EBOOK
, NUMERICAL METHODS FOR ENGINEERS, EIGHTH EDITION
Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2021 by McGraw-Hill Education.
All rights reserved. Printed in the United States of America. Previous editions © 2015, 2010, and 2006. No part of this
publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system,
without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other
electronic storage or transmission, or broadcast for distance learning.
Some ancillaries, including electronic and print components, may not be available to customers outside the United States.
This book is printed on acid-free paper.
1 2 3 4 5 6 7 8 9 LCR 24 23 22 21 20
ISBN 978-1-260-23207-3 (bound edition)
MHID 1-260-23207-7 (bound edition)
ISBN 978-1-260-48458-8 (loose-leaf edition)
MHID 1-260-48458-0 (loose-leaf edition)
Portfolio Manager: Beth Bettcher
Product Developer: Heather Ervolino
Senior Marketing Manager: Shannon O’Donnell
Content Project Managers: Jeni McAtee, Samantha Donisi-Hamm
Buyer: Susan K. Culbertson
Design: Matt Diamond
Content Licensing Specialist: Abbey Jones
Cover Image: © iurii/Shutterstock
Compositor: Aptara®, Inc
All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.
Library of Congress Cataloging-in-Publication Data
Names: Chapra, Steven C., author. | Canale, Raymond P., author.
Title: Numerical methods for engineers / Steven C. Chapra, Berger Chair in
Computing and Engineering, Tufts University, Raymond P. Canale Professor
Emeritus of Civil Engineering, University of Michigan.
Description: Eighth edition. ∣ New York, NY : McGraw-Hill Education, [2021] ∣
Includes bibliographical references and index.
Identifiers: LCCN 2019017090| ISBN 9781260232073 (hard cover : acid-free
paper) ∣ ISBN 1260232077 (hard cover : acid-free paper)
Subjects: LCSH: Engineering mathematics—Data processing. ∣ Numerical
calculations—Data processing ∣ Microcomputers—Programming.
Classification: LCC TA345 .C47 2021 | DDC 518.024/62—dc23 LC record
available at https://lccn.loc.gov/2019017090
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by
the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.
mheducation.com/highered
@Seismicisolation
@Seismicisolation
cha32077_fm_i-xviii.indd 2 11/7/1
, ABOUT THE AUTHORS
Steve Chapra teaches in the Civil and Environmental Engineering Department at Tufts
University, where he holds the Louis Berger Chair in Computing and Engineering. His
other books include Surface Water-Quality Modeling and Applied Numerical Methods
with MATLAB.
Dr. Chapra received engineering degrees from Manhattan College and the University
of Michigan. Before joining the faculty at Tufts, he worked for the Environmental Protec-
tion Agency and the National Oceanic and Atmospheric Administration, and taught at
Texas A&M University, the University of Colorado, and Imperial College London. His
general research interests focus on surface water-quality modeling and advanced com-
puter applications in environmental engineering.
He is a Fellow of the ASCE, and has received a number of awards for his scholarly
contributions, including the Rudolph Hering Medal (ASCE), and the Meriam-Wiley
Distinguished Author Award (American Society for Engineering Education). He has also
been recognized as the outstanding teacher among the engineering faculties at Texas
A&M University, the University of Colorado, and Tufts University.
Raymond P. Canale is an emeritus professor at the University of Michigan. During
his over 20-year career at the university, he taught numerous courses in the areas of comput-
ers, numerical methods, and environmental engineering. He also directed extensive research
programs in the area of mathematical and computer modeling of aquatic ecosystems. He
has authored or coauthored several books and has published over 100 scientific papers and
reports. He has also designed and developed personal computer software to facilitate engi-
neering education and the solution of engineering problems. He has been given the Meriam-
Wiley Distinguished Author Award by the American Society for Engineering Education for
his books and software and several awards for his technical publications.
Professor Canale is now devoting his energies to applied problems, on which he
works with engineering firms and industry and governmental agencies as a consultant
and expert witness.
iv
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, CONTENTS
ABOUT THE AUTHORS iv
PREFACE xv
PART ONE
MODELING, PT1.1 Motivation 2
COMPUTERS, AND PT1.2 Mathematical Background 4
ERROR ANALYSIS 2 PT1.3 Orientation 7
CHAPTER 1
Mathematical Modeling and Engineering Problem Solving 11
1.1 A Simple Mathematical Model 11
1.2 Conservation Laws and Engineering 18
Problems 21
CHAPTER 2
Programming and Software 28
2.1 Packages and Programming 28
2.2 Structured Programming 29
2.3 Modular Programming 38
2.4 Excel 40
2.5 MATLAB 44
2.6 Mathcad 48
2.7 Other Languages and Libraries 49
Problems 50
CHAPTER 3
Approximations and Round-Off Errors 57
3.1 Significant Figures 58
3.2 Accuracy and Precision 60
3.3 Error Definitions 61
3.4 Round-Off Errors 67
Problems 81
v
@Seismicisolation
@Seismicisolation
cha32077_fm_i-xviii.indd 5 11/7/1
, NUMERICAL METHODS FOR ENGINEERS, EIGHTH EDITION
Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2021 by McGraw-Hill Education.
