基于 MATLAB 的数值方法应用指南

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Applied Numerical Methods with MATLAB for Engineers and Scientists Applied Numerical Methods with MATLAB for Engineers and Scientists 是一本经典的电子书，专门介绍数值方法的应用，适合工学、理学等领域。该书籍涵盖了数值方法的基础知识和 MATLAB 的应用，旨在帮助读者理解和掌握数值方法的原理和应用。数值方法是科学和工程领域中一种常用的研究方法，它通过离散化和近似来解决复杂的问题。该方法广泛应用于物理、工程、经济、金融等领域。数值方法的应用可以帮助研究人员和工程师解决复杂的问题，提高研究效率和准确性。 MATLAB 是一种流行的编程语言和开发环境，广泛应用于科学和工程领域。 MATLAB 提供了强大的数值计算功能和可视化工具，能够帮助用户快速开发和实现数值方法的应用。本书籍涵盖了数值方法的基础知识，包括线性代数、微积分、差分方程、优化方法等。同时，该书籍还介绍了 MATLAB 的应用，包括 MATLAB 的基本语法、数据类型、函数编程等。读者可以通过本书籍学习数值方法的基础知识和 MATLAB 的应用，从而提高自己的研究和开发能力。数值方法的应用领域非常广泛，包括物理、工程、经济、金融等领域。在物理领域，数值方法可以用于模拟复杂的物理现象，例如气体动力学、流体力学等。在工程领域，数值方法可以用于设计和优化工程系统，例如机械设计、电气工程等。在经济领域，数值方法可以用于经济模型的建立和分析，例如经济增长模型、金融模型等。 Applied Numerical Methods with MATLAB for Engineers and Scientists 是一本非常有价值的电子书籍，对于工学、理学等领域的研究人员和工程师非常有帮助。该书籍涵盖了数值方法的基础知识和 MATLAB 的应用，能够帮助读者提高自己的研究和开发能力。

FIGURE P.1

An outline of this edition. The shaded areas represent new material. In addition, several of the original chapters have been supplemented with

new topics.

xiv

PART ONE PART TWO PART THREE PART FOUR PART FIVE PART SIX

Modeling, Computers, Roots and Linear Systems Curve Fitting Integration and Ordinary Differential

and Error Analysis Optimization Differentiation Equations

CHAPTER 1 CHAPTER 5 CHAPTER 8 CHAPTER 14 CHAPTER 19 CHAPTER 22

Mathematical Roots: Bracketing Linear Algebraic Linear Regression Numerical Integration Initial-Value

Modeling, Numerical Methods Equations Formulas Problems

Methods, and Problem and Matrices

Solving

CHAPTER 2 CHAPTER 6 CHAPTER 9 CHAPTER 15 CHAPTER 20 CHAPTER 23

MATLAB Roots: Open Gauss Elimination General Linear Numerical lntegration Adaptive Methods

Fundamentals Methods Least-Squares and of Functions and Stiff Systems

Nonlinear Regression

CHAPTER 3 CHAPTER 7 CHAPTER 10 CHAPTER 16 CHAPTER 21 CHAPTER 24

Programming Optimization LU Factorization Fourier Analysis Numerical Boundary-Value

with MATLAB Differentiation Problems

CHAPTER 4 CHAPTER 11 CHAPTER 17

Roundoff and Matrix Inverse Polynomial

Truncation Errors and Condition Interpolation

CHAPTER 12 CHAPTER 18

Iterative Methods Splines and Piecewise

Interpolation

CHAPTER 13

Eigenvalues

cha01102_fm_i-xviii.qxd 12/17/10 8:58 AM Page xiv

PREFACE xv

to move this material up to what I consider to be its more natural mathematical po-

sition at the end of the section on linear algebraic equations. By stressing applica-

tions (in particular, the use of eigenvalues to study vibrations), I have found that

students respond very positively to the subject in this position. In addition, it allows

me to return to the topic in subsequent chapters which serves to enhance the

students’ appreciation of the topic.

• FourierAnalysis. In past years, if time permitted, I also usually presented a lecture

at the end of the semester on Fourier analysis. Over the past two years, I have begun

presenting this material at its more natural position just after the topic of linear least

squares. I motivate the subject matter by using the linear least-squares approach to

fit sinusoids to data. Then, by stressing applications (again vibrations), I have found

that the students readily absorb the topic and appreciate its value in engineering and

science.

It should be noted that both chapters are written in a modular fashion and could

be skipped without detriment to the course’s pedagogical arc. Therefore, if you

choose, you can either omit them from your course or perhaps move them to the

end of the semester. In any event, I would not have included them in the current

edition if they did not represent an enhancement within my current experience in

the classroom. In particular, based on my teaching evaluations, I find that the

stronger, more motivated students actually see these topics as highlights. This is

particularly true because MATLAB greatly facilitates their application and inter-

pretation.

2. New Content. Beyond the new chapters, I have included new and enhanced sections on a

number of topics. The primary additions include sections on animation (Chap. 3), Brent’s

method for root location (Chap. 6), LU factorization with pivoting (Chap. 8), ran-

dom numbers and Monte Carlo simulation (Chap. 14), adaptive quadrature (Chap. 20),

and event termination of ODEs (Chap. 23).

3. New Homework Problems. Most of the end-of-chapter problems have been modi-

fied, and a variety of new problems have been added. In particular, an effort has been

made to include several new problems for each chapter that are more challenging and

difficult than the problems in the previous edition.

