≠x Mathematica Demystified CHAPTeR 8 Solving equations 209 8.1 Polynomial Equations 8.2 Systems of Polynomial Equations 215 8.3 Systems of Linear Equations 217 8.4 Nonpolynomial Equations 223 8.5 Differential Equations 8.6 Find Out more 235 Quiz chaPTeR 9 Working with Data 239 9.1 Country Data 240 9.2 Word Play 248 9.3 Graphs 252 9. 4 A Glimpse of Other Data Sets 9.5 Find out more 264 Qu CHAPTER 10 Dynamical Systems and fractals 267 10.1 Iterating a Function 10.2 Graphical analysis 10.3 The Quadratic Family 10. Julia Sets 287 10.5 Custom Coloring 295 10.6 Making Movies 10.7 The mandelbrot set 300 10.8 What is a fractal? 10.9 Find Out more Qu 306 CHAPTER 11 Looking Good 307 Cell Styling 11.2 The Option Inspector 11.3 Cell Properti
x Mathematica Demystified CHAPTER 8 Solving Equations 209 8.1 Polynomial Equations 209 8.2 Systems of Polynomial Equations 215 8.3 Systems of Linear Equations 217 8.4 Nonpolynomial Equations 223 8.5 Differential Equations 227 8.6 Find Out More 235 Quiz 235 CHAPTER 9 Working with Data 239 9.1 Country Data 240 9.2 Word Play 248 9.3 Graphs 252 9.4 A Glimpse of Other Data Sets 261 9.5 Find Out More 264 Quiz 264 CHAPTER 10 Dynamical Systems and Fractals 267 10.1 Iterating a Function 268 10.2 Graphical Analysis 271 10.3 The Quadratic Family 276 10.4 Julia Sets 287 10.5 Custom Coloring 295 10.6 Making Movies 297 10.7 The Mandelbrot Set 300 10.8 What Is a Fractal? 304 10.9 Find Out More 305 Quiz 306 CHAPTER 11 Looking Good 307 11.1 Cell Styling 308 11.2 The Option Inspector 310 11.3 Cell Properties 312
Contents xi P 11.4 Using Palettes 313 11.5 Cell Grouping 11.6 Hyperlinks 318 11.7 Adding Graphics to Notebooks 11.8 Creating Slideshows 325 11.9 Find Out more 329 UIZ Final Exam 331 335 Index 379
Contents xi 11.4 Using Palettes 313 11.5 Cell Grouping 315 11.6 Hyperlinks 318 11.7 Adding Graphics to Notebooks 321 11.8 Creating Slideshows 325 11.9 Find Out More 329 Quiz 330 Final Exam 331 Answers 335 Index 379
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PREFACE · What Is mathematica? Mathematica is a program for doing mathematics. Using Mathematica it is easy to Make numeric and symbolic calculations Simplify complicated mathematical expressions Plot the graphs of functions as well as curves and surfaces in 3-space Create sophisticated color graphic Compute derivatives and integrals Solve equations, including differential equations Work with large data sets Create animations Write programs to carry out any algorithm Create slideshow presentations The latest version of Mathematica, Version 7.0, is packed with all sorts of new capabilities including a dynamic interface that allows the user to inter act with graphics, as well as other kinds of output in real time. The new version of Mathematica is also fast. Many of the underlying routines have been optimized for greater speed. Whether you are a high school student or a Ph. D. mathematician, physicist, or engineer, Mathematica is an ideal tool for meeting your computational needs · Who is this book for? This book is intended primarily for Mathematica newcomers-people whe used Mathematica, or who have used it very little. We'll take you from your very first calculation all the way to plotting beautiful fractals The book includes hundreds of examples each with step-by-step explana- tions. Using this book, you can progress from knowing nothing at all about
PREFACE • What Is Mathematica? Mathematica is a program for doing mathematics. Using Mathematica it is easy to – Make numeric and symbolic calculations – Simplify complicated mathematical expressions – Plot the graphs of functions as well as curves and surfaces in 3-space – Create sophisticated color graphics – Compute derivatives and integrals – Solve equations, including differential equations – Work with large data sets – Create animations – Write programs to carry out any algorithm – Create slideshow presentations The latest version of Mathematica, Version 7.0, is packed with all sorts of new capabilities including a dynamic interface that allows the user to interact with graphics, as well as other kinds of output in real time. The new version of Mathematica is also fast. Many of the underlying routines have been optimized for greater speed. Whether you are a high school student or a Ph.D. mathematician, physicist, or engineer, Mathematica is an ideal tool for meeting your computational needs. • Who Is This Book for? This book is intended primarily for Mathematica newcomers—people who have never used Mathematica, or who have used it very little. We’ll take you from your very first calculation all the way to plotting beautiful fractals. The book includes hundreds of examples each with step-by-step explanations. Using this book, you can progress from knowing nothing at all about
