MATLAB数值计算·修订版

　　

　　Numerical Computing with MATLAB revised in 2013（MATLAB数值计算-2013修订版 英文版）
　　MATLAB之父Cleve B. Moler的经典之作，经Cleve本人正式授权，中国首印。
　　
　　

海报：
　　

　　《MATLAB数值计算·2013修订版（英文版）》已得到MATLAB、数值分析和科学计算之父Cleve Moler 本人正式授权。该书不以深奥的数值分析理论为内容，而以易于理解的数学思维和便于掌握的数学计算编程技术为教学素材。该书摒弃以往数值分析教材中常见的程式性定理、定理证明、收敛性理论和冗长公式推演。该书数值算法原理的表述，言简意骇、层次丰富、见解独到、精辟；数学计算软件的教学内容易学易懂，构思巧妙而循循善诱。
　　全书正文共11 章，包括：MATLAB 入门、线性方程组、插值、零点和根、小二乘、定积分、常微分方程、随机数、傅立叶分析、特征值和奇异值、偏微分方程。每章后都配置了大量习题。与本书正文及习题匹配的70 多个M 文件都由Cleve Moler 本人编写，并被其本人赞为引以自傲的软件作品。该书所有代码都适配于MATLAB R2014a。
　　该书是Cleve Moler 专为高校研究生、本科生编写的数值计算、MATLAB 教材。该书也是所有MATLAB 用户理解MATLAB 算法原理的好指南，也是广大科技人员自学、精读或随时查阅的可信赖的参考书。

　　Cleve B.Moler，是MathWorks公司的董事长和首席科学家。Moler先后在密歇根大学、斯坦福大学、新墨西哥大学担任数学和计算机科学教授达20余年。1989年全职加入MathWokrs公司之前，他先后在Intel Hypercube和Ardent Computer这计算机硬件生产公司工作了五年。Cleve先后就读于加州理工和斯坦福并获博士学位。
　　作为MATLAB创始人，他同时也是LINPACK和EISPACK科学子程序库的作者之一。他与别人合作出版了三本关于数值方法的书，同时也独立编写了Numerical Computing with MATLAB 和 Experiments with MATLAB。
　　Cleve长期服务于美国工业与应用数学学会，并于2007-2009任主席。Cleve于1997年当选美国国家工程院院士，并获多项荣誉，包括瑞典林学平大学荣誉学位，加拿大滑铁卢大学荣誉数学博士学位，丹麦科技大学荣誉博士等。Cleve还获得IEEE计算机学会的2012年计算机先驱奖。

Preface
1Introduction to MATLAB
1.1 The Golden Ratio
1.2 Fibonacci Numbers
1.3 Fractal Fern
1.4 Magic Squares
1.5 Cryptography
1.6 The 3n+1 Sequence
1.7 Floating-Point Arithmetic
1.8 Further Reading
Exercises
2 Linear Equations
2.1 Solving Linear Systems
2.2 The MATLAB Backslash Operator
2.3 A 3-by-3 Example
2.4 Permutation and Triangular Matrices
2.5 LU Factorization
2.6 Why Is Pivoting Necessary?
2.7 lutx, bslashtx, lugui
2.8 Effect of Roundoff Errors
2.9 Norms and Condition Numbers
2.10 Sparse Matrices and Band Matrices
2.11 PageRank and Markov Chains
2.12 Further Reading
Exercises
3 Interpolation
3.1 The Interpolating Polynomial
3.2 Piecewise Linear Interpolation
3.3 Piecewise Cubic Hermite Interpolation
3.4 Shape-Preserving Piecewise Cubic
3.5 Cubic Spline
3.6 pchiptx, splinetx
3.7 interpgui
Exercises
4 Zeros and Roots
4.1 Bisection
4.2 Newton's Method
4.3 A Perverse Example
4.4 Secant Method
4.5 Inverse Quadratic Interpolation
4.6 Zeroin
4.7 fzerotx
4.8 fzerogui
4.9 Value Finding and Reverse Interpolation
4.10 Optimization and fmintx
Exercises
5 Least Squares
5.1 Models and Curve Fitting
5.2 Norms
5.3 censusgui
5.4 Householder Reflections
5.5 The QR Factorization
5.6 Pseudoinverse
5.7 Rank De ciency
5.8 Separable Least Squares
5.9 Further Reading
Exercises
6 Quadrature
6.1 Adaptive Quadrature
6.2 Basic Quadrature Rules
6.3 quadtx, quadgui
6.4 Specifying Integrands
6.5 Performance
6.6 Integrating Discrete Data
6.7 Further Reading
Exercises
7 Ordinary Differential Equations 193
7.1 Integrating Differential Equations
7.2 Systems of Equations
7.3 Linearized Differential Equations
7.4 Single-Step Methods
7.5 The BS23 Algorithm
7.6 ode23tx
7.7 Examples
7.8 Lorenz Attractor
7.9 Stiffness
7.10 Events
7.11 Multistep Methods
7.12 The MATLAB ODE Solvers
7.13 Errors
7.14 Performance
7.15 Further Reading
Exercises
8 Fourier Analysis
8.1 Touch-Tone Dialing
8.2 Finite Fourier Transform
8.3 fftgui
8.4 Sunspots
8.5 Periodic Time Series
8.6 Fast Finite Fourier Transform
8.7 ffttx
8.8 fftmatrix
8.9 Other Fourier Transforms and Series
8.10 Further Reading
Exercises

