Math S1202: Calculus IV (Summer 2018, Section 2)

Logistics

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.


Grading

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.


Resources

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.


Syllabus and Schedule

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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