Department of Mathematics

Columbia University

Math UN1201: Calculus III (Sections 007 and 008)
Fall 2021

Time and location: Section 007: Tuesdays and Thursdays 2:40-3:55pm in 207 Mathematics. Section 008: Tuesdays and Thursdays 4:10-5:25pm in 207 Mathematics.

Instructor: Inbar Klang (, pronouns: she/her/hers

Office hours: Tuesdays and Thursdays 5:40-7:10pm, or by appointment (in person or online meetings available.) Tuesdays: 622 Mathematics, Thursdays: 629 Mathematics.

Teaching assistants: Graduate TAs: Haodong Yao ( and Avi Zeff ( Undergraduate TAs: Inesse Jibre (, Melissa Juarez (, Jeremy Kohler (, Thomas Lim (, and Andrew Park (

TA Office Hours: Held in the math help room.

Textbook: Calculus: Early Transcendentals, 8th Edition, by James Stewart

Prerequisite: The prerequisite for this course is Calculus I or an equivalent. For more information on calculus at Columbia, read about the calculus sequence.

Overview: Welcome to Calculus III! We will cover the following topics:

Alternate classes: Are you wondering whether this is the right class for you? Here are some other options:


Detailed syllabus: here.

Course notes: Here.


  Assignment Due Date
1 HW 1 Sep 14 at 11pm
2 HW 2 Sep 21 at 11pm
3 HW 3 Sep 28 at 11pm
4 HW 4 Oct 12 at 11pm
5 HW 5 Oct 19 at 11pm
6 HW 6 Oct 26 at 11pm
7 HW 7 Nov 4 at 11pm
8 HW 8 Nov 16 at 11pm
9 HW 9 Nov 23 at 11pm
10 HW 10 Nov 30 at 11pm
11 HW 11 Dec 7 at 11pm
12 HW 12 Dec 14 at 11pm

Material for midterm 1

10.1 pages 640-642, 10.3 pages 658-661, 10.5, 12.1-12.6 (no torque or work or direction angles / cosines), 15.7 pages 1040-1041, 15.8 pages 1045-1046.

Material for midterm 2

Sections: 13.1 pages 848-851, 13.2, 13.3 (no osculating circle), 13.4 pages 870-875, 14.1, 14.2 (no epsilon-delta definition or arguments), 14.3 pages 911-920, 14.4.

Material for the final exam

All previous material, and: Sections 14.5, 14.6, 14.7 pages 959-966, 14.8, and Appendix H pages A57-A62.

Course structure

This course will have an "active learning" structure. Students will be responsible for engaging with the course material before class sessions, by reading the notes posted on Courseworks, watching the videos posted on Courseworks, or some combination thereof. I highly recommend attempting the exercises given in the notes as you come upon them. Each Monday and Wednesday night, a pre-class reading questionnaire will be due, to help me determine which topics to focus on in class. Class will be devoted to reviewing concepts according to the reading questionnaire, Q & A, and working on problems in small groups. Please do not attend class if you are unwell, quarantined, or have tested positive for COVID-19. The TAs and I will be happy to help you make up any material you've missed.


The default weights will be as follows:

Contract weighting: You have the opportunity to individualize the weight you would like each component of this course to have, within constraints. To opt in, email me by Thursday, September 23, with subject line "weighting", with your preferred weights. The sum of weights must be 100%, subject to the constraints below. There will be a "renegotiation" period (October 24-31) in which you can modify the weights of everything except midterm 1.


There will be two midterms and a final exam. Exams will take place via timed quizzes on Courseworks, which you can take at any point during a time period of a few days. Midterm 1 will be available October 6-8, and midterm 2 will be available November 10-12. The exams will be open-book and open-notes, and any calculator may be used. You are allowed to look up information online during the exam, but you may not ask a person or website about a specific exam question.

Optional project. Students may choose to replace the final exam with a group project, to be completed in groups of 3-5 students. You can opt-in to this about halfway through the semester, and the projects will be due at the beginning of exam week. Projects will typically include studying and providing a clear exposition on a topic related to course material, and providing detailed solutions to several problems. Projects must be typed, not handwritten.

Homework Policies

There will be 12 homework assignments. The homework grade will be obtained as 0.1 x (sum of problem set scores), so you can miss up to two problem sets and still obtain a full grade on homework. Please submit your homework on Gradescope, as a pdf file if possible, either typed or handwritten clearly and legibly. Homework will be due every Tuesday (except exam weeks) at 11pm Eastern time, and the submission box will close promptly at that time.

Late homework is highly discouraged, to avoid placing an undue burden on graders. I recognize, however, that this is a difficult semester; if you are experiencing extraordinary circumstances, please reach out to me and we will figure out a solution. You are allowed and encouraged to collaborate on homework, but you must write up your own solutions. Please cite any references used (e.g. websites.) Homework assignments may feature more challenging or involved problems that will count for extra credit.


The topic for each class session indicates which material you should read beforehand. Exception: you will not be expected to have completed readings before the first class (but it is recommended that you do, if possible.)

Date Book Sections Topics Homework
Sep 9
12.1, 10.3,
15.7 p.1040-1041, 15.8 p.1045-1046
Overview, coordinate systems  
Sep 14
12.2, 12.3
Vectors and dot product HW 1 due
Sep 16
Cross Product  
Sep 21
10.1, 12.5
Parametric curves, equations of lines HW 2 due
Sep 23
Equations of planes  
Sep 28
Conic sections HW 3 due
Sep 30
Quadric surfaces  
Oct 5
Oct 7   no class (midterm 1)  
Oct 12
13.1, parts of Ch.2
Vector functions, review of limits HW 4 due
Oct 14
Derivatives and integrals of vector functions  
Oct 19
Arc length and curvature HW 5 due
Oct 21
Motion in space  
Oct 26
Functions of several variables, limits and continuity HW 6 due
Oct 28
Partial derivatives  
Nov 4
Tangent planes HW 7 due Nov 3 at 11pm
Nov 9
Nov 11   no class (midterm 2)  
Nov 16
The chain rule HW 8 due
Nov 18
14.6 part 1
Directional derivatives and the gradient  
Nov 23
14.6 part 2
Directional derivatives and the gradient cot'd HW 9 due
Nov 30
14.7 part 1
Maxima and minima HW 10 due
Dec 2
14.7 part 2
Maxima and minima cot'd  
Dec 7
Lagrange multipliers HW 11 due
Dec 9
Appendix H
Complex numbers HW 12 due Dec 14 at 11pm