This is the catalog description of the course:

The methods of the course grow out of multivariable calculus and power series. 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 theoretical computer science) relies on results from complex analysis. The essential prerequisites for the course include acquaintance with partial derivatives, line integrals, and power series, and students must know this material fairly well at the beginning of the course to be successful. I'll check on this knowledge with an entrance exam to be handed out on the first day of class.
While some parts of calculus with complex numbers resemble routine elements of calculus 1, there are profound differences, most of which consist of amazing simplifications and apparent coincidences. These actually signal significant ideas! Many of the techniques of complex analysis are now incorporated in such programs as Maple and Mathematica, but any use of these programs will be a rather minor part of the course. My last observation here is a restatement: the material of this course is beautiful and my ambition is to help you discover this beauty.

Text The text is Complex Variables by Stephen D. Fisher, 2^nd edition (1999) published by Dover Books, list price $18.95, ISBN 0-486-40679-2. Amazon sells it for $12.89. I hope to cover essentially all of chapters 1 and 2, most of chapter 3, and a significant part of chapter 4. This is subject to change as I learn more about the preparation, abilities, and interest of the students.
There are certainly hundreds of books on elementary complex analysis. You may want to browse in the Math Library some time (QA 331). Many of the books are very good, and some of them have radically different approaches to the subject. Some people have felt rather strongly about the correct exposition of complex analysis. Here is a discussion of some texts I wrote in fall 2007 before the last time I taught the graduate complex analysis course. Although the material is very well-known and the core material in its present form is almost a century old, authors still feel "the market" needs more books. Almost every year several additional complex analysis texts are published.

Prerequisites As mentioned previously, students must have excellent command of all three semesters of calculus. Any additional experience with partial differential equations and geometric reasoning will be useful. Further background in mathematical physics will also be helpful.

Exams, grades, etc. There will be two in-class exams, which will be announced well in advance, and a final exam on Friday, May 7, from 4 to 7 PM. While exam grades will be the principal source of the course grade, there will also be graded homework and probably some in-class work.

Instructor S. Greenfield
Office: Hill 542; (732) 445-3074;
greenfie@math.rutgers.edu
Office hours: Wednesday 2 to 3:30 and Thursday from 10 to 11:30 and by appointment (e-mail is best for arranging appointments). I will try to answer e-mail promptly and that might be the simplest way to get a rapid response to questions.

Maintained by greenfie@math.rutgers.edu and last modified 1/18/2010.