Math 13, Fall 2021

Multivariable Calculus


This course is a sequel to MATH 8 and provides an introduction to calculus of vector-valued functions. Topics include differentiation and integration of parametrically defined functions with interpretations of velocity, acceleration, arc length and curvature. Other topics include iterated, double, triple and surface integrals including change of coordinates. The remainder of the course is devoted to vector fields, line integrals, Green's theorem, curl and divergence, and Stokes' theorem.


Math 8 or equivalent.

Lecture Information

Instructor:Justin Miller
Time:(2) MWF 2:10-3:15 PM
Location:Kemeny 006
Email:Justin Miller
Office:315 Kemeny Hall
Office Hours:Monday 12-1pm, Thursday 1:20-2:10pm


The course shall use two textbooks in addition to online materials found on this site. You will only need one of the texts, not both.

"Calculus Early Transcendentals Multivariable", by Rogawski & Adams, 3rd Edition, ISBN: 978-1464171758

"Openstax Calculus Volume 3", a free learning resource provided by Rice University. It is strongly recommended that students consider this before spending money on a textbook.


There will be two midterm exams and a final exam. Unless otherwise stated, all exams are to be completed without any outside assistance, including but not limited to communicating with other people, electronics, the internet, calculators, or notes.

Midterm #1October 5thCarson Hall L017-9pm
Midterm #2October 26thCarson Hall L017-9pm
FinalNovember 19thTBD3-6pm


Homework will consist of short WebWork problem sets assigned each lecture day, and six longer written assignments assigned semi-weekly. Written assignments will be due on Wednesdays during weeks in which we do not have an exam. Homework assignments will cover material from the previous week of lectures. Collaborating with and assisting your fellow students is strongly encouraged, however all students must submit their own work.

Calculators are allowed on homework, but be aware that they will not be allowed during exams. For written assignments, you are required to show your work for full credit.

Office Hours

I will be holding office hours on Mondays from 12-1pm and Thursdays from 1:20-2:10pm. Office hours will be held at the following Zoom link:

Occasionally, Thursday office hours will be held in person in our classroom 006 Kemeny. I will notify you in advance on days which this is the case.


Brian Mintz [Email] will be running Tutorial and office hour study sessions on Tuesdays from 3-6pm and Friday from 10am-1pm. He will be available to answer your questions and help with homework problems, as well as explain concepts from class. Sessions will be held at the following zoom link:

Honor Policy

As with all courses at Dartmouth, this course relies on Dartmouth's Academic Honor Principle. Additionally, mathematics is a discipline driven by collaboration and working together. Both of these principles apply to this course. Students are strongly encouraged to work together to understand and complete homework assignments, however all students are required to submit their own work. You may come up with a solution to a problem as a group, however each student is required to submit the solution in their own words to demonstrate that they understand the solution.

All exams are to be completed with no external help from other people, notes, electronic devices, audio recordings, et cetera.

Helpful Learning Resources

COVID-19 Information


You are expected to attend class in person unless you have made alternative arrangements due to illness, medical reasons, or the need to isolate due to COVID-19.

For the health and safety of our class community, please: do not attend class when you are sick, nor when you have been instructed by Student Health Services to stay home.


In accordance with current College policy, all members of the Dartmouth community are required to wear a suitable face covering when indoors, regardless of vaccination status. This includes our classroom and other course-related locations, such as labs, studios, and office hours. If you need to take a quick drink during class, please dip your mask briefly for each sip. Eating is never permitted in the classroom. (The only exception to the mask requirement is for students with an approved disability-related accommodation; see below.) If you do not have an accommodation and refuse to comply with masking or other safety protocols, I am obligated to assure that the Covid health and safety standards are followed, and you will be asked to leave the classroom. You remain subject to course attendance policies, and dismissal from class will result in an unexcused absence. If you refuse to comply with masking or other safety protocols, and to ensure the health and safety of our community, I am obligated to report you to the Dean’s office for disciplinary action under Dartmouth’s Standards of Conduct. Additional COVID-19 protocols may emerge. Pay attention to emails from the senior administrators at the College.


This course is meant to be welcoming and accessible to students from all backgrounds. Please schedule a meeting as soon as possible to discuss any potential conflicts arising from religious observances, planned medical procedures, or other life events. There is no guarantee that accommodations can be made if you wait until the last minute, so please be proactive.

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me as soon as possible, or before the end of the second week of the term—at the latest, to discuss appropriate adjustments.

All students are encouraged to take care of their well-being. Dartmouth's Counseling Center and Wellness Center are available for student use. Please do not hesitate reach out to me about any difficulties you have in the course, or other stressors external to the course if you need someone to talk to.

Sexual respect, safety, and well-being are critical to Dartmouth's environment. Any and all forms of sexual assault, gender-based harassment, domestic violence, dating violence, and stalking are unacceptable and hostile to other members of the community. For more information, please visit Dartmouth's Sexual Respect website. Please note that, as a faculty member, I am a mandatory reporter under Title IX. That means that I must share any disclosures regarding conduct governed by Title IX to Dartmouth's Title IX coordinator. The Title IX office provides many resources to assist students who need them, which you can view here.

Disability and COVID-19 Accommodations

Students requesting disability-related accommodations and services for this course are required to register with Student Accessibility Services (SAS; Getting Started with SAS webpage;; 1-603-646-9900) and to request that an accommodation email be sent to me in advance of the need for an accommodation. Then, students should schedule a follow-up meeting with me to determine relevant details such as what role SAS or its Testing Center may play in accommodation implementation. This process works best for everyone when completed as early in the quarter as possible. If students have questions about whether they are eligible for accommodations or have concerns about the implementation of their accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.