Math 20550 Calculus III (Fall 2020)
Multivariable Calculus

Course information

Overview: Calc III gives a comprehensive treatment of differential and integral calculus of several variables. Topics include space curves, surfaces, functions of several variables, partial derivatives, multiple integrals, line integrals, surface integrals, Stokes theorem, and applications. See the syllabus for more detail.

Because of the unique nature of this semester, our class format will be somewhat non-traditional. Some students might be taking the class remotely, and we need to be prepared for some or all students (or instructors) reverting to online learning at any point in the semester. Each lecture will be taught simultaneously online (via zoom) and in person. Lectures will focus on outlining the key concepts and intuition, and providing as many examples as possible. Short videos will be available which delve more deeply into each topic, and students may be expected watch some of these videos before class. Worksheets will be provided to give an outline and some example problems for the week's material. The worksheets will also point out the relevant videos for the week. Tutorials will be for group work, all done remotely. In lieu of exams, we will have short, 30min quizzes each Monday (starting August 17) in class. Homework is online on webassign. All office hours will all be remote, in the same zoom room. A math help room will be staffed on zoom for students to work with tutors and other students. See below for details.

Our remotely learning will be through the zoom platform. You will need to download the (free) zoom client, and log in using your Notre Dame ID. Lectures, tutorials, and office hours will all have a designated zoom meeting room, just as they may have a designated room on campus. You can find the zoom links on our Sakai web page.

The covid19 situation is unpredictable, uncontrollable, and might force changes in various different aspects of this class. We might practice meeting completely remotely several times to be prepared.

Textbook: Stewart: Multi-variable Calculus, 8th Edition, Chapters 12-16. For more info look at the textbook and webassign section.

Other suggested material: We suggest that all students have a 11 inch by 17 inch white board and a set of markers. We do not care where you get them. The bookstore should have some ordered. You will use them so that we can see your work either via Zoom or when physically distancing. We will see how useful these prove.

Lectures: Each class will have lectures 3 times per week, MWF. Every lecture should be accessible to both in person and online students. Unless you have permission or are ill, you are expected to attend all lectures. The lectures will be recorded so that students may rewatch them later. The recorded lectures, along with the shorter pre-recorded videos focusing on key parts of the material, can be found on the Sakai class page. See this calendar for the scheduled lecture times and locations.

Tutorials: Tutorials are on Thursdays. See the calendar for tutorial times. Since all tutorials will focus on active learning, they will be held remotely via Zoom. The total for tutorials is 30 points and will be counted as a quiz. More details will be discussed during your first tutorial.

Quizzes: After the first Monday, every Monday for the first 30 minutes of lecture there will be a quiz. The material which can appear on a Monday quiz will have been covered by preceding Thursday tutorial. The final will be 3 quizzes taken together with a 15 minutes break between them. One of the 3 quizzes for the final will be on past week's material. The other two will cover all the material covered. The lowest two quiz scores will be dropped. Each quiz will have 3 multichoice questions worth 6 points each, and one free response question worth 12 points for a total of 30 points. The total for the quizzes is 450 points. Be careful as the semester progresses the quizzes will get harder. Calculators are not allowed on the quizzes. Makeups should not be needed but will be discussed on a case by case basis and will need a valid reason.

Everyone will be using this template to provide answers for the quizzes. Please print off 16 copies and have one available for every quiz. On Monday after the quiz the instructor will be collecting these. If you are taking the quiz remotely please followig these instructions. Your quiz grades will also be posted to Sakai. As a reminder, it is your responsibility to make sure that your quizzes are clear and readable.

Honor code: As members of the Notre Dame community, we will not tolerate academic dishonesty. The honor code is in effect for all quizzes. The quizzes are to reflect your work and you cannot use your book, a calculator, other software packages, the internet, a phone, etc to solve the problems. You may not talk about a quiz with anyone who has not already taken it. Even though the quizzes are all taken on Monday, people in different classes will take them at different times. We take the honor code very seriously and will follow up any possible violations. Please let's avoid any violations. It gets ugly for everyone.

Homework: Homework is online, through the Enhanced Web Assign (EWA) software. See webassign access to see details on setting up your account. There will be a homework assignment due each week on Friday at 11:59pm. Don't leave it until the last minute! You can set Webassign to send you reminders of due homework (once in Webassign, click on Notifications on the top right on the screen). Except for health reasons, we will not accept late homework.

Homework will be worth 50 points in total. You will be able to drop the lowest 3 scores. Although the homework doesn't count nearly as much as quizzes, keeping up with the homework will give you crucial practice. Like any skill, you won't get better at math just by watching instructors do it, you need to practice it yourself! We recommend writing out your solutions and keeping them in a notebook, so you can review them later.

