It has been twenty years since we published the first edition of this book. Over that period,
our original contention that numerical methods and computers would figure more prominently
in the engineering curriculum—particularly in the early parts—has been dramatically
borne out. Many universities now offer freshman, sophomore, and junior courses in
both introductory computing and numerical methods. In addition, many of our colleagues
are integrating computer-oriented problems into other courses at all levels of the curriculum.
Thus, this new edition is still founded on the basic premise that student engineers
should be provided with a strong and early introduction to numerical methods. Consequently,
although we have expanded our coverage in the new edition, we have tried to
maintain many of the features that made the first edition accessible to both lower- and
upper-level undergraduates. These include:
Problem Orientation. Engineering students learn best when they are motivated by
problems. This is particularly true for mathematics and computing. Consequently, we
have approached numerical methods from a problem-solving perspective.
Student-Oriented Pedagogy. We have developed a number of features to make this
book as student-friendly as possible. These include the overall organization, the use of
introductions and epilogues to consolidate major topics and the extensive use of worked
examples and case studies from all areas of engineering. We have also endeavored to
keep our explanations straightforward and oriented practically.
“Clear Box” Approach. Although we emphasize problem solving, we believe that it is
self-limiting for engineers to approach numerical algorithms as “black boxes.” Thus, we
include sufficient theory to allow users to understand the basic concepts behind the methods.
In particular,we stress theory related to error analysis, the limitations of the methods,
and trade-offs among methods.
Personal Computing Orientation. When we first wrote this book, there was a great
chasm between the batch world of mainframe computers and the interactive world of
PCs. Today, as PC performance grows, the distinctions are falling away. That said, this
book still emphasizes visualization and interactive calculations, which are the hallmarks
of personal computing.
Empowering Students. We obviously introduce students to the standard “point-andshoot”
problem-solving capabilities of packages like Excel and MATLAB software.
However, students are also shown how to develop simple, well-structured programs to
extend the base capabilities of those environments. This knowledge carries over to standard
programming languages such as Visual Basic, Fortran 90 and C/C++. We believe
that the current flight from computer programming represents something of a “dumbing
down” of the engineering curriculum. The bottom line is that as long as engineers are
not content to be tool limited, they will have to write code. Only now they may be called
“macros” or “M-files.” This book is designed to empower them to do that.
Beyond these five original principles, the primary enhancement in the fifth edition is a
major revision and expansion of the end-of-chapter problem sets. Most of the problems
have been modified so that they yield different numerical solutions from previous editions.
In addition, a variety of new problems have been included. As with previous editions, we
include both mathematical and applied problems from all branches of engineering. In all
cases, our intent is to provide students with exercises to check their understanding and to
illustrate how numerical methods can help them become better problem solvers.
As always, our primary intent in writing this book is to provide students with a sound
introduction to numerical methods. We believe that motivated students who enjoy numerical
methods, computers, and mathematics will, in the end, make better engineers. If our
book fosters an enthusiasm for these subjects, we will consider our efforts a success.
Acknowledgments. We would like to thank our friends at McGraw-Hill. In particular,
Amanda Green, Suzanne Jeans, and Peggy Selle, who provided a positive and supportive
atmosphere for creating this edition. As usual, Beatrice Sussman did a masterful job of
copyediting the manuscript. Special thanks to Professors Wally Grant, Olga Pierrakos,
Amber Phillips, Justin Griffee and Kevin Mace (Virginia Tech) and Professor Theresa Good
(Texas A&M), who have contributed problems to our book over the years. As in past editions,
David Clough (University of Colorado) and Jerry Stedinger (Cornell University) generously
shared their insights and suggestions. Useful suggestions were also made by Bill
Philpot (Cornell University), Jim Guilkey (University of Utah), Dong-Il Seo (Chungnam
National University, Korea), and Raymundo Cordero and Karim Muci (ITESM, Mexico).
The present edition has also benefited from the reviews and suggestions provided by the
following colleagues:
Ella M. Atkins, University of Maryland
Betty Barr, University of Houston
Florin Bobaru, University of Nebraska–Lincoln
Ken W. Bosworth, Idaho State University
Anthony Cahill, Texas A&M University
Raymond C. Y. Chin, Indiana University–Purdue, Indianapolis
Jason Clark, University of California, Berkeley
John Collings, University of North Dakota
Ayodeji Demuren, Old Dominion University
Cassiano R. E. de Oliveira, Georgia Institute of Technology
Subhadeep Gan, University of Cincinnati
Aaron S. Goldstein, Virginia Polytechnic Institute and State University
Gregory L. Griffin, Louisiana State University
Walter Haisler, Texas A&M University
Don Hardcastle, Baylor University
Scott L. Hendricks, Virginia Polytechnic Institute and State University
David J. Horntrop, New Jersey Institute of Technology
Tribikram Kundu, University of Arizona
Hysuk Lee, Clemson University
Jichun Li, University of Nevada, Las Vegas
Jeffrey S. Marshall, University of Iowa
cha1873X_fm.qxd 4/5/05 07:12 PM Page xiv
George Novacky, University of Pittsburgh
Dmitry Pelinovsky, McMaster University
Siva Parameswaran, Texas Technical University
Greg P. Semeraro, Rochester Institute of Technology
Jerry Sergent, Faifield University
Dipendra K. Sinha, San Francisco State University
Scott A. Socolofsky, Texas A&M University
Robert E. Spall, Utah State University
John C. Strikwerda, University of Wisconsin-Madison
Karsten E. Thompson, Louisiana State University
Kumar Vemaganti, University of Cincinnati
Peter Wolfe, University of Maryland
Nader Zamani, University of Windsor
Viktoria Zoltay, Tufts University
It should be stressed that although we received useful advice from the aforementioned
individuals, we are responsible for any inaccuracies or mistakes you may detect in this edition.
Please contact Steve Chapra via e-mail if you should detect any errors in this edition.
Finally, we would like to thank our family, friends, and students for their enduring
patience and support. In particular, Cynthia Chapra and Claire Canale are always there
providing understanding, perspective, and love.
Steven C. Chapra
Medford, Massachusetts
steven.chapra@tufts.edu
Raymond P. Canale
Lake Leelanau, Michigan
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