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.
Textbook
James Stewart, Calculus: Early Transcendentals, 9th Edition, Cengage Learning, 2021.
(1) Register WebAssign and eBook through the Canvas course.
You want to register and access WebAssign and eBook through your Canvas account. Please use your UMass email when registering into WebAssign. Students get a 14-day free trial of WebAssign and eBook that starts the first day of the course. You can purchase access directly from your WebAssign account after you register into WebAssign. $124.96 for multi-term access (recommended) or $88.92 for single-term access. If you want/need to purchase a printed textbook separately,
(2) Purchasing Textbook: The eBook is within WebAssign but you can purchase a printed textbook through the link below,
If you choose https://www.cengage.
Note: there is no need to purchase/rent a textbook, you do *not* need to buy any other materials for the course once you register WebAssign through the Canvas course.
Topics
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
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
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
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
The following is meant to give a general idea of which sections are covered in which weeks. Coverage may be different depending on such factors as MWF vs. TuTh schedule, different paces of individual instructors, etc. However, it is expected that all these sections will be covered.
|
Week |
Lecture |
Events |
Memo |
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Sept 2 |
Intro, 2.1 |
First day of the semester is on Tuesday, Sept 3 |
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Sept 9 |
2.2-2.4 |
9/9 is the last day to add/drop |
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Sept 16 |
2.5-2.7 |
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Sept 23 |
2.8, 3.1, 3.2 |
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Sep 30 |
3.3-3.5 |
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Oct 7 |
Review, 3.6 |
Exam 1 Wednesday Oct 9,7-9pm Make-up exam: Thursday Oct 10,7-9pm |
Exam 1 covers 2.1-2.8
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Oct 14 |
3.7-3.9 |
Monday 10/14 is a Holiday; Tuesday is Monday schedule. |
return exam 1 to students |
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Oct 21 |
3.10, 4.1, 4.2 |
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Oct 28 |
4.3 |
Last day to Drop with ‘W’ and select 'P/F' - Undergraduate, is Tuesday 10/29 |
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Nov 4 |
Review, 4.4 (part I) |
Exam 2 Wednesday Nov 6, 7-9pm; Make-up exam: Thursday, Nov 7,7-9pm. |
Exam 2 covers Chapter 3 |
|
Nov 11 |
4.4(end), 4.7 (part I) |
11/11 holiday |
return exam 2 to students |
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Nov 18 |
4.7 (end), 4.9, 5.1 |
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Nov 25 |
5.1 |
Tuesday 11/26, Thanksgiving Recess begins |
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Dec 2 |
5.2, Review |
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Dec 9 |
Review |
The last class is Tuesday 12/10. |
Final exam covers entire materials |
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Dec 12 |
Final exam: 12/16 |
Final grade is due by midnight 12/24 |
Your grade will be posted on SPIRE. |
Requirements
1.Take three 2-hours Exams (Exam1, Exam2 and Final Exam)-total 65%
2. Complete online homework on time-15%.
3. Attend classes regularly and complete in-class written teamwork-10%.
4. Attend discussion sections, take in-class written quizzes-10%.
Exams
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 written exams. Be sure to bring your Umass student ID card and any other exam allowed supplies (like pens, pencils and erasers) when you attend the Exam. All 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 the procedure of make-up request. As long as an exam has been taken, it can NOT be retaken.
Make-up request: All students should check your travel plan and exam schedules of your courses carefully. If you have any schedule conflicts, you may log on the Spire page, go to "Student Home" and then to "Evening Exam Conflict". This will allow you to fill out a conflict form and submit it. Then the registrar will email your instructor who needs to provide a makeup exam. Please do so at least two weeks before the exam, then your instructor will collect all make-up requests and report a whole list to the course chair, then the course chair will reserve a classroom for the make-up students based on the total number of requests, so any late requests will be refused by the course chair. The course chair assistant will notify you when and where to take the make-up exam 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 log on the Spire page, go to "Student Home" and then to "Evening Exam Conflict". This will allow you to fill out a conflict form and submit it. Then the registrar will email your instructor who needs to provide a makeup exam.