Mathematica Demystified Mathematica to being able to use mathematica for all of the tasks listed above and more. Experienced Mathematica users who have yet to learn all the new features of Versions 6.0 and 7.0 should also find the book helpful. While we assume you know nothing about Mathematica, we do assume that you know a little mathematics, at least high school algebra. A high school student who has yet to learn calculus may find the chapter on calculus a bit mysterious, but there are plenty of neat things to learn in the other chapters College students who are currently taking calculus, linear algebra, or differ ential equations can use this book as a companion text, and do your homework with mathematica In addition to teaching you Mathematica, the examples will introduce you to some beautiful and exciting mathematics. The book provides glimpses of some real mathematical gems including a few conjectures that have vexed mathematicians for hundreds of years. So, you'll not only learn Mathematica but some neat mathematics too ·What’ s in This book? Mathematica is huge, really, really big. Any book can cover only a small fraction of Mathematica. Our goal is to cover enough material so that after reading this book you can do quite a few things with Mathematica, probably as much as most people would ever want to do. Plus, you don' t have to read the whole book. If, for example, you mainly want to use Mathematica to pro- duce graphics, you can skip the later chapters that dont deal with graphics But perhaps more important than teaching you a specific set of Mathematica features, we'll be teaching you how to use the online Mathematica documen tation so that you can teach yourself to go beyond the basics of this guides and tutorials in the Mathematica Documentation Center that elaborate on the material in that chapter For the most part, each chapter deals with a specific topic within Mathe- natica, for example, three-dimensional graphics, or solving equations. The one exception is Chapter 10 that instead focuses on a mathematical topic, in this case, dynamical systems and fractals, and shows how to use Mathematica to draw beautiful fractals including Julia sets and the famous mandlebrot set with only one exception, the chapters are ordered so that each Mathematica function is thoroughly explained when it is first introduced and before it is used in later chapters. Still, it is not necessary to read the chapters in the given order. However, if you are a complete beginner, you should at least read Chapters I to 5(or perhaps at least 1 to 4) before skipping around. You could probably read the chapter on three-dimensional graphics right after the chapter on two-dimensional graphics, especially if you are willing to
xiv Mathematica Demystified Mathematica to being able to use Mathematica for all of the tasks listed above and more. Experienced Mathematica users who have yet to learn all the new features of Versions 6.0 and 7.0 should also find the book helpful. While we assume you know nothing about Mathematica, we do assume that you know a little mathematics, at least high school algebra. A high school student who has yet to learn calculus may find the chapter on calculus a bit mysterious, but there are plenty of neat things to learn in the other chapters. College students who are currently taking calculus, linear algebra, or differential equations can use this book as a companion text, and do your homework with Mathematica. In addition to teaching you Mathematica, the examples will introduce you to some beautiful and exciting mathematics. The book provides glimpses of some real mathematical gems including a few conjectures that have vexed mathematicians for hundreds of years. So, you’ll not only learn Mathematica, but some neat mathematics too! • What’s in This Book? Mathematica is huge, really, really big. Any book can cover only a small fraction of Mathematica. Our goal is to cover enough material so that after reading this book you can do quite a few things with Mathematica, probably as much as most people would ever want to do. Plus, you don’t have to read the whole book. If, for example, you mainly want to use Mathematica to produce graphics, you can skip the later chapters that don’t deal with graphics. But perhaps more important than teaching you a specific set of Mathematica features, we’ll be teaching you how to use the online Mathematica documentation so that you can teach yourself to go beyond the basics of this book. Each chapter contains a section titled “Find Out More” that will direct you to guides and tutorials in the Mathematica Documentation Center that elaborate on the material in that chapter. For the most part, each chapter deals with a specific topic within Mathematica, for example, three-dimensional graphics, or solving equations. The one exception is Chapter 10 that instead focuses on a mathematical topic, in this case, dynamical systems and fractals, and shows how to use Mathematica to draw beautiful fractals including Julia sets and the famous Mandlebrot set. With only one exception, the chapters are ordered so that each Mathematica function is thoroughly explained when it is first introduced and before it is used in later chapters. Still, it is not necessary to read the chapters in the given order. However, if you are a complete beginner, you should at least read Chapters 1 to 5 (or perhaps at least 1 to 4) before skipping around. You could probably read the chapter on three-dimensional graphics right after the chapter on two-dimensional graphics, especially if you are willing to