General information about Math 403:02, spring 2005

This is the catalog description of the course:

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. 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 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. 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 will be a rather minor part of the course. My final observation 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, 2nd edition (1999) published by Dover Books, list price $18.95, ISBN 0-486-40679-2. Amazon sells it for $12.89. 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 a few months ago before teaching 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. For example, I found information about three new complex analysis texts in the latest edition of the Notices of the American Math Society!

Prerequisites 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 Thursday, May 5 from 8-11 PM. While exam grades will be the principal source of the course grade, there will also be graded homework and some in-class work.

Instructor S. Greenfield
Office: Hill 542; (732) 445-3074;
Office hours: To be announced.

Maintained by and last modified 1/23/2008.