – What is calculus?

Chapter 2 – Limits and derivatives

2.1   The tangent and velocity problems
2.2   The limit of a function
2.3   Calculating limits using the limit laws
2.4   The precise definition of a limit
2.5   Continuity
2.6   Limits at infinity; horizontal asymptotes
2.7   Derivatives and rates of change
2.8   The derivative as a function

Chapter 3 – Differentiation Rules

3.1   Derivatives of polynomials and exponential functions
3.2   The Product and Quotient Rules
3.3   Derivatives of trigonometric functions
3.4   The Chain Rule
3.5   Implicit differentiation
3.6   Derivatives of logarithmic functions
3.7   Rates of change in the natural and social sciences
3.8   Exponential growth and decay
3.9   Related rates **
3.10 Linear approximations and differentials

Chapter 4 – Applications of Differentiation

4.1   Maximum and minimum values
4.2   The Mean Value Theorem
4.3   How derivatives affect the shape of a graph
4.4   Indeterminate forms and L’Hospital’s Rule
4.7   Optimization problems
4.8   Newton’s Method **
4.9   Antiderivatives

Chapter 5 – Integrals (introduction)

5.1  Areas and distances
5.2  The definite integral and Riemann sums


** Topics will be omitted if time is lost from emergency campus closing.

Weekly Schedule

Week Lecture Events
Aug. 24 Intro, 2.1, 2.2  First lecture is on Monday, Aug 24
Aug. 31 2.3-2.5  
Sept 7 2.6-2.8 Monday September 7, Labor Day - Classes will be held; Last day to drop: Mon Sep 7
Sept 14 3.1-3.3  
Sep. 21 review, 3.4(start)

Exam 1 Wednesday Sep 23,7-9pm; Make-up Exam time is TBA; Exam 1 covers section 2.1-2.8

sep. 28 3.4(end)-3.6   

Oct 5

Oct 12 3.9(end)-4.1  Monday  October 12, Columbus Day - Classes will be held Last day for W: Friday Oct 16.
Oct 19 4.2 -4.3(start)  
Oct 26 review-4.3(end)  
Nov 2 4.4, 4.7

 Exam 2 Wednesday Nov 4, 7-9pm; Make-up exam 2 is TBA; Exam 2 covers section 3.1-4.2

Nov 9 4.9, 5.1  Wednesday November 11, Veterans' Day - Classes will be held
Nov 16 5.2, Review

 Nov 20: Last day of classes. Thanksgiving recess begins after end of classes

Nov 23  Nov 27-28: Reading Days
Nov 30-Dec 4  Final exam period  Final exam is TBA; Final make-up exam is TBA
Dec  14    Final grade is due by midnight Monday, 12/14



1.Take three 2-hours Exams (Exam1, Exam2 and Final Exam)-total 65%

2. Complete online homework on time-15%.

3. Watch the preview lecture video, attend classes regularly and complete in-class written teamwork-10%.

4. Attend discussion sections, take in-class written quizzes-10%.


All three exams are closed book; there is no calculator allowed in any exams; Exam dates and materials covered are listed in the weekly schedule, which are the same for all lecture sections of the course. All exams are online exams through gradescope. Be sure to bring your Umass student ID card and any other exam allowed supplies (like pens, penciles and erasers) when you attend the Exam. All of students must take the regular exam unless you are qualified to take an official make-up exam which has been permitted by your instructor, which follows procedure of make-up request. As long as an exam has been taken, it can NOT be retaken.

Make-up request: All of students should check your travel plan and exam schedules of your courses carefully. If you have any schedule conflicts, you should hand in a written request with your name, student ID, section number, brief reason and an official support document to your instructor at least two weeks before the exam, then your instructor will collect all  make-up requests and report a whole list to course chair, then course chair will reserve a online make-up exam based on the total number of requests, so any late requests will be refused by course chair. The course chair assistant will notify you when and where to take the make-up exam in a few days before the exam.

Which case and where is the official support document for the make-up request?

(1) if you have an exam (or a class) schedule conflicts with the regular exam, you should contact Office of University Registrar (213 Whitmore Administration Building, University of Massachusetts, 181 Presidents Drive Amherst, MA 01003-9313) 8:00am - 5:00pm Monday through Friday to get an "evening exam conflicts form" as the official document or take a snapshot of your course schedule on SPIRE and send it to your instructor with a written request.

