Math S1202: Calculus IV (Summer 2015, 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: 408 Mathematics
Office Hours: Monday 2 pm to 4 pm, or by appointment

Teaching Assistant: Alvin Peizhe Li
Email: pl2488 "at" columbia.edu
Help Room: 406 Mathematics
Help Room Hours: Wednesday 7 pm to 10 pm, Thursday 7 pm to 10 pm
(For more information about the Help Room, see below.)

Textbook: James Stewart, Calculus: Early Transcendentals, 7th Edition
(More information about the textbook is available here. Please make sure you have access to the corrrect edition when working on the homework problems.)

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 at the end of class every Tuesday and Thursday (except on the second and last days of class). You may either turn them in to me in class, or leave them in the homework dropbox (located outside of 408 Mathematics) 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, 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.


Resources

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 Alvin'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.


Syllabus and Schedule

The following is subject to change as the course moves along.

  Date  Topics  Reading  Homework 
Lecture 1  July 6 (Mon)  Introduction; Double integrals over rectangles  15.1   
Lecture 2  July 7 (Tue)  Iterated integrals  15.2   
Lecture 3  July 8 (Wed)  Double integrals over general regions  15.3   
Lecture 4  July 9 (Thu)  Double integrals in polar coordinates  15.4  Homework 1 (covering 15.1, 15.2) due: Solutions, Extra Solutions 
Lecture 5  July 13 (Mon)  Applications of double integrals; Surface area  15.5, 15.6   
Lecture 6  July 14 (Tue)  Surface area; Triple integrals  15.6, 15.7  Homework 2 (covering 15.3, 15.4) due: Solutions 
Lecture 7  July 15 (Wed)  Triple integrals in cylindrical coordinates  15.8   
Lecture 8  July 16 (Thu)  Triple integrals in spherical coordinates  15.9  Homework 3 (covering 15.5, 15.6, 15.7) due: Solutions, Extra Solutions 
Lecture 9  July 20 (Mon)  Midterm Exam 1 (Solutions   Practice Exam and Solutions 
Lecture 10  July 21 (Tue)  Change of variables in multiple integrals (Notes 15.10  Homework 4 (covering 15.8, 15.9) due: Solutions, Extra Solutions, Solutions to optional problems 
Lecture 11  July 22 (Wed)  Change of variables in multiple integrals; Vector fields  15.10, 16.1   
Lecture 12  July 23 (Thu)  Vector fields; Line integrals  16.1, 16.2  Homework 5 (covering 15.10) due: Solutions, Extra Solutions, Solutions to optional problems 
Lecture 13  July 27 (Mon)  Line integrals (Notes 16.2   
Lecture 14  July 28 (Tue)  The fundamental theorem for line integrals (Notes 16.3   
Lecture 15  July 29 (Wed)  Green's theorem  16.4   
Lecture 16  July 30 (Thu)  Curl and divergence (Notes 16.5  Homework 6 (covering 16.1, 16.2, 16.3) due: Solutions 
Lecture 17  August 3 (Mon)  Midterm Exam 2 (Solutions   Practice Exam and Solutions 
Lecture 18  August 4 (Tue)  Green's theorem in vector forms; Parametric surfaces  16.5, 16.6  Homework 7 (covering 16.4, 16.5) due: Solutions, Solutions to optional problems 
Lecture 19  August 5 (Wed)  Parametric surfaces and their areas; Surface integrals  16.6, 16.7   
Lecture 20  August 6 (Thu)  Surface integrals  16.7  Homework 8 (covering 16.6) due: Solutions 
Lecture 21  August 10 (Mon)  Stokes' theorem  16.8  Homework 9 (covering 16.6, 16.7) due: Solutions, Solutions to optional problems 
Lecture 22  August 11 (Tue)  The divergence theorem  16.9   
Lecture 23  August 12 (Wed)  Review    Homework 10 (covering 16.8, 16.9) due: Solutions, Solutions to optional problems 
Lecture 24  August 13 (Thu)  Final Exam    Practice Exam and Solutions 

Last updated: August 12, 2015.

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