　　Preface
　　Numerical Computing with MATLAB is a textbook for an introductory coursein numerical methods Matlab and technical computing. The emphasis is on in-formed use of mathematical software. We want you learn enough about the mathe-matical functions in Matlab that you will be able to use them correctly appreciatetheir limitations and modify them when necessary to suit your own needs. Thetopics include
　　introduction to Matlab
　　linear equations
　　interpolation
　　zero and roots
　　least squares
　　quadrature
　　ordinary differential equations
　　random numbers
　　Fourier analysis
　　eigenvalues and singular values
　　partial differential equations.
　　George Forsythe initiated a software-based numerical methods course at Stan-ford University in the late 1960s. The textbooks by Forsythe Malcolm and Moler[20] and Kahaner Moler and Nash [34] that evolved from the Stanford course werebased upon libraries of Fortran subroutines.
　　This textbook is based upon Matlab. NCM a collection of over 70 M-files forms an essential part of the book. Many of the over 200 exercises involvemodifying and extending the programs in NCM. The book also makes extensiveuse of computer graphics including interactive graphical expositions of numericalalgorithms.
　　The prerequisites for the course and the book include
　　calculus
　　some familiarity with ordinary differential equations
　　some familiarity with matrices
　　some computer programming experience.
　　If you've never used Matlab before the rst chapter will help you get started. Ifyou're already familiar with Matlab you can glance over most of the rst chapterquickly. Everyone should read the section in the rst chapter about oating-point
　　arithmetic.
　　There is probably too much material here for a one-quarter or one-semestercourse. Plan to cover the rst several chapters and then choose the portions of thelast four chapters that interest you.
　　Make sure that the NCM collection is installed on your network or your per-sonal computer as you read the book. The software is available from a Web sitedevoted to the book [47]:
　　http://www.mathworks.cn/moler
　　There are three types of NCM files:
　　gui files: interactive graphical demonstrations;
　　tx files: textbook implementations of built-in Matlab functions;
　　others: miscellaneous files primarily associated with exercises.When you have NCM available
　　ncmgui
　　produces the figure shown on the next page. Each thumbnail plot is actually a pushbutton that launches the corresponding gui.
　　This book would not have been possible without the people at The MathWorksand at SIAM. Both groups are professional creative and delightful to work with.They have been especially supportive of this book project. Out of the many friendsand colleagues who have made speci c contributions I want to mention five inparticular. Kathryn Ann Moler has used early drafts of the book several times incourses at Stanford and has been my best critic. Tim Davis and Charlie Van Loanwrote especially helpful reviews. Lisl Urban did an immaculate editing job. My wifePatsy has lived with my work habits and my laptop and loves me anyway. Thankseveryone.
　　A revised reprint in 2008 included a change in the section on Google PageRankthat improves the handling of web pages with no out links a short new section inthe Random Numbers chapter removal of material on inline and feval andcorrection of a few dozen minor typographical errors.
　　A significant update in September 2013 incorporates over 60 changes. Manyof them have been recommended by Professor Zhiyong Zhang of Nanjing Univer-sity of Posts and Telecommunications in China (NJUPT) who prepared a Chinesetranslation for BUAA press. The census example in section 5.3 includes the 2010census. Output from format long shows 16 signi cant digits. Symbolic Toolboxusage re
　　ects the MuPad connection. Many thanks to Prof. Zhang.
　　Cleve Moler
　　Sept. 16 2013