Course background material 

A list of students in the course 
Student information sheet  [Postscript  PDF]  A sheet passed out on the first day of class so that I could learn about the students.  1/20/2002 
The Entrance "exam"  [Postscript  PDF]  The purpose of this assignment is to give insight to students very early in the course about some of the methods to be used. Familiarity with all of the material tested here is necessary for success in this course.  1/20/2002 
Locate some complex numbers  [Postscript  PDF]  A small group exercise to see if people know how to sketch some complex numbers.  1/28/2002 
How to "locate" some complex numbers  [Postscript  PDF]  The answers to the questions shown with the previous link.  1/30/2002 
Draw some pictures  [Postscript  PDF]  Work with expressions in complex notation to sketch some sets in the plane and answer questions about them.  2/4/2002 
How to "draw" some pictures  [Postscript  PDF]  The answers to the questions shown with the previous link.  2/6/2002 
Questions about exp and log  [Postscript  PDF]  Computing some values of log & exp; learning where z's with real log & exp values are.  2/11/2002 
Answers about exp and log  [Postscript  PDF]  The answers to the questions shown with the previous link.  2/13/2002 
Course expectations  [Postscript  PDF]  A detailed discussion of what is expected of the students (and the instructor!) in this course.  2/13/2002 
Review problems for the first exam  [Postscript  PDF]  Review problems. A review session will be held on Tuesday evening, March 5 (time/place to be announced here).  2/27/2002 
A Fourier series example  [Postscript  PDF]  An example to show that simple properties of power series may need some understanding and verification.  3/2/2002 
The first exam  [Postscript  PDF]  A slight misstatement in the second question (the instructor wanted students to compute certain values of sine and cosine) has been "corrected". This mistake should reduce the instructor's grade to 98.  3/6/2002 
Answers to the first exam  [Postscript  PDF]  Student grades ranged from 36 to 94. The mean grade was 72.76 and the median grade was 78. 17 students took the exam.  3/8/2002 
Some integrals  [Postscript  PDF]  An exercise in class to see if people can use Cauchy's Theorem and various Cauchy Integral Formulas. The horrible misstatement in the original version given out in class (which resulted in an improper integral in problem 2!) has been modified.  2/27/2002 
Computing a definite integral  [Postscript  PDF]  A workshop in class on using the Residue Theorem to compute a definite integral.  4/10/2002 
Review problems for the second exam  [Postscript  PDF]  Review problems for the second exam which will be given in class on Monday, 4/22/2002, at the standard class time and place.  4/15/2002 
The bald answers for those review problems  [Postscript  PDF]  Here are numerical answers or brief hints to help people trying to solve the review problems for the second exam.  4/15/2002 
An extended discussion of the answers to the review problems  [Postscript  PDF]  Since we won't be able to have a review session, I have written an extended discussion of the answers to the review problems for the second exam.  4/16/2002 
The second exam  [Postscript  PDF]  The instructor's grade would be 96, since he made some arithmetic errors and gave an inadequate citation in his reasoning to answer one question (based on his own grading "rubric" [his scoring scheme]).  4/28/2002 
Answers to the second exam  [Postscript  PDF]  Student grades ranged from 10 to 99. The mean grade was 75.86 and the median grade was 85. 15 students took the exam.  4/28/2002 
Review problems for the final exam  [Postscript  PDF]  Review sessions will be held in Hill 525 on Wednesday, May 8, from 10 to 11:30 AM and on Thursday, May 9, from 3:30 to 5 PM.  5/2/2002 
The final exam  [Postscript  PDF]  This is a compact form of the final. Extended discussion of the grading of the final is available.  5/13/2002 
01:640:403. Introductory Theory of Functions of a Complex
Variable (3) Prerequisite CALC4 First course in the theory of a complex variable. Cauchy's integral theorem and its applications. Taylor and Laurent expansions, singularities, conformal mapping. 
The methods of the course grow out of multivariable calculus and power series, and the results of the course are both extremely beautiful and enormously applicable. Applications abound in physics and engineering, and any field which studies asymptotics (such as parts of computer science) relies on results from complex analysis. The essential subject matter prerequisites for the course include partial derivatives, line integrals, and power series, and students must be well acquainted with this material at the beginning of the course to be successful in it.
Instructor S. Greenfield, email: greenfie@math.rutgers.edu
Meeting time(s) and place Section 1 of Math 403 meets Monday and Wednesday 4:305:50 (sixth period) in SEC 203, Busch Campus. Students are expected to attend all classes.
Text We changed textbooks this year. We will use Complex Variables by Stephen D. Fisher, 2^{nd} edition (1999) published by Dover Books, list price $16.95 (which should be welcomed by students, since the list price for the text formerly used was more than five times this!).
Syllabus Here is a tentative schedule which will probably need adjusting during the semester. Here is a list of problems students should do as the sections in the book are covered. Students will be required to hand in some problems to be graded.
Office hour(s) I have two offices in Hill Center: Hill 304 and Hill 542. I'm in the Hill 304 office most days, much of the time, as part of my job in charge of the Graduate Program in Mathematics. You can see me there most days. It would be useful if you confirmed a visit by email first, though, to make sure that I'm there and I'm available. I will try to reserve Wednesdays 1:102:30 (fourth period) as an office hour for this course, but I also encourage you to ask questions via email or after almost any class or to make an appointment at a mutually convenient time.
Web pages from the past The instructor has given Math 403 several times before, and records for two previous instances are on the web. Students are cautioned that the text and the order and selection of topics will be different this semester.


Maintained by greenfie@math.rutgers.edu and last modified 5/13/2002.