The mathematica book / Stephen Wolfram.

Format:

Book

Author/Creator:

Wolfram, Stephen, 1959-

Language:

English

Subjects (All):

Mathematica (Computer file).

Mathematics--Data processing.

Mathematics.

Physical Description:

xxvi, 1470 pages : illustrations (some color) ; 24 cm

Edition:

Fourth edition.

Place of Publication:

Champaign, IL : Wolfram Media ; New York : Cambridge University Press, [1999]

Summary:

The Mathematica Book is a must-have purchase for anyone who wants to understand the opportunities in science, technology, business, and education made possible by Mathematica 4. This encompasses a broad audience of scientists and mathematicians, engineers, computer professionals, financial analysts, medical researchers, and students at high school, college, and graduate levels. Written by the creator of the system, The Mathematica Book includes both a tutorial introduction and complete reference information, and contains a comprehensive description of how to take advantage of Mathematica's ability to solve myriad technical computing problems and its powerful graphical and typesetting capabilities. New to this version: -- Major efficiency enhancements in handling large volumes of numerical data-- Internal packed array technology to make repetitive operations on large numerical datasets radically more efficient in speed and memory-- Improved algebraic computation facilities, including support for assumptions within Simplify, and related functions, and specification of domains for variables, as well as full support of symbolic Laplace, Fourier, and Z transforms-- Additional mathematical functions, including Dirac Delta, Stuve, Harmonic numbers, etc.-- Enhanced graphics and sound capabilities, including faster graphic generation and additional format support for graphics and sound-- Full-function spell checking including special technical dictionaries

Contents:

Mathematica as a Calculator

Power Computing with Mathematica

Accessing Algorithms in Mathematica

Mathematical Knowledge in Mathematica

Building Up Computations

Handling Data

Visualization with Mathematica

Mathematica Notebooks

Palettes and Buttons

Mathematical Notation

Mathematica and Your Computing Environment

The Unifying Idea of Mathematica

Mathematica as a Programming Language

Writing Programs in Mathematica

Building Systems with Mathematica

Mathematica as a Software Component

The World of Mathematica

Part 1. A Practical Introduction to Mathematica

1.0 Running Mathematica 26

Notebook Interfaces

Text-Based Interfaces

1.1 Numerical Calculations 29

Arithmetic

Exact and Approximate Results

Some Mathematical Functions

Arbitrary-Precision Calculations

Complex Numbers

Getting Used to Mathematica

Mathematical Notation in Notebooks

1.2 Building Up Calculations 38

Using Previous Results

Defining Variables

Making Lists of Objects

Manipulating Elements of Lists

The Four Kinds of Bracketing in Mathematica

Sequences of Operations

1.3 Using the Mathematica System 44

The Structure of Mathematica

Differences between Computer Systems

Special Topic: Using a Text-Based Interface

Doing Computations in Notebooks

Notebooks as Documents

Active Elements in Notebooks

Special Topic: Hyperlinks and Active Text

Getting Help in the Notebook Front End

Getting Help with a Text-Based Interface

Mathematica Packages

Warnings and Messages

Interrupting Calculations

1.4 Algebraic Calculations 62

Symbolic Computation

Values for Symbols

Transforming Algebraic Expressions

Simplifying Algebraic Expressions

Advanced Topic: Putting Expressions into Different Forms

Advanced Topic: Simplifying with Assumptions

Picking Out Pieces of Algebraic Expressions

Controlling the Display of Large Expressions

The Limits of Mathematica

Using Symbols to Tag Objects

1.5 Symbolic Mathematics 78

Basic Operations

Differentiation

Integration

Sums and Products

Equations

Relational and Logical Operators

Solving Equations

Differential Equations

Power Series

Limits

Integral Transforms

Packages for Symbolic Mathematics

Advanced Topic: Generic and Non-Generic Cases

1.6 Numerical Mathematics 100

Numerical Sums, Products and Integrals

Numerical Equation Solving

Numerical Differential Equations

Numerical Optimization

Manipulating Numerical Data

Statistics Packages

1.7 Functions and Programs 108

Defining Functions

Functions as Procedures

Repetitive Operations

Transformation Rules for Functions

1.8 Lists 113

Collecting Objects Together

Making Tables of Values

Vectors and Matrices

Getting Pieces of Lists

Testing and Searching List Elements

Adding, Removing and Modifying List Elements

Combining Lists

Advanced Topic: Lists as Sets

Rearranging Lists

Grouping Together Elements of Lists

Advanced Topic: Alignment and Padding in the Partitioning of Lists

Mathematical Operations on Lists

Advanced Topic: Rearranging Nested Lists

Advanced Topic: Combinatorial Operations

1.9 Graphics and Sound 133

Basic Plotting

Special Topic: How Graphics Are Output

Options

Redrawing and Combining Plots

Advanced Topic: Manipulating Options

Contour and Density Plots

Three-Dimensional Surface Plots

Converting between Types of Graphics

Plotting Lists of Data

Parametric Plots

Some Special Plots

Special Topic: Animated Graphics

Sound

1.10 Input and Output in Notebooks 178

Entering Greek Letters

Entering Two-Dimensional Input

Editing and Evaluating Two-Dimensional Expressions

Entering Formulas

Entering Tables and Matrices

Subscripts, Bars and Other Modifiers

Special Topic: Non-English Characters and Keyboards

Other Mathematical Notation

Forms of Input and Output

Mixing Text and Formulas

Displaying and Printing Mathematica Notebooks

Creating Your Own Palettes

Setting Up Hyperlinks

Automatic Numbering

Exposition in Mathematica Notebooks

1.11 Files and External Operations 208

Reading and Writing Mathematica Files

Advanced Topic: Finding and Manipulating Files

Importing and Exporting Data

Exporting Graphics and Sounds

Exporting Formulas from Notebooks

Generating TEX

Converting Notebooks to HTML

Generating C and Fortran Expressions

Splicing Mathematica Output into External Files

Running External Programs

MathLink

1.12 Special Topic: The Internals of Mathematica 220

Why You Do Not Usually Need to Know about Internals

Basic Internal Architecture

The Algorithms of Mathematica

The Software Engineering of Mathematica

Testing and Verification

Part 2. Principles of Mathematica

2.1 Expressions 232

Everything Is an Expression

The Meaning of Expressions

Special Ways to Input Expressions

Parts of Expressions

Manipulating Expressions like Lists

Expressions as Trees

Levels in Expressions

2.2 Functional Operations 242

Function Names as Expressions

Applying Functions Repeatedly

Applying Functions to Lists and Other Expressions