(2) if you have a university travel for univerisity business during the regular exam date, like an athletic competition or academic conference etc., you should ask your supervisor or your coach to write an explanation letter including his/her phone number to your instructor as the official written document. Your instructor may verify the event by phone call.

(3) if you have a religious observance on regular exam date and can NOT take the exam, you should write an explanation letter yourself and attach the invitation letter or relevent information as the official document.

(4) if you have a medical reason and can not take the regular exam, you should ask a medical professional's statement including his/her phone number which indicate that you were unable for medical reason to take the scheduled exam. If the medical professional's statement is not given before the exam, you instructor may refuse your make-up request.

 Accommodation Statement

The University of Massachusetts Amherst is committed to providing an equal educational opportunity for all students.  If you have a documented physical, psychological, or learning disability on file with Disability Services (DS), you may be eligible for reasonable academic accommodations to help you succeed in this course.  If you have a documented disability that requires an accommodation, please notify your instructor within the first two weeks of the semester so that we may make appropriate arrangements. 

Academic Honesty Statement

Since the integrity of the academic enterprise of any institution of higher education requires honesty in scholarship and research, academic honesty is required of all students at the University of Massachusetts Amherst.  Academic dishonesty is prohibited in all programs of the University.  Academic dishonesty includes but is not limited to: cheating, fabrication, plagiarism, and facilitating dishonesty.  Appropriate sanctions may be imposed on any student who has committed an act of academic dishonesty.  Instructors should take reasonable steps to address academic misconduct.  Any person who has reason to believe that a student has committed academic dishonesty should bring such information to the attention of the appropriate course instructor as soon as possible.  Instances of academic dishonesty not related to a specific course should be brought to the attention of the appropriate department Head or Chair.  Since students are expected to be familiar with this policy and the commonly accepted standards of academic integrity, ignorance of such standards is not normally sufficient evidence of lack of intent (

Exam review sessions: TAs will run at least three review sessions before each Exam. The review sessions will mainly go over solutions of old exams or homework questions. Your instructor will notify you the schedule of review sessions one week before the exam.

Exam review materials:  Fall 2019 Exam1    Fall 2018 Exam 1     Fall 2019 Exam 2    Fall 2018 Exam 2     Fall 2019 Final Exam      Fall 2018 Final Exam


A graphing calculator may be useful for the webassign online homework. There is no calculator allowed in any exams. If you never have one, then we recommend you to buy TI-89, you may see the online tutoring about  TI-89 at If you already have a TI series calculator, like TI-83,84, this should be adequate for the course.


All students require the webassign online homework system, which you may self-enroll the online homework system with a class key. Your instructor will tell you the class key of your section , then you should follow the instruction at to create a webassign account. You can do homework with others, but you have to enter answers yourself. There is no make-up for homework unless there is some certified special accommodation from disability service center or if there is a medical reason, then you have to provide a mdeical professional's statement.  

How to log on the webassign homework system?

All lecture sections require the WebAssign on-line system for homework. If you have had a cengage account, then you may directly go to and type your username and password to sign in.

Otherwise, All of students have to enroll your online homework system using a class key. See the following instruction.

Your instructor might give you a class key like umass 1234 5678 to enroll in your class. A class key does not verify payment.
Enroll yourself in each class section only once.
1). Go to and click Enroll with Class Key.
2). Enter your class key and click Enroll.
3). If the correct class and section is listed, click Yes, this is my class.
4). Sign in or create your account.
If you have a Cengage Account, then
1). Type your Cengage username and password.
2). Click Sign In.
3). If prompted, either sign in to your existing account or create a new Cengage account.
If you Don't Have a Cengage Account
1). Click Create Account.
2). Type your UMass campus email, first name, last name (please use the exactly same first name and last name as you used in SPIRE) for your new Cengage account.
3). Enter your student ID, Birth year, choose yes for receiving exclusive Cengage offers and discounts, then set your passwords.
4). Read and acknowledge your acceptance of the Cengage service agreement.
5). Click Create Account.
You are signed in to WebAssign with your new account and enrolled in your class  

Please do NOT buy the ebook and access code through webassign, you should buy the ebook and access code through the link which we provide on textbook part.

Webassign access code

Webassign will give you two weeks grace period. After the grace period, you will have to provide access code to do homework, therefore, you should buy access code as soon as you can.


