Day and Time: MTWR 1:00 pm - 2:35 pm
Location: 417 Mathematics
Instructor: Pak-Hin Lee
Email: phlee "at" math.columbia.edu
Office: 408 Mathematics
Office Hours: By appointment
Teaching Assistant: Garrett Kaighn
Email: grk2114 "at" columbia.edu
Help Room: 406 Mathematics
Help Room Hours: Mondays 4 pm to 6 pm, Thursdays 4 pm to 6 pm
(For more information about the Help Room, see below.)
Textbook: James Stewart, Calculus: Early Transcendentals, 8th Edition
(More information about the textbook is available here. Please note that you are not required to have the latest edition, as all homework problems will be typed out completely in the problem sets.)
Course Description: Double and triple integrals. Change of variables. Line and surface integrals. Grad, div, and curl. Vector integral calculus: Green's theorem, divergence theorem, Stokes' theorem. (Chapters 15 and 16 of Stewart.)
Prerequisites: Calculus I, II, III. (Chapters 1 to 14 of Stewart, but 9 and 11 are of little relevance.) Integration techniques are especially important, so brush up on them early on!
Important Dates: For more details, please refer to the summer calendar. This course falls under Session D.
Homework: There will be ten written problem sets, due generally every Tuesday and Friday at 2:35 pm. You may turn in your work in class, leave it in the homework dropbox (located outside of 408 Mathematics), or email a scan to me by 2:35 pm. The majority of the problems will be taken from the textbook, with a few extra problems. Solutions will be posted after the homework is due. No late submission will be accepted, but the lowest homework score will be dropped. Collaboration is encouraged, but you must write up your own solutions independently. You must cite any resources you consult other than the textbook (Google, Wikipedia, Help Room, classmates, etc.); failure to do so is considered plagiarism.
Examinations: There will be two midterms (20% each) and one final (30%) held in class. The topics to be covered in each exam will be announced later. If you have a conflict with any of the exam dates, you must contact me at least one week in advance for alternative arrangements. If you are unable to take the exam because of a medical problem, you must go to the health center and get a note from them, and contact me as soon as you can. The use of books, cell phones, calculators, or notes of any sort is not permitted in any of the exams.
CourseWorks: All course materials (homework, solutions, supplementary notes, etc.) and grades will be posted on CourseWorks. Important announcements will also be emailed via CourseWorks.
Plagiarism: Any work plagiarized from outside sources or between classmates will receive no credit and potentially result in disciplinary actions.
Help Room: The Help Room is open 9 am to 10 pm Mondays through Thursdays, and 9 am to 4 pm on Fridays. The full schedule is available here. Feel free to seek help from any other TA's who are on duty, if you cannot make Garrett's hours.
WebAssign: We will not be using WebAssign. If you want to use it for practice, please refer to the information here.
Disability Services: In order to receive disability-related academic accommodations, students must first be registered with the Disability Services (DS). More information on the DS registration process is available online here. Registered students must present an accommodation letter to the instructor before exam or other accommodations can be provided. Students who have, or think they may have, a disability are invited to contact DS for a confidential discussion.
Tutoring Services: Information is available here.
The following is subject to change as the course moves along.
|Lecture 1||May 22 (Mon)||Introduction; Double integrals over rectangles||15.1||Homework 1 (covering 15.1) due on May 26 (Fri): Solutions|
|Lecture 2||May 23 (Tue)||Double integrals over rectangles||15.1|
|Lecture 3||May 24 (Wed)||Double integrals over general regions||15.2||Homework 2 (covering 15.2, 15.3) due on May 30 (Tue): Solutions|
|Lecture 4||May 25 (Thu)||Double integrals over general regions; Double integrals in polar coordinates||15.2, 15.3|
|No class||May 29 (Mon)||Memorial Day Holiday|
|Lecture 5||May 30 (Tue)||Applications of double integrals||15.4||Homework 3 (covering 15.4, 15.5, 15.6) due on June 2 (Fri): Solutions|
|Lecture 6||May 31 (Wed)||Surface area; Triple integrals||15.5, 15.6|
|Lecture 7||June 1 (Thu)||Triple integrals||15.6|
|Lecture 8||June 2 (Fri)||Triple integrals in cylindrical coordinates; Triple integrals in spherical coordinates||15.7, 15.8||Homework 4 (covering 15.7, 15.8) due on June 6 (Tue): Solutions, Solutions to practice problems|
|Lecture 9||June 5 (Mon)||Midterm Exam 1 (Solutions)||Practice Exam and Solutions|
|Lecture 10||June 6 (Tue)||Change of variables in multiple integrals (Notes)||15.9||Homework 5 (covering 15.9) due on June 9 (Fri): Solutions, Solutions to practice problems|
|Lecture 11||June 7 (Wed)||Change of variables in multiple integrals; Overview of vector calculus||15.9|
|Lecture 12||June 8 (Thu)||Vector fields; Line integrals||16.1, 16.2||Homework 6 (covering 16.1, 16.2) due on June 13 (Tue): Solutions|
|Lecture 13||June 12 (Mon)||Line integrals (Notes)||16.2||Homework 7 (covering 16.2, 16.3) due on June 16 (Fri): Solutions|
|Lecture 14||June 13 (Tue)||The fundamental theorem for line integrals (Notes)||16.3|
|Lecture 15||June 14 (Wed)||Green's theorem||16.4||Homework 8 (covering 16.4, 16.5) due on June 20 (Tue): Solutions, Solutions to practice problems|
|Lecture 16||June 15 (Thu)||Curl and divergence (Notes)||16.5|
|Lecture 17||June 19 (Mon)||Midterm Exam 2 (Solutions)||Review Notes, Practice Exam and Solutions|
|Lecture 18||June 20 (Tue)||Green's theorem in vector forms; Parametric surfaces||16.5, 16.6||Homework 9 (covering 16.6, 16.7) due on June 23 (Fri): Solutions|
|Lecture 19||June 21 (Wed)||Parametric surfaces and their areas; Surface integrals of scalar functions||16.6, 16.7|
|Lecture 20||June 22 (Thu)||Surface integrals of vector fields||16.7|
|Lecture 21||June 26 (Mon)||Stokes' theorem||16.8||Homework 10 (covering 16.8, 16.9) due on June 28 (Wed): Solutions, Solutions to practice problems|
|Lecture 22||June 27 (Tue)||The divergence theorem||16.9|
|Lecture 23||June 28 (Wed)||Review|
|Lecture 24||June 29 (Thu)||Final Exam||Review Notes, Practice Exam and Solutions|
Last updated: June 27, 2017.Back to my homepage