Math UN1201, Section 001
Lecture: Mondays and Wednesdays from 10:10am to 11:25am in 207 Mathematics Building. All lectures will be held on Zoom at the usual class time, from Wednesday, March 11, through the end of the semester. To access the lecture, go to Courseworks and click on the Zoom tab. The lecture should be scheduled for you there. All lectures will be recorded. You can see past lectures in Courseworks (one is in the Files section, and the others are in the Zoom section, by clicking on the Recordings tab). If you have difficulties accessing Zoom or finding the recorded lectures, please let me know.
Office Hours: Mondays and Wednesdays from 11am to 12:30pm in my office (629 Mathematics building). Due to COVID19, I am holding office hours at these times via Zoom. See Courseworks for the link and Meeting ID to join (there is a single link/ID that will work for my office hours for the rest of the semester), under Announcements.
Teaching Assistants: TAs will hold their office hours in the Help Room. The Help Room will start holding hours via Zoom on Thursday, May 26. A link to their Zoom account will be posted on Courseworks (under Announcements) as soon as it is available. You will be able to break out into rooms to meet with one of our TAs. Some TAs will also hold office hours by appointment on Zoom. That information will also be posted on Courseworks.
Detailed Syllabus: Available here.
Textbook: James Stewart, Calculus: Early Transcendentals, 8th Edition. This is available for purchase at the Columbia bookstore, or you can acquire it as an ebook online.
Prerequisites: Calculus I or equivalent.
Course Website: This website will be the primary source of information for the course. Grades will be posted on CourseWorks.
Course Overview: In Calculus III we will cover the following topics:
Homework: Homework will be assigned weekly and will be due on Wednesdays. There will be 12 homework assignments throughout the semester. These assignments will be due on Wednesdays by 8pm, unless otherwise noted. Update: Starting with HW#8, all homework assignments should be uploaded to Gradescope. You must SCAN your work (consider using a free scanning app for your phone such as iScanner if you do not have a scanner) and upload a single file to Gradescope.
[You should leave your homework in the appropriate Calculus III box outside room 410, on the 4th floor of the math department. Be sure to write your full name (first and last), UNI, and the section number on your homework, and staple all of the pages securely together. Graded homework can be picked up from the appropriate basket outside room 517 (in the Math building). ]
No late homework will be accepted. However, I understand that due to external circumstances, it may not always be possible to complete your assignments on time. To account for this, the lowest two homework scores will be dropped.
You are encouraged to collaborate on and discuss the homework with other students. However, you must independently write up your own solutions.
Homework assignments will posted below at least one week before the due date. All problems are from Stewart. Solutions will be posted here the morning after the assignment is due.
Office Hours: Mondays and Wednesdays from 11am to 12:30pm in my office (629 Mathematics building). Due to COVID19, I am holding office hours at these times via Zoom. See Courseworks for the link and Meeting ID to join (there is a single link/ID that will work for my office hours for the rest of the semester), under Announcements.
Teaching Assistants: TAs will hold their office hours in the Help Room. The Help Room will start holding hours via Zoom on Thursday, May 26. A link to their Zoom account will be posted on Courseworks (under Announcements) as soon as it is available. You will be able to break out into rooms to meet with one of our TAs. Some TAs will also hold office hours by appointment on Zoom. That information will also be posted on Courseworks.
 Mrudul Thatte: Office hours Wednesdays 25pm. Email: mrudul@math.columbia.edu
 Francesco Grechi: Office hours Mondays 35pm. Email: francesco.grechi@columbia.edu
 Sophia Cornell: Office hours Mondays 13pm. Email: sc4127@columbia.edu
Detailed Syllabus: Available here.
Textbook: James Stewart, Calculus: Early Transcendentals, 8th Edition. This is available for purchase at the Columbia bookstore, or you can acquire it as an ebook online.
Prerequisites: Calculus I or equivalent.
Course Website: This website will be the primary source of information for the course. Grades will be posted on CourseWorks.
Course Overview: In Calculus III we will cover the following topics:
 Vectors and the geometry of space (Chapter 12)
 Vector functions (Chapter 13)
 Functions of several variables and partial derivatives (Chapter 14)
Homework: Homework will be assigned weekly and will be due on Wednesdays. There will be 12 homework assignments throughout the semester. These assignments will be due on Wednesdays by 8pm, unless otherwise noted. Update: Starting with HW#8, all homework assignments should be uploaded to Gradescope. You must SCAN your work (consider using a free scanning app for your phone such as iScanner if you do not have a scanner) and upload a single file to Gradescope.
[You should leave your homework in the appropriate Calculus III box outside room 410, on the 4th floor of the math department. Be sure to write your full name (first and last), UNI, and the section number on your homework, and staple all of the pages securely together. Graded homework can be picked up from the appropriate basket outside room 517 (in the Math building). ]
No late homework will be accepted. However, I understand that due to external circumstances, it may not always be possible to complete your assignments on time. To account for this, the lowest two homework scores will be dropped.
You are encouraged to collaborate on and discuss the homework with other students. However, you must independently write up your own solutions.
Homework assignments will posted below at least one week before the due date. All problems are from Stewart. Solutions will be posted here the morning after the assignment is due.
HW#1 


