Numerical Analysis and Graphic Visualization with MATLAB

Numerical Analysis and Graphic Visualization with MATLAB

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PREFACE WHAT THIS BOOK DESCRIBES This book is intended to introduce numerical analysis and graphic visualization using MATLAB to college students majoring in engineering and science.It can also be a handbook of MATLAB applications for professional engi-neers and scientists. The goal is not to teach the mathematics of numericalanalysis, but rather to teach the knowledge and skills of solving equationsand presenting them graphically so that readers can easily handle equationsand results of the computations. With its unique and fascinating capabilities, MATLAB has changed theconcept of programming for numerical and mathematical analyses. Therefore, MATLAB is a superb vehicle to achieve our goal. This book fullyimplements the mathematical and graphic tools in the most recent versionof MATLAB. 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, particularly for the beginner or entry-level collegestudent. Indeed, these two chapters have been most significantly enhancedin this edition compared to the first edition. In Chapter 1, understandingand developing programming skills on MATLAB are emphasized particularlybecause, unless the reader has knowledge and experience with another pro-gramming language, these are tough hurdles for the beginner to overcome.To acquire the knowledge and skills necessary to read the rest of the book, solving the problems at the end of each chapter is very important. Chapter 2 starts out with the elements of graphics on MATLAB, whichis easy to follow. Yet, toward the end of the chapter, three-dimensionalgraphics on the professional level are achieved. Not only is the programmingtechnique of plotting functions mentioned, but also skills of presenting mathematical and scientific material using graphics are developed throughout thechapter. The graphics knowledge acquired in this chapter are foundationsin learning and applying the numerical methods described in the remainderof the book. Again, practice on the computer is important. Some studentstry to memorize scripts without understanding why and how they work, but such an effort is utterly meaningless. More important is to play with afew new commands, understand how they work and how they may fail, andfinally become a master of the commands. Chapters 3 through 11 cover numerical methods and their implementations with MATLAB. All the numerical methods described are illustratedwith applications on MATLAB. Appendices describe special topics, including advanced three-dimensional graphics with colors, motion pictures, imageprocessing, and graphical user interface. Readers should feel free to use thescripts in this book in any way desired. However, the beginning studentsare advised not to u se these scripts blindly. The students should write theirown scripts. Using the lists of the scripts and function, readers can run most examples and figures on their own computers. The m-files of the scripts can bedownloaded as mentioned later. 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 outstandingfeatures for numerical analyses, however, are: Significantly simpler programming Continuity among integer, real, and complex values Extended range of numbers and their accuracy A comprehensive mathematical library Extensive graphic tools including graphic user interface functions Capability of linking with traditional programming languages Transportability of MATLAB programs An extraordinary feature of MATLAB is that there is no distinction amongreal, complex, and integer numbers. All numbers are in double precision. InMATLAB, all kinds of numbers are continuously connected, as they should be. It means that in MATLAB, any variable can take any type of numberwithout special declaration in programming. This makes programming fasterand more productive. In Fortran, a different subroutine is necessary for eachsingle, double, real or complex, or integer variable, while in MATLAB thereis no need to separate them. The mathematical library in MATLAB makes mathematical analyseseasy. Yet the user can develop additional mathematical routines significantlymore easily than in other programming languages because of the continuitybetween real and complex variables. Among numerous mathematical functions, linear algebra solvers play central roles. Indeed, the whole MATLABsystem is founded upon linear algebra solvers. IMPORTANCE OF GRAPHICS Graphic presentation of mathematical analysis helps the reader to under-stand mathematics and makes it enjoyable. Although this advantage hasbeen well known, presenting computed results with computer graphics wasnot without substantial extra effort in the past. With MATLAB, however, graphic presentations of mathematical material is possible with just a fewcommands. Scientific and even artistic graphic objects can be created on thescreen using mathematical expressions. It has been found that MATLABgraphics motivate and excite students to learn mathematical and numericalmethods that could otherwise be dull. MATLAB graphics are easy and great fun for readers. This book alsoillustrates image processing and production of motion pictures for scientific computing as well as for artistic or hobby material. WILL MATLAB ELIMINATE THE NEED FOR FORTRAN OR C? The answer is no. Fortran and C are still important for high-performancecomputing that requires a large memory or long computing time. The speedof MATLAB computation is significantly slower than that with Fortran orC because MATLAB is paying the high price for the nice features. Learn-ing Fortran or C, however, is not a prerequisite for understanding MATLAB. REFERENCE BOOKS THAT ARE HELPFUL TO LEARN MATLAB This book explains many MATLAB commands but is not intended to be acomplete guide to MATLAB. Readers interested in further information onMATLAB are advised to read User's Guide and Reference Guide. Also, youshould know that over 400 books for use with MATLAB, Simulink, Tool-boxes, and Blocksets have been written. See WEB SITE FOR READERS OF THIS BOOK A Web site for readers of this book has been opened at http://olen.eng.ohio-state.ed/matlab This Web site includes additional examples, hints, and color graphics thatcannot be printed in the book. If there are corrections to the text material, they will appear on this Web site. Links to other relevant sites are alsoprovided. HOW TO OBTAIN M-FILES PACKAGE The m-files package that includes all the scripts and functions developed inthe present book are available from the download site of the publisher, whichcan be accessed via the Web site in the foregoing paragraph. The packageincludes the following files: All m-files listed at the end of chapters. All scripts illustrated in the book (except short ones). Scripts to plot typical figures in the book. SOLUTION KEYS Solution keys for the problems for each chapter are available at the end ofthis book. Further help may also be available at the Web site for the readers. HOW TO OBTAIN MORE INFORMATION ABOUT MATLAB The best way to start collecting more information about MATLAB is to visitthe Web site of MATHWORKS at For other communication with MathWorks, their address is: The MathWorks, Inc., 3 Apple Hill Drive, Natick , MA 01760-2098, United StatesPhone: 508-647-7000, Fax: 508-647-7001. LIST OF REVIEWERS The first edition of this book was reviewed by: Professor T. Aldemir, Nuclear Engineering, The Ohio State University, Columbus, Ohio Professor M. Darwish, Mechanical Engineering Department, American University of Beirut, Beirut, Lebanon The MathWorks Inc., Natick, Massacusetts Professor J.K. Shultis, Nuclear Engineering, Kansas State University, Manhattan, Kansas Professor S.V. Sreenivasan, Department of Mechanical Engineering, University of Texas, Austin, Texas10.3.5 Fourth-Order Runge-Kutta Method Derivation of the fourth-order Runge- Kutta method is similar to that of the ... There are several alternative choices for the numerical integration scheme to be used in Eq.( 10.3.2). ... The first version is based on Simpsona#39;s 1/3 rule and is written as fa = hf(yn, tn) fa = hf(yn + fa/2, tn+i/2) fa = hf(yn + fa/2, tn+l/2) ... We then find that Eq.( 10.3.20) agrees with the Taylor expansion of the exact solution to the third-order term if 9 = ~ 1. using the fourth- orderanbsp;...

Title:Numerical Analysis and Graphic Visualization with MATLAB
Author:Shoichiro Nakamura
Publisher:Prentice Hall - 2002


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