(2) if you have a university trip for university 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 a regular exam date and can NOT take the exam, you should write an explanation letter yourself and attach the invitation letter or relevant 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 indicates that you were unable for medical reason to take the scheduled exam. If the medical professional's statement is not given before the exam, your instructor may refuse your make-up request.
Special Accommodation
The University of Massachusetts Amherst is committed to making reasonable, effective and appropriate accommodations to meet the needs of students with disabilities and help create a barrier-free campus. If you have a disability and require accommodations, please register with Disability Services (161 Whitmore Administration building; phone 413-545-0892), meet with an Access Coordinator and send an accommodation letter to your faculty. Information on services and materials for registering are also available on the website www.umass.edu/disability.
Special accommodation request: new disability students should be certified by Umass disability service center (DSC) at first, then you should ask DSC to send the special accommodation documents to your instructor at least two weeks before exam 1 or exam 2, after that you may contact DSC,
Trisha Link
Exam Proctoring Coordinator
examsaccess@admin.umass.edu
413-545-0892
169A Whitmore
directly to schedule an appointment, DSC will notify you when and where to take the exam in a few days before the exam . For the documented disability students, DSC will notify you when you should schedule the final exam in DSC.
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 (http://www.umass.edu/dean_students/codeofconduct/acadhonesty/).
Title IX Statement
In accordance with Title IX of the Education Amendments of 1972 that prohibits gender-based discrimination in educational settings that receive federal funds, the University of Massachusetts Amherst is committed to providing a safe learning environment for all students, free from all forms of discrimination, including sexual assault, sexual harassment, domestic violence, dating violence, stalking, and retaliation. This includes interactions in person or online through digital platforms and social media. Title IX also protects against discrimination on the basis of pregnancy, childbirth, false pregnancy, miscarriage, abortion, or related conditions, including recovery. There are resources here on campus to support you. A summary of the available Title IX resources (confidential and non-confidential) can be found at the following link: https://www.umass.edu/titleix/resources. You do not need to make a formal report to access them. If you need immediate support, you are not alone. Free and confidential support is available 24 hours a day / 7 days a week / 365 days a year at the SASA Hotline 413-545-0800.
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 2022 Exam1 Fall 2023 Exam 1 Fall 2022 Exam 2 Fall 2023 Exam 2 Fall 2022 Final Exam Fall 2023 Final Exam
Calculator
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 http://www.prenhall.com/esm/app/graphing/ti89/. If you already have a TI series calculator, like TI-83,84, this should be adequate for the course.
Homework
Homework: All students require the WebAssign online homework system, which you may self-enroll in the online homework system through the Canvas course. Please watch the instruction video at https://startstrong.
Need Help registering into WebAssign? Get LIVE help on campus:
Date / UMass Location / Time:
Virtual Office Hours for Students needing help Get Registered into WebAssign!
Link to Virtual Office Hours for Students: https://cp.cengage.
or you can contact Frank Cronin at frank.cronin@cengage.com anytime.
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 the disability service center or if there is a medical reason, then you have to provide a medical professional's statement.
Grading
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 without round:
| A | A− | B+ | B | B− | C+ | C | C− | D+ | D | F |
| 90 | 87 | 83 | 79 | 75 | 71 | 67 | 63 | 59 | 55 | <55 |
For example, since 90-100 is A and 87-90 is A- this means 89.999 is still an A- and not rounded up to a 90.000 which is an A.
Help and Tutoring
A quick way to get help is to visit the mth131 tutoring center (LGRT140), the information about course-wide tutoring can be found on each student's Math 131 Canvas course in the second week.
Another option is to visit the UMass Learning Resource Center on the 10th floor of the DuBois Library, where you may find free tutors who can help with Math131 materials. Of course you are very welcome to schedule a meeting with your instructor or TA during their office hours for help.
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 its 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 the 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.