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Numerical Analysis and Graphic Visualization with MATLAB, 2nd Edition

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Numerical Analysis and Graphic Visualization with MATLAB, 2nd Edition


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  • NEW - Focus on MATLAB-6—Modifies many explanations and implements the new features of MATLAB into the software in the book (the previous edition was based on MATLAB 4).
    • Keeps students up to date on the latest version of the software. Ex.___

  • NEW - Additional introductory coverage of MATLAB—Revises explanation in Chapter 1 of MATLAB commands, examples, and exercise problems, and increases the number of problems, so that beginning students can understand the programming.
    • Makes material more accessible for beginning students and makes book more adaptable to students at different levels. Ex.___

  • NEW - New graphic capabilities in MATLAB-6—Updates Chapter 2 on Graphics to incorporate new features of MATLAB.
    • Keeps students up to date on the latest version of the software. Ex.___

  • NEW - Redrawn figures with better captions—Includes subscripts, superscripts, and legends.
    • Appeals to students' need to learn visually and supports text material. Ex.___

  • NEW - Solution keys provided.
    • Helps students assess their progress and understanding of the material. Ex.___

  • Comprehensive tutorials of MATLAB commands and graphic tools.
    • Gives students a well-rounded understanding of fundamental concepts. Ex.___

  • Coverage of numerical methods with their implementations in MATLAB—Illustrates all numerical methods described with applications in MATLAB.
    • Demonstrates realistic applications of principles. Ex.___

  • Lists of scripts and functions—Enables students to run most examples and figures on their own computers.
    • Gives students firsthand, hands-on practice with the material. Ex.___


  • Copyright 2002
  • Dimensions: K
  • Pages: 544
  • Edition: 2nd
  • Book
  • ISBN-10: 0-13-065489-2
  • ISBN-13: 978-0-13-065489-2

Leverage the power of MATLAB 6 in all your technical computation and measurement applications

Now, there is a complete introduction to numerical methods and visualization with the latest, most powerful version of MATLAB, Version 6.0. Dr. Shoichiro Nakamura introduces the skills and knowledge needed to solve numerical equations with MATLAB, understand the computational results, and present them graphically.

This book brings together all four cornerstones of numerical analysis with MATLAB: the fundamental techniques of MATLAB programming; the mathematical basis of numerical methods; the application of numerical analysis to engineering, scientific, and mathematical problems; and the creation of scientific graphics. Coverage includes:

  • Complete introductory tutorials for both MATLAB 6.0 programming and professional-quality 3D graphics
  • Linear algebra applications: matrices, vectors, Gauss elimination, Gauss-Jordan elimination, LU decomposition, and more
  • Polynomials and interpolation, including interpolation with Chebyshev points; cubic hermite, 2D and transfinite interpolation; and M-files
  • Numerical integration, differentiation, and roots of nonlinear equations
  • Advanced techniques, including curve fitting, spline functions, and boundary value problems

Whether you are a student, engineer, scientist, researcher, or economic analyst, MATLAB 6 offers you unprecedented power for defining and solving problems. Put that power to work — with Numerical Analysis and Graphical Visualization with MATLAB, second edition.

Sample Content

Table of Contents


1. MATLAB Primer.

Before Starting Calculations. How to Do Calculations. Branch Statements. Loops with for/end or while/end. Reading and Writing. Array Variables. Unique Aspect of Numbers in MATLAB. Mathematical Functions of MATLAB. Functions That Do Chores. Developing a Program as an M-File. How to Write Your Own Functions. Saving and Loading Data. How to Make Hard Copies.

2. Graphics with MATLAB.

Simple Plotting. Interactive Editing of Figures. How to Print or Record Graphs. Plotting of Two-Dimensional Functions. Triangular Grid and Contours. Curvilinear Grid and Contours. Plotting Curved Surfaces. MATLAB as a Drawing Board. Interactive Graphics. M-Files.

3. Linear Algebra.

Matrices and Vectors. Matrix and Vector Operations in MATLAB. Inverse Matrix. Linear Equations. Unsolvable Problems. The Determinant. Ill-conditioned Problems. Gauss Elimination. Gauss-Jordan Elimination and Matrix Inversion. LU Decomposition. Iterative Solution. Matrix Eigenvalues.

4. Polynomials and Interpolation.

MATLAB Commands for Polynomials. Linear Interpolation. Polynomial Interpolation with Power Series. Lagrange Interpolation Polynomial. Error of Interpolation Polynomials. Differentiation and Integration of Lagrange Interpolation Formula. Interpolation with Chebyshev Points. Cubic Hermite Interpolation. Two-Dimensional Interpolation. Transfinite Interpolation. M-Files.

5. Numerical Integration.

Trapezoidal Rule. Simpson's Rules. Other Quadratures. Numerical Integration with Infinite Limits or Singularities. MATLAB Commands for Integrations. Numerical Integration on a Two-Dimensional Domain. M-Files.

6. Numerical Differentiation.

Derivatives of Interpolation Polynomials. Difference Approximations. Taylor Expansion Method. Algorithms to Automate Derivations. Difference Approximation for Partial Derivatives. Numerical Evaluation of High-Order Derivatives. M-Files.

7. Roots of Nonlinear Equations.

Graphical Method. Bisection Method. Newton Iteration. Secant Method. Successive Substitution Method. Simultaneous Nonlinear Equations. M-Files.

8. Curve Fitting To Measured Data.

Line Fitting. Nonlinear Curve Fitting with a Power Function. Curve Fitting with a Higher-Order Polynomial. Curve Fitting by a Linear Combination of Known Functions.

9. Spline Functions and Nonlinear Interpolation.

C-Spline Interpolation. Cubic B-Spline. Interpolation with a Nonlinear Function. M-Files.

10. Initial-Value Problems of Ordinary Differential Equations.

First-Order ODEs. Euler Methods. Runge-Kutta Methods. Shooting Method. Method of Lines.

11. Boundary-Value Problems of Ordinary Differential Equations.

Introduction. Boundary-Value Problems for Rods and Slabs. Solution of Tridiagonal Equations. Variable Coefficients and Nonuniform Grids. Cylinders and Spheres. Nonlinear Ordinary Differential Equations.

Appendix A: Colors.

Appendix B: Drawing Three-Dimensional Objects.

Appendix C: Movies.

Appendix D: Image Processing.

Appendix E: Graphical User Interface.

Appendix F: Answer Key.

Subject Index.




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.


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.


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.


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.


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



A Web site for readers of this book has been opened at


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.


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:

  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 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.


The best way to start collecting more information about MATLAB is to visitthe Web site of MATHWORKS at http://www.mathworks.com

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.


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, Texas


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