Image of a successful calculus student by Ryan Armand.
Instructor: Mike Miller Eismeier
Email: smm2344@columbia.edu
Classroom/time: ???, T/Th 1:10-2:25PM
Webpage: here! homework will also be posted to Courseworks
Office: Math 427
Office hours: TBA.
Teaching assistants: Your course will have undergraduate TAs (who grade homework and hold help hours), and one graduate TA (who grades exams, holds help hours, and answers emails).
You may attend any of their help hours. You may (and should!) email your graduate TA with any questions, but not your undergraduate TAs.
Your TAs will be announced at around the beginning of the second week of classes.
Recordings: So long as it is technically possible, I will be posting recordings of each lecture on CourseWorks.
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, or online. 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. These won't appear until about 1/3 into the course, but once they do, they never go away.
Homework: 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 on Courseworks. 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.
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: October 7
Midterm 2: November 16
(tentative) Final: December 21, 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.
Project: In lieu of a final exam, you and 1-3 other students may write an expository paper on a topic related to Calculus III, and explain it with some examples (which may be calculations like on your homework assignments but more involved, or they may be computer demonstrations such as in Mathematica or Desmos; what form this takes will depend on your project).
In the week after Midterm 1, you will be able to opt in or out of a final project. If you opt in, you will have periodic deadlines until the end of the semester, including choosing a topic, outlining your paper, and sending me a draft for comments. I try to give very detailed and explicit feedback.
Grading: The final course grade is weighted as:
Homework: 15%
Midterm 1: 20%
Midterm 2: 25%
Final: 40%
Your bottom two 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 |
|---|---|---|---|
| 9/9 | Notation and coordinate systems (12.1, 10.3, 15.7) | ||
| 9/14 | Vectors (12.2) | ||
| 9/16 | Dot product (12.3) | ||
| 9/21 | Cross Product (12.4) | HW1 due; | |
| 9/23 | Equations of lines and planes (12.5) | ||
| 9/28 | Parametric curves in the plane and space (10.1, 13.1) | HW2 due | |
| 9/30 | Derivatives and integrals of vector functions (13.2) | ||
| 10/5 | Review | HW3 due; | |
| 10/7 | Midterm 1 | Covers all material to this point | |
| 10/12 | Functions of several variables (14.1) | Drop date: Barnard, CC, GS, SPS | |
| 10/14 | Limits and continuity in multivariable calculus (14.2) | ||
| 10/19 | Partial derivatives (14.3) | HW 4 due | |
| 10/21 | Linear algebra (my notes) | ||
| 10/26 | Differentiability and linear approximation (14.4, my notes) | HW5 due | |
| 10/28 | Linear transformations and matrix multiplication (my notes) | ||
| 11/2 | Academic holiday | ||
| 11/4 | The multivariable chain rule (14.5, notes) | HW6 due | |
| 11/9 | Chain rule continuned (14.5, notes) | ||
| 11/11 | Review | HW 7 due (~36h later, on Friday 11/12 at midnight) | |
| 11/16 | Midterm 2 | ||
| 11/18 | Directional derivatives and the gradient vector (14.6) | P/F deadline. Drop deadline: GSAPP; SEAS. | |
| 11/23 | Directional derivatives and gradients cont'd (14.6) |
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| 11/25 | Academic holiday | ||
| 11/30 | Local maxima, minima, and critical points (14.7) | HW 8 due | |
| 12/2 | Lagrange multipliers (14.8) | ||
| 12/7 | Lagrange multipliers with multiple constraints (14.8) | HW 9 due | |
| 12/9 | Extreme critical points and global maximization (14.7 redux) | ||
| [TBA] | Review session | HW10 due on Monday 12/13 at midnight |
Image of a successful calculus student by Ryan Armand.