Image of an aspirational calculus student by Ryan Armand.
Instructor: Mike Miller
Time: Tuesday/Thursday 10:10am-11:25am EST
Email: smm2344@columbia.edu
Webpage: here! Homework will be posted to Courseworks
Office: My dining room table
Office hours: There will be two Zoom office hours per week, Monday 4-5PM and Friday 11-12PM (all EST). You can access them in the Zoom Class sessions tab. (I may occasionally be a few minutes late on Thursday, as I teach beforehand, but if so I will stay late, too.)
Teaching assistants: Hyun Woo Park (hwp2108@columbia.edu) holds office hours Wednesday 7-9PM (EST), at the following link: https://columbiauniversity.zoom.us/j/98777483473
Textbook: Calculus: Early Transcendentals, 8th Edition, by James Stewart. See here for more information.
This course does not require the textbook. The textbook is very expensive, and most students do not refer back to it after they finish the calculus sequence. It may be useful to have on-hand to look at in addition to your notes from the course; I recommend either finding an online copy or an older edition of the textbook; very little changes except for the problems.
Problems will be provided on Courseworks weekly, not assigned out of the textbook.
If you would like access to the textbook but are having trouble finding a copy that is either free or reasonably priced, please contact me.
Some material in the class will not be covered in the textbook. There will be notes posted for this material on Courseworks.
Prerequisites: This is the final calculus course, and uses all previous material; thus Calculus I-III or equivalent are prerequisite. See here for more information on what constitutes an equivalent.
Piazza: This term we will be using Piazza for class discussion. The system is designed to get you help fast from me, your TAs, and your classmates. Rather than emailing questions to me or your TAs, you should post your questions on Piazza; we will respond as quickly as we would via email. Sometimes your fellow students will be able to help out more quickly than we can, too.
Homework: There will be a total of 10 homework assignments. Most homework will be assigned on Tuesday and due by the following Tuesday. To submit your homework, you will need to scan it (either with a scanner or with a scanning app on your phone), and upload it on Courseworks; if your homework is not readable, it will not be accepted.
In my experience, homework is not useful as an evaluative tool --- it is important because the only real way to learn and understand math is with practice. To encourage this, homework is graded entirely on completion; the graders will, however, still give weekly comments.
You can work together with other students on the assignments (I encourage it - explaining math helps you understand and remember math), but answers must be written up in your own words, and you must write down who you collaborated with.
Calculus IV is significantly more difficult than your previous Calculus classes. It is very important that you not only do all of the homework, but that eventually you also understand all of the individual problems: how we arrived at the solutions, and what the underlying ideas are. If you approach homework by copying (either from an online resource or a classmate), you will inevitably not understand the material well enough to succeed at this course.
Late homework will not be accepted.
Tests: There will be two midterm exams and one final exam. The exams will not be administered in class; they will be available online for the specified time period.
The tests are open-book, and open-note (in the sense that you can refer to your own notes), but nothing else; you may not collaborate with classmates or use any online tools.
Each midterm is available for a 12-hour period, but should take no longer than 90 minutes to complete and submit. The final is available for a 24-hour period, but should take no longer than 4 hours to complete and submit.
The exams must be submitted on time, before the end of the available period. Late exams will not be accepted. Therefore, you should be sure to start submitting at least an hour before the end of the period, and contact me the moment you run into technical issues.
The midterms only cover the material between the tests; the final is cumulative.
(tentative)
Midterm 1: October 4, (9AM-9PM EST)
Midterm 2: November 15 (9AM-9PM EST)
Final: Thursday Dec 17, all day (12AM-11:59PM EST)
There are no make-up exams, and there are no exceptions to this policy.
Grading: The final course grade is weighted as:
Homework: 15%
Midterm 1: 25%
Midterm 2: 25%
Final: 35%
Your bottom homework score will automatically be dropped.
Students with disabilities: To receive accomodations for exams (or otherwise), you must register with the Disability Services office and present an accomodation letter.
More information is available here.
Getting help: Math, and college, can be hard; anybody who's done a lot of math will tell you that they've struggled. If you're finding that you're struggling with the course, you should get help immediately.
If you're finding yourself overwhelmed but don't get help, then the tide may very well sweep you away and leave you completely lost!
You can come to my office hours (listed on my main page and this syllabus), or to the help room, where there is always TA - your specific TA's help room hours will be posted as well. And as mentioned above, I recommend working with your friends! Lastly, please do not hesitate to reach out to me.
There is information here about tutoring services. I will warn that private tutoring, especially in NYC, can be extremely expensive.
| Date | Book Section(s) | Homework | Notes |
|---|---|---|---|
| 9/8 | Double integrals over rectangles (15.1-2) | ||
| 9/10 | Double integrals over more general regions (15.3) | ||
| 9/15 | Polar coordinates, applications of double integrals (15.4-5) | HW 1 due | |
| 9/17 | More applications, triple integrals (15.5-6) | ||
| 9/22 | Cylindrical and spherical coordinates (15.7-8) | HW 2 due | |
| 9/24 | Spherical coordinates and change of variables (15.8-9) | ||
| 9/29 | Change of variables (15.9) | ||
| 10/1 | Review |
HW 3 due on 10/4 (day of midterm 1) |
|
| 10/6 | Vector fields (16.1) | ||
| 10/8 | Line integrals (16.2) | Drop deadline | |
| 10/13 | FTC for line integrals (16.3) | HW 4 due | |
| 10/15 | Green's theorem (16.4) | ||
| 10/20 | Curl and divergence (16.5) | HW 5 due | |
| 10/22 | Parametric surfaces and surface area (16.6) | ||
| 10/27 | Surface integrals (16.7) | HW 6 due | |
| 10/29 | Stokes' theorem (16.8) | ||
| 11/3 | Election day! (no class) | ||
| 11/5 | Divergence theorem (16.9) | ||
| 11/10 | Stokes' theorem in general (notes) | HW 7 due | |
| 11/12 | Review | ||
| 11/17 | Complex numbers (Appendix H; notes) | ||
| 11/19 | Complex functions (notes) | ||
| 11/24 | Cauchy-Riemann equations (notes) | HW 8 due | |
| 11/26 | Thanksgiving! (no class) | ||
| 12/1 | Cauchy-Riemann equations II (notes) | ||
| 12/3 | Contour integrals (notes) | HW 9 due | |
| 12/8 | Cauchy's thoerem (notes) | ||
| 12/10 | Final review | HW 10 due |
Image of an aspirational calculus student by Ryan Armand.