| Course background material |
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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, e-mail: greenfie@math.rutgers.edu
Meeting time(s) and place Section 1 of Math 403 meets Monday and Wednesday 4:30-5:50 (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, 2nd 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 e-mail first, though, to make sure that I'm there and I'm available. I will try to reserve Wednesdays 1:10-2:30 (fourth period) as an office hour for this course, but I also encourage you to ask questions via e-mail 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.
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Maintained by greenfie@math.rutgers.edu and last modified 5/13/2002.