## Numerical Analysis and Graphic Visualization with MATLAB (2nd Edition)

### Shoichiro Nakamura

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This textbook for engineering students introduces the commands and graphical tools of MATLAB and their application to performing numerical analysis. The numerical methods include linear algebra, numerical differentiation, successive substitution, Newton iteration, curve fitting to measured data, Eul

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From the Publisher:

This book explores using MATLAB for numerical methods and graphic visualization. It offers a complete tutorial of MATLAB, covering numerical methods with MATLAB and advanced three-dimensional graphics with colors.

From the Inside Flap:

Preface This book is intended to introduce numerical analysis and graphic visualization using MATLAB to college students in engineering and science. It can also be a handbook of MATLAB applications to professional engineers and scientists.

With its unique and fascinating capabilities, MATLAB has changed the concept of programming for numerical and mathematical analyses. It has been found difficulty, however, to teach its application in numerical analysis with a text written previously. For this reason, developing a text that fully implements the mathematical and graphic tools of MATLAB in application of numerical analysis became desirable. The following four fundamental elements are integrated in this book: (1) programming in MATLAB, (2) mathematical basics of numerical analysis, (3) application of numerical methods to engineering, scientific, and mathematical problems, and (4) scientific graphics with MATLAB.

The first two chapters are comprehensive tutorials of MATLAB commands and graphic tools. Chapters 3 through 11 cover numerical methods with their implementations with MATLAB. All the numerical methods described are illustrated with applications on MATLAB. Using the lists of the scripts and functions or copying from the diskette (available to readers free from MathWorks), readers can run most examples and figures on their own computers.

Appendices describe special topics, including advanced three-dimensional graphics with colors, motion pictures, image processing, and graphical user interface. This book is based on MATLAB Student Edition 4, or MATLAB Professional Edition 4.1 or higher.

WHAT IS UNIQUE ABOUT MATLAB? MATLAB may be regarded as a programming language like Fortran or C, although describing it in a few words is difficult. Some of its outstanding features for numerical analyses, however, are: pah

Significantly simpler programming pah

Continuity among integer, real, and complex values pah

Extended range of numbers and their accuracy pah

Comprehensive mathematical library pah

Extensive graphic tools including graphic user interface functions pah

Transportability of MATLAB programs

An extraordinary feature of numbers in MATLAB is that there is no distinction among real, complex, integer, single, and double. In MATLAB, all these numbers are continuously connected, as they should be. It means that in MATLAB, any variable can take any types of numbers without special declaration in programming. This makes programming faster and more productive. In Fortran, a different subroutine is necessary for each of single, double, real or complex, or integer variable, while in MATLAB there is no need to separate them. The mathematical library in MATLAB makes mathematical analyses easy.

Yet the user can develop additional mathematical routines significantly more easily than in other programming languages because of the continuity between real and complex variables. Among numerous mathematical functions, linear algebra solvers play central roles. Indeed, the whole MATLAB system is founded upon linear algebra solvers.

IMPORTANCE OF GRAPHICS Visual analysis of mathematical analyses helps understand mathematics and makes it enjoyable. Although this advantage has been well known, presenting computed results with computer graphics was not without substantial extra effort. With MATLAB, however, graphic presentations of mathematical material is possible with a few commands. Scientific and even artistic graphic objects can be created on the screen using mathematical expressions. It has been found that MATLAB graphics motivate and even excite students to learn mathematical and numerical methods that could otherwise often be dull. MATLAB graphics is easy and will be great fun for readers. This book also illustrates image processing and production of motion pictures for scientific computing as well as for artistic or hobby material.

COMMAND AND FUNCTION NAMES IN THIS BOOK

The command and function names peculiar to this book all include {stt _} for example {stt rotx_.m}. The functions and commands that do not include the underscore are original from MATLAB.

WILL MATLAB ELIMINATE THE NEED FOR FORTRAN OR C?} The answer is no.

Fortran and C are still important for high-performance computing that requires large memory or long computing time. The speed of MATLAB computation is significantly slower than that with Fortran or C because MATLAB is paying the high price for the nice features.

Learning Fortran or C, however, is not a prerequisite for understanding MATLAB.

REFERENCE BOOKS THAT ARE IMPORTANT TO LEARN MATLAB This book explains many MATLAB commands but is not intended to be a complete guide to MATLAB. Readers interested in further information on MATLAB are advised to read the following literature on MATLAB: *** The MathWorks, The Student Edition of MATLAB, } *** hspace{0.5in} Version 4, User's Guide,} Prentice-Hall 1995 *** MATLAB, Reference Guide, MathWorks, 1992 *** MATLAB, User's Guide, MathWorks, 1992 *** MATLAB, Building a Graphical User Interface, MathWorks, 1993

HOW TO OBTAIN M-FILES DISKETTE All the scripts and functions developed in the present book are included in the diskette available from MathWorks. Please mail the diskette request card inserted at the end of this book. If the request card is missing, MathWorks' address appears on the next page. The diskette includes the following files: *** (1) All M-files listed at the end of chapters. *** (2) All scripts illustrated in the book (except short ones). *** (3) Scripts to plot typical figures in the book. SOLUTION KEYS

Solution keys for the problems at the end of chapters will be included in the M-Files Diskette.

ftp.mathworks (144.212.100.10).
The FAQ and the Technical Notes can be found in the directories {stt /pub/doc/faq and {stt /pub/tech-support/tech-notes respectively. Pagebreak You may also receive the following information free of charge:

* The MathWorks Newsletter (quarterly publication)

* The MATLAB News Digest (distributed via email)

* Technical Support

Send email to {stt subscribe@mathworks. Include in the email your name, company/university, address, phone number, email address, and license or serial number, which can be found by entering "ver" at the MATLAB prompt. For other communication with MathWorks, their address is: The MathWorks, Inc., 24 Prime Park Way, Natick, MA 01760, Phone: 508-653-1415, Fax: 508-653-2997. LIST OF REVIEWERS This book has been reviewed by:

*** Professor T. Aldemir, Nuclear Engineering,

The Ohio State University, Columbus, Ohio *** Professor M. Darwish, Mechanical Engineering Degment,

American University of Beirut, Beirut, Lebanon ***The MathWorks Inc., Natick, Massachusetts

*** Professor J. K. Shultis, Nuclear Engineering,

Kansas State University, Manhattan, Kansas *** Professor S. V. Sreenivasan, Degment of Mechanical Engineering,

University of Texas, Austin, Texas

Image Alchemy is a registered trademark of Handmade Software, Inc. MATLAB is a registered trademark of MathWorks, Inc.

Qtake is a registered trademark of Apple, Inc. Unix is a registered trademark of AT\$&\$T Bell Laboratories.

Windows is a registered trademark of Microsoft, Inc.

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