Image of a successful calculus student by Ryan Armand.
Instructor: Mike Miller Eismeier
Email: smm2344@columbia.edu
Classroom/time: Math 312, T/Th 2:40-3:55PM
Webpage: here! homework will be posted to the Files tab on Courseworks
Office: Math 427
Office hours: TBA. I will hold three office hours per week, one on zoom.
Teaching assistants: Your course will have three undergraduate TAs (who grade homework and hold help hours), and two graduate TA (who grade exams, holds help hours, answers emails, and grade concept questions).
You may attend any of their help hours. You may (and should!) email your graduate TA with any questions, but not your undergraduate TAs.
Graduate TAs: Yash Deshmukh (deshmukh@math.columbia.edu), Shalin Parekh (sp3577@columbia.edu)
Undergraduate TAs: Maya Raghavan, Sangeetha Bharath, Gurnoor Virdi
Recordings: So long as it is technically possible, I will be posting high-quality recordings of each lecture on CourseWorks. (The quality last semester was subpar.)
Illness: If you feel at all ill, please do not come to class, and instead join over Zoom. I don't want to get sick and neither do your classmates, and a single lecture is hardly important enough to risk that. I am very hopeful that the recordings will be sufficient for you to catch up. You do not need to let me know if you're missing class, there's certainly no attendance policy. If you are ill during an exam week, get in touch with me and we will make alternate arrangements.
Textbook (not mandatory but very strongly suggested): Calculus: Early Transcendentals, 8th Edition, by James Stewart. See here for more information.
We will hop around the textbook a lot and my lectures will not follow it. However, the most successful students read the textbook as well as my lecture notes. Because I am writing the assignments this semester, the textbook is useful but not mandatory.
New editions of the textbook are 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.
If you are not sure how to find a cheap or free copy, please get in touch with me: I want to help.
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. I will take for granted that you remember all of the material of that couse: how to compute derivatives and limits (and quickly), and that you have an intuitive sense of what a limit is.
Homework: I will post PDFs with around 10-15 problems each week. Around 20% of these will be concept questions, where you need to carefully explain your logic. (Understanding the concepts is more important than any computation.)
Most homework will be assigned on Tuesday and due by the beginning of class the following Tuesday. To submit your homework, you need to upload it to Courseworks or Gradescope (TBA which we use). You have two options: write neatly, and scan using a good scanner (or scanner app on your phone / tablet), or learn to TeX your homework. If your homework is not readable, it will not be accepted.
The homework will be posted on Courseworks. 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.
Homework will be graded as follows. One random concept question will be graded (and you will receive comments), amounting to 20% of the grade on a homework assignment. A selection of around 5 random problems will be graded (with fewer comments), amounting to 50% of the grade. And the remaining 30% is awarded for fully completing the assignment, with partial credit for partial completion.
Late homework will not be accepted.
Tests: It is currently expected that we will have in-person exams. I will update this immediately if our course modality is expected to change. There will be two 70-minute midterm exams and a 170-minute final exam. The midterms only cover the material between the tests; the final is cumulative. I aim to get results back within a day or two, and before any major deadlines.
Midterm 1: February 17
Midterm 2: March 24
(tentative) Final: May 12, 1:10-4PM
The test dates cannot be moved. You must plan your travel well in advance to not conflict with exam dates. There are no make-up exams, and there are no exceptions to this policy. In case of emergency, please contact me as soon as possible: the later you get in touch, the less likely I will be able to help.
The tentative final date almost never changes.
Grading: The final course grade is weighted as:
Homework: 15%
Midterm 1: 20%
Midterm 2: 25%
Final: 40%
Your two bottom homework scores will automatically be dropped.
Students with disabilities: In order to receive disability-related academic accommodations for this course, students must first be registered with their school Disability Services (DS) office. Detailed information is available online for both the Columbia and Barnard registration processes.
Refer to the appropriate website for information regarding deadlines, disability documentation requirements, and drop-in hours(Columbia)/intake session (Barnard).
For this course, students are not required to have testing forms or accommodation letters signed by faculty. However, students must do the following:
· The Instructor section of the form has already been completed and does not need to be signed by the professor.
· The student must complete the Student section of the form and submit the form to Disability Services.
· Master forms are available in the Disability Services office or online: https://health.columbia.edu/
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!
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 |
|---|---|---|---|
| 1/18 | Points, coordinates, and vectors (12.1 and 12.2) | ||
| 1/20 | Vector arithmetic and geometry (12.2) | ||
| 1/25 | Parametric curves and moving particles (10.1, 13.1) | HW1 due | |
| 1/27 | Derivatives and velocity (10.2, 13.2) | ||
| 2/1 | Functions of multiple variables (14.1) | HW2 due | |
| 2/3 | Transformations and changes of variables (15.9, my notes) | ||
| 2/8 | Multivariable limits 1 (14.2) | HW3 due | |
| 2/10 | Multivariable limits 2 (14.2) | ||
| 2/15 | Partial derivatives (14.3) | HW4 due (great review for midterm) | |
| 2/17 | Midterm 1 | Covers all material through 2/10 | |
| 2/22 | Linear functions and matrices (my notes) | HW5 due | Drop date: Barnard, CC, GS, SPS |
| 2/24 | Total derivatives and linear approximation (14.4, my notes) | ||
| 3/1 | Multivariable differentiability (14.4, my notes) | HW6 due | |
| 3/3 | Composition and matrix multiplication (my notes) | ||
| 3/8 | Multivariable chain rule 1 (my notes, 14.5) | HW7 due | |
| 3/10 | Chain rule and directional derivatives (14.5, 14.6) | ||
| 3/15 | Academic holiday | ||
| 3/17 | Academic holiday | ||
| 3/22 | Dot products and gradient vectors (12.3, 14.6) | HW8 due (again: good practice for MT2) | |
| 3/24 | Midterm 2 | Covers 2/15-3/10. | |
| 3/29 | Determinants and cross products (12.4) | ||
| 3/31 | Lines and planes 1 (12.5) | ||
| 4/5 | Lines and planes 2 (12.5) | HW9 due (longer) | |
| 4/7 | Surfaces: parameterizations and constraints (14.1, 16.6) | ||
| 4/12 | Tangent lines and tangent planes 1 (13.2, 14.4) | HW10 due | |
| 4/14 | Tangent planes 2 (14.4, 14.6) | ||
| 4/19 | Critical points and local maxima (14.7) | HW11 due | |
| 4/21 | Lagrange multipliers (14.8) | ||
| 4/26 | Absolute maxima: the compactness principle (14.7) | ||
| 4/28 | Multiple constraints, and domains with corners (14.7, 14.8) | HW12 due on Monday 5/2 at midnight |
Image of a successful calculus student by Ryan Armand.