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Cover type: Paperback

Edition: 2ND 99

Copyright: 1999

Publisher: Prentice Hall, Inc.

Published: 1999

International: No

Edition: 2ND 99

Copyright: 1999

Publisher: Prentice Hall, Inc.

Published: 1999

International: No

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"Nancy Blachman's book opens up the world of Mathematica. She has a down-to-earth lucid style of writing and real experience with the system. This belongs on your bookshelf."--William R. Hearst III

"Nancy Blachman's book is an indispensable resource for anyone who wants to do serious work with Mathematica."--Hal R. Varian, Dean, School of Information Management & Systems University of California at Berkeley

"Many people that I know have asked me how to get started using Mathematica. I always point them to *Mathematica: A Practical Approach*.--Dr. Henry Cejtin, One of the eight original Mathematica developers

"This book offers a systematic introduction to Mathematica for people who want to get up to speed quickly. It provides the best presentation that I have seen. It covers all important features of Mathematica thoroughly, with clear explanations, excellent examples, and challenging and instructive problem sets."--Dr. Cameron Smith, Author of *The Mathematica Graphics Guidebook*

"This book is very user-friendly. Not only did I use it to learn Mathematica, but I find myself using it to upgrade my skills."--Vrinda Kadiyali, Assistant Professor of Economics and Marketing Cornell's Johnson School of Management

There are over 100 books published about Mathematica. One of my personal favorites is *Mathematica: A Practical Approach.*--Ian Collier, Member of Technical Staff Wolfram Research, Inc.

*Mathematica: A Practical Approach* is the most popular introductory tutorial book on Mathematica. It has been translated into Japanese, Spanish, Dutch, and Portuguese. The new edition, is loaded with even more examples and exercises to get you up and running with Mathematica version 3!

This book teaches how to:

- solve differential equations

- solve partial differential equations

- solve complicated integrals

- create graphics, sounds and animations

- write functional, rule-based & procedural programs

- define palettes, buttons & hyperlinks

- make your own packages

- interact with the user & with files

- plot functions and data

- fit curves & doing data analysis

- <193>and much much more<193>

**Blachman, Nancy R. : Variable Symbols, Inc. / Stanford University**

Nancy R. Blachman is one of the nation's leading Mathematica trainers. In 1989, after working at Wolfram Research Inc., Ms. Blachman founded her own company, Variable Symbols, Inc., to provide both individual and group training in Mathematica to scientists and engineers. She teaches classes in Mathematica at Stanford University and is an invited speaker at conference and workshops on Mathematica. She has written four popular Mathematica books. She holds degrees in mathematics, operations research, and computer science from the University of Birmingham (UK), the University of California at Berkeley, and Stanford University.

**Williams, Colin P. : Stanford University**

Colin P. Williams has used Mathematica intensively since 1990 and has given numerous Mathematica tutorials to banks and engineering research labs. He recently co-wrote *CalcLabs with Mathematica* with Nancy Blachman, and *Explorations in Quantum Computing* with Scott Clearwater. Colin also teaches Mathematica at Stanford University. Colin holds a Ph.D. is artificial intelligence and advanced degrees in physics and atmospheric dynamics. He was a research scientist at Xerox PARC and a former research assistant to Prof. Stephen Hawking of Cambridge University.

(NOTE: Most chapters end with a Summary and Exercises).

**I. USING MATHEMATICA INTERACTIVELY.**

**1. Getting Started with Mathematica.**

Starting Mathematica.

The In's and Out's of Mathematica.

Using On-Line Help.

Using Palettes to Enter Formulae.

Notation Conventions.

Saving Your Work and Quitting.

A Quick Tour of Some Commands.

Using the Standard Packages.

**2. Numerical Capabilities.**

Arithmetic Operations.

Types of Numbers.

Random Numbers.

Numerical Precision.

Integer Functions.

Finding Roots of Equations.

Numerical Integration.

Numerical Differential Equations.

**3. Symbolic Capabilities.**

Manipulating and Simplifying Expressions.

Trigonometry.

Solving Equations.

Differential Calculus.

Series.

Integral Calculus.

Symbolic Sums, Products, and Limits.

Symbolic Differential Equations.

**4. Plotting Functions.**

Two-Dimensional Plots.

Changing the Appearance of Plots.

Combining Plots.

Parametric, Implicit and Polar Plots.