HW#2 


HW#3 

Due Wednesday, 2/12, by 8pm Solutions to HW#3 
HW#4 

Due Wednesday, 2/26, by 8pm Solutions to HW#4 
HW#5 

Due Wednesday, 3/4, by 8pm Solutions to HW#5 
HW#6 

Due Wednesday, 3/11, by 8pm Solutions to HW#6 
HW#7 


HW#8 


HW#9 


HW#10 


HW#11 


HW#12 

Due Wednesday, 5/6, by 8pm Solutions to HW#12 
Exams: There will be 2 inclass midterm exams and 1 final exam.
Midterm#1: Here is a copy of Midterm #1, and here are the solutions.
You may use a nongraphing (nonprogrammable) calculator and can bring a 3x5 index card to the exam (this can just be a sheet of paper cut to be 3 inches by 5 inches, or it can be an actual index card). You can write (or type) anything you want on the index card, but you must put your name on it. I will collect it at the end of the exam to check that it is the appropriate size.
The exam will cover all material through class on Wednesday, 2/12. Precisely, the material on the exam will include everything that we have covered in class as well as the following sections of the textbook: 12.1, 10.3 (p.658662), 15.7 (p.10401041), 15.8 (p.10451046), 12.2, 12.3 (skip "Direction angles and direction cosines"), 12.4 (skip "Torque"), 12.5, 12.6 (drawing traces only  see the worksheet from Homework#4 for sample problems), 10.5 (only what we did in class: given an equation in one of the forms presented in class, you need to know how to graph the curve, and you need to know how to shift the curve  you do not need to know the formal definition or anything about the focus or directrix). [Note: this may be updated after class on Wednesday 2/12 if we do not cover everything planned.].
The following are practice exams to help you prepare for the exam. These are taken from actual exams that have been given in past semesters. Note that every instructor structures the course a little differently, so I have noted questions which you should skip. Also, do not assume that every topic you need to know is covered on one of these exams, and do not assume that these exams will cover every type of question that will be asked. I suggest you take at least one practice exam in an exam setting (75 minutes, one notecard of notes, a nongraphing calculator).
Midterm#2: Here is a copy of the exam, and the solutions. At the end of the solutions, there are comments on common mistakes that I saw while grading.
This will be a takehome exam. The exam will available for download on Courseworks at noon on Thursday, April 2. Your completed exam must be uploaded to Courseworks by 11:59pm on Thursday, April 9 (one minute before midnight on Thursday evening). All times are local to New York City (EST). There is no restriction on how much time you can spend on the exam during that week.
You have three choices for completing and uploading the exam:
The exam will be open book, open notes, and open internet. You can look up anything you'd like using any resource, including online resources. If you can find a solution to the problem online, I ask that you use the same guidelines as for the homework: feel free to read the solution, but close the website before you write up your own solution. You are also allowed to use a nongraphing calculator, but you may NOT use a graphing calculator or any graphing software on your computer. You are not allowed to talk to any one else about the exam while you are taking it. I cannot monitor whether or not you adhere to these guidelinesyou are on the honor system.
The exam will cover all material through class on Wednesday, April 1. Precisely, the material on the exam will include everything we have covered in class as well as the following sections of the textbook: 12.6, 13.1, 13.2, 13.3, 13.4 (skip Kepler's Laws of Planetary Motion), 14.1, and 14.2. [Note that this is subject to change, depending on how much we cover between now and April 1.]
The exam is not cumulative, but much of the material from Midterm#1 is still relevant and will be tested. For example, I could ask you to write the equation of the osculating plane to a curve at a point  for this you need to know how to write the equation of a plane, which is material from the first midterm. However, there will be no questions on the exam that are exclusively about the material from Midterm#1.
The following are practice exams to help you prepare for the exam. These are taken from actual exams that have been given in past semesters. Note that every instructor structures the course a little differently, so I have noted questions which you should skip. Also, do not assume that every topic you need to know is covered on one of these exams, and do not assume that these exams will cover every type of question that will be asked.
Final Exam: The exam will be open book, open notes, and open internet. You can look up anything you'd like using any resource, including online resources. If you can find a solution to the problem online, I ask that you use the same guidelines as for the homework: feel free to read the solution, but close the website before you write up your own solution. You are also allowed to use a nongraphing calculator, but you may NOT use a graphing calculator or any graphing software on your computer. You are not allowed to talk to any one else about the exam while you are taking it. I cannot monitor whether or not you adhere to these guidelinesyou are on the honor system.
