Mathematica Navigator 2009 3rd Edition [godsogood]

VERT IMPORTANT NOTE: PLEASE, PLEASE, PLEASE IF YOU LIKE THIS BOOK YOU MUST BUY IT PLEASE, PLEASE, PLEASE IF YOU WANT TO USE THIS BOOK YOU MUST BUY IT DO NOT FORGET THAT THE AUTHOR OF THIS BOOK WORKED VERY HARD TO MAKE IT SEED PLEASE, SEED PLEASE 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. SEED PLEASE, SEED PLEASE

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godsogood (2010-01-21)

SEED PLEASE, SEED PLEASE

bobmagic (2011-05-31)

This is a magnificent book that explains nearly every feature of Mathematica in simple terms. Study the examples and notebooks. If you can't find it here you don't need it!
Thank you godsogood.
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FreiTod (2012-04-20)

Thanks very much indeed.

maxjasper (2012-07-22)

Thanks a lot bro