Calculus III (Math UN1201)

Instructor: Mike Miller
Classroom/time: Math 312, T/Th 1:10-2:25PM
Webpage: here! homework will also be posted to Courseworks
Office: Math 427
Office hours: Monday, Thursday, 12-1PM and Friday 9-10AM

Teaching assistants: Your course has three 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 graduate TA is Song Yu, His help room hours are Wednesday 9-12.

Your undergraduate TAs are Jonnathan Baquero, Maria Thompson, and Lekha Yesantharao. Their help room hours are Monday 1-3 (JB), Monday/Tuesday 9-10 (MT), and Thursday 9-11 (LY) respectively.

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.

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. 

Homework: Most homework will be assigned on Tuesday and due by the beginning of class the following Tuesday. Your homework must be dropped off in drop-boxes on the 4th floor of the math building; it will not be accepted electronically.
The homework will be posted here and on Courseware. 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.

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Homework 7

Homework 8

Homework 9

Homework 10

Homework 11


Tests: 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.

Midterm 1: February 20
(tentative) Final: Tuesday May 12, 1:10-4:00PM

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.


The tentative final date almost never changes. The structure of the final will be announced later in the course, but will be open book.

Grading: The final course grade is weighted as:

Homework: 20%
Midterm 1: 30%
Final: 50%

Your bottom three 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:


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.

Tentative schedule (as of 3/12)

Date Book Section(s) Homework Notes
1/21 Notation and coordinate systems (12.1, 10.3, 15.7)    
1/23 Vectors (12.2)    
1/28 Dot product (12.3) HW1 due  
1/30 Cross Product (12.4)    
2/4 Equations of lines and planes (12.5) HW 2 due  
2/6 Parametric curves in the plane and space (10.1, 13.1)    
2/11 Derivatives and integrals of vector functions (13.2) HW 3 due  
2/13 Acceleration, curvature, and osculating planes (13.3, 13.4)    
2/18 Review HW 4 due  
2/20 Midterm 1   Covers all material to this point
2/25 Functions of several variables (14.1)   Drop date: Barnard, CC, GS, SPS
2/27 Limits and continuity in multivariable calculus (14.2)    
3/3 Partial derivatives (14.3) HW 5 due  
3/5 Linear algebra (notes)    
3/10 CANCELED     
3/12 Differentiability and linear approximation (14.4, notes)    
3/17 Academic holiday HW 6 due (Mon 3/16)  
3/19 Academic holiday    
3/24 CANCELED    
3/26 Tangent planes and linear approximations (14.4)    
3/31 Linear algebra (notes)

HW 7 due

4/2 The multivariable chain rule (notes)    
4/7 The multivariable chain rule continued (14.5)


4/9 Directional derivatives and the gradient vector (14.6)    
4/14 Directional derivatives and the gradient vector continued (14.6) HW 8 due  
4/16 Maxima and minima (14.7)    
4/21 Lagrange multipliers (14.8) HW 9 due  
4/23 Lagrange multipliers continued (14.8)    
4/28 Maximization: global behavior (14.7) HW10 due  
4/30 Review HW 11 due following Tues, 5/5  

Image of a successful calculus student by Ryan Armand.

Homework 9