Math V1202: Calculus IV

Spring 2012

Time and place: TR 1:10--2:15, in 407 Mathematics.
Instructor: Qile Chen (Office 628 Mathematics).
Office hours: Tentatively Wednesday 10:00 -- 12:00 am in 628 Math, or by email appointment.
Email: q_chen@math.columbia.edu
Grader: Shazia Dharssi, she has office hours in Math 406 from 10:30 am - 12:30 pm on Mondays.

This is a fourth semester calculus course. Prerequisites are Calculus I -- III or the equivalent. In particular, you should be familiar with standard techniques of differentiation and integration and with the basic properties of functions of several variables, including partial derivatives.

The course begins with integration of functions of two and three variables. Next, we study the calculus of vector fields: the various differential operators (grad, curl, div) that can be applied to a function or vector field, types of integrals of vector fields (line integrals, surface integrals), and the fundamental theorems (Green, Stokes, divergence or Gauss) relating differentiation and integration of vector fields. If time allows, we will give an introduction to the theory of functions of a complex variable.

Textbook: James Stewart, Calculus: Early Transcendentals, seventh edition, Thomson Brooks Cole, 2012. ISBN 9781111649579.


The homework assignments and due days will be posted here: [ Homework ]


Homework: There will be weekly problem sets, due at the beginning of class on every Tuesday. The first problem set will be due on Tuesday, January 24. The Midterm and final exams will be closely related to the homework assignments. You should understand how to do every problem correctly. Collaboration and discussion with your classmates is encouraged, but you must write up assignments individually.

Graded homework will be available on the table outside 625 Mathematics. Late homework will not be accepted.

Exams: There will be two 75-minute midterm exams and a final. The dates for the midterms are as follows:

  • First Midterm, Tuesday, February 28, in class
  • Second Exam, Thursday, April 12, in class
  • Final: Tuesday, May 08, 1:10 -- 3:10 pm at MAT 407. This is scheduled by the university. It must be taken at the scheduled time.
If you have two final examinations scheduled at the same time, it is the responsibility of the other department to provide an alternate exam. Examinations will not be rescheduled because of travel arrangements -- it is your responsibility to schedule travel appropriately. Makeup midterms will be given only under exceptional circumstances and you will need a note from a doctor or a dean.

Grading: The final course grade will be determined by:

Homework: 10%
Midterm exams each: 20%
Final exam: 50%.


Help: Besides my office hours, help is also available without appointment in the Mathematics Help Room (406 Mathematics) whenever it is open.The Help Room is staffed both by faculty and teaching assistants, who will be able to help you with questions related to this course.

Useful links for the schedule:

Master University Examination Schedule
University Academic Calendar


Homework:

The assignments will be posted before each Tuesday.

Date
Reading
Homework
  Jan. 17, 19   15.1-15.3: Double integrals.  HW#1 due Jan. 24: 
 15.2: 4, 5, 17, 20, 26
  Jan. 24, 26   15.4-15.5: Polar coordinates & Applications of double integrals  HW#2 due Jan. 31: 
 15.3: 5, 6, 17, 26, 48
 15.4: 6, 16, 26
 15.5: 6, 24, 29
  Jan. 31, Feb. 6   15.6, 15.7, 15.8: surface area, triple integral, cylindrical coordinates  HW#3 due Feb. 7: 
 15.6: 2, 11, 23
 15.7: 5, 6, 18, 20, 21, 34
 15.8: 20, 24, 25
  Feb. 7, 9   15.9, 15.10: Spherical coordinates, change of variables  HW#4 due Feb. 14: 
 15.9: 8, 10, 22, 26, 29
 15.10: 4, 8, 16, 24
  Feb. 14, 16   16.1, 16.2 Vector fields, line integrals  HW#5 due Feb. 21: 
 16.1: 21, 22, 23, 24
 16.2: 2, 4, 8, 22, 28, 36, 40
  Feb. 21, 23   16.3 The Fundamental theorem for line integrals, Review  HW#6 due Mar. 6: 
 16.3: 4, 6, 8, 12, 14, 18, 24
  Feb. 28, Mar. 1   1st mid-term (15.1 - 16.2), 16.4 Green's theorem  HW#7 due Mar. 6 : 
 16.4: 2, 6, 10, 14, 18 (No home work due on Feb 28)
  Mar. 6, 8   16.5 & 16.6  HW#8 due Mar. 20 : 
 16.5: 4, 6, 14, 16, 18
 16.6: 22, 34, 36, 40, 48
  Mar. 20, 22   16.7 & 16.8  HW#9 due Mar. 27 : 
 16.7: 10, 14, 20, 40, 44
 16.8: 2, 4, 6, 10, 16
  Mar. 27, 29   16.9 & Review  HW#10 due Apr. 3 : 
 16.9: 2, 4, 12, 14, 18, 24, 26
  Apr. 3, 5   Complex Functions I  HW#11 due Apr. 10 : 
 Problems in : Complex Functions I
  Apr. 10, 12   Complex Functions II & Second Midterm (Chapter 16 & Complex Functions I)  HW#12 due Apr. 24 : 
 Problems in : Complex Functions II
  Apr. 17, 19   Complex Functions III  HW#13 (do not submit) : 
 Problems in : Complex Functions III
 Homework Problems in Complex Functions III will be explained on Apr. 24 during the class. This homework will not be graded.
  Apr. 24, 26   Review  No Homework  
  May. 8   Final Exam (Chapter 15, 16, and Complex Functions I, II, III)   1:10 -- 3:10 pm at MAT 407  

The template of this Syllabus is copied from http://www.math.columbia.edu/department/syllabi/CalcIVsyllabus.html