The pdf syllabus contains a slightly more expanded version of the following.

It is not mandatory but strongly recommended to read the textbook, as the course will closely follow it. On the other hand, I will post the lecture notes I wrote.

It is indeed very helpful to read the textbook for a better understanding of the material. On the other hand, the same content can be found in an older edition of the textbook. If you choose to use an older version of the textbook, be mindful that the section/exercise numbers are often different.

- Vectors and the geometry of space (Section 10.5 and Chapter 12)

- Vector functions (Chapter 13)

- Functions of several variables and partial derivatives (Chapter 14)

If you are wondering if this is the right class for you, there are alternatives to this course, like MATH UN1205 (Accelerated Multivariable Calculus; covers Chapters 12-16 of Stewart), MATH UN1207 (Honors Math A; proof-based), and APMA 2000 (Multivariable Calculus; for SEAS students).

- Homework, 25%

- Midterm 1, 20%

- Midterm 2, 25%

- Final, 30%

Also, there will be several opportunities to obtain supplementary bonus grades, up to 11% of the total grade.

- Weekly feedback surveys, 3%

- Optional homework assignments, 4%

- Individual project, 4%

Although attendance is not part of the grade, per University policy, students are expected to attend all classes.

The letter grade will be decided based on the sum of everything (Homework + Midterms + Final + Supplementary activities), maxed out at 100%, and will not be curved. The only exception is A+, which I will decide in a relative fashion based on the sum of everything (out of 111%).

We also offer you to configure your own alternative grading scheme for the major grading components. Your final grade will be the highest of the two (one using the default grading scheme, one using your own alternative grading scheme). Your grading scheme should satisfy the following conditions.

- The sum of the following four weights must be 100%, and the weights should be in the following range.

- Homework, 10-30%

- Midterm 1, 10-25%

- Midterm 2, 15-30%

- Final, 20-45%

Please email the Head TA (Taeseok Lee, taeseok.lee@columbia.edu) your alternative grading scheme by Friday, September 27.

Homework

Homework will be out every Tuesday, except exam weeks, and due most of the time on the following Tuesday by 11:59 PM.

There will be 11 homework assignments. Each homework assignment is worth 1/9 of the total homework grade, so you can miss up to two problem sets and still obtain a full grade on homework.

Please submit your homework on Gradescope, as a pdf file if possible, either typed or handwritten clearly and legibly. You are encouraged to collaborate on homework, but you must write up your own solutions in your words. Please cite any references used.

Except in extraordinary circumstances, late homework will not be accepted, to avoid placing an undue burden on graders.

Tests

There will be two in-class midterms (75 minutes) and a final exam (170 minutes).

Midterm 1: Oct 1 (Tue), in-class

Midterm 2: Oct 31 (Thu), in-class

Projected Final Exam Date (To be confirmed in November)

Section 005 (TR 11:40AM-12:55PM): Dec 19 (Thu), 4:10-7PM

Section 006 (TR 1:10-2:25PM): Dec 17 (Tue), 1:10-4PM

If you think you cannot make one of the two in-class midterms, make-up exams may be arranged within 2 days of the originally scheduled dates. Please let me know as soon as possible.

Unlike midterms, the Final exam cannot be moved at the instructor's discretion. If you have foreseeable difficulty in accommodating the current schedule of the Finals, please consult your advisor.

You may bring your own formula sheet during the exams, no longer than two sides of a single A4 paper. For the final, you can bring up to three sheets of A4 paper (max 6 sides in total). No electronic device (e.g. calculators) can be used during the exam.

Supplementary activities

Weekly feedback surveys

There will be a short survey posted every week regarding the past week's course content. I will ask questions like "was X confusing to you?" etc. You can get up to 3% of the total grade as a bonus (namely, not affecting the main four grading components) if you participate in the surveys. More precisely, you will get the full bonus grade of 3% if you participate in 6 or more surveys.

Optional homework assignments

There will be 2 optional homework assignments in addition to the regular weekly ones, which will contain a little more adventurous problems.

Individual project

This individual project aims to explore how to use calculus beyond what we have learned (in mathematics, science, engineering, economics, etc.).

After Midterm 2, I will post a list of problems you can choose for the extra assignment. The problems will be quite different from the regular homework assignments. For example, many problems will have several sub-problems to build up for a conclusion. Some problems may even ask you to write a short essay!

You can choose a topic of your interest to work on this project. This will be due on 12/9 (Mon).

Feel free to suggest the topics of your interest! As a mathematician, I certainly do not know all the applications of calculus in other disciplines. Please email me if you are interested. We can talk about what might be of interest to you over the semester.

Please note that the schedule is subject to change, especially during the first few weeks of the semester.

Date	Topic	Textbook	Homework
-	Review of prerequisites | Exercise solutions, 1-7, 8-14, 15-21	Calculus I, Precalculus
9/3 (Tue)	Overview, coordinate systems | Exercises	12.1, 10.3, 15.7, 15.8
9/5 (Thu)	Vectors | Exercises	12.2
9/10 (Tue)	Dot product + Trigonometry review | Exercises | Dot product and cosine	12.3	HW 1 due
9/12 (Thu)	Cross product | Exercises | Cross product and sine | Parallelepiped	12.4
9/17 (Tue)	Lines and curves | Exercises	10.1, 12.5	HW 2 due
9/19 (Thu)	Planes and surfaces | Exercises | Distance between a point and a plane	12.5
9/24 (Tue)	Planes and surfaces, continued | Exercises	12.5
9/26 (Thu)	Review	-	HW 3 due
10/1 (Tue)	In-class Midterm 1 (No class)	-
10/3 (Thu)	Derivatives and integrals of vector functions | Exercises	13.2
10/8 (Tue)	Calculus for curves and motions | Exercises	10.2, 13.3, 13.4	HW 4 due
10/10 (Thu)	Functions of several variables | Exercises	14.1
10/15 (Tue)	Limits and continuity in several variables | Exercises	14.2	HW 5 due
10/17 (Thu)	Partial derivatives | Exercises	14.3
10/22 (Tue)	Tangent planes and approximations | Exercises	14.4	HW 6 due
10/24 (Thu)	Chain rule | Exercises	14.5
10/29 (Tue)	Review	-	HW 7 due
10/31 (Thu)	In-class Midterm 2 (No class)	-
11/5 (Tue)	Election Day (University Holiday; no class)	-
11/7 (Thu)	Directional derivatives and the gradient | Exercises	14.6
11/12 (Tue)	Local maxima and minima, critical points | Exercises	14.7	HW 8 due
11/14 (Thu)	Global maxima and minima I: Lagrange multipliers | Exercises	-
11/19 (Tue)	Global maxima and minima II: Lagrange multipliers, multiple equalities | Exercises	-	HW 9 due
11/21 (Thu)	Global maxima and minima III: Fun with boundaries | Exercises	-
11/26 (Tue)	Global minima of coercive functions | Exercises	-	HW 10 due
11/28 (Thu)	Thanksgiving (University Holiday; no class)	-
12/3 (Tue)	Review of Global maxima and minima	-
12/5 (Thu)	Review	-	HW 11 due