Complex Variables - Complex Analysis

Chapter 1. Complex Numbers

Chapter 2. Complex Functions

Chapter 3. Analytic and Harmonic Functions

Chapter 4. Sequences, Series, and Julia and Mandelbrot Sets

Chapter 5. Elementary Functions

Chapter 6. Complex Integration

Chapter 7. Taylor and Laurent Series

Chapter 8. Residue Theory

Chapter 9. The z-Transforms and Applications

Chapter 10. Conformal Mapping

Chapter 11. Applications of Harmonic Functions

Chapter 12. Fourier Series and the Laplace Transform

The undergraduate modules were started in 2003, and since that early beginning it has been replaced

several times. The current version is under continuous upgrading and improvement. If you are one to notice

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

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 books 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 , and the new 3-D graphical visualizations

for the residue calculus involving
Trigonometric Integrals , Rational Functions, Improper Trig. Integrals,

Indented Contours, and Branch Points. 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.

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