Chapter 1      Complex Numbers
Section 1.1    The Origin of Complex Numbers download
Section 1.2    The Algebra of Complex Numbers download
Section 1.3    The Geometry of Complex Numbers download
Section 1.4    The Geometry of Complex Numbers, Continued download
Section 1.5    The Algebra of Complex Numbers, Revisited download
Section 1.6    The Topology of Complex Numbers download

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

Chapter 3      Analytic and Harmonic Functions
Section 3.1    Differentiable and Analytic Functions download
Section 3.2    The Cauchy-Riemann Equations download
Section 3.3    Analytic Functions and Harmonic Functions download

Chapter 4      Sequences, Series, and Julia and Mandelbrot Sets
Section 4.1    Sequences and Series download
Section 4.2    Julia and Mandelbrot Sets download
Section 4.3    Geometric Series and Convergence Theorems download
Section 4.4    Power Series Functions download

Chapter 5      Elementary Functions
Section 5.1    The Complex Exponential Function download
Section 5.2    The Complex Logarithm Function download
Section 5.3    Complex Exponents download
Section 5.4    Trigonometric and Hyperbolic Functions download
Section 5.5    Inverse Trigonometric and Hyperbolic Functions download

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

Chapter 7      Taylor and Laurent Series
Section 7.1    Uniform Convergence download
Section 7.2    Taylor Series Representations download
Section 7.3    Laurent Series Representations download
Section 7.4    Singularities, Zeros and Poles download
Section 7.5    Applications of Taylor and Laurent Series download

Chapter 8      Residue Theory
Section 8.1    The Residue Theorem download
Section 8.2    Calculation of Residues download
Section 8.3    Trigonometric Integrals download
Section 8.4    Improper Integrals of Rational Functions download
Section 8.5    Improper Integrals Involving Trigonometric Functions download
Section 8.6    Indented Contour Integrals download
Section 8.7    Integrands with Branch Points download
Section 8.8    The Argument Principle and Rouche's Theorem download

Chapter 9      Conformal Mapping
Section 9.1    Basic Properties of Conformal Mappings download
Section 9.2    Bilinear Transformations download
Section 9.3    Mappings Involving Elementary Functions download
Section 9.4    Mappings by Trigonometric Functions download

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

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

Complimentary software to accompany our textbook:

COMPLEX ANALYSIS: for Mathematics and Engineering
4th Edition,  2001,  ISBN: 0-7637-1425-9
Jones & Bartlett Publishers, Inc.
40 Tall Pine Drive, Sudbury, MA 01776  
Tele.  (800) 832-0034, FAX:  (508)  443-8000  
E-mail:  mkt@jbpub.com  
Internet:  http://www.jbpub.com/  
This free software is compliments of the authors.
John H. Mathews,   mathews@fullerton.edu
Russell W. Howell,  howell@westmont.edu

    All Rights reserved.  No portion of this supplement may be reproduced in any form or by any means without permission in writing from the publisher or the authors. Duplicated in the United States of America 

Jones and Bartlett Publishers, Inc.
40  Tall  Pine  Drive
Sudbury,  MA  01776

Preface

      This disk contains complex analysis software coded in theMathematica programming language. The examples are described in the text "Complex Analysis: for Mathematics and Engineering," 4th Edition, 2001.  The authors appreciate correspondence regarding the book.  You are welcome to correspond by mail or electronic mail.

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:   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:   howell@westmont.edu

(c) John H. Mathews 2006