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Title...........: Mathematica® Navigator. Mathematics, Statistics, and Graphics
Edition.........: THIRD EDITION
Year............: 2009
Pages...........: 1135
Type............: Ebook
Reader..........: PDF Reader
Size............: 18.6 MB
Posted by.......: [godsogood]


Mathematica® Navigator

Mathematics, Statistics, and Graphics

THIRD EDITION

Heikki Ruskeepää
Department of Mathematics
University of Turku, Finland

Copyright © 2009, Elsevier Inc. All rights reserved.

Printed in the United States of America

Contents:

Preface xi

1 Starting 1
	1.1 What Is Mathematica 2
	1.2 First Calculations 6
	1.3 Important Conventions 12
	1.4 Getting Help 15
	1.5 Editing 22
2 Sightseeing 25
	2.1 Graphics 26
	2.2 Expressions 31
	2.3 Mathematics 40
3 Notebooks 51
	3.1 Working with Notebooks 52
	3.2 Editing Notebooks 59
	3.3 Inputs and Outputs 70
	3.4 Writing Mathematical Documents 78
4 Files 93
	4.1 Loading Packages 94
	4.2 Exporting and Importing 100
	4.3 Saving for Other Purposes 109
	4.4 Managing Time and Memory 112
5 Graphics for Functions 115
	5.1 Basic Plots for 2D Functions 116
	5.2 Other Plots for 2D Functions 132
	5.3 Plots for 3D Functions 139
	5.4 Plots for 4D Functions 147
6 Graphics Primitives 151
	6.1 Introduction to Graphics Primitives 152
	6.2 Primitives and Directives 155
7 Graphics Options 179
	7.1 Introduction to Options 180
	7.2 Options for Form, Ranges, and Fonts 189
	7.3 Options for Axes, Frames, and Primitives 195
	7.4 Options for the Curve 203
	7.5 Options for Surface Plots 210
	7.6 Options for Contour and Density Plots 226
8 Graphics for Data 231
	8.1 Basic Plots 232
	8.2 Scatter Plots 249
	8.3 Bar Charts 253
	8.4 Other Plots 260
	8.5 Graph Plots 267
	8.6 Plots for 3D Data 275
9 Data 283
	9.1 Chemical and Physical Data 284
	9.2 Geographical and Financial Data 293
	9.3 Mathematical and Other Data 300
10 Manipulations 315
	10.1 Basic Manipulation 316
	10.2 Advanced Manipulation 338
11 Dynamics 357
	11.1 Views and Animations 357
	11.2 Advanced Dynamics 369
12 Numbers 395
	12.1 Introduction to Numbers 396
	12.2 Real Numbers 403
	12.3 Options of Numerical Routines 409
13 Expressions 413
	13.1 Basic Techniques 414
	13.2 Manipulating Expressions 419
	13.3 Manipulating Special Expressions 427
	13.4 Mathematical Functions 435
14 Lists 443
	14.1 Basic List Manipulation 444
	14.2 Advanced List Manipulation 459
15 Tables 4670
	15.1 Basic Tabulating 467
	15.2 Advanced Tabulating 470
16 Patterns 4910
	16.1 Patterns 491
	16.2 String Patterns 505
17 Functions 5110
	17.1 User-Defined Functions 512
	17.2 More about Functions 523
	17.3 Contexts and Packages 531
18 Programs 5410
	18.1 Simple Programming 542
	18.2 Procedural Programming 553
	18.3 Functional Programming 568
	18.4 Rule-Based Programming 584
	18.5 Recursive Programming 596
19 Differential Calculus 6150
	19.1 Derivatives 615
	19.2 Taylor Series 624
	19.3 Limits 630
20 Integral Calculus 6330
	20.1 Integration 634
	20.2 Numerical Quadrature 644
	20.3 Sums and Products 666
	20.4 Transforms 670
21 Matrices 6770
	21.1 Vectors 677
	21.2 Matrices 686
22 Equations 709
	22.1 Linear Equations 710
	22.2 Polynomial and Radical Equations 716
	22.3 Transcendental Equations 730
23 Optimization 7410
	23.1 Global Optimization 743
	23.2 Linear Optimization 753
	23.3 Local Optimization 759
	23.4 Classical Optimization 768
	23.5 Special Topics 777
24 Interpolation 791
	24.1 Usual Interpolation 792
	24.2 Piecewise Interpolation 797
	24.3 Splines 803
	24.4 Interpolation of Functions 806
25 Approximation 811
	25.1 Approximation of Data 812
	25.2 Approximation of Functions 824
26 Differential Equations 829
	26.1 Symbolic Solutions 830
	26.2 More about Symbolic Solutions 841
	26.3 Numerical Solutions 849
	26.4 More about Numerical Solutions 865
27 Partial Differential Equations 885
	27.1 Symbolic Solutions 886
	27.2 Series Solutions 893
	27.3 Numerical Solutions 909
28 Difference Equations 923
	28.1 Solving Difference Equations 924
	28.2 The Logistic Equation 935
	28.3 More about Discrete Systems 950
29 Probability 961
	29.1 Random Numbers and Sampling 962
	29.2 Discrete Probability Distributions 966
	29.3 Continuous Probability Distributions 976
	29.4 Stochastic Processes 987
30 Statistics 1003
	30.1 Descriptive Statistics 1004
	30.2 Frequencies 1011
	30.3 Confidence Intervals 1020
	30.4 Hypothesis Testing 1024
	30.5 Regression 1030
	30.6 Smoothing 1041
	30.7 Bayesian Statistics 1046
References 1063
Index 1067