For each homework question part, you are allowed 5 submissions for the answer. You can submit parts individually; when you wish to make a submission, click Submit Answers. You do not need to complete your homework or a question in one sitting - you may click Save Work if you wish to return to your work later. When you think you have completed an assignment, it is a good idea to make one last check to be sure that you have submitted each answer.

You may work together on homework, but you must submit your own work. Each of you may get different questions for an assignment so a correct solution for one may not be a correct solution for another. Group work will help you learn what "similar" questions look like and may help you isolate what are the important points the problem is testing. Never give your EWA password to someone else to "help" you with your homework. If you suspect your password has been compromised, change it immediately if you can and alert your instructor. Only you should enter material into your EWA account.

It is a good idea to write out your solutions to homework problems and the worksheet in a notebook and save them for reference.

Office hours: Office hours will be held online. All office hours will be held at the same zoom meeting room. See this calendar for scheduled office hours for each instructor and TA, and see Sakai web page for the zoom links.

Extra credit: Students have the option of earning 1 extra credit point once a week, up to 10 total, for each office hour they attend.

Grades: Your final grade will be out of 500 points, which consist of 450 points for quizzes and tutorials (30 points each quiz and 30 points for all tutorials) and 50 points for homework. You will be able to drop the lowest two quiz scores (the tutorial points will count as one quiz score), and the lowest 3 HW scores. You may receive up to 10 bonus points for attending office hours (1 point per attendance, up to 1 point per week).

Earning 470 (94%) or more of the 500 points will result in an A; earning 420 (84%) or more of the 500 points will result in an A-, B+, or B; earning 370 (74%) or more of the 500 points will result in a B-, C+, or C; and earning 320 (64%) or more of the 500 points will result in a C- or a D. The plus and minuses will only be used for the final course grade.

The grades in Sakai represent the grade that you are currently earning. Those grades will be used for midterm grades or any other required reporting of grades.

Worksheets: Each week a worksheet will be made available to guide lectures and tutorials. Every worksheet will have three parts: a summary of the material we will cover that week, a number of problems for examples in lecture and some problems for tutorial. We do not expect to work though all problems and the unworked problems are intended as review for the quizzes, and may include older material. The worksheets will also suggest some relevant videos to be viewed prior to class. Worksheets will be posted in on Sakai webpage as they are released.

Attendance and Seating: We will not take attendance, but barring health issues, you are expected to attend your assigned class and tutorial. You will only be hurting yourself if you don't. If your performance or attendance to lectures or tutorials is subpar we might track your attendance and if you miss 3 classes we can ask you to drop this class. We will be asking everyone to fill out a seating chart the first 4 days of lecture and after the fourth day remain in that seat the rest of the semester. This is for contact tracing. The students in the same dorm should be close to each other. Fill in the seating from the back of the room forward.

Software: The use of mathematical software/hardware is not required but can be very helpful. Understanding the qualitative behavior of graphs, functions, surfaces, etc. is often easier using software than by hand. Some useful programs we recommend are: Wolfram alpha, Grapher (comes by default on Macs), Mathematica (available for download on the OIT website). There are many other tools out there, both free and paid. If you have a graphing calculator, that is also very powerful.

Math help room: In addition to tutorials and office hours, a math help room will be staffed over zoom for students to find help from tutors and other students. The help room is available for students from all the calculus classes. See this calendar for the math help room schedule.


Health and Safety Protocols

In this class, as elsewhere on campus, students must comply with all University health and safety protocols, including:

  1. Face masks that completely cover the nose and mouth will be worn by all students and instructors;
  2. Physical distancing will be maintained in all instructional spaces;
  3. Students will sit in assigned seats throughout the semester; and
  4. Protocols for staged entry to and exit from classrooms and instructional spaces will be followed.

Every morning, members of the Notre Dame Community will be asked to complete a daily health check and submit their information via the Return to Campus Advisor application. The health check application will indicate one of the following:

  1. Student is cleared for class and should attend class in person; or
  2. Student is advised to stay home to monitor symptoms and should participate in class virtually and complete all assignments and assessments; or
  3. Student must consult a healthcare provider and should contact University Health Services (UHS) for an assessment. In the meantime, the student should participate in class virtually and complete all assignments and assessments. Depending on the medical assessment, UHS will follow the University's standard protocol for obtaining an excused absence for medical reasons.

Compliance with these protocols is an expectation for everyone enrolled in this course. If a student refuses to comply with the University's health and safety protocols, the student must leave the classroom and will earn an unexcused absence for the class period and any associated assignments/assessments for the day. Persistent deviation from expected health and safety guidelines may be considered a violation of the University's "Standards of Conduct," as articulated in du Lac: A Guide for Student Life, and will be referred accordingly.


Textbook and Webassign access

Textbook: We will be using Stewart: Multi-variable Calculus, 8th Edition and we will be using the online homework homework system Enhanced Webassign (EWA) provided by the book publisher. Note: we do NOT use the early transcendentals version of Stewart.

