Department of Mathematics

Columbia University

Math UN1201: Calculus III (Section 007 and 008)
Fall 2019

Time and location: Section 7: Tuesdays and Thursdays 4:10-5:25pm, 207 Mathematics.
Section 8: Tuesdays and Thursdays 6:10-7:25pm, 323 Milbank Hall.

Instructor: Inbar Klang (klang@math.columbia.edu, office: 629 Mathematics), pronouns: she/her/hers

Office hours: Tuesdays 2-3:30pm in 520 Mathematics, and Thursdays 2-3:30pm in 629 Mathematics

Teaching assistants: Section 7: Isaac Fingerson (ipf2107@columbia.edu), Dmitrii Piozhkov (dp2782@columbia.edu), Lekha Yesantharao (lvy2002@columbia.edu).
Section 8: Kyle Creech (kcc2150@columbia.edu).

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:

• 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.

Homework

Material for midterm 1

10.1 (excluding graphing devices), 10.3 pages 658-662, 10.5, 12.1-12.5 (no torque or work), 15.7 pages 1040-1041, 15.8 pages 1045-1046.

Practice exams

Here are some practice exams for midterm 1, all taken from exams or practice exams in past years. I would recommend attempting one of them under exam conditions (75 minutes, 2-sided formula sheet, no programmable calculator.)

• practice exam A, Solutions
• practice exam B, Solutions
• practice exam C, Solutions
• practice exam D, Solutions
• practice exam E, Solutions

Material for midterm 2

Sections 12.6, 13.1 (no computers), 13.2, 13.3 (no normal and binormal vectors), 13.4 pages 870-874, 14.1, 14.2, 14.3 pages 911-920, 14.4.

Practice exams

Here are some practice exams for midterm 2, all taken from exams or practice exams in past years.

• practice exam A. Disregard problems 1(e) and 5. Solutions.
• practice exam B. Disregard exercise 1. Solutions.
• practice exam C. Disregard problems 2 and 7. Solutions.
• practice exam D. Disregard problems 2(c)(e), 3, and 5(e). For 2(b), just compute the unit tangent vector. For 4(c), assume a=1 and b=2. Solutions.
• practice exam E. Solutions.
• In addition, do the quadric surface questions from:
• (just problem 6.)
• (just problem 5.)
• (just problem 5.)
• (just problem 5)

Material for the final exam

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

Practice exams

Here are some practice exams for the final, all taken from exams or practice exams in past years.

• practice exam A. Disregard problems 1(e) and 9. Solutions. Note that there are errors in the cross product computations in the solutions.
• practice exam B. Solutions.
• practice exam C. Solutions.
• practice exam D. Disregard problems 1(b) and 8(a). Solutions.
• practice exam E. Disregard problems 2 and 5(b). Solutions.

Here is an "in-format" practice final. All questions are taken from the above practice exam, but the exam is roughly in the format that ours will be in. I recommend trying it under exam conditions after you've studied and made a formula sheet.

Grading

The default weights will be as follows:

• Homework, 25%
• Midterm 1, 25%
• Midterm 2, 25%
• Final exam, 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 17, 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 22-29) in which you can modify the weights of homework, midterm 2, and the final exam.

• Homework, 10-25%
• Midterm 1, 15-35%
• Midterm 2, at least 15%
• Final exam, at least 20%

Exams

There will be two in-class midterms, on September 26 and October 31, and a final exam on December 17. The final exam is scheduled by the university and cannot be rescheduled; a make-up final will only be possible under specific circumstances, such as an exam conflict or a university athletics commitment. If you are unable to take one of the midterms at the scheduled time, please let me know as soon as possible so that we can figure out a solution.
You may use a formula sheet during the exams, no longer than two sides of an A4 page. The only electronic device you may use is a calculator (e.g. scientific calculator), but programmable or graphing calculators are not allowed. Collaboration during exams is considered cheating and is taken very seriously. Cheating during a midterm or final entails failing the course.

Homework Policies

There will be 12 homework assignments. All homework must be submitted by 8pm on Thursdays, unless otherwise noted. Please submit your homework to the Calculus III box corresponding to your section on the 4th floor of the math building. Make sure to clearly write your name, UNI, and section number, and to staple all the pages together securely. You can pick up your graded homework from the bin labeled with our class and section number, outside room 520 of the math building.

To avoid creating an undue burden on graders, late homework will not be accepted. To mitigate this, your homework grade will be obtained by dividing the sum of your homework scores by 10. 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 schedule below is tentative and subject to change.