Calculus II
Math 132 - Fall 2026

Santiago Arango-Piñeros, Ph.D. (He/Him).

My office is in LGRT 1238, and you can contact me via email at:

• sarangopiner@umass.edu.

Bryan Silva. Their office is in LGRT 1325, and you can contact them via email at:

• bryansilva@umass.edu.

Bryan teaches both discussion sections.

The best way to get help is to come to our office hours. No appointment is needed, and you are welcome to bring your classmates and work on problems together.

If the times above are not convenient, or if you would like to discuss a private matter, send me an email and we will find a time to meet.

MATH 131 or equivalent.

• [S] J. Stewart, Calculus: Early Transcendentals, 9th edition.

Enhanced WebAssign (access code + e-book) is required: your homework is done there. The e-book and the access code are bundled together inside your Canvas course, so a physical copy of the textbook is not required.

By the end of this course, you will be able to:

1. Apply integration techniques to evaluate definite and indefinite integrals.
2. Use integration in applications such as computing areas, volumes, and arc lengths.
3. Represent functions as power series, and find Taylor and Maclaurin series.
4. Analyze curves and solve problems using parametric equations and polar coordinates.

This page collects the things you will need week to week. The official course syllabus is the authoritative document, and it also contains the required university statements (Title IX, academic honesty and integrity, accommodations, the full make-up exam policy, and the General Education R1/R2 learning outcomes):

• Math 132 syllabus (pdf), also posted on Canvas.

• All exams are closed-book.
• Calculators, textbooks, notes, formula sheets, cell phones, smartwatches, and all other electronic devices are strictly prohibited. Any electronic device visible during the exam will lead to an assumption of cheating.
• Bring your student ID to every exam.

You are expected to take the exams at the scheduled times. Make-up exams are offered in excusable situations: extenuating circumstances, religious reasons (tell me at the beginning of the semester), athletic events, field trips and performances, health reasons, and exam conflicts. Tell me as early as possible, and bring supporting documents when necessary.

• Exam conflicts. University policy says that you cannot be expected to take two exams at the same time, or three exams in one day. Submit the Evening Exam Conflict or Final Exam Conflict form through SPIRE (Class & Finals Schedule, in the Manage Classes tile) at least two weeks before the scheduled exam.
• There are no exam retakes in this course, for any reason. If an emergency prevents you from taking an exam, contact me within 24 hours of the scheduled exam.
• The full policy is in the official syllabus.

If you are approved for testing accommodations, you take your midterms on the same day as everyone else, but starting at 6:00 PM instead of 7:00 PM. The final exam is also on the same day, starting at 8:00 AM.

You do not need to schedule anything with the Disability Services Exam Proctoring Center or through Clockwork; no exams are given there. You will be emailed your exam location at least three days before each exam.

If you miss a deadline, you can still complete the assignment for up to 7 days after the due date by requesting an automatic extension through WebAssign. A 30% late penalty applies to the portion of the assignment submitted during those 7 days. Beyond that, late homework is generally not accepted or extended without penalty.

If you join the course late, catching up on the assignments is your responsibility. The schedule is arranged so that the first assignment is due one day after the last day to add or drop.

You are expected to attend all classes regularly, and you are responsible for any material, announcements, or assignments you miss. Attendance is not taken, but let me know if illness or other extenuating circumstances prevent you from attending. Absences for university-approved conflicts or other excusable reasons do not excuse you from meeting the course requirements.

This course uses Canvas as its learning management system; log in with your NetID@umass.edu and password. WebAssign and the e-book are reached from Canvas, and exams are graded in Gradescope. No course entry code is needed.

UMass Amherst uses Navigate360 to identify students who may need additional support. You may receive emails from Navigate360 about your grades and academic performance during the semester. Check your UMass email regularly, and if you get an alert, read it carefully and connect with the resources it lists. Alerts are meant to help you, not to punish you.

• Last day to add or drop with no record: <2026-09-14 Mon>.
• Last day to drop with a "W" and to select P/F: <2026-11-04 Wed>.
• See the academic calendar for other important dates.
• An Incomplete is possible only if: (1) you had a compelling personal reason, e.g. serious illness; (2) your work has clearly been passing; and (3) there is a good chance you will complete the course with a passing grade within the allotted time. Failing work is not in itself a reason for an Incomplete.

Academic honesty is required of all students at UMass Amherst, and academic dishonesty — cheating, fabrication, plagiarism, and facilitating dishonesty — is prohibited in all programs of the University. The formal definitions, examples, and procedures are on the Academic Honesty website, and the full statement is in the official syllabus. You are expected to be familiar with this policy: ignorance of these standards is not normally sufficient evidence of lack of intent.

UMass 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, you may be eligible for reasonable academic accommodations. If you have a documented disability that requires an accommodation, please notify me within the first two weeks of the semester so that we can make the appropriate arrangements. See also testing accommodations for the exams.

UMass Amherst is committed to providing a safe learning environment for all students, free from all forms of discrimination. A summary of the available Title IX resources, confidential and non-confidential, is at 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 24/7 at the SASA Hotline 413-545-0800.

Your effort and attitude determine your abilities. Embrace challenges and failure as an opportunity to grow. Find inspiration in other people's success.

Paraphrasing Galileo:

``You cannot teach a person anything; you can only help them find it within themselves.''

We are all here to understand. My job as a more experienced learner is to assist you on your journey. But you are responsible for investing the time and effort necessary to learn.

This is hard work, and it will be frustrating at times. In my opinion, the reward is well worth the investment, as is often the case with challenging endeavors. In the words of JFK:

``We choose to go to the Moon in this decade and do the other things, not because they are easy, but because they are hard; because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one we intend to win, and the others, too.''

We will subscribe to Federico's axioms.

• Axiom 1. Mathematical potential is equally present in different groups, irrespective of geographic, demographic, and economic boundaries.
• Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
• Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
• Axiom 4. Every student deserves to be treated with dignity and respect.