Frames, Grids, Backgrounds and Ticks.

Inserting Annotations to a Plot.

Three Dimensional Plots.

Contour Plots and Density Plots.

**5. Visualizing Data.**

Plotting Data in Two Dimensions.

Error Plots.

Log Plots.

Bar Charts and Pie Charts.

Two-Dimensional Fields.

**6. Data Manipulation and Analysis.**

Lists and Nested Lists As Data Structures.

Re-ordering and Partitioning Data.

Inserting, Replacing, and Deleting Elements.

Selecting Subsets of the Data.

Counting and Binning Elements.

Mapping Functions over Data.

Statistical Analyses.

Curve Fitting.

Data Interpolation.

**7. Getting Around with Notebooks.**

Initialization Cells.

Default Output Form for Formulae.

Interacting with Outputs.

Cell Brackets.

Menus in Notebooks.

**II. PROGRAMMING.**

**8. Writing Your Own Programs.**

A Simple Program.

Multi-Line Programs.

Localizing Variables.

Programs with Multiple Calling Patterns.

Logical Operators and Tests.

Conditional Execution.

Adding Usage Messages.

Adding Error Messages.

**9. Rule-Based Programming.**

Local Rewrite Rules.

Rules Don't Always Work As Expected.

Controlling How Rules Are Applied.

Types of Patterns.

Uses of Patterns.

**10. Functional Programming.**

Nesting Function Calls.

Recursive Functions.

Anonymous (Pure) Functions.

Variants of Map.

Apply.

Select.

Functional Alternatives to Loops.

**11. Procedural Programming.**

Arrays.

Counter Variables.

Loops and Iteration.

Conditionals.

**12. Graphics, Animation and Sound.**

Two-Dimensional Graphics Primitives.

Setting Styles for Graphics Primitives.

Three-Dimensional Graphics Primitives.

Creating Animations.

Creating Sounds.

**13. Writing Interactive Programs.**

Asking Questions and Getting Replies.

Strings.

Checking a User's Answer.

Managing User Interaction.

**14. Notation, Buttons, and Palettes.**

Special Notation.

Defining Buttons.

Creating Palettes.

**III. Building Larger Applications.**

**15. Speeding Up Your Programs.**

Timing Your Programs.

Avoid Exact Arithmetic.

Avoid Evaluating Data Structures.

Avoid the Procedural Style.

Compile Numerical Functions.

**16. Writing Your Own Packages.**

Why Write a Package?

Contexts.

Package Style.

Loading Packages.

Accidental Shadowing.

**17. Working with Files.**

Telling Mathematica where to Look.

Importing Data from Files.

Exporting Data.

Low-Level File Interaction.

Exporting Special Formats.

Exporting Graphics.

Exporting HTML Files.

Exporting Function Definitions.

Searching the Contents of a File.

**18. Example Applications.**

Monte Carlo Simulations.

Cryptography.

Appendix A: Answers to Odd-Numbered Exercises.

Appendix B: Suggestions for Further Reading.

Appendix C: Index.

shop us with confidence

Summary

"Nancy Blachman's book opens up the world of Mathematica. She has a down-to-earth lucid style of writing and real experience with the system. This belongs on your bookshelf."--William R. Hearst III

"Nancy Blachman's book is an indispensable resource for anyone who wants to do serious work with Mathematica."--Hal R. Varian, Dean, School of Information Management & Systems University of California at Berkeley

"Many people that I know have asked me how to get started using Mathematica. I always point them to *Mathematica: A Practical Approach*.--Dr. Henry Cejtin, One of the eight original Mathematica developers

"This book offers a systematic introduction to Mathematica for people who want to get up to speed quickly. It provides the best presentation that I have seen. It covers all important features of Mathematica thoroughly, with clear explanations, excellent examples, and challenging and instructive problem sets."--Dr. Cameron Smith, Author of *The Mathematica Graphics Guidebook*

"This book is very user-friendly. Not only did I use it to learn Mathematica, but I find myself using it to upgrade my skills."--Vrinda Kadiyali, Assistant Professor of Economics and Marketing Cornell's Johnson School of Management

There are over 100 books published about Mathematica. One of my personal favorites is *Mathematica: A Practical Approach.*--Ian Collier, Member of Technical Staff Wolfram Research, Inc.