All math131 sections must follow the universal grading policy to determine a student's total score. For your total scores: each of Exam1 and Exam 2 is 20%, the final exam is 25%, online homework is 15%, discussion section 10%, and class participation 10%. If your final exam score exceeds the average of your Exam 1 and Exam 2 scores, then your final exam will count 30% (instead of 25%) and each of Exams 1 and 2 will count only 17.5% (instead of 20%).  The course letter-grade scale after round to nearest integer is: 

A A− B+ B B− C+ C C− D+ D F
90 87 83 79 75 71 67 63 59 55 <55

Help and Tutoring

 A better way to get help is to schedule a zoom meeting with your instructor or TA during their office hours for help. Another option is to schedule an appointment with Learning Resource Center in the Dubois Library where you may find free tutors who can help with Math131 materials.

 General Education Designation

 MATH 131 is a four-credit General Education course that satisfies the R1 (Basic Math Skills) and R2 (Analytic Reasoning) general education requirements for graduation.

The General Education Program at the University of Massachusetts Amherst offers students a unique opportunity to develop critical thinking, communication, and learning skills that will benefit them for a lifetime. For more information about the General Education Program, please visit the GenEd web page.

 Learning Outcomes for all General Education courses

 Math 131 satisfies the following General Education objectives:


·         Content:  Know fundamental questions, ideas, and methods of inquiry/analysis used in mathematics: Students will learn limits and continuity of functions, use these to compute rates of change, and analyze their real-life and theoretical applications.


·         Critical Thinking: Students demonstrate creative, analytical, quantitative, & critical thinking through inquiry, problem solving, & synthesis: Students will use critical thinking skills to develop and understand rates of change of functions using limits, and computational skills to find these rates of change efficiently. Students will demonstrate an understanding of various methods of differentiation in order to compute the rate of change for many types of functions.


·         Communication: Develop informational and technological literacy: Students will develop their writing skills by articulating their reasoning for computations throughout the course. 


·         Demonstrate capacity to apply disciplinary perspectives and methods of analysis to real world problems (the larger society) or other contexts: Students will apply the theoretical concepts of calculus to real-world and theoretical problems.  Students will use the derivative to find where a function reaches is maximum and minimum values, and apply this to various contexts such as finding the maximum height of an object travelling through the air.

 Learning Outcomes for the R1 and R2 Designations

 Because Math 131 presupposes basic math skills, it carries the designation for the Basic Math Skills requirement (R1). In addition, the course satisfies the following objectives of the Analytic Reasoning requirement (R2):

·         Advance a student’s formal or mathematical reasoning skills beyond the level of basic competence:  In learning Calculus in Math 131, students will think critically about the overarching idea of rates of change.  Students will advance their mathematical literacy and analyzing skills by learning to limits of mathematical functions and using these limits to construct accurate and efficient ways of computing rates of change, called derivatives.


·         Increase the student’s sophistication as a consumer of numerical information:  Students will connect the ideas of rates of change to various disciplines by analyzing and solving problems in both real life and theoretical applications.


·         Indicate the limits of formal, numerical, quantitative, or analytical reasoning and discuss the potential for the abuse of numerical arguments:  Students will learn methods of both estimating and computing cumulative change.  Students will analyze when it is appropriate to use an estimation, as well as the accuracy and efficiency of their estimations.


Math 131, Weekly Schedule (approximate)
Week Lecture Events
Sept 4 Intro, 2.1, 2.2 First lecture Tues/Wed
Sept 11 2.3-2.5  
Sept 18 2.6-2.8 Last day to drop: Mon Sep 18
Sept 25 3.1-3.3  
Oct. 2 review, 3.4(start)

Exam 1 Wednesday Oct 4,7-9pm       Make-up exam 1 Tuesday Oct 3, 7-9pm

Oct 9 3.4(end)-3.6   Holiday Mon;Tues = Mon
Oct 16 3.7-3.9(start)   Last day for W: Thurs Oct 19
Oct 23 3.9(end)-4.1  
Oct 30 4.2 -4.3(start)  
Nov 6 review-4.3(end)  
Nov 13 4.4

  Exam 2 Monday Nov 13, 7-9pm                      Make-up exam 2 Tuesday Nov 14, 7-9pm

Nov 20
 Thanksgiving  Recess
Nov 27 4,7, 4.9, 5.1  
Dec 4 5.1, 5.2  
Dec 11 review   Last class Tuesday12/12