vi PREFACEsetting of this new edition should likewise enhance reading. The answers to all
odd-numbered exercises should help instructors as they deliberate on problem as-
signments, and should help students as they review material. We present confor-
mal mapping in a visual and geometric manner so that compositions and images
of curves and regions can be more easily understood. We first solve boundary-
value problems for harmonic functions in the upper half-plane so that we can
use conformal mapping by elementary functions to obtain solutions in other do-
mains. We carefully develop the Schwarz- Christoffel transformation and present
applications. Two-dimensional mathematical models are used for applications
in the areas of ideal fluid flow, steady-state temperatures, and elect rostatics.
We accurately portray streamlines, isothermals, and equipotential curves with
computer-drawn figures.
An early introduction to sequences and series appears in Chapter 4 and
facilitates the definition of the exponential function via series. We include a
section on Julia and Mandelbrot sets, showing how complex analysis is con-
nected to contemporary topics in mathematics. We keep in place the modern
computer-generated illustrations introduced in the third and fourth editions, in-
cluding Rlemann surfaces, contour and surface graphics for harmonic functions,
the Dirichlet problem, streamlines involving harmonic and analytic functions,
and conformal mapping. We also include a section on the Joukowski airfoil.
The website, http://math.jbpub.com/catalog/0763737488/supplements.
htm, contains supplementary materials for both PC and Macintosh computers
using the software products F(Z)™, lvlATLAB®, Maple TM, and Mathematica TM.
The authors' website, http://mat h.fullerton.edu/mathews/complex.html, con-
tains additional important materials, such as Mathematica notebooks and graph-
ical enhancements to the exercises.
Finally, we support the emphasis currently being placed in undergraduate
research. To help in this effort we have prepared a rather extensive list of research
proj ects for students. They are listed on the Jones and Bartlett website for this
book, given above.
Acknowledgments We would like to express our gratitude to all the peo-
ple whose efforts contributed to the development and preparation of the first
edition of this book, and thank those students who used a preliminary copy of
the manuscript. Robert A. Calabretta (formerly at California State University-
F\lllerton, and now with Boeing Corporation) proofread the manuscript, and
Charles L. Belna (Syracuse University) offered many useful suggestions and
changes. Edward G. Thurber (Biola University) used the manuscript in his course
and offered encouragement. We also want to thank Richard A. Alo (Lamar Uni-
versity), Ario Davis (Indiana. University of P ennsylvania), Holland Filgo (North-
eastern University), Donald Hadwin (University of New Hampshire), E. Robert
Heal (Utah State University), Melvin J. Jacobsen (Rensselaer Polytechnic Insti-
tute), Charles P. Luehr (University of Florida), John Trienz (United States Naval