*Mathematica: A Practical Approach* is the most popular introductory tutorial book on Mathematica. It has been translated into Japanese, Spanish, Dutch, and Portuguese. The new edition, is loaded with even more examples and exercises to get you up and running with Mathematica version 3!

This book teaches how to:

- solve differential equations

- solve partial differential equations

- solve complicated integrals

- create graphics, sounds and animations

- write functional, rule-based & procedural programs

- define palettes, buttons & hyperlinks

- make your own packages

- interact with the user & with files

- plot functions and data

- fit curves & doing data analysis

- <193>and much much more<193>

Author Bio

**Blachman, Nancy R. : Variable Symbols, Inc. / Stanford University**

Nancy R. Blachman is one of the nation's leading Mathematica trainers. In 1989, after working at Wolfram Research Inc., Ms. Blachman founded her own company, Variable Symbols, Inc., to provide both individual and group training in Mathematica to scientists and engineers. She teaches classes in Mathematica at Stanford University and is an invited speaker at conference and workshops on Mathematica. She has written four popular Mathematica books. She holds degrees in mathematics, operations research, and computer science from the University of Birmingham (UK), the University of California at Berkeley, and Stanford University.

**Williams, Colin P. : Stanford University**

Colin P. Williams has used Mathematica intensively since 1990 and has given numerous Mathematica tutorials to banks and engineering research labs. He recently co-wrote *CalcLabs with Mathematica* with Nancy Blachman, and *Explorations in Quantum Computing* with Scott Clearwater. Colin also teaches Mathematica at Stanford University. Colin holds a Ph.D. is artificial intelligence and advanced degrees in physics and atmospheric dynamics. He was a research scientist at Xerox PARC and a former research assistant to Prof. Stephen Hawking of Cambridge University.

Table of Contents

(NOTE: Most chapters end with a Summary and Exercises).

**I. USING MATHEMATICA INTERACTIVELY.**

**1. Getting Started with Mathematica.**

Starting Mathematica.

The In's and Out's of Mathematica.

Using On-Line Help.

Using Palettes to Enter Formulae.

Notation Conventions.

Saving Your Work and Quitting.

A Quick Tour of Some Commands.

Using the Standard Packages.

**2. Numerical Capabilities.**

Arithmetic Operations.

Types of Numbers.

Random Numbers.

Numerical Precision.

Integer Functions.

Finding Roots of Equations.

Numerical Integration.

Numerical Differential Equations.

**3. Symbolic Capabilities.**

Manipulating and Simplifying Expressions.

Trigonometry.

Solving Equations.

Differential Calculus.

Series.

Integral Calculus.

Symbolic Sums, Products, and Limits.

Symbolic Differential Equations.

**4. Plotting Functions.**

Two-Dimensional Plots.

Changing the Appearance of Plots.

Combining Plots.

Parametric, Implicit and Polar Plots.

Frames, Grids, Backgrounds and Ticks.

Inserting Annotations to a Plot.

Three Dimensional Plots.

Contour Plots and Density Plots.

**5. Visualizing Data.**

Plotting Data in Two Dimensions.

Error Plots.

Log Plots.

Bar Charts and Pie Charts.

Two-Dimensional Fields.

**6. Data Manipulation and Analysis.**

Lists and Nested Lists As Data Structures.

Re-ordering and Partitioning Data.

Inserting, Replacing, and Deleting Elements.

Selecting Subsets of the Data.

Counting and Binning Elements.

Mapping Functions over Data.

Statistical Analyses.

Curve Fitting.

Data Interpolation.

**7. Getting Around with Notebooks.**

Initialization Cells.

Default Output Form for Formulae.

Interacting with Outputs.

Cell Brackets.

Menus in Notebooks.

**II. PROGRAMMING.**

**8. Writing Your Own Programs.**

A Simple Program.

Multi-Line Programs.

Localizing Variables.

Programs with Multiple Calling Patterns.

Logical Operators and Tests.

Conditional Execution.

Adding Usage Messages.

Adding Error Messages.

**9. Rule-Based Programming.**

Local Rewrite Rules.

Rules Don't Always Work As Expected.

Controlling How Rules Are Applied.

Types of Patterns.

Uses of Patterns.

**10. Functional Programming.**

Nesting Function Calls.

Recursive Functions.

Anonymous (Pure) Functions.

Variants of Map.