Buying a hard copy of the book for this course is optional. You may prefer to use just an e-book, or an e-book and a hardcopy of an older (used) edition. It is advisable to register for online homework (see below) to preview the e-book and attached media files before you make your decision on what to purchase.

To register for the online homework system Enhanced WebAssign (EWA), follow the instructions below. You will get the class key from your class Sakai webpage. You can register any time after Sunday, August 9. You will have a grace period of about 2 weeks to do your EWA homework and view the e-book. You will need to purchase an Enhanced WebAssign access code within that period in order to continue doing homework and have your work saved.

Options for purchasing book/access code:

  1. Hard Copy directly from the Cengage webasite. $299.95 (free shipping).
  2. An access code to webassign and e-book through Cengage Unlimited. $119.99 (for 4 months access that you will need). For more information see: "What is Cengage Unlimited?".
  3. You may also purchase an access code online through webassign after you register for online homework. Single term access for $100 or Multi-Term access for $125. If you need access to Cengage for other classes then Cengage Unlimited is a better deal than the Multi-Term access.
  4. If you have had Calc I or II at ND then you have access to the needed online homework problems on EWA. When you sign up with WebAssign be sure to use the same username as you used in the past. This will also provide you with access to the e-book.
For the first 3 options you will need access to a debit or credit card.

Webassign (EWA) access: You will need a class identifier key to register for the correct section in Webassign. You can find this in your Sakai course page. Below are step-by-step instructions on how to set up your webassign account. You may register anytime after August 9.

  1. Go to webassign, click on Enter Class Key on the top right.
  2. Enter your class key identifier, and press Submit.
  3. Verify your information and click Yes this is my class.
  4. If you don't have a Webassign account click on Continue and follow to the next step. If you already have a WebAssign account check the appropriate button, click on Continue and you should be set.
  5. You will be asked to fill out an information form. Choose your username and password. We recommend using your Notre Dame ID as your username. If you forget your password at some point throughout the summer, contact the WebAssign Support Center to obtain a new one. Enter you first name and last name as they appear on your Notre Dame ID. Since EWA is not integrated into Sakai, this allows us to match your homework and you. The student ID number is not required.


Lecture and tutorial times, locations, emails

The calendar below has links to the actual locations and will be used to note a substitute instructor or teaching assistant. All tutorials will be held remotely. The zoom links can be found on the Sakai class page.

Lecture schedule:
Section Instructor Email Time Room
1 P. Cholak MWF 8:00am 102 DeBartolo Hall
2 S. Stolz MWF 9:10am 190BC Morris Inn
3 S. Zhang MWF 5:40pm 101 Stepan Center
4 B. Mulholland MWF 11:40am 101 Jordan Hall of Science
5 N. Edelen MWF 2:30pm 101 DeBartolo Hall
6 N. Edelen MWF 1:00pm 213 DeBartolo Performing Arts Ctr.
7 S. Zhang MWF 4:05pm 101 DeBartolo Hall

Tutorial schedule (all tutorials are remote):
Section TA Email Time
11 P. Heslin Th 12:45pm
12 P. Heslin Th 2:30pm
21 L. Moncada Morales Th 11:10am
22 L. Jones Th 2:30pm
31 E. Addison Th 9:35am
32 A. Tyrrell Th 5:40pm
41 L. Jones Th 12:45pm
42 A. Tyrrell Th 4:05pm
51 P. LeVan Th 2:30pm
52 L. LeGare Th 5:40pm
61 P. LeVan Th 12:45pm
62 E. Addison Th 8:25am
71 L. Moncada Morales Th 9:35am
72 L. LeGare Th 4:05pm

Lecture and tutorial calendar:


Calendar of Office hours and Math help room

Office hours and math help zooms: See the Sakai class webpage.

You may go to any instructor or teaching assistant for office hours. You can also make an appointment via email to meet with an instructor or teaching assistant outside office hours. There is also the math help room available. Between office hours and the help room we have provided over 33 hours of office help. Please use them! You can earn a bonus point each week by asking a question in office hours or the help room.

All office hours are held in the same zoom room, linked above. If you make an individual appointment outside normal office hours you should use the Zoom link associated with the instructor or TA's class. Note that you will need to log into zoom via your Notre Dame account to access lecture, tutorial, and office hour zoom meetings. There will be a waiting room, so if you are not immediately let in it is because the person staffing the office hour is busy with another student. The passwords to these zoom meetings can be found on the Sakai class webpage.

