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Math UN 1201
Calculus III (Section 006 and 007)
Fall 2020
Time and location: Section 006: TR 2:40-3:55pm online. Section 007: TR 4:10-5:25pm online.
Instructor: Inbar Klang (email: klang@math.columbia.edu), pronouns: she/her/hers. You can
call me Prof. Klang, Dr. Klang, or Inbar.
Office hours: Tuesdays and Thursdays 5:40-7:10pm online.
Teaching assistants: TBA.
Their office hours will be held in the virtual math help room; see here for hours.
Textbook: James Stewart, Calculus: Early Transcendentals, 8th^ Edition. This is available for
purchase at the Columbia bookstore, or you can acquire it as an ebook online.
Prerequisites: Calculus I or equivalent.
Course overview: Welcome to Calculus III! In this class, 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)
You can find a detailed outline on the last page of the syllabus.
On help hours: An essential part of learning mathematics is asking questions. Office hours (whether the instructor’s, the TAs’, or those of other TAs in the help room) are an opportunity to go over material covered in class, get homework help, and ask any other class-related questions. Other academic resources include the Columbia tutoring services, which can match you with a tutor for this course, and Khan academy, which has a variety of multivariable calculus videos and texts.
Structure of the course:
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 policy:
There will be weekly homework, twice-weekly pre-class questionnaires, two midterms, and a final exam (which students may choose to replace by a group project.) Their default weight will be as follows, although there is some flexibility (see “contract weighting” below):
- Homework: 30%
- Pre-class questionnaires: 5%
- Midterm 1: 20%
- Midterm 2: 20%
- Final exam / 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. (If you do not email me, your weights will be as above.) The sum of weights must be 100%, subject to these constraints:
- Homework: 10-30%
- Pre-class questionnaires: 2-8%
- Midterm 1: 10-30%
- Midterm 2: at least 10%
- Final exam / project: at least 20%
There will be a “renegotiation” period (October 24-31) in which you can modify the weights of everything except midterm 1.
Homework: There will be 12 homework assignments. The homework grade will be obtained as
- 1 ×(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.
Pre-class questionnaires: Pre-class questionnaires will comprise 3-5 questions about the
reading material for the following day’s class. A questionnaire will be due every Monday and Wednesday at 11pm, except for the first week and election week (only a Wednesday questionnaire),
Tentative Course Outline:
Week Content
- 1046, 12.1-12. Sep 8, 10 • Overview, coordinate systems, vectors; 10.3, 15.7 p. 1040-1041, 15.8 p.1045- - Sep 15, 17 • Dot product, cross product; 12.3-12. - • HW 1 due Tuesday Sep - Sep 22, 24 • Parametric curves, equations of lines and planes; 10.1, 12. - • HW 2 due Tuesday Sep
- Sep 29, Oct 1 • Conic sections, quadric surfaces; 10.5, 12. - • HW 3 due Tuesday Sep - Oct 6, 8 • Review, Midterm - • review Oct 6, no class Oct - Oct 13, - • Vector functions and their derivatives and integrals, review of limits; 13.1-13. - and some Chapter - • HW 4 due Tuesday Oct - Oct 20, 22 • Arc length, curvature, motion in space; 13.3-13. - • HW 5 due Tuesday Oct - Oct 27, - 14. • Functions of several variables, limits and continuity, partial derivatives; 14.1- - • HW 6 due Tuesday Oct - Nov 5 • Tangent planes; 14. - • HW 7 due Wednesday Nov
- Nov 10, 12 • Review, Midterm - • review Nov 10, no class Nov
- Nov 17, 19 • Chain rule, directional derivatives and gradient; 14.5-14. - • HW 8 due Tuesday Nov - Nov 24 • Directional derivatives and gradient cot’d; 14. - • HW 9 due Tuesday Nov - Dec 1, 3 • Maxima and minima; 14. - • HW 10 due Tuesday Dec - • HW 11 due Tuesday Dec 8; HW 12 due Tuesday Dec Dec 8, 10 • Lagrange multipliers, complex numbers; 14.8 and Appendix H