The final will cover all material from the class, with approximately half the exam covering material from Midterms #1 and #2, and the other half covering new material (starting with class on Monday, April 6). Precisely, the material on the exam will include everything we have covered in class as well as the following sections of the textbook: 12.1, 10.3 (p.658662), 15.7 (p.10401041), 15.8 (p.10451046), 12.2, 12.3 (skip "Direction angles and direction cosines"), 12.4 (skip "Torque"), 12.5, 12.6, 10.5 (only what we did in class: given an equation in one of the forms presented in class, you need to know how to graph the curve, and you need to know how to shift the curve  you do not need to know the formal definition or anything about the focus or directrix), 13.1, 13.2, 13.3, 13.4 (skip Kepler's Laws of Planetary Motion), 14.1, 14.2, 14.3 (skip "The CobbDouglas Production Function"), 14.4, 14.5, 14.6, 14.7, 14.8, and Appendix H. Note that we did more with optimization using contour maps and gradient vector fields than is covered in 14.7; there are additional notes on these topics in the calendar below.
The following are practice exams to help you prepare for the exam. These are (mostly) taken from actual exams that have been given in past semesters. Do not assume that every topic you need to know is covered on one of these exams, and do not assume that these exams will cover every type of question that will be asked.
Grading Policy: Your grade will be calculated as follows.
UPDATE: The course is now Pass/Fail. I will calculate your numerical grades as described above, and then choose the cutoff for a grade of Pass.
Getting Help: I strongly encourage you to come to my office hours or the TA's office hours if you need help (see schedule above). You may also stop by the Help Room (502 Milstein Center) outside of the TA's office hours and get help. See here for the Help Room schedule. Finally, the math department has a list of graduate students who do private tutoring.
Academic Honesty Policy: Please read the Columbia University Undergraduate Guide to Academic Integrity.
Accessibility and accommodations: Your success in this class is important to me. We all learn differently. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. We can develop strategies to meet both your needs and the requirements of the course.
If you have an accommodation letter, please present it to me as soon as possible. If you think you might need official accommodations, I encourage you to contact the Office of Disability Services for a confidential discussion. Once you register with them, they can provide you with an accommodation letter.
Student wellbeing: Your wellbeing is of primary importance. If you are facing challenges related to your physical or mental health, or obstacles like housing or food insecurity, you are encouraged to contact your advising dean and/or the Student Health Service. If you feel comfortable doing so, please do not hesitate to get in touch with me to discuss ways we can put you in the best possible position to succeed.
Inclusivity: We are part of a learning community and must treat one another with respect at all times. This is especially important with regard to race, religion, nationality, sexual orientation, gender, disability, age, immigration status, parental status, and any other aspect of identity. I am committed to ensuring that this class is a supportive, inclusive, and safe environment for all students, and that all students are treated with dignity and respect. See also the Columbia College Notice of NonDiscrimination.
Tentative Course Schedule: This schedule is subject to change as the semester progresses and will be updated if and when changes are made. In parentheses you will find the section(s) of the book that we will cover that week. I strongly suggest you read the section before coming to class. I do not expect that you will understand everything, but it will better prepare you for the day's lecture. After each class, I strongly suggest you reread the section and, in particular, work through the examples in the text (without first looking at the solution in the book!) and check your work. This is a great way to check that you've understood the material and are ready to start the homework problems for that section.
 Midterm #1: Wednesday, February 19
 Midterm #2: TAKEHOME. The exam will become available for download on Courseworks on 4/2 and will be due by 11:59pm on 4/9.
 Final Exam: Wednesday, May 13, 9am  12pm (This will not be a takehome exam.) Contact me ASAP if the timing of this exam does not work for you in your current timezone.
Midterm#1: Here is a copy of Midterm #1, and here are the solutions.
You may use a nongraphing (nonprogrammable) calculator and can bring a 3x5 index card to the exam (this can just be a sheet of paper cut to be 3 inches by 5 inches, or it can be an actual index card). You can write (or type) anything you want on the index card, but you must put your name on it. I will collect it at the end of the exam to check that it is the appropriate size.
