《Mathematica Navigator》完整版下载指南：学习MATHEMATICA的权威教程

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"《Mathematica® Navigator》是一本详细介绍Mathematica编程和应用的优秀教材，适合对数学、统计学以及图形处理感兴趣的读者。本书由Heikki Ruskeepää撰写，他是芬兰图尔库大学数学系的教授，以其深厚的学术背景和实践经验，为读者提供了深入理解Mathematica的实用指南。该书第三版反映了作者对Mathematica的最新理解和技巧，旨在帮助用户充分利用其强大的功能进行数据处理、符号计算、可视化以及解决实际问题。这本书的特点在于其内容的实用性与理论相结合，不仅包含了基础知识，如函数定义、表达式操作、数据结构等，还涵盖了高级主题，如数值分析、机器学习算法实现以及图形设计。由于Mathematica版本的更新，书中可能包含了针对最新版本特性的讲解，确保读者能够跟上技术的步伐。值得注意的是，这本书是由Mathematica软件本身生成的PDF文件，这体现了Mathematica的强大功能，也暗示了读者可以通过这本书的学习来提升对Mathematica的掌握程度。版权方面，所有复制或传播必须得到Elsevier出版社的书面许可，以尊重作者的知识产权。对于那些在CSDN网站上寻找资源的用户，虽然提供了分章节下载的选项，这里提供的是一本完整的单文件版本，方便读者一次性获取所有内容。无论是初学者还是进阶用户，都能从中找到适合自己的学习资料和实例，提升在Mathematica环境下的编程能力。《Mathematica® Navigator》是一本值得投资的书籍，它不仅是学习Mathematica的强大工具，也是扩展数学技能、进行数据分析和探索复杂图形的理想资源。通过阅读这本书，读者不仅能掌握Mathematica的基本操作，还能了解到如何将其应用于解决实际问题，提升工作效率。"

‡ Depth

To give an impression of the depth of various topics, we next describe some special topics in various

cha

ters of the book.

• Chapter 3, Notebooks: An introduction to Mathematica as an environment for preparing technical

documents; writing mathematical formulas

• Chapter 5, Graphics for Functions: Stereographic figures; graphics for four-dimensional functions

• Chapter 8, Graphics for Data: Visualizations of several real-life data; dot plots; statistical plots

• Chapter 18, Programs: Four styles of programming (procedural, functional, rule-based, and

recursive); emphasis on functional programming; many examples of programs

• Chapter 22, Equations: Iterative methods of solving linear equations; programs for nonlinear

equations

• Chapter 23, Optimization: A program for numerical minimization; a program for classical optimiza-

tion with equality and inequality constraints; dynamic programming

• Chapter 25, Approximation: Graphical diagnostics of least-squares fits

• Chapter 26, Differential Equations: Analyzing and visualizing solutions of systems of nonlinear

differential equations; study of a predator

-prey model, a competing species model, and the Lorenz

model; numerical solution of linear and nonlinear boundary value problems; estimation of

nonlinear differential equations from data; solving integral equations

• Chapter 27, Partial Differential Equations: Series solutions for partial differential equations; solving

parabolic and hyperbolic problems by the method of lines; solving elliptic problems by the finite

difference method

• Chapter 28, Difference Equations: The logistic model as an example of nonlinear difference

equations; bifurcation diagrams, periodic points, Lyapunov exponents; a discrete-time preda-

tor

-prey model as an example of a system of nonlinear difference equations; estimation of

nonlinear difference equations from data; fractal images; Lindenmayer systems

• Chapter 29, Probability: Simulation of several stochastic processes

• Chapter 30, Statistics: Visualizing confidence intervals and types of errors in statistical tests;

confidence intervals and tests for probabilities; local regression; Bayesian statistics; Gibbs sampling;

Markov chain Monte Carlo

‡ Programs

Mathematica has a large number of ready-to-use commands for symbolic and numerical calculations and

for graphics. Nevertheless, in this book we also present approximately 130 of our own programs.

Indeed, programming is one of the strongest points of Mathematica. It is often amazing how concisely

and efficiently we can write a program even for a somewhat complex problem. We think that our own

programs can be of some value, despite the fact that they are not so fine and powerful as Mathematica’s

built-in commands. We have included our own programs for the following reasons:

1. A self-made implementation shows clearly how the algorithm works. You know (or should know)

exactly what you are doing when you use your own implementation. The ready-made commands

are often like black (or gray) boxes because we do not know much about the methods.

2. Writing our own implementations teaches us programming. We present short programs through-

out the book (especially in the mathematical chapters). In this way, we hope that you will become

steadil

more familiar with

rammin

and that

ou are encoura

ed to

ractice

ram writin

Preface xv

3. A self-made implementation can be pedagogically worthwhile. For example, we implement Euler’s

method for differential equations. It has almost no practical value, but as the simplest numerical

method for initial value problems, it has a certain pedagogical value. Also, programming a simple

method first may help us to tackle a more demanding method later.

‡ Other Special Aspects

We have integrated the so-called packages tightly into the material covered in this book. Instead of

resentin

a se

arate cha

ter about

acka

es, each

acka

e is ex

lained in its

er context.

We have tried to make the structure of the book such that finding a topic is easy. Usually a topic is

considered in one and only one chapter or section so that you need not search in several places to find

the whole story. Each numerical routine is also presented in the proper context after the corresponding

symbolic methods. This helps you to find material for solving a given problem: It is usually best to try a

symbolic method first and, if this fails, to then resort to a numerical method.

Some topics of a “pure” nature, such as finite fields, quaternions, combinatorics, computational

geometry, and graph theory, are not considered in this book; Mathematica has packages for these topics.

Commands for box and notebook manipulation are treated only briefly. We do not consider MathLink (a

part of Mathematica that enables interaction between Mathematica and external programs), J/Link (a

product that integrates Mathematica and Java), XML (a metamarkup language for the World Wide Web),

or MathML (an XML-based markup language for representing mathematics). Also, we do not consider

any of the many other Mathematica-related products, such as webMathematica, gridMathematica,

CalculationCenter, or the Applications Library packages.

Mathematica 6

‡ Introduction

Mathematica 6 contains a huge amount of new functionality. The following is a part of an on-line

document:

Mathematica 6.0 fundamentally redefines Mathematica and introduces a major new paradigm for

computation. Building on Mathematica’s time-tested core symbolic architecture, version 6.0 adds

nearly a thousand new functions~almost doubling the total number of functions in the system~

dramatically increasing both the breadth and depth of Mathematica’s capabilities, as well as introduc-

ing hundreds of major original algorithms, and perhaps a thousand new ideas, large and small.

To study the new features, see the following on-line documentation (the use of the Documentation

Center is explained in Section 1.4.2, p. 17):

• Help @ Startup Palette, the What’s New in 6 link to Wolfram’s website

• Help @ Documentation Center, the New in 6 links in the home page

• Help @ Documentation Center, the

guideêSummaryOfNewFeaturesIn60 document

• Help @ Documentation Center, the

guideêNewIn60AlphabeticalListing document

• Help @ Function Navigator, the New In 6 item

If you are a new user of Mathematica and would like to study the basics of Mathematica 6, see the

following documents:

• Help @ Startup Palette: the First Five Minutes with Mathematica button

• Hel

@ Virtual Book: the Introduction item

xvi Mathematica Navigator

‡ New Properties of Version 6

Because the new features are numerous, we do not list them all here. However, we mention some of the

most remarkable new commands and features, classified accordin

to the cha

ters of the book:

• Chapter 1, Starting: documentation is on-line in the form of Documentation Center, Function

Navigator and Virtual Book (we do not have a printed manual); documentation is automatically

updated via the Internet; writing Mathematica inputs is helped by syntax coloring

• Chapter 3, Notebooks:

Style, Text, Hyperlink

• Chapter 4, Files: commands of many packages are now built-in; the remaining packages are rebuilt;

look at Compatibility/guide/StandardPackageCompatibilityGuide in the Documentation Center

to obtain information about how to replace the functionality of the old packages

• Chapter 5, Graphics for Functions:

GraphicsRow, GraphicsGrid, Tooltip; graphics is handled like

other expressions; the default font in graphics is Times instead of Courier; 3D graphics is adaptive;

contours in contour plots have tooltips; density plots, by default, do not have meshes; 2D graphics

can be interactively drawn and edited; 3D graphics can be interactively manipulated (e.g., rotated);

for animation, use

Manipulate or Animate

• Chapter 6, Graphics Primitives: Arrow, Opacity, Inset

• Chapter 7, Graphics Options: Directive, BaseStyle, Filling; the default value of AspectRatio in

Graphics and ParametricPlot is Automatic instead of 1/GoldenRatio

• Chapter 8, Graphics for Data: ListLinePlot, GraphPlot; plotting of several data sets

• Chapter 9, Data:

ElementData, CountryData, PolyhedronData, etc.

• Chapter 10, Manipulations:

Manipulate (for creating interactive dynamic interfaces)

• Chapter 11, Dynamics:

Dynamic (for advanced dynamic interfaces), MenuView, TabView, etc.

• Chapter 15, Tables:

Grid, Row, Column

• Chapter 16, Patterns: DictionaryLookup

• Chapter 21, Matrices: Accumulate, PositiveDefiniteMatrixQ

• Chapter 23, Optimization: FindShortestTour

• Chapter 29, Probability: RandomReal, RandomInteger, RandomChoice, RandomSample

• Chapter 30, Statistics: Tally, BinCounts, FindClusters

In my opinion, the most impressive new commands in version 6 are Manipulate, Dynamic,

GraphPlot, and Grid.

Note that many familiar commands, such as

NIntegrate or NDSolve, have also been enhanced in

version 6.

In the forthcoming chapters, we mark with (Ÿ6) the properties and commands of Mathematica

available for the first time in version 6.

‡ Obsolete Properties in Version 6

Version 6 makes obsolete some old commands and features, especially in graphics. First, here are some

changes that relate to the display and arrangement of graphics:

• To prevent the display of graphics, end the plotting command with

; instead of using the

DisplayFunction option.

• In programs, enclose a plotting command with

Print if that command is not the last command of

the program and you would like the program to show that plot.

•

GraphicsArray is obsolete. To show, for example, two plots p1 and p2 side by side, use one of the

following ways:

{p1, p2}, Row[{p1, p2}], or GraphicsRow[{p1, p2}]. Use GraphicsGrid for

arrays of plots.

Preface xvii

• To show two plots side by side, you can also simply give a list of plotting commands {Plot[…],

Plot[…]}

• To show two plots on top of each other, simply write

Show[Plot[…], Plot[…]]; the

DisplayFunction option is no longer needed.

•

Graphics and Graphics3D no longer need Show to display the graphics. Thus, write

Graphics[{…}] instead of Show[Graphics[{…}].

• Use Inset[gr, pos] instead of Rectangle[{x1, y1}, {x2, y2}, gr].

Some changes that relate to plotting of data are as follows:

• To plot data by connecting the points with lines, use

ListLinePlot[data] instead of

ListPlot[data, PlotJoined Ø True].

• To plot data by points and connecting lines, use

ListLinePlot[data, Mesh Ø All] instead of

ListPlot[data, PlotJoined Ø True, Epilog Ø {PointSize[s], Map[point, data]}].

• To plot data by points and vertical lines, use

ListPlot[data, Filling Ø Axis] instead o

resorting to Prolog or Epilog.

• To plot several data sets, use

ListPlot[{data1, data2, … }] or ListLinePlot[{data1, data2, …

}]

instead of resorting to MultipleListPlot in a package.

• To

lot several

oints, sim

write Point[points] instead of Map[Point, points].

Here are some changes that relate to styles and options of graphics:

• Use

Style instead of StyleForm.

• Use the

BaseStyle option instead of the TextStyle option or the $TextStyle global constant.