Applying Functions to Parts of Expressions

Pure Functions

Building Lists from Functions

Selecting Parts of Expressions with Functions

Expressions with Heads That Are Not Symbols

Advanced Topic: Working with Operators

Structural Operations

Sequences

2.3 Patterns 261

Finding Expressions That Match a Pattern

Naming Pieces of Patterns

Specifying Types of Expression in Patterns

Putting Constraints on Patterns

Patterns Involving Alternatives

Flat and Orderless Functions

Functions with Variable Numbers of Arguments

Optional and Default Arguments

Setting Up Functions with Optional Arguments

Repeated Patterns

Verbatim Patterns

Patterns for Some Common Types of Expression

An Example: Defining Your Own Integration Function

2.4 Transformation Rules and Definitions 285

Applying Transformation Rules

Manipulating Sets of Transformation Rules

Making Definitions

Special Forms of Assignment

Making Definitions for Indexed Objects

Making Definitions for Functions

The Ordering of Definitions

Immediate and Delayed Definitions

Functions That Remember Values They Have Found

Associating Definitions with Different Symbols

Defining Numerical Values

Modifying Built-in Functions

Advanced Topic: Manipulating Value Lists

2.5 Evaluation of Expressions 310

Principles of Evaluation

Reducing Expressions to Their Standard Form

Attributes

The Standard Evaluation Procedure

Non-Standard Evaluation

Evaluation in Patterns, Rules and Definitions

Evaluation in Iteration Functions

Conditionals

Loops and Control Structures

Tracing Evaluation

Advanced Topic: The Evaluation Stack

Advanced Topic: Controlling Infinite Evaluation

Advanced Topic: Interrupts and Aborts

Compiling Mathematica Expressions

Advanced Topic: Manipulating Compiled Code

2.6 Modularity and the Naming of Things 363

Modules and Local Variables

Local Constants

How Modules Work

Advanced Topic: Variables in Pure Functions and Rules

Dummy Variables in Mathematics

Blocks and Local Values

Blocks Compared with Modules

Contexts

Contexts and Packages

Setting Up Mathematica Packages

Automatic Loading of Packages

Manipulating Symbols and Contexts by Name

Advanced Topic: Intercepting the Creation of New Symbols

2.7 Strings and Characters 391

Properties of Strings

Operations on Strings

String Patterns

Characters in Strings

Special Characters

Advanced Topic: Newlines and Tabs in Strings

Advanced Topic: Character Codes

Advanced Topic: Raw Character Encodings

2.8 Textual Input and Output 409

How Input and Output Work

The Representation of Textual Forms

The Interpretation of Textual Forms

Short and Shallow Output

String-Oriented Output Formats

Output Formats for Numbers

Tables and Matrices

Styles and Fonts in Output

Representing Textual Forms by Boxes

Adjusting Details of Formatting

String Representation of Boxes

Converting between Strings, Boxes and Expressions

The Syntax of the Mathematica Language

Operators without Built-in Meanings

Defining Output Formats

Advanced Topic: Low-Level Input and Output Rules

Generating Unstructured Output

Generating Styled Output in Notebooks

Requesting Input

Messages

International Messages

Documentation Constructs

2.9 The Structure of Graphics and Sound 472

The Structure of Graphics

Two-Dimensional Graphics Elements

Graphics Directives and Options

Coordinate Systems for Two-Dimensional Graphics

Labeling Two-Dimensional Graphics

Making Plots within Plots

Density and Contour Plots

Three-Dimensional Graphics Primitives

Three-Dimensional Graphics Directives

Coordinate Systems for Three-Dimensional Graphics

Plotting Three-Dimensional Surfaces

Lighting and Surface Properties

Labeling Three-Dimensional Graphics

Advanced Topic: Low-Level Graphics Rendering

Formats for Text in Graphics

Graphics Primitives for Text

Advanced Topic: Color Output

The Representation of Sound

Importing Graphics and Sounds

2.10 Manipulating Notebooks 558

Cells as Mathematica Expressions

Notebooks as Mathematica Expressions

Manipulating Notebooks from the Kernel

Manipulating the Front End from the Kernel

Advanced Topic: Executing Notebook Commands Directly in the Front End

Button Boxes and Active Elements in Notebooks

Advanced Topic: The Structure of Cells

Styles and the Inheritance of Option Settings

Options for Cells

Text and Font Options

Advanced Topic: Options for Expression Input and Output

Options for Graphics Cells

Options for Notebooks

Advanced Topic: Global Options for the Front End

2.11 Files and Streams 613

External Programs

Advanced Topic: Streams and Low-Level Input and Output

Naming and Finding Files

Files for Packages

Manipulating Files and Directories

Importing and Exporting Files

Reading Textual Data

Searching Files

Searching and Reading Strings

2.12 MathLink and External Program Communication 647

How MathLink Is Used

Installing Existing MathLink-Compatible Programs

Setting Up External Functions to Be Called from Mathematica