Apply.

Select.

Functional Alternatives to Loops.

**11. Procedural Programming.**

Arrays.

Counter Variables.

Loops and Iteration.

Conditionals.

**12. Graphics, Animation and Sound.**

Two-Dimensional Graphics Primitives.

Setting Styles for Graphics Primitives.

Three-Dimensional Graphics Primitives.

Creating Animations.

Creating Sounds.

**13. Writing Interactive Programs.**

Asking Questions and Getting Replies.

Strings.

Checking a User's Answer.

Managing User Interaction.

**14. Notation, Buttons, and Palettes.**

Special Notation.

Defining Buttons.

Creating Palettes.

**III. Building Larger Applications.**

**15. Speeding Up Your Programs.**

Timing Your Programs.

Avoid Exact Arithmetic.

Avoid Evaluating Data Structures.

Avoid the Procedural Style.

Compile Numerical Functions.

**16. Writing Your Own Packages.**

Why Write a Package?

Contexts.

Package Style.

Loading Packages.

Accidental Shadowing.

**17. Working with Files.**

Telling Mathematica where to Look.

Importing Data from Files.

Exporting Data.

Low-Level File Interaction.

Exporting Special Formats.

Exporting Graphics.

Exporting HTML Files.

Exporting Function Definitions.

Searching the Contents of a File.

**18. Example Applications.**

Monte Carlo Simulations.

Cryptography.

Appendix A: Answers to Odd-Numbered Exercises.

Appendix B: Suggestions for Further Reading.

Appendix C: Index.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 1999

International: No

Published: 1999

International: No

"Nancy Blachman's book opens up the world of Mathematica. She has a down-to-earth lucid style of writing and real experience with the system. This belongs on your bookshelf."--William R. Hearst III

"Nancy Blachman's book is an indispensable resource for anyone who wants to do serious work with Mathematica."--Hal R. Varian, Dean, School of Information Management & Systems University of California at Berkeley

"Many people that I know have asked me how to get started using Mathematica. I always point them to *Mathematica: A Practical Approach*.--Dr. Henry Cejtin, One of the eight original Mathematica developers

"This book offers a systematic introduction to Mathematica for people who want to get up to speed quickly. It provides the best presentation that I have seen. It covers all important features of Mathematica thoroughly, with clear explanations, excellent examples, and challenging and instructive problem sets."--Dr. Cameron Smith, Author of *The Mathematica Graphics Guidebook*

"This book is very user-friendly. Not only did I use it to learn Mathematica, but I find myself using it to upgrade my skills."--Vrinda Kadiyali, Assistant Professor of Economics and Marketing Cornell's Johnson School of Management

There are over 100 books published about Mathematica. One of my personal favorites is *Mathematica: A Practical Approach.*--Ian Collier, Member of Technical Staff Wolfram Research, Inc.

*Mathematica: A Practical Approach* is the most popular introductory tutorial book on Mathematica. It has been translated into Japanese, Spanish, Dutch, and Portuguese. The new edition, is loaded with even more examples and exercises to get you up and running with Mathematica version 3!

This book teaches how to:

- solve differential equations

- solve partial differential equations

- solve complicated integrals

- create graphics, sounds and animations

- write functional, rule-based & procedural programs

- define palettes, buttons & hyperlinks

- make your own packages

- interact with the user & with files

- plot functions and data

- fit curves & doing data analysis

- <193>and much much more<193>

**Blachman, Nancy R. : Variable Symbols, Inc. / Stanford University**

Nancy R. Blachman is one of the nation's leading Mathematica trainers. In 1989, after working at Wolfram Research Inc., Ms. Blachman founded her own company, Variable Symbols, Inc., to provide both individual and group training in Mathematica to scientists and engineers. She teaches classes in Mathematica at Stanford University and is an invited speaker at conference and workshops on Mathematica. She has written four popular Mathematica books. She holds degrees in mathematics, operations research, and computer science from the University of Birmingham (UK), the University of California at Berkeley, and Stanford University.

**Williams, Colin P. : Stanford University**

Colin P. Williams has used Mathematica intensively since 1990 and has given numerous Mathematica tutorials to banks and engineering research labs. He recently co-wrote *CalcLabs with Mathematica* with Nancy Blachman, and *Explorations in Quantum Computing* with Scott Clearwater. Colin also teaches Mathematica at Stanford University. Colin holds a Ph.D. is artificial intelligence and advanced degrees in physics and atmospheric dynamics. He was a research scientist at Xerox PARC and a former research assistant to Prof. Stephen Hawking of Cambridge University.