The exam will cover all material through class on Wednesday, 2/12. Precisely, the material on the exam will include everything that we have covered in class as well as the following sections of the textbook: 12.1, 10.3 (p.658662), 15.7 (p.10401041), 15.8 (p.10451046), 12.2, 12.3 (skip "Direction angles and direction cosines"), 12.4 (skip "Torque"), 12.5, 12.6 (drawing traces only  see the worksheet from Homework#4 for sample problems), 10.5 (only what we did in class: given an equation in one of the forms presented in class, you need to know how to graph the curve, and you need to know how to shift the curve  you do not need to know the formal definition or anything about the focus or directrix). [Note: this may be updated after class on Wednesday 2/12 if we do not cover everything planned.].
The following are practice exams to help you prepare for the exam. These are taken from actual exams that have been given in past semesters. Note that every instructor structures the course a little differently, so I have noted questions which you should skip. Also, do not assume that every topic you need to know is covered on one of these exams, and do not assume that these exams will cover every type of question that will be asked. I suggest you take at least one practice exam in an exam setting (75 minutes, one notecard of notes, a nongraphing calculator).
 Practice Exam 1, Solutions: Skip the "Surface" column in problem 5.
 Practice Exam 2, Solutions: Skip problem 6(b)(c)
 Practice Exam 3, Solutions: Skip problem 5(b)(c)
 Practice Exam 4, Solutions: Skip problem 1(b)(c), 4
 Practice Exam 5, Solutions: Skip problem 5(c)
Midterm#2: Here is a copy of the exam, and the solutions. At the end of the solutions, there are comments on common mistakes that I saw while grading.
This will be a takehome exam. The exam will available for download on Courseworks at noon on Thursday, April 2. Your completed exam must be uploaded to Courseworks by 11:59pm on Thursday, April 9 (one minute before midnight on Thursday evening). All times are local to New York City (EST). There is no restriction on how much time you can spend on the exam during that week.
You have three choices for completing and uploading the exam:
 If you have a tablet, you can open the exam and write your solutions directly on the tablet. Then upload the pdf to Courseworks.
 If you have a printer, you can print the exam and do the work directly on the printed exam. Then SCAN your exam and upload to Courseworks. You must upload a single file, so be sure you know how to do that ahead of time if you are taking pictures (I sent out an email with instructions for a mac).
 If you don't have a tablet or printer, then you can read the problems off the screen and do your work on your own paper. Please put only one problem on each page to keep it organized. Then SCAN your pages and upload to Courseworks. You must upload a single file, so be sure you know how to do that ahead of time.
The exam will be open book, open notes, and open internet. You can look up anything you'd like using any resource, including online resources. If you can find a solution to the problem online, I ask that you use the same guidelines as for the homework: feel free to read the solution, but close the website before you write up your own solution. You are also allowed to use a nongraphing calculator, but you may NOT use a graphing calculator or any graphing software on your computer. You are not allowed to talk to any one else about the exam while you are taking it. I cannot monitor whether or not you adhere to these guidelinesyou are on the honor system.
The exam will cover all material through class on Wednesday, April 1. Precisely, the material on the exam will include everything we have covered in class as well as the following sections of the textbook: 12.6, 13.1, 13.2, 13.3, 13.4 (skip Kepler's Laws of Planetary Motion), 14.1, and 14.2. [Note that this is subject to change, depending on how much we cover between now and April 1.]
The exam is not cumulative, but much of the material from Midterm#1 is still relevant and will be tested. For example, I could ask you to write the equation of the osculating plane to a curve at a point  for this you need to know how to write the equation of a plane, which is material from the first midterm. However, there will be no questions on the exam that are exclusively about the material from Midterm#1.
The following are practice exams to help you prepare for the exam. These are taken from actual exams that have been given in past semesters. Note that every instructor structures the course a little differently, so I have noted questions which you should skip. Also, do not assume that every topic you need to know is covered on one of these exams, and do not assume that these exams will cover every type of question that will be asked.
 Practice Exam A, Solutions: Skip #5
 Practice Exam B, Solutions
 Practice Exam C, Solutions: Skip #4c, 5, 8 (Note that #7 is a bit harder than what we covered in class and what will be on our exam, but it's a good idea to give it a try)
 Practice Exam D, Solutions: For #1b, the "TNB frame" is just the 3 vectors T, N, and B; skip #5
 Also complete the following problems from the practice exams for Midterm#1: Practice Exam 1 #5, Practice Exam 2 #6(b)(c), Practice Exam 3 #5(b)(c), Practice Exam 4 #1(c), and Practice Exam 5 #5(c).