Handling Lists, Arrays and Other Expressions

Special Topic: Portability of MathLink Programs

Using MathLink to Communicate between Mathematica Sessions

Calling Subsidiary Mathematica Processes

Special Topic: Communication with Mathematica Front Ends

Two-Way Communication with External Programs

Special Topic: Running Programs on Remote Computers

Special Topic: Running External Programs under a Debugger

Manipulating Expressions in External Programs

Advanced Topic: Error and Interrupt Handling

Running Mathematica from Within an External Program

2.13 Global Aspects of Mathematica Sessions 692

The Main Loop

Dialogs

Date and Time Functions

Memory Management

Advanced Topic: Global System Information

Advanced Topic: Customizing Your Mathematica Configuration

Part 3. Advanced Mathematics in Mathematica

3.1 Numbers 714

Types of Numbers

Numeric Quantities

Converting between Different Forms of Numbers

Numerical Precision

Arbitrary-Precision Numbers

Machine-Precision Numbers

Advanced Topic: Interval Arithmetic

Advanced Topic: Indeterminate and Infinite Results

Advanced Topic: Controlling Numerical Evaluation

3.2 Mathematical Functions 736

Naming Conventions

Numerical Functions

Pseudorandom Numbers

Integer and Number-Theoretical Functions

Combinatorial Functions

Elementary Transcendental Functions

Functions That Do Not Have Unique Values

Mathematical Constants

Orthogonal Polynomials

Special Functions

Elliptic Integrals and Elliptic Functions

Mathieu and Related Functions

Working with Special Functions

Statistical Distributions and Related Functions

3.3 Algebraic Manipulation 789

Structural Operations on Polynomials

Finding the Structure of a Polynomial

Structural Operations on Rational Expressions

Algebraic Operations on Polynomials

Polynomials Modulo Primes

Advanced Topic: Polynomials over Algebraic Number Fields

Trigonometric Expressions

Expressions Involving Complex Variables

Simplification

Using Assumptions

3.4 Manipulating Equations 811

The Representation of Equations and Solutions

Equations in One Variable

Advanced Topic: Algebraic Numbers

Simultaneous Equations

Equations Involving Functions

Getting Full Solutions

Advanced Topic: Existence of Solutions

Eliminating Variables

Solving Equations with Subsidiary Conditions

Advanced Topic: Solving Logical Combinations of Equations

Advanced Topic: Equations Modulo Integers

3.5 Calculus 830

Total Derivatives

Derivatives of Unknown Functions

Advanced Topic: The Representation of Derivatives

Defining Derivatives

Indefinite Integrals

Integrals That Can and Cannot Be Done

Definite Integrals

Manipulating Integrals in Symbolic Form

Integral Transforms and Related Operations

Generalized Functions and Related Objects

3.6 Series, Limits and Residues 860

Making Power Series Expansions

Advanced Topic: The Representation of Power Series

Operations on Power Series

Advanced Topic: Composition and Inversion of Power Series

Converting Power Series to Normal Expressions

Solving Equations Involving Power Series

Summation of Series

Finding Limits

Residues

3.7 Linear Algebra 871

Constructing Matrices

Getting Pieces of Matrices

Scalars, Vectors and Matrices

Operations on Scalars, Vectors and Matrices

Multiplying Vectors and Matrices

Matrix Inversion

Basic Matrix Operations

Solving Linear Systems

Eigenvalues and Eigenvectors

Advanced Topic: Matrix Decompositions

Advanced Topic: Tensors

3.8 Numerical Operations on Data 893

Curve Fitting

Approximate Functions and Interpolation

Fourier Transforms

Convolutions and Correlations

3.9 Numerical Operations on Functions 909

Numerical Mathematics in Mathematica

The Uncertainties of Numerical Mathematics

Numerical Integration

Numerical Evaluation of Sums and Products

Numerical Solution of Polynomial Equations

Numerical Root Finding

Numerical Solution of Differential Equations

Numerical Minimization

Linear Programming

Advanced Topic: Functions with Sensitive Dependence on Their Input

3.10 Mathematical and Other Notation 939

Names of Symbols and Mathematical Objects

Letters and Letter-like Forms

Operators

Structural Elements and Keyboard Characters

Formula Gallery 969

Graphics Gallery 979

Appendix A. Mathematica Reference Guide

A.1 Basic Objects 1000

Expressions

Symbols

Atomic Objects

Numbers

Character Strings

A.2 Input Syntax 1005

Entering Characters

Types of Input Syntax

Symbol Names and Contexts

Bracketed Objects

Operator Input Forms

Two-Dimensional Input Forms

Input of Boxes

The Extent of Input Expressions

Special Input

Front End Files

A.3 Some General Notations and Conventions 1027

Function Names

Function Arguments

Part Numbering

Sequence Specifications

Level Specifications

Iterators

Scoping Constructs

Ordering of Expressions

Mathematical Functions

Protection

A.4 Evaluation 1034

The Standard Evaluation Sequence

Non-Standard Argument Evