COMPLEX ANALYSIS: Mathematica 3.0 Notebooks
(c) John H. Mathews, and Russell W. Howell, 1998

Complimentary software to accompany our textbook:

COMPLEX ANALYSIS: for Mathematics and Engineering, 
3rd Edition,  1997,  ISBN: 0-7637-0270-6
Jones & Bartlett Publishers, Inc.
40 Tall Pine Drive, Sudbury, MA 01776
Tele.  (800) 832-0034, FAX:  (508)  443-8000
E-mail:  mkt@jbpub.com,     http://www.jbpub.com/

This free software is compliments of the authors.
mathews@fullerton.edu,  howell@westmont.edu


Prof.  John  H.  Mathews
Department of Mathematics
California State University Fullerton
Fullerton, CA  92634
(714) 278-3196  Office
(714) 278-3631  Secretary
(714) 278-3972  FAX
E-mail:  in%"mathews@fullerton.edu"

Prof. Russell W. Howell
Mathematics & Computer Science Dept.
Westmont  College
Santa Barbara,  CA  93108
(805)  565-6178  Office
(805)  565-6174  Secretary
(805)  565-6220  FAX
E-mail:  in%"howell@westmont.edu"

Contents

CHAPTER 1  COMPLEX NUMBERS
Section 1.1  The Origin of Complex Numbers
Section 1.2  The Algebra of Complex Numbers
Section 1.3  The Geometry of Complex Numbers
Section 1.4  The Geometry of Complex Numbers, Continued
Section 1.5  The Algebra of Complex Numbers, Revisited
Section 1.6  The Topology of Complex Numbers

CHAPTER 2   COMPLEX FUNCTIONS
Section 2.1  Functions of a Complex Variable
Section 2.2  Transformations and Linear Mappings
Section 2.3  The Mappings  w =z^n  and  w = z^n
Section 2.4  Limits and Continuity
Section 2.5  Branches of Functions
Section 2.6 The Reciprocal Transformation  w = 1/z

CHAPTER 3  ANALYTIC and HARMONIC FUNCTIONS
Section 3.1  Differentiable Functions
Section 3.2  The Cauchy-Riemann Equations
Section 3.3  Analytic Functions and Harmonic Functions

CHAPTER 4  SEQUENCES, SERIES, and JULIA and MANDELBROT SETS
Section 4.1  Definitions and Basic Theorems for Sequences and Series
Section 4.2  Power Series Functions
Section 4.3  Julia and Mandelbrot Sets

CHAPTER 5  ELEMENTARY FUNCTIONS
Section 5.1  The Complex Exponential Function
Section 5.2  Branches of the Complex Logarithm Function
Section 5.3  Complex Exponents
Section 5.4  Trigonometric and Hyperbolic Functions
Section 5.5  Inverse Trigonometric and Hyperbolic Functions

CHAPTER 6  COMPLEX INTEGRATION
Section 6.1  Complex Integrals
Section 6.2  Contours and Contour Integrals
Section 6.3  The Cauchy-Goursat Theorem
Section 6.3  The Cauchy-Goursat Theorem
Section 6.4  The Fundamental Theorems of Integration
Section 6.5  Integral Representations for Analytic Functions
Section 6.6  The Theorems of Morera and Liouville and Some Applications

CHAPTER 7  TAYLOR AND LAURENT SERIES
Section 7.1  Uniform Convergence
Section 7.2  Taylor series Representations
Section 7.3  Laurent series Representations
Section 7.4  Singularities, Zeros and Poles
Section 7.5  Applications of Taylor and Laurent Series

CHAPTER 8   RESIDUE THEORY
Section 8.1  The Residue Theorem
Section 8.2  Calculation of Residues
Section 8.3  Trigonometric Integrals
Section 8.4  Improper Integrals of Rational Functions
Section 8.5  Improper Integrals involving Trigonometric Functions
Section 8.6  Indented Integrals

CHAPTER 9  CONFORMAL MAPPING
Section 9.1  Basic Properties of Conformal Mappings
Section 9.2  Bilinear Transformations
Section 9.3  Mapping Involving Elementary Functions
Section 9.4  Mapping Involving Trigonometric Functions

CHAPTER 10  APPLICATIONS of HARMONIC FUNCTIONS
Section 10.1  Preliminaries
Section 10.2  Invariance of Laplace's Equation and the Dirichlet Problem
Section 10.3  Poisson's Integral for the Upper Half-Plane
Section 10.4  Two-Dimensional Mathematical Models
Section 10.5  Steady State Temperatures
Section 10.6  Two Dimensional Electrostatics
Section 10.7  Two-Dimensional Fluid Flow
Section 10.8  The Joukowski Airfoil
Section 10.9  Schwarz-Christoffel Transformation
Section 10.10  Images of a Fluid Flow
Section 10.11  Sources and Sinks

CHAPTER 11  FOURIER SERIES and the LAPLACE TRANSFORM
Section 11.1  Fourier Series
Section 11.2  The Dirichlet Problem for the Unit Disk
Section 11.3  Vibrations in Mechanical Systems
Section 11.4  The Fourier Transform
Section 11.5  The Laplace Transform
Section 11.6  Laplace Transforms of Derivatives and Integrals
Section 11.7  Shifting Theorems and the Step Function
Section 11.8  Multiplication  and  Division  by  t
Section 11.9  Inverting the Laplace Transform
Section 11.10  Convolution