**Research
Experience for Undergraduates**

This page contains links which are intended to help students find
additional resources for

studying various topics in complex analysis. All of the original
links were created in 2003 and

were a complementary resource that accompanied the 2001 edition of
our textbook.

COMPLEX ANALYSIS: for Mathematics and Engineering, Fourth Edition, 2001

John H. Mathews and Russell W. Howell

ISBN: 0-7637-4125-9

Jones and Bartlett Pub. Inc.

Sudbury, MA

Since this part of our complex analysis project was created nine
years ago, it has been

almost impossible to keep it up to date. However a few of the pages
have been updated in

recent years. We apologize for any inconveniences that you might
experience with dead links.

It is very time consuming to keep this section of the project up to
date. Please be patient.

Complex Numbers

- Complex Numbers
- DeMoivre's Theorem
- Roots of Cubic Equations
- Roots of Quartic Equations
- Complex Roots of Polynomials
- Quaternions
- History of Complex Numbers

Complex Functions

Analytic and Harmonic Functions

- Analytic Functions
- Mean Value Theorem and Rolle's Theorem
- Cauchy-Riemann Equations
- Harmonic Functions
- Polya Vector Field
- Entire Functions
- Holomorphic Functions
- Meromorphic Functions

Sequences, Series, and Julia and Mandelbrot Sets

Elementary Functions

Complex Integration

- Complex Integral
- Contour Integrals
- Green's Theorem
- Cauchy-Goursat Theorem
- Cauchy's Integral Formula
- Fundamental Theorem of Calculus
- Morera's Theorem
- Maximum Modulus Principle
- Liouville's Theorem
- Fundamental Theorem of Algebra
- Schwarz Lemma

Taylor and Laurent Series

- Taylor Series
- Laurent Series
- Poles and Singularity
- Infinite Products
- Analytic Continuation
- Bieberbach Conjecture
- Riemann Hypothesis

Residue Theory

- Residue Calculus
- Contour Integrals
- Cauchy Principal Value
- Hilbert Transformation
- Argument Principle
- Rouche's Theorem
- Nyquist Stability Criterion
- Z-Transform

Conformal Mapping

Applications of Harmonic Functions

- Dirichlet Problem
- Neumann Problem
- Poisson Integral
- Electrostatics
- Ideal Fluid Flow
- Steady State Temperature
- Joukowski Transformation and Airfoils
- Schwarz-Christoffel transformation
- Complex Potential
- Green's Function

Fourier Series and the Laplace Transform

Return to the Complex Analysis Project

Finally, we would like to emphasize that the above materials are
supplements that are coordinated

with the various editions of our textbook "Complex Analysis for
Mathematics and Engineering".

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