This is the catalog description of the course:

01:640:403. Introductory Theory of Functions of a Complex
Variable (3) Prerequisite CALC4First 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,
2^{nd} edition (1999) published by Dover Books, list price
$18.95, ISBN 0-486-40679-2. `Amazon` sells
it for $12.89. There are certainly *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;

`greenfie@math.rutgers.edu`

Office hours: To be announced.

**
Maintained by
greenfie@math.rutgers.edu and last modified 1/23/2008.
**