Day and Time: MTWR 4:30 pm - 6:05 pm
Location: 417 Mathematics
Instructor: Pak-Hin Lee
Email: phlee "at" math.columbia.edu
Office Hours Location: 408 Mathematics (my office) or 406 Mathematics (Help Room)
Office Hours: Tuesdays 3:30 pm to 4:30 pm, Thursdays 3:30 pm to 4:30 pm, or by appointment
Teaching Assistant: Byung Chan Ko
Email: b.ko "at" columbia.edu
Help Room: 406 Mathematics
Help Room Hours: Mondays 10 am to 12 pm, Thursdays 10 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 in your work in class, leave it in the homework dropbox (located outside of 408 Mathematics), or email a scan 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 (30%) held in class. The topics to be covered in each exam will be announced later. The use of books, notes, cell phones, calculators, or other electronic devices is not permitted in any of the exams. If you have a conflict with any of the exam dates, you must contact me at least one week in advance for alternative arrangements. In case of medical or family emergency, you must contact me as soon as possible and provide a note from your doctor or dean.
Plagiarism: Any work plagiarized from outside sources or between classmates will receive no credit and potentially result in disciplinary actions.
Canvas: All course materials (homework, solutions, supplementary notes, etc.) and grades will be posted on Canvas, with links on this webpage. Important announcements will also be sent out via Canvas.
Help Room: The Help Room is open 9 am to 9 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 Byung'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.
Date | Topics | Reading | Notes | Homework | |
Lecture 1 | July 2 (Mon) | Introduction; Double integrals over rectangles | 15.1 | Homework 1 (covering 15.1) due on July 6 (Fri): Solutions over email | |
Lecture 2 | July 3 (Tue) | Double integrals over rectangles | 15.1 | ||
No class | July 4 (Wed) | Independence Day Holiday | |||
Lecture 3 | July 5 (Thu) | Double integrals over general regions | 15.2 | Homework 2 (covering 15.2, 15.3) due on July 10 (Tue): Solutions over email | |
Lecture 4 | July 6 (Fri) | Double integrals over general regions; Double integrals in polar coordinates | 15.2, 15.3 | ||
Lecture 5 | July 9 (Mon) | Applications of double integrals | 15.4 | Homework 3 (covering 15.4, 15.5, 15.6) due on July 13 (Fri): Solutions over email | |
Lecture 6 | July 10 (Tue) | Surface area; Triple integrals | 15.5, 15.6 | ||
Lecture 7 | July 11 (Wed) | Triple integrals | 15.6 | ||
Lecture 8 | July 12 (Thu) | Triple integrals in cylindrical coordinates; Triple integrals in spherical coordinates | 15.7, 15.8 | Notes | Homework 4 (covering 15.7, 15.8) due on July 17 (Tue): Solutions to practice problems, Solutions over email |
Lecture 9 | July 16 (Mon) | Midterm Exam 1 (Solutions) | Announcement; Practice Exam and Solutions | ||
Lecture 10 | July 17 (Tue) | Change of variables in multiple integrals | 15.9 | Notes | Homework 5 (covering 15.9) due on July 20 (Fri): Solutions to practice problems, Solutions over email |
Lecture 11 | July 18 (Wed) | Change of variables in multiple integrals; Overview of vector calculus | 15.9 | ||
Lecture 12 | July 19 (Thu) | Vector fields; Line integrals | 16.1, 16.2 | Homework 6 (covering 16.1, 16.2) due on July 24 (Tue): Solutions over email | |
Lecture 13 | July 23 (Mon) | Line integrals | 16.2 | Notes | Homework 7 (covering 16.2, 16.3) due on July 27 (Fri): Solutions over email |
Lecture 14 | July 24 (Tue) | Line integrals; The fundamental theorem for line integrals | 16.2, 16.3 | Notes | |
Lecture 15 | July 25 (Wed) | Green's theorem | 16.4 | Homework 8 (covering 16.4, 16.5) due on July 31 (Tue): Solutions to practice problems, Solutions over email | |
Lecture 16 | July 26 (Thu) | Curl and divergence | 16.5 | Notes | |
Lecture 17 | July 30 (Mon) | Midterm Exam 2 (Solutions) | Review | Announcement; Practice Exam and Solutions | |
Lecture 18 | July 31 (Tue) | Green's theorem for regions with holes; Green's theorem in vector forms; Parametric surfaces | 16.4, 16.5, 16.6 | Homework 9 (covering 16.6, 16.7) due on August 5 (Sun): Solutions over email | |
Lecture 19 | August 1 (Wed) | Parametric surfaces and their areas | 16.6 | ||
Lecture 20 | August 2 (Thu) | Surface integrals | 16.7 | ||
Lecture 21 | August 6 (Mon) | Stokes' theorem | 16.8 | Homework 10 (covering 16.8, 16.9) due on August 8 (Wed): Solutions to practice problems, Solutions over email | |
Lecture 22 | August 7 (Tue) | The divergence theorem | 16.9 | ||
Lecture 23 | August 8 (Wed) | Review | Announcements: Loose ends and typos, Partial integration in 3 variables | ||
Lecture 24 | August 9 (Thu) | Final Exam | Review | Announcement; Practice Exam and Solutions |
Last updated: August 9, 2018.
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