Department of Mathematics
Time and location: Tuesdays and Thursdays 6:10-7:25pm, online starting March 12
Instructor: Inbar Klang (klang@math.columbia.edu, office: 629 Mathematics), pronouns: she/her/hers
Office hours: Tuesdays and Thursdays 4:15-5:45pm online
Teaching assistants:
Graduate TAs: Donghan Kim (dk2571@columbia.edu) and Renata Picciotto (rp2752@columbia.edu).
Undergraduate TAs: Kyle Creech (kcc2150@columbia.edu), Vanessa Ho (hoiwan.ho@columbia.edu), Yunpeng Liu (yl4409@columbia.edu), and Manasi Sharma (ms5510@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:
Detailed syllabus: here.
| Assignment | Due Date | |
|---|---|---|
| 1 |
10.3 #12,16 15.7 #4,6 15.8 #4,6 12.1 #14,20,30 12.2 #20,28,36 |
Jan 28 at 8pm |
| 2 |
12.3 #12,18,26,32,44,48 12.4 #2,18,20,30,36,38 |
Feb 4 at 8pm |
| 3 |
10.1 #14,18,38,46(a)(c) 12.5 #6,14,22,26,34,64,72,78 |
Feb 11 at 8pm |
| 4 |
10.5 #4,20,30,48,55 12.6 #4,12,14,18,30,34,38 |
Feb 25 at 8pm |
| 5 |
2.3 #38,42 13.1 #6,8,32,44,49 13.2 #8,20,26,41,50 |
March 3 at 8pm |
| 6 |
13.3 #4,15,24,46,50,56 13.4 #6,14,18(a),24,30,42 |
March 11 at 10am Eastern time |
| 7 |
14.1 #12,18,30,48,52,70 14.2 #10,18,22,30,32,44(a)(b) |
March 26 at 10am Eastern time |
| 8 |
14.3: #20,26,44,48,54,82 14.4: #2,14,26,36,46 Ch. 14 Review exercises (p. 982): 8(b)(c) |
April 7 at 8pm Eastern time |
| 9 |
14.5: #4,10,22,30,32,40 14.6: #4,8,12,14,19,30 |
April 21 at 8pm Eastern time |
| 10 |
14.6: #22,32,44,56,60,66 14.7: #4,6,10,12,16,20 |
April 28 at 8pm Eastern time |
| 11 |
14.7 #34,38,42,46,54,57 14.8 #1,8,10,18,21,34 |
May 5 at 8pm Eastern time |
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.
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 C (which was midterm 1 last semester) is most similar in format to our exam, but note that it does not cover quadric surfaces.
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.
Here are some practice exams for midterm 2, all taken from exams or practice exams in past years. If you would like more practice with multiple choice questions, you can try for example Albert.io. For more practice with true/false questions, you can try the True / False quizzes at the end of Chapter 13 and Chapter 14.
All previous material, and sections 14.5, 14.6, 14.7 pages 959-966, 14.8.
Here are some practice exams for the final exam, all taken from exams or practice exams in past years. If you would like more practice with multiple choice questions, you can try for example Albert.io. See also Khan academy for good fill-in-the-blank questions to practice with.
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 Tuesday, February 4, 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 (March 24-April 2) in which you can modify the weights of homework, midterm 2, and the final exam.
There was an in-class midterm, on February 20. The second midterm is online and optional, and can be taken at any time between April 2 at 7:30pm and April 9 at 6pm. Each student can make two attempts, and the higher score of the two will be taken. The final exam is planned to be online, to be taken anytime during the week of May 8 to May 15. Two attempts will be possible, and the higher score of the two will be taken.
You may use a formula sheet during an in-class exam, 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. During the online exam, any resource may be used, but receiving help from other people is not permitted. Collaboration during exams is considered cheating and is taken very seriously. Cheating during a midterm or final entails failing the course.
There will be 11 homework assignments. All homework must be submitted by 8pm on Tuesdays, 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. After March 10: Homework is due online on Courseworks.
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 9. 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 schedule below is tentative and subject to change.
| Date | Book Sections | Topics | Homework |
|---|---|---|---|
| Jan 21 |
15.7 p.1040-1041 |
Brief overview, coordinate systems | |
| Jan 23 |
|
Spherical coordinates, Vectors | |
| Jan 28 |
|
Dot Product | HW 1 due |
| Jan 30 |
|
Cross Product | |
| Feb 4 |
|
Parametric curves, equations of lines | HW 2 due |
| Feb 6 |
|
Equations of planes | |
| Feb 11 |
|
Conic sections | HW 3 due |
| Feb 13 |
|
Quadric surfaces | |
| Feb 18 |
|
Review | |
| Feb 20 | Midterm 1 | ||
| Feb 25 |
|
Vector functions, review of limits | HW 4 due |
| Feb 27 |
|
Review of limits, derivatives and integrals of vector functions | |
| March 3 |
|
Arc length and curvature | HW 5 due |
| March 5 |
|
Motion in space | |
| March 10 |
|
CANCELLED | HW 6 due March 11 at 10am |
| March 12 |
|
Functions of several variables, limits and continuity | |
| March 24 |
|
CANCELLED | |
| March 26 |
|
Partial derivatives, tangent planes | HW 7 due March 26 at 10am |
| March 31 | 14.4 | Tangent planes | |
| April 2 | Review | ||
| April 7 |
|
Review | HW 8 due |
| April 9 |
|
Chain rule | |
| April 14 |
|
Directional derivatives and the gradient | |
| April 16 |
|
Directional derivatives and the gradient | |
| April 21 |
|
Maxima and minima | HW 9 due |
| April 23 |
|
Maxima and minima | |
| April 28 |
|
Lagrange multipliers | HW 10 due |
| April 30 | Review | HW 11 due Tuesday May 5 |