Contents Parts:

The 30 chapters of the book can be divided into nine main parts:

Introduction
	1. Starting
	2. Sightseeing
Files
	3. Notebooks
	4. Files
Graphics
	5. Grahics for Functions
	6. Graphics Primitives
	7. Graphics Options
	8. Graphics for Data
Data
	9. Data
Dynamics
	10. Manipulations
	11. Dynamics
Expressions
	12. Numbers
	13. Expressions
	14. Lists
	15. Tables
	16. Patterns
Programs
	17. Functions
	18. Programs
Mathematics
	19. Differential Calculus
	20. Integral Calculus
	21. Matrices
	22. Equations
	23. Optimization
	24. Interpolation
	25. Approximation
	26. Differential Equations
	27. Partial Differential Equations
	28. Difference Equations
Statistics
	29. Probability
	30. Statistics


Preface

Welcome

The goals of this book, the third edition of Mathematica Navigator: Mathematics, Statistics, 

Graphics, and
Programming, are as follows:
•􀀁to introduce the reader to Mathematica; and
•􀀁to emphasize mathematics (especially methods of applied mathematics), statistics, 

graphics,
programming, and writing mathematical documents.
Accordingly, we navigate the reader through Mathematica and give an overall introduction. 

Often we
slow down somewhat when an important or interesting topic of mathematics or statistics is 

encountered
to investigate it in more detail. We then often use both graphics and symbolic and numerical 

methods.
Here and there we write small programs to make the use of some procedures easier. One 

chapter is
devoted to Mathematica as an advanced environment of writing mathematical documents.
The online version of the book, which can be installed from the enclosed CD-ROM, makes the
material easily available when working with Mathematica.
Changes in this third edition are numerous and are explained later in the Preface. The 

current edition
is based on Mathematica 6. On the CD-ROM, there is material that describes the new 

properties of
Mathematica 7.



‡ Readership

The book may be useful in the following situations:
•􀀁for courses teaching Mathematica;
•􀀁for several mathematical and statistical courses (given in, for example, mathematics, 

engineering,
physics, and statistics); and
•􀀁for self-study.
Indeed, the book may serve as a tutorial and as a reference or handbook of Mathematica, and 

it may
also be useful as a companion in many mathematical and statistical courses, including the 

following:
differential and integral calculus • linear algebra • optimization • differential, partial 

differential,
and difference equations • engineering mathematics • mathematical methods of physics •
mathematical modeling • numerical methods • probability • stochastic processes • statistics 

•
regression analysis • Bayesian statistics


‡ Previous Knowledge

No previous knowledge of Mathematica is assumed. On the other hand, we assume some knowledge 

of
various topics in pure and applied mathematics. We study, for example, partial differential 

equations
and statistics without giving detailed introductions to these topics. If you are not 

acquainted with a
topic, you can simply skip the chapter or section of the book considering that topic.
Also, to understand the numerical algorithms, it is useful if the reader has some knowledge 

about the
simplest numerical methods. Often we introduce briefly the basic ideas of a method (or they 

may
become clear from the examples or other material presented), but usually we do not derive 

the methods.
If a topic is unfamiliar to you, consult a textbook about numerical analysis, such as Skeel 

and Keiper
(2001).


‡ Recommendations

If you are a newcomer to Mathematica, then Chapter 1, Starting, is mandatory, and Chapter 2, 

Sightseeing,
is strongly recommended. You can also browse Chapter 3, Notebooks, and perhaps also Chapter 

4,
Files, so that you know where to go when you encounter the topics of these chapters. After 

that you can
proceed more freely. However, read Section 13.1, “Basic Techniques,” because it contains 

some very
common concepts used constantly for expressions.
If you have some previous knowledge of Mathematica, you can probably go directly to the 

chapter or
section you are interested in, with the risk, however, of having to go back to study some 

background
material. Again, be sure to read Section 13.1.



‡ Introduction, Files, Graphics, Data, Dynamics, Expressions, and Programs

The first two chapters introduce Mathematica and give a short overview.
The next two chapters consider files, particularly files created by Mathematica, which are 

called
notebooks. We show how Mathematica can be used to write mathematical documents. We also 

explain
how to load packages, how to export and import data and graphics into and from Mathematica, 

and how
to manage memory and computing time. You may skip these two chapters until you need them.
Then we go on to graphics. One of the finest aspects of Mathematica is its high-quality 

graphics, and
one of the strongest motivations for studying Mathematica is to learn to illustrate 

mathematics with
figures. We consider separately graphics for functions and graphics for data. In addition, 

we have
chapters about graphics primitives and graphics options.
New in Mathematica 6 are the built-in data sources, covering topics such as chemistry, 

astronomy,
particles, countries, cities, finance, polyhedrons, graphs, words, and colors.
The main new topic in Mathematica 6 is dynamics. This allows us to easily build interactive 

interfaces.
The user of such an interface can choose some parameters or other options and the output 

will be
changed dynamically, in real time. This helps in studying various models and phenomena.
Then we study various types of expressions, from numbers to strings, mathematical 

expressions,
lists, tables, and patterns.
We have two chapters relating to programming. The first studies functions and the next 

various
styles of programming. Four styles are considered: procedural, functional, rule-based, and 

recursive.


‡ Mathematics and Statistics

In the remaining 12 chapters, we study different areas of pure and applied mathematics and 

statistics.
The mathematical chapters can be divided into four classes, with each class containing 

chapters of more
or less related topics. Descriptions of these classes follow.
Topics of traditional differential and integral calculus include derivatives, Taylor series, 

limits,
integrals, sums, and transforms.
Then we consider vectors and matrices; linear, polynomial, and transcendental equations; and 

global,
local, and classical optimization.
In interpolation we have the usual interpolating polynomial, a piecewise-calculated 

interpolating
polynomial, and splines. In approximation we distinguish the approximation of data and 

functions. For
the former, we can use the linear or nonlinear least-squares method, whereas for the latter 

we have, for
example, minimax approximation.
Mathematica solves differential equations both symbolically and numerically. We can solve 

first- and
higher-order equations, systems of equations, and initial and boundary value problems. For 

partial
differential equations, we show how some equations can be solved symbolically, how to handle 

series
solutions, and how to numerically solve problems with the method of lines or with the finite 

difference
method. Then we consider difference equations. For linear difference equations, we can 

possibly find a
solution in a closed form, but most nonlinear difference equations have to be investigated 

in other ways,
such as studying trajectories and forming bifurcation diagrams.
Lastly, we study probability and statistics. Mathematica contains information about most of 

the
well-known probability distributions. Simulation of various random phenomena (e.g., 

stochastic
processes) is done well with random numbers. Statistical topics include descriptive 

statistics, frequencies,
confidence intervals, hypothesis testing, regression, smoothing, and Bayesian statistics.


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