Honors Calc IV, Spring 2021

Prof. Jo Nelson
Math 222

Email: jo [dot] nelson [at] rice [dot] edu
Discussion/Lectures: TTh 1.30-2.50pm CST
Location: PCF 3 + Zoom
Office Hours:
TTh 2.30-3pm CST (Outside + Zoom)
T 6-6.30pm CST (Zoom only)
W 7.15-7.45am (Zoom only)


Doyin Aderele is the Math 222 Tech TA. She'll be helping by bringing my attention to student questions, helping manage break out rooms and other Zoom function, and aiding with Zoomer engagement and cameras during hybrid instruction.
Cameron Noorbakhsh and Leo Liu are the Math 222 TAs. They will be grading homework, holding a weekly recorded problem session, and providing hints to homework as requested in Canvas. Leo is in the China time zone, so he'll have a short unrecorded weekly gathering for the asynchronous international students, which will be the primary way for asynchronous international students to earn their participation points. Cameron is in the Central time zone, so he'll be hosting a live weekly recorded problem session, which students are encouraged to attend in real time. Recordings will be posted to the Canvas Zoom page.
Please extend the same courtesy and respect that you do for me to Doyin, Cameron, and Leo.

Assessment, % of Course Grade

Homework, 40%; Discussion, 13%; Midterm Exam, 20%; Final Exam, 27%.
The cutoff for a B- in this course is 55%.

Participation Assessment

Students will be assessed on their participation during the regularly scheduled TTh class time time, and each week of participation is worth 1% of the course grade. Successful participation includes asking clarifying questions about the lecture material, providing solutions or hints to the in lecture problems, forming small study groups to work on homework, and/or actively participating in instructor office hours or TA problem sessions at least once per week. Uncollegial behavior towards other students, the instructor, or the TAs will result in a 0% discussion assessment for the week. Students will keep track of their participation each week and submit a spreadsheet to Prof Jo prior to the midterm and final exam.


Homework will count for 40% of your final grade. There will be weekly written homeworks, which you must scan and upload to Gradescope on Thursdays by 11pm local time (tentatively). During any weeks containing sprinkle days, you will have an additional day to complete the homeworks. No homework will be due the week following move-in, which is presently slated as Feb 15.

Your TWO lowest/nonexistent homework scores will be dropped. I will also grant individuals one extension up to 2 days on a homework set of their choice. To request an extension please email myself and the course TAs with your request at least 24 hours ahead of the deadline and indicate your desired due date and if the extension is requested for personal reasons (no need to elaborate), unusually heavy workload in other classes, or other mitigating circumstances (no need to elaborate). Additional extensions will be granted for serious illness (including COVID-19) and family emergency, though these will require documentation from your magister.

Clearly print your first and last name on your written assignment. The homework is not pledged and you are encouraged to work together with your classmates on the assignments. However, you must write up your solutions individually. Legible handwritten and LaTeX-ed solution sets are both acceptable. Not all homework problems will be graded each week, but you will receive additional credit for completeness. Homework assessment will include credit for good composition (or neatly organizing a computation). The use of full sentences, proper grammar, and overall neatness counts towards ‘good composition’.

You are not allowed to look up solutions in any written form; in particular, you are not allowed to look up solutions online. Students caught violating this rule will be reported to the Honor Council. Do not use calculators or outside software unless otherwise specified. Late homework will not be accepted without prior authorization and at least 24 hours ahead of the deadline.

Midterm and Final Exam

There will be one pledged take home midterm exam. It is open books and open notes, but you may not use the internet, calculators, or outside software such as wolfram alpha. It will be a 90 minute exam, which you will have 7-10 days to complete and upload to Gradescope. We will set the week for the midterm during the first class of the spring semester to better accommodate your schedules.

There will be one pledged take home final exam. It is open books and open notes, but you may not use the internet. It will be a three hour exam, which you will have a week to complete and upload to Gradescope. The deadline for submitting the final exam will be determined by the registrar, and we will discuss an agreeable release date for the final exam. It is your responsibility to inform me in writing as soon as possible and no later than three weeks before the exam if you have a conflict. In the event of illness or family emergency I must be notified ideally at least 24 hours in advance of the deadline and documentation from your magister must be provided to me.


If you find yourself confused, please seek help sooner rather than later. I will be available to answer questions during my office hours. Additionally, the TAs and I will monitor canvas discussions to provide additional clarification and homework help. There will be a weekly recorded problem session given by TAs.


Comportment Expectations. The Department of Mathematics supports an inclusive learning environment where diversity and individual differences are understood, respected, and recognized as a source of strength. Racism, discrimination, harassment, and bullying will not be tolerated. We expect all participants in mathematics courses (students and faculty alike) to treat each other with courtesy and respect, and to adhere to the Mathematics Department Standards of Collegiality, Respect, and Sensitivity as well as the Rice Student Code of Conduct. If you think you have experienced or witnessed unprofessional or antagonistic behavior, then the matter should be brought to the attention of the instructor and/or department chair. The Ombudsperson is also available as an intermediate, informal option, and contacting them will not necessarily trigger a formal inquiry.

Title IX Responsible Employee Notification. Rice University cares about your wellbeing and safety. Rice encourages any student who has experienced an incident of harassment, pregnancy discrimination or gender discrimination or relationship, sexual, or other forms interpersonal violence to seek support through The SAFE Office. Students should be aware when seeking support on campus that most employees, including myself, as the instructor/TA, are required by Title IX to disclose all incidents of non-consensual interpersonal behaviors to Title IX professionals on campus who can act to support that student and meet their needs. For more information, please visit safe.rice.edu or email titleixsupport@rice.edu.