The default office hour schedule is below but office hours may change, and so we recommend using the calendar to find office hours and hours our TAs are in the math help room.
Instructor/TA Times
P. Cholak WF 3-4pm
N. Edelen Sun 12-2pm, Th 4-6pm
B. Mulholland WF 1-2pm
S. Stolz W 6-7pm, F 2-3pm
S. Zhang Tu, Sat 6-8pm
E. Addison F 5-7pm
P. Heslin Sun 7-8pm, F 8-9pm
L. Jones Tu 1-3pm
L. LeGare Th 3-4pm , F 4-5pm
P. LeVan Sun 2-4pm
L. Moncada Morales W 2-3pm, Th 1-2pm
A. Tyrrell Sun 4-5pm, F 7-8pm

The math help room is an additional resource available to all calculus students. The room is staffed over zoom, and provides a platform for students to work with tutors and other students. All the TAs from all math classes with tutorials and some upper level undergrads will take turns staffing the help room. You will be able to work with other students from Calc 3 via using the breakout rooms. The link can be found on the Sakai webpage. There will be a waiting room, so if you are not immediately let in it is because the tutor is busy with another student. The default math help room schedule is below, however as with office hours these times may change, so we recommend using the calendar below to verify when the math help room is open.
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
1-9pm 1-9pm 1-9pm 1-9pm 1-4pm closed 4-9pm

Office hour calendar. This calendar also lists when our TAs will be staffing help room:



After the first Monday, every Monday for the first 30 minutes there will be a quiz. The lines represent the cutoff for the legal material on the following Monday. Any material presented prior to the cutoff is legal. The EWA homework assoicated with the new material for the weekly quiz is due Friday at 11:59pm.
Date Section Topic
August 10 12.1 Introduction and 3D coordinates
12 12.2 Vectors
13 Tutorial (Introduction, some group work, and if time start Dot Products)
14 12.3 Dot Product
Monday 17 12.4 Cross Product and Distance (no Torque)
19 12.5 Lines
20 Tutorial
21 12.5 Planes
Monday24 13.1 Vector Functions, Space Curves
26 13.2 Derivatives, Integrals
27 Tutorial
28 13.3 Arc Length (No Curvature), TNB frame
Monday 31 13.4 Motion in Space
September 2 Catch up or Review
3 Tutorial
4 14.1-2 Functions of Several Variables, Limits (only nonexistence) and Continuity
Monday 7 14.3 Partial Derivatives
9 14.5 Chain Rule
10 Tutorial
11 14.6 Directional Derivatives, Gradients
Monday 14 14.6 Gradients, Tangent Planes, Normal Lines
16 14.7 Local Maxima, Local Minima, Saddle Points
17 Tutorial
18 14.7 Maxima and Minima on Bounded Regions
Monday 21 14.8 Lagrange Multipliers (one constraint)
23 14.8 Lagrange Multipliers (two constraints)
24 Tutorial
25 15.1 Double Integrals over Rectangles
Monday 28 15.2 Double Integrals over General Regions
30 15.3 Polar Coordinates
October 1 Tutorial
2 15.4 Mass, Centers of Mass, and Moments
Monday 5 15.6 Triple Integrals
7 15.7 Triple Integrals in Cylindrical Coordinates
8 Tutorial
9 15.8 Triple Integrals in Spherical Coordinates
Monday 12 15.9 Change of Variables in Multiple Integrals
14 16.1 Vector Fields
15 Tutorial
16 16.2 Line Integrals
Monday 19 16.3 Fundamental Theorem of Line Integrals I
21 16.3 Fundamental Theorem of Line Integrals I
22 Tutorial
23 16.4 Green's Theorem
Monday 26 16.5 Curl, Divergence
28 16.6 Parametric Surfaces, Tangent Planes
29 Tutorial
30 16.6 Surface Area
Monday, November 2 16.7 Surface Integrals
4 16.7 Flux Integrals
5 Tutorial
6 16.8 Stokes' Theorem
Monday 9 16.9 Divergence Theorem
11 Catch up or Review
12 Tutorial
November 16-20 Hopefully a 2 hour time slot for a final


New instructions taking quizzes remotely

During class, the quiz will be shared via zoom so you can view the questions. You will take the quiz in the allotted time, writing your answers in the provided quiz answer sheet. Upon completion, you will scan your answer sheet using either a scanner or phone you will upload your answer sheet to Gradescope. You can access directly Gradescope using your ND credentials or through Sakai. If you don't upload your answer sheet within 7 minutes of finishing the quiz, you will receive a 0. For more details on how to upload a PDF to Gradescope look at this document provided by Gradescope.

There are several apps that allow you to scan documents with your smart phone. These may be the easiest option for many people. Below are our recommend apps, but you can also download and follow a similar process with any other scanning app that produces high-quality PDFs.

For more details on scanning and uploading look at this document provided by Gradescope.

As a reminder, it is your responsibility to make sure that your quizzes are clear and readable. It is recommended everyone practicing using these scanning apps and uploadoing.