(NOTE: Most chapters end with a Summary and Exercises).

**I. USING MATHEMATICA INTERACTIVELY.**

**1. Getting Started with Mathematica.**

Starting Mathematica.

The In's and Out's of Mathematica.

Using On-Line Help.

Using Palettes to Enter Formulae.

Notation Conventions.

Saving Your Work and Quitting.

A Quick Tour of Some Commands.

Using the Standard Packages.

**2. Numerical Capabilities.**

Arithmetic Operations.

Types of Numbers.

Random Numbers.

Numerical Precision.

Integer Functions.

Finding Roots of Equations.

Numerical Integration.

Numerical Differential Equations.

**3. Symbolic Capabilities.**

Manipulating and Simplifying Expressions.

Trigonometry.

Solving Equations.

Differential Calculus.

Series.

Integral Calculus.

Symbolic Sums, Products, and Limits.

Symbolic Differential Equations.

**4. Plotting Functions.**

Two-Dimensional Plots.

Changing the Appearance of Plots.

Combining Plots.

Parametric, Implicit and Polar Plots.

Frames, Grids, Backgrounds and Ticks.

Inserting Annotations to a Plot.

Three Dimensional Plots.

Contour Plots and Density Plots.

**5. Visualizing Data.**

Plotting Data in Two Dimensions.

Error Plots.

Log Plots.

Bar Charts and Pie Charts.

Two-Dimensional Fields.

**6. Data Manipulation and Analysis.**

Lists and Nested Lists As Data Structures.

Re-ordering and Partitioning Data.

Inserting, Replacing, and Deleting Elements.

Selecting Subsets of the Data.

Counting and Binning Elements.

Mapping Functions over Data.

Statistical Analyses.

Curve Fitting.

Data Interpolation.

**7. Getting Around with Notebooks.**

Initialization Cells.

Default Output Form for Formulae.

Interacting with Outputs.

Cell Brackets.

Menus in Notebooks.

**II. PROGRAMMING.**

**8. Writing Your Own Programs.**

A Simple Program.

Multi-Line Programs.

Localizing Variables.

Programs with Multiple Calling Patterns.

Logical Operators and Tests.

Conditional Execution.

Adding Usage Messages.

Adding Error Messages.

**9. Rule-Based Programming.**

Local Rewrite Rules.

Rules Don't Always Work As Expected.

Controlling How Rules Are Applied.

Types of Patterns.

Uses of Patterns.

**10. Functional Programming.**

Nesting Function Calls.

Recursive Functions.

Anonymous (Pure) Functions.

Variants of Map.

Apply.

Select.

Functional Alternatives to Loops.

**11. Procedural Programming.**

Arrays.

Counter Variables.

Loops and Iteration.

Conditionals.

**12. Graphics, Animation and Sound.**

Two-Dimensional Graphics Primitives.

Setting Styles for Graphics Primitives.

Three-Dimensional Graphics Primitives.

Creating Animations.

Creating Sounds.

**13. Writing Interactive Programs.**

Asking Questions and Getting Replies.

Strings.

Checking a User's Answer.

Managing User Interaction.

**14. Notation, Buttons, and Palettes.**

Special Notation.

Defining Buttons.

Creating Palettes.

**III. Building Larger Applications.**

**15. Speeding Up Your Programs.**

Timing Your Programs.

Avoid Exact Arithmetic.

Avoid Evaluating Data Structures.

Avoid the Procedural Style.

Compile Numerical Functions.

**16. Writing Your Own Packages.**

Why Write a Package?

Contexts.

Package Style.

Loading Packages.

Accidental Shadowing.

**17. Working with Files.**

Telling Mathematica where to Look.

Importing Data from Files.

Exporting Data.

Low-Level File Interaction.

Exporting Special Formats.

Exporting Graphics.

Exporting HTML Files.

Exporting Function Definitions.

Searching the Contents of a File.

**18. Example Applications.**

Monte Carlo Simulations.

Cryptography.

Appendix A: Answers to Odd-Numbered Exercises.

Appendix B: Suggestions for Further Reading.

Appendix C: Index.