Complex Analysis Project

for

Complementary Materials for Math 412

Modules for Complex Variables & Complex Analysis

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 60th

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

it's 30th 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 MapleTM and MathematicaTM 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

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