Day and Time: MTWR 4:30 pm - 6:05 pm
Location: 417 Mathematics
Instructor: Pak-Hin Lee
Email: phlee "at" math.columbia.edu
Office: 408 Mathematics
Office Hours: By appointment
Teaching Assistant: João Guerreiro
Email: guerreiro "at" math.columbia.edu
Help Room: 406 Mathematics
Help Room Hours: Monday 9 am to 12 pm, Wednesday 9 am to 12 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 Q.
Homework: There will be ten written problem sets, due generally every Tuesday and Friday at 6:15 pm. You may turn them in to me in class, leave them in the homework dropbox (located outside of 408 Mathematics), or email a scan of your work to me by 6:15 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 (40%) 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 Monday to Friday. The full schedule is available here. Feel free to seek help from any other TA's who are on duty, if you cannot make João's hours.
WebAssign: We will not be using WebAssign. If you want to use it for practice, please refer 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.
Date | Topics | Reading | Homework | |
Lecture 1 | July 5 (Tue) | Introduction; Double integrals over rectangles | 15.1 | Homework 1 (covering 15.1) due on July 8 (Fri): Solutions |
Lecture 2 | July 6 (Wed) | Double integrals over rectangles | 15.1 | |
Lecture 3 | July 7 (Thu) | Double integrals over general regions | 15.2 | Homework 2 (covering 15.2, 15.3) due on July 12 (Tue): Solutions |
Lecture 4 | July 8 (Fri) | Double integrals in polar coordinates | 15.3 | |
Lecture 5 | July 11 (Mon) | Applications of double integrals; Surface area | 15.4, 15.5 | Homework 3 (covering 15.4, 15.5, 15.6) due on July 15 (Fri): Solutions |
Lecture 6 | July 12 (Tue) | Surface area; Triple integrals | 15.5, 15.6 | |
Lecture 7 | July 13 (Wed) | Triple integrals; Triple integrals in cylindrical coordinates | 15.6, 15.7 | Homework 4 (covering 15.7, 15.8) due on July 19 (Tue): Solutions, Solutions to practice problems |
Lecture 8 | July 14 (Thu) | Triple integrals in spherical coordinates | 15.8 | |
Lecture 9 | July 18 (Mon) | Midterm Exam 1 (Solutions) | Practice Exam and Solutions | |
Lecture 10 | July 19 (Tue) | Change of variables in multiple integrals (Notes) | 15.9 | Homework 5 (covering 15.9) due on July 22 (Fri): Solutions, Solutions to practice problems |
Lecture 11 | July 20 (Wed) | Change of variables in multiple integrals; Overview of vector calculus; Vector fields | 15.9, 16.1 | Homework 6 (covering 16.1, 16.2) due on July 26 (Tue): Solutions |
Lecture 12 | July 21 (Thu) | Line integrals | 16.2 | |
Lecture 13 | July 25 (Mon) | Line integrals (Notes) | 16.2 | Homework 7 (covering 16.2, 16.3) due on July 29 (Fri): Solutions |
Lecture 14 | July 26 (Tue) | The fundamental theorem for line integrals (Notes) | 16.3 | |
Lecture 15 | July 27 (Wed) | Green's theorem | 16.4 | Homework 8 (covering 16.4, 16.5) due on August 2 (Tue): Solutions, Solutions to practice problems |
Lecture 16 | July 28 (Thu) | Curl and divergence (Notes) | 16.5 | |
Lecture 17 | August 1 (Mon) | Midterm Exam 2 (Solutions) | Practice Exam and Solutions | |
Lecture 18 | August 2 (Tue) | Green's theorem in vector forms; Parametric surfaces | 16.5, 16.6 | Homework 9 (covering 16.6, 16.7) due on August 5 (Fri): Solutions |
Lecture 19 | August 3 (Wed) | Parametric surfaces and their areas; Surface integrals | 16.6, 16.7 | |
Lecture 20 | August 4 (Thu) | Surface integrals | 16.7 | |
Lecture 21 | August 8 (Mon) | Stokes' theorem | 16.8 | Homework 10 (covering 16.8, 16.9) due on August 10 (Wed): Solutions, Solutions to practice problems |
Lecture 22 | August 9 (Tue) | The divergence theorem | 16.9 | |
Lecture 23 | August 10 (Wed) | Review | ||
Lecture 24 | August 11 (Thu) | Final Exam | Practice Exam and Solutions |
Last updated: August 10, 2016.
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