Aside from the new material and problems, the third edition is very similar to the second.

In particular, I have endeavored to maintain most of the features contributing to its pedagog-

ical effectiveness including extensive use of worked examples and engineering and scien-

tific applications. As with the previous edition, I have made a concerted effort to make this

book as “student-friendly” as possible. Thus, I’ve tried to keep my explanations straightfor-

ward and practical.

Although my primary intent is to empower students by providing them with a sound

introduction to numerical problem solving, I have the ancillary objective of making this

introduction exciting and pleasurable. I believe that motivated students who enjoy engi-

neering and science, problem solving, mathematics—and yes—programming, will ulti-

mately make better professionals. If my book fosters enthusiasm and appreciation for these

subjects, I will consider the effort a success.

cha01102_fm_i-xviii.qxd 12/17/10 8:58 AM Page xv

Acknowledgments. Several members of the McGraw-Hill team have contributed to

this project. Special thanks are due to Lorraine Buczek, and Bill Stenquist, and Melissa

Leick for their encouragement, support, and direction. Ruma Khurana of MPS Limited, a

Macmillan Company also did an outstanding job in the book’s final production phase. Last,

but not least, Beatrice Sussman once again demonstrated why she is the best copyeditor in

the business.

During the course of this project, the folks at The MathWorks, Inc., have truly demon-

strated their overall excellence as well as their strong commitment to engineering and

science education. In particular, Courtney Esposito and Naomi Fernandes of The Math-

Works, Inc., Book Program have been especially helpful.

The generosity of the Berger family, and in particular Fred Berger, has provided me

with the opportunity to work on creative projects such as this book dealing with computing

and engineering. In addition, my colleagues in the School of Engineering at Tufts, notably

Masoud Sanayei, Lew Edgers, Vince Manno, Luis Dorfmann, Rob White, Linda Abriola,

and Laurie Baise, have been very supportive and helpful.

Significant suggestions were also given by a number of colleagues. In particular, Dave

Clough (University of Colorado–Boulder), and Mike Gustafson (Duke University) pro-

vided valuable ideas and suggestions. In addition, a number of reviewers provided useful

feedback and advice including Karen Dow Ambtman (University of Alberta), Jalal Behzadi

(Shahid Chamran University), Eric Cochran (Iowa State University), Frederic Gibou (Uni-

versity of California at Santa Barbara), Jane Grande-Allen (Rice University), Raphael

Haftka (University of Florida), Scott Hendricks (Virginia Tech University), Ming Huang

(University of San Diego), Oleg Igoshin (Rice University), David Jack (Baylor Univer-

sity), Clare McCabe (Vanderbilt University), Eckart Meiburg (University of California at

Santa Barbara), Luis Ricardez (University of Waterloo), James Rottman (University of

California, San Diego), Bingjing Su (University of Cincinnati), Chin-An Tan (Wayne State

University), Joseph Tipton (The University of Evansville), Marion W. Vance (Arizona

State University), Jonathan Vande Geest (University of Arizona), and Leah J. Walker

(Arkansas State University).

It should be stressed that although I received useful advice from the aforementioned

individuals, I am responsible for any inaccuracies or mistakes you may find in this book.

Please contact me via e-mail if you should detect any errors.

Finally, I want to thank my family, and in particular my wife, Cynthia, for the love,

patience, and support they have provided through the time I’ve spent on this project.

Steven C. Chapra

Tufts University

Medford, Massachusetts

steven.chapra@tufts.edu

xvi PREFACE

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PEDAGOGICAL TOOLS

Theory Presented as It Informs Key Concepts. The text is intended for Numerical Meth-

ods users, not developers. Therefore, theory is not included for “theory’s sake,” for example no

proofs. Theory is included as it informs key concepts such as the Taylor series, convergence,

condition, etc. Hence, the student is shown how the theory connects with practical issues in

problem solving.

Introductory MATLAB Material. The text includes two introductory chapters on how to

use MATLAB. Chapter 2 shows students how to perform computations and create graphs

in MATLAB’s standard command mode. Chapter 3 provides a primer on developing

numerical programs via MATLAB M-file functions. Thus, the text provides students with

the means to develop their own numerical algorithms as well as to tap into MATLAB’s

powerful built-in routines.

Algorithms Presented Using MATLAB M-files. Instead of using pseudocode, this book

presents algorithms as well-structured MATLAB M-files. Aside from being useful com-

puter programs, these provide students with models for their own M-files that they will

develop as homework exercises.

Worked Examples and Case Studies. Extensive worked examples are laid out in detail

so that students can clearly follow the steps in each numerical computation. The case stud-

ies consist of engineering and science applications which are more complex and richer than

the worked examples. They are placed at the ends of selected chapters with the intention of

(1) illustrating the nuances of the methods, and (2) showing more realistically how the

methods along with MATLAB are applied for problem solving.

Problem Sets. The text includes a wide variety of problems. Many are drawn from engi-

neering and scientific disciplines. Others are used to illustrate numerical techniques and

theoretical concepts. Problems include those that can be solved with a pocket calculator as

well as others that require computer solution with MATLAB.

Useful Appendices and Indexes. Appendix A contains MATLAB commands, and

Appendix B contains M-file functions.

Textbook Website. A text-specific website is available at www.mhhe.com/chapra. Re-

sources include the text images in PowerPoint, M-files, and additional MATLAB resources.

PREFACE xvii

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