Image of a successful calculus student by Ryan Armand.
Instructor: Mike Miller
Time: MTWR 6:15pm-7:50pm EST
Email: smm2344@columbia.edu
Webpage: here! homework will also be posted to Courseworks
Office: My dining room table
Office hours: There will be three Zoom office hours per week (all EST):
Mon 2-3PM; Thurs 9-10AM; Fri 3-4PM.
Teaching assistants: Your course has two TAs (who grade homework and hold office hours).
Gabriel Agostini, gsa2117@columbia.edu. Office hours: 8-10AM, at this link.
Christian Serio, cds2185@columbia.edu. Office hours: Thursday 8-9PM, Friday 8-9PM, at this link.
Textbook: Calculus: Early Transcendentals, 8th Edition, by James Stewart. See here for more information.
The textbook is very expensive, and most students do not refer back to it after they finish the calculus sequence. It is much cheaper to purchase an older edition of the textbook; very little changes except for the problems.
However, problems are assigned out of the 8th edition.
You should make sure to get the correct problems either from the library or from a friend. If you have trouble getting access to the book, 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: The only prerequisite course is Calculus I (Math UN1101) or equivalent; 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 six homework assignments. Most homework will be assigned on Thursday and due by the following Monday. 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.
I encourage you to start working before the end of the week --- homework assignments in a summer course are usually about twice as long as assignments during the normal term.
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. The final is available for a 24-hour period, but should take no longer than 4 hours to complete.
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: July 19, (9AM-9PM EST)
Midterm 2: August 2 (9AM-9PM EST)
Final: August 16, 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 |
|---|---|---|---|
| 7/6 | Notation and coordinate systems (12.1, 10.3, 15.7, 15.8) | ||
| 7/7 | Vectors (12.2) | ||
| 7/8 | Dot product (12.3) | ||
| 7/9 | Cross Product (12.4) | ||
| 7/13 | Equations of lines and planes (12.5) | HW 1 due | |
| 7/14 | Parametric curves in the plane and space (10.1, 13.1) | ||
| 7/15 | Derivatives and integrals of vector functions (13.2) | ||
| 7/16 | Acceleration, curvature, and osculating planes (13.3, 13.4) |
|
|
| 7/20 | Functions of several variables (14.1) | HW 2 due | |
| 7/21 | Limits and continuity in multivariable calculus (14.2) | ||
| 7/22 | Partial derivatives (14.3) | ||
| 7/23 | Linear functions and systems of equations (notes) | ||
| 7/27 | Differentiability and linear approximations (14.4) | HW 3 due | |
| 7/28 | Linear transformations and matrix multiplication (notes) | ||
| 7/29 | The multivariable chain rule (14.5, notes) | ||
| 7/30 | Chain rule continued (14.5, notes) | ||
| 8/3 | Directional derivatives and the gradient vector (14.6) | HW 4 due | Drop date |
| 8/4 | More on directional derivatives and the gradient vector (14.6) | ||
| 8/5 | Local maxima, minima, and critical points (14.7) | ||
| 8/6 | Lagrange multipliers (14.8) | ||
| 8/10 | Lagrange multipliers with multiple constraints (14.8) | HW 5 due | |
| 8/11 | Extreme critical points and global maximization (14.7 redux) | ||
| 8/12 | Complex numbers (Appendix H) | ||
| 8/13 | Final review |
HW 6 due on day of final |
Image of a successful calculus student by Ryan Armand.