All rights reserved. Printed in the United States of America. Previous editions © 2015, 2010, and 2006. No part of this
publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system,
without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other
electronic storage or transmission, or broadcast for distance learning.
Some ancillaries, including electronic and print components, may not be available to customers outside the United States.
This book is printed on acid-free paper.
1 2 3 4 5 6 7 8 9 LCR 24 23 22 21 20
ISBN 978-1-260-23207-3 (bound edition)
MHID 1-260-23207-7 (bound edition)
ISBN 978-1-260-48458-8 (loose-leaf edition)
MHID 1-260-48458-0 (loose-leaf edition)
Portfolio Manager: Beth Bettcher
Product Developer: Heather Ervolino
Senior Marketing Manager: Shannon O’Donnell
Content Project Managers: Jeni McAtee, Samantha Donisi-Hamm
Buyer: Susan K. Culbertson
Design: Matt Diamond
Content Licensing Specialist: Abbey Jones
Cover Image: © iurii/Shutterstock
Compositor: Aptara®, Inc
All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.
Library of Congress Cataloging-in-Publication Data
Names: Chapra, Steven C., author. | Canale, Raymond P., author.
Title: Numerical methods for engineers / Steven C. Chapra, Berger Chair in
Computing and Engineering, Tufts University, Raymond P. Canale Professor
Emeritus of Civil Engineering, University of Michigan.
Description: Eighth edition. ∣ New York, NY : McGraw-Hill Education, [2021] ∣
Includes bibliographical references and index.
Identifiers: LCCN 2019017090| ISBN 9781260232073 (hard cover : acid-free
paper) ∣ ISBN 1260232077 (hard cover : acid-free paper)
Subjects: LCSH: Engineering mathematics—Data processing. ∣ Numerical
calculations—Data processing ∣ Microcomputers—Programming.
Classification: LCC TA345 .C47 2021 | DDC 518.024/62—dc23 LC record
available at https://lccn.loc.gov/2019017090
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by
the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.
mheducation.com/highered
@Seismicisolation
@Seismicisolation
cha32077_fm_i-xviii.indd 2 11/7/1
, ABOUT THE AUTHORS
Steve Chapra teaches in the Civil and Environmental Engineering Department at Tufts
University, where he holds the Louis Berger Chair in Computing and Engineering. His
other books include Surface Water-Quality Modeling and Applied Numerical Methods
with MATLAB.
Dr. Chapra received engineering degrees from Manhattan College and the University
of Michigan. Before joining the faculty at Tufts, he worked for the Environmental Protec-
tion Agency and the National Oceanic and Atmospheric Administration, and taught at
Texas A&M University, the University of Colorado, and Imperial College London. His
general research interests focus on surface water-quality modeling and advanced com-
puter applications in environmental engineering.
He is a Fellow of the ASCE, and has received a number of awards for his scholarly
contributions, including the Rudolph Hering Medal (ASCE), and the Meriam-Wiley
Distinguished Author Award (American Society for Engineering Education). He has also
been recognized as the outstanding teacher among the engineering faculties at Texas
A&M University, the University of Colorado, and Tufts University.
Raymond P. Canale is an emeritus professor at the University of Michigan. During
his over 20-year career at the university, he taught numerous courses in the areas of comput-
ers, numerical methods, and environmental engineering. He also directed extensive research
programs in the area of mathematical and computer modeling of aquatic ecosystems. He
has authored or coauthored several books and has published over 100 scientific papers and
reports. He has also designed and developed personal computer software to facilitate engi-
neering education and the solution of engineering problems. He has been given the Meriam-
Wiley Distinguished Author Award by the American Society for Engineering Education for
his books and software and several awards for his technical publications.
Professor Canale is now devoting his energies to applied problems, on which he
works with engineering firms and industry and governmental agencies as a consultant
and expert witness.
iv
@Seismicisolation
@Seismicisolation
cha32077_fm_i-xviii.indd 4 11/7/1
, CONTENTS
ABOUT THE AUTHORS iv
PREFACE xv
PART ONE
MODELING, PT1.1 Motivation 2
COMPUTERS, AND PT1.2 Mathematical Background 4
ERROR ANALYSIS 2 PT1.3 Orientation 7
CHAPTER 1
Mathematical Modeling and Engineering Problem Solving 11
1.1 A Simple Mathematical Model 11
1.2 Conservation Laws and Engineering 18
Problems 21
CHAPTER 2
Programming and Software 28
2.1 Packages and Programming 28
2.2 Structured Programming 29
2.3 Modular Programming 38
2.4 Excel 40
2.5 MATLAB 44
2.6 Mathcad 48
2.7 Other Languages and Libraries 49
Problems 50
CHAPTER 3
Approximations and Round-Off Errors 57
3.1 Significant Figures 58
3.2 Accuracy and Precision 60
3.3 Error Definitions 61
3.4 Round-Off Errors 67
Problems 81
v
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