Department of Mathematics

Columbia University

Math UN1201: Calculus III (Sections 006 and 007)
Fall 2020

Time and location: Section 006: Tuesdays and Thursdays 2:40-3:55pm online. Section 007: Tuesdays and Thursdays 4:10-5:25pm online.

Instructor: Inbar Klang (klang@math.columbia.edu), pronouns: she/her/hers

Office hours: Tuesdays and Thursdays 5:40-7:10pm online

Teaching assistants: TBA

TA Office Hours: Held in the virtual 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:

• Vectors and the geometry of space (Section 10.5 and Chapter 12)
• Vector functions (Chapter 13)
• Functions of several variables and partial derivatives (Chapter 14)

Detailed syllabus: here.

Course notes: Here.

Homework

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

To best adapt the course for the online format, it 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.

Grading

The default weights will be as follows:

• Homework, 30%
• Pre-class questionnaires, 5%
• Midterm 1, 20%
• Midterm 2, 20%
• Final exam or project 25%

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 Tuesday, September 22, 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.

• Homework, 10-30%
• Midterm 1, 10-30%
• Pre-class questionnaires, 2-8%
• Midterm 2, at least 10%
• Final exam / project, at least 20%

Exams

The exams will be online, multiple choice exams on Courseworks. Each midterm will be 90 minutes long, and the final exam will be 3 hours long. Students can make two attempts at each exam, and the higher score of the two will be taken. Any resource may be used (textbook, notes, online) except for asking another person or website about an exam question. Midterm 1 can be taken at any time during the week of October 5-12. Midterm 2 can be taken at any time during the week of November 9-16. The final exam can be taken at any time during finals week. Collaboration during exams is considered cheating and is taken very seriously. Cheating during a midterm or final entails failing the course.

Optional project. Students may choose to replace the final exam with a group project, to be completed in groups of 3-5 students. Project topics will be posted about halfway through the semester, and the projects will be due at the beginning of exam week. Projects will typically include studying a topic related to course material, and providing detailed solutions to several textbook 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 Courseworks, as a pdf file if possible. 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.

Schedule

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.)