Final Exam: The exam will be open book, open notes, and open internet. You can look up anything you'd like using any resource, including online resources. If you can find a solution to the problem online, I ask that you use the same guidelines as for the homework: feel free to read the solution, but close the website before you write up your own solution. You are also allowed to use a nongraphing calculator, but you may NOT use a graphing calculator or any graphing software on your computer. You are not allowed to talk to any one else about the exam while you are taking it. I cannot monitor whether or not you adhere to these guidelinesyou are on the honor system.
The final will cover all material from the class, with approximately half the exam covering material from Midterms #1 and #2, and the other half covering new material (starting with class on Monday, April 6). Precisely, the material on the exam will include everything we have covered in class as well as the following sections of the textbook: 12.1, 10.3 (p.658662), 15.7 (p.10401041), 15.8 (p.10451046), 12.2, 12.3 (skip "Direction angles and direction cosines"), 12.4 (skip "Torque"), 12.5, 12.6, 10.5 (only what we did in class: given an equation in one of the forms presented in class, you need to know how to graph the curve, and you need to know how to shift the curve  you do not need to know the formal definition or anything about the focus or directrix), 13.1, 13.2, 13.3, 13.4 (skip Kepler's Laws of Planetary Motion), 14.1, 14.2, 14.3 (skip "The CobbDouglas Production Function"), 14.4, 14.5, 14.6, 14.7, 14.8, and Appendix H. Note that we did more with optimization using contour maps and gradient vector fields than is covered in 14.7; there are additional notes on these topics in the calendar below.
The following are practice exams to help you prepare for the exam. These are (mostly) taken from actual exams that have been given in past semesters. Do not assume that every topic you need to know is covered on one of these exams, and do not assume that these exams will cover every type of question that will be asked.
 Practice Exam A, Solutions
 Practice Exam B, Solutions
 Practice Exam C, Solutions
 Practice Exam D, Solutions
 Practice Exam E, Solutions
Grading Policy: Your grade will be calculated as follows.
 Homework: 10%
 Midterms: 25% each
 Final: 40%
UPDATE: The course is now Pass/Fail. I will calculate your numerical grades as described above, and then choose the cutoff for a grade of Pass.
Getting Help: I strongly encourage you to come to my office hours or the TA's office hours if you need help (see schedule above). You may also stop by the Help Room (502 Milstein Center) outside of the TA's office hours and get help. See here for the Help Room schedule. Finally, the math department has a list of graduate students who do private tutoring.
Academic Honesty Policy: Please read the Columbia University Undergraduate Guide to Academic Integrity.
Accessibility and accommodations: Your success in this class is important to me. We all learn differently. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. We can develop strategies to meet both your needs and the requirements of the course.
If you have an accommodation letter, please present it to me as soon as possible. If you think you might need official accommodations, I encourage you to contact the Office of Disability Services for a confidential discussion. Once you register with them, they can provide you with an accommodation letter.
Student wellbeing: Your wellbeing is of primary importance. If you are facing challenges related to your physical or mental health, or obstacles like housing or food insecurity, you are encouraged to contact your advising dean and/or the Student Health Service. If you feel comfortable doing so, please do not hesitate to get in touch with me to discuss ways we can put you in the best possible position to succeed.
Inclusivity: We are part of a learning community and must treat one another with respect at all times. This is especially important with regard to race, religion, nationality, sexual orientation, gender, disability, age, immigration status, parental status, and any other aspect of identity. I am committed to ensuring that this class is a supportive, inclusive, and safe environment for all students, and that all students are treated with dignity and respect. See also the Columbia College Notice of NonDiscrimination.
Tentative Course Schedule: This schedule is subject to change as the semester progresses and will be updated if and when changes are made. In parentheses you will find the section(s) of the book that we will cover that week. I strongly suggest you read the section before coming to class. I do not expect that you will understand everything, but it will better prepare you for the day's lecture. After each class, I strongly suggest you reread the section and, in particular, work through the examples in the text (without first looking at the solution in the book!) and check your work. This is a great way to check that you've understood the material and are ready to start the homework problems for that section.
Dates 

1/22 

1/27 & 1/29 

2/3 & 2/5 

2/10 & 2/12 

2/17 & 2/19 

2/24 & 2/26 

3/2 & 3/4 

3/9 & 3/11 

3/23 & 3/25 

3/30 & 4/1 

4/6 & 4/8 

4/13 & 4/15 

4/20 & 4/22 

4/27 & 4/29 

5/4 
