Math V1202: Calculus IVSpring 2012Instructor: 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 75minute midterm exams and a final. The dates for the midterms are as follows:
Grading: The final course grade will be determined by: Homework: 10%
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
Homework: 
The assignments will be posted before each Tuesday. 



Jan. 17, 19  15.115.3: Double integrals. 
HW#1 due Jan. 24: 15.2: 4, 5, 17, 20, 26 
Jan. 24, 26  15.415.5: 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 midterm (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