**Complex
Analysis Project**

**for**

**Undergraduate
Students**

**Complementary
Materials for Math 412**

Modules for Complex Variables & Complex Analysis

Research Experience for Undergraduates

History of the Complex Analysis Project

The motivation for this project started with the software program
F(z) which was designed by

Martin Lapidus and is available from Lascaux
Software. In
1988 we distributed an F(Z) supplement

for
our textbook and the web page Complex
Analysis - Complex Variables,
Explorations with F(Z).

In 2000 a web project titled Complex Analysis: Mathematica 4.0
Notebooks was made, and then

the web project titled Complex Analysis: Maple 7 Worksheets was made.
For the 2001 edition of our

book, a CD-ROM titled "Complex Analysis for Mathematics and
Engineering," ISBN: 0-7637-1530-1,

was packaged free with each copy and contained color plate pictures
of the Julia and Mandelbrot sets

and all the computer software supplemnts: the F(Z) files, Maple
worksheets and Mathematica notebooks.

This version of our complex analysis web project was started in 2003,
and since that early beginning

it has been updated several times and it is under continuous
upgrading and improving. If you are one to notice

all the details then you probably will find some remnants dated 2003
and the most current version of modules

are dated 2012. But you need not worry about the time line because
the core material in complex analysis has

not changed much in the past sixty years and some currently available
textbooks have actually made their 60^{th}

year milestone. We cannot brag to have such longevity and are just
thankful that our textbook has just achieved

it's 30^{th} year milestone. There have been significant
improvements in the textbook since 1982. Noteworthy is

the new Chapter 9: The
Z-transform
and it's applications to Difference
Equations and
Digital
Signal Filters.

We try to keep things up to date and this complex analysis web site
is one way to do it. You will find

several instances where the content of the web site goes
significantly beyond the material in the textbook:

e. g. Harmonic
Functions and their Riemann Sheets
in Section
3.3; 3-D
graphical visualizations for the residue

calculus involving Trigonometric
Integrals,
Rational
Functions,
Improper
Trig. Integrals,
Indented
Contours,
and

Branch
Points; the argument
principle and winding number is
associated with Riemann surfaces; new 3-D graphs

for the Dirichlet
problem, and conformal
mapping. This
is intentional since it allows us to present more details for

the solutions to the examples and exercises. Also you will notice
that we have illustrated how to use Mathematica

and Maple as a pedagogical tool for teaching and exploring concepts
the in complex analysis. Although these

details are much too extensive to print in any textbook, they are
easy to squeeze in on the web pages.

For certain we can say that our book is the first to have included
Maple^{TM }and Mathematica^{TM} supplements.

We started
encouraging the use of computer algebra software since we made our
first complementary

Computer
Software Supplements,
the Maple Version 4 worksheets in 1997, and Mathematica Version 3

notebooks in 1998. They have been improved for the past 15 years and
can serve as a tutorial on how to

learn to use Maple and Mathematica to study Complex Analysis. You may
want to get the new copies of the

latest Mathematica
Version 8 and Maple Version 15 supplements, which are available as
complementary

student supplement to our textbook from the Jones
and Bartlett
web page.

We find that there is a
tendency to teach complex analysis with pencil and paper, and it is
the hope of this

web site to overcome this inertia. Perhaps you will find useful
computer illustrations that will encourage students

to explore complex analysis using Mathematica and Maple. Since we are
a bellwether in this movement we hope

that you will follow us through the pages in this web site and see
the beautiful explorations that can be made.

Hopefully you will gain some insight as to how this can help you
teach complex analysis and the benefits your

students can gain by making their own computer explorations.

Finally, we would like to
emphasize that this web site is a complementary supplement that is
coordinated

with the current version of our textbook Complex
Analysis for Mathematics and Engineering,
Sixth Ed., 2012.

You are welcome to correspond with us on matters regarding the
content and any suggestions you have or typos

you may find. You are welcome to correspond with us by
mail or e-mail.

Prof.
John H. Mathews

Department
of Mathematics

California
State University Fullerton

Fullerton,
CA 92634

mathews@fullerton.edu

Prof.
Russell W. Howell

Mathematics
& Computer Science Department

Westmont College

Santa
Barbara, CA 93108

howell@westmont.edu

This material is coordinated with our book Complex Analysis for Mathematics and Engineering.

(c) 2012 John H. Mathews, Russell W. Howell