• Use the MaxRecursion option instead of the PlotDivision option.

• Use the

DataRange option instead of the MeshRange option.

• Use the Filling option instead of the FilledPlot command.

Some other changes are as follows:

• Use

RandomReal[…], RandomInteger[…], and RandomComplex[…] instead of Random[Real, …],

etc.

• For random numbers from probability distributions, use

RandomReal[contDist, n] or

RandomInteger[discrDist, n] instead of resorting to Random or RandomArray.

• Use

Tally instead of Frequencies in a package.

The Third Edition

‡ Main Changes

The text has been revised throughout. Indeed, Mathematica 6 brings up so much new and changed

features that almost every topic has undergone a revision and new topics are included. Recall that the

second edition of this book was based on Mathematica 5.

The main change in the structure of the book is that we have six new chapters: Chapter 6, Graphics

Primitives; Chapter 9, Data; Chapter 10, Manipulations; Chapter 11, Dynamics; Chapter 15, Tables; and

Chapter 16, Patterns. On the other hand, some chapters have been merged and the result is that the

current edition has but one chapter about the following topics: graphics for functions, graphics for data,

and graphics options (the second edition had two chapters for each of these topics, one for two-

dimensional and one for three-dimensional graphics).

xviii Mathematica Navigator

The main change in the contents of the book is the transition from version 5 to version 6. In addition,

we have some other enhancements. The chapter on programming is much enhanced and enlarged and

contains much more examples. The chapter about matrix calculus is also enhanced. The chapter about

optimization now includes the method of dynamic programming. Chapters about graphics for data and

timization have under

one a restructurin

Note that this book fully utilizes the new features of Mathematica 6. Because version 6 differs so much

from earlier versions, this book cannot practically be used with older versions of Mathematica. If you

have Mathematica 5.2 or an earlier version, please use the second edition of Mathematica Navigator.

The CD-ROM contains Help Browser material that describes the new properties of Mathematica 7.

‡ Some Notes

New Features

Some of the new features of version 6 would have warranted a broader and deeper treatment and more

examples of use throughout the book. These features include the creation of dynamic interfaces and the

use of the built-in data sources. However, to keep the book at a reasonable size, we had to limit the

treatment and the number of examples. We suggest that the reader consults the built-in documentation.

The website http://demonstrations.wolfram.com contains thousands of examples of dynamic interfaces.

Environment

During the writing of this book, I used a Macintosh with MacOS X. Mathematica works in much the same

way in various environments, but the keyboard shortcuts of menu commands vary among different

environments. To some extent, we mention the shortcuts for the Microsoft Windows and Macintosh

environments.

Options

Many commands of Mathematica have options for modifying them. All options have a default value, but

we can input other values. When listing the options, we give either all possible values of them or some

examples of possible values, but we do not explicitly mention the default values, to save space. In the

context of this book, the default value of an option is always the first value mentioned. After that are other

possible values or examples of other values.

Simulations

In several places in the book, we simulate various random phenomena. Usually, each time a simulation

is run, a slightly different result is obtained. However, in experimenting with the examples of the book,

the reader may want to get exactly the same result as printed in the book. This can be achieved by using

a seed to the random number generator with

SeedRandom[n] for a given integer n. With the same seed,

the result of a simulation remains the same in repeated executions. We use

SeedRandom quite often in

this book. If you want to get other results of simulation than those of this book, give different seeds or

do not execute

SeedRandom[n] at all (in the latter case, the default seed is used).

CD-ROM

The entire book is contained on the CD-ROM that comes with it. With a few easy steps you can install

the book into the Help Browser of Mathematica (the CD-ROM contains installation instructions). With

the Help Browser you can easily find and read sections of the book, experiment with the commands,

and copy material from the book to your document. You can see all of the figures of the book in color

and interactively study the manipulations and animations. The material about the new properties of

Mathematica 7 can also be installed into the Help Browser. In addition, the CD-ROM contains some data

files that are used in the book.

Preface xix

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