Disability-related Academic Accommodations. In order to receive disability-related academic accommodations, students must first be registered with the Disability Resource Center (DRC). Students who may need accommodations in this course should give me a written letter from the DRC within the first two weeks. More information on the DRC registration process is available online at https://drc.rice.edu/. Registered students must present an accommodation letter to the professor before exams or other accommodations can be provided. Students who have, or think they may have, a disability are invited to contact DRC for a confidential discussion.


The basic plan is to make sure that we have enough time to understand, prove, and do computations involving Green's theorem, Stokes' theorem, and Gauss' theorem. Since 2020 has thrown us all for a loop, and then some, that means that we will be spending less time on integration. Instead of theoretical integration, we will be doing practical integration.

Practical integration means we will have flipped class style virtual board discussions during our shortened meeting times, since you will additionally watch prerecorded videos from Prof. Michael Hutchings, my longtime research collaborator and voice of UC Berkeley's online multivariable calculus. We will skip Chapters 9-11 from Dr. Jones' book. In March 2020, I shared Hutchings' videos with Dr. Jones' and they're certified to be used in Math 222 for 2021!

We will start the semester with Dr. Jones' book:
  • Jones 7: Cross product
  • Jones 8: Volumes of parallelograms
Then we mostly skip Jones 9-11 and switch to Dr. Hutchings' videos and in class overviews by Prof Jo:
  • Hutchings Part 3: Integration
  • Hutchings Part 4: Vector Calculus
After we cover line integrals, we will supplement Hutchings' videos and Prof Jo's Overviews with Dr. Jones' book:
  • Jones 12: Green's theorem
  • Jones 13: Stokes' theorem
  • Jones 14: Gauss' theorem
Our in person meetings will be discussion and problem based. Problems for the midterm and final exam will be similar to those worked out in Hutchings' videos, those from Prof. Jo's classes, and the occasional short proof. Prof. Jo will additionally provide her old exams from her Fall 2018: Multi - Math 212 course.

Schedule & Assignments

Prerequisites: Math 221 (or Math 354 with High School Multi)
Textbook: Dr. Jones' Honors Calculus Book, free digitial pdf.
Videos: Prof. Hutchings' Multi Videos, YouTube (inform me of any needed digital accommodations).

Optional Zero Content and Theory ProblemsLaTeX

Date   Section and Topics  In Class Problems      HW, tentatively
due Thurs 11pm
1/26 Basics of the cross product
Survey Logistics
Setting week for Midterm 1
Finalizing time and day for homework
Week 1LaTeX
1/28 Jones 7: The Cross product
Hutchings 1.3.5, 1.3.6 (optional)
Due 2/4
2/2 Jones 7.D: Orientations Week 2LaTeX
2/4 Jones 7.F: Rotations
Due 2/11
2/9 Jones 8: Volumes of Parallelograms Week 3LaTeX
2/11 Jones 8: Volumes of Parallelograms HW 3LaTeX
Due Friday 2/26
2/16 SNOW DAY ☃️
So much for PCF 3
2/18 SNOW DAY ☃️
2/23 Prof Jo and Folland: Multi-Integration Overview + Fubini
Hutchings 3.1: Basics of Double Integrals
Week 4LaTeX HW 4LaTeX
Due Saturday 3/6
2/25 Prof Jo: Partitions and 1-D Riemann Sums
Hutchings 3.2: Polar double integrals
OMIT Hutchings 3.2.6
OMIT Hutchings 3.3.4 Center of Mass
3/2 Prof Jo: 1-D integration
Hutchings 3.3: Cartesian triple integrals
Hutchings 3.4: Triple integrals
Week 5LaTeX
3/4 Prof Jo: non rectangular regions
Prof Jo: Cylindrical triple integrals
Hutchings 3.4: Triple integrals
Week 6-7LaTeX
No 222 class because its Monday
Midterm released (tentatively)
Contact Prof Jo to request earlier release or later submission
Midterm includes but does not go beyond Cartesian Triple Integrals
Due 3/15
3/9 Prof Jo: Spherical triple integrals
Folland: Change of variables
Hutchings 3.5: Change of variables, Jacobians
Break from homework
because of Midterm
3/11 Folland: Change of variables
Hutchings 3.5: Change of variables, Jacobians
Week 8LaTeX HW 5LaTeX
Due 3/18
No 222 class because its Monday
Midterm due at 11pm (tentatively)
3/18 Folland: Change of Variables
Due 3/25
3/23 Hutchings 4.1: Vector fields
Hutchings 4.2: Line Integrals
Week 9LaTeX
3/25 Fundamental Theorem of Line Integrals HW 7LaTeX
Due FRIDAY 4/2
3/30 Jones 12 + Hutchings 4.3:
Green's theorem I
Week 10LaTeX
4/1 Green's Theorem II HW 8LaTeX
Due MONDAY 4/12
4/6 Hutchings 4.5: Parametrized surfaces and infinitesimal surface area
Klein Bottles and Möbius Bands
The Hopf fibration visualizes S^3
Week 11LaTeX
4/13 Jones 13 + Hutchings 4.6:
Surface integrals and Stokes' Theorem I
Cult Classic: Sphere Eversion
Week 12LaTeX HW 9LaTeX
Due 4/22
4/15 Jones 13 + Hutchings 4.6:
Stokes' Theorem II
Bonus Week 12 (Higher Dimensional Manifolds)LaTeX
4/20 Hutchings 4.4: Gradient, Curl, and Divergence
4/22 Jones 14 + Hutchings 4.7: Divergence Theorem I Week 13LaTeX HW 10LaTeX
Due 4/29
4/27 Divergence Theorem II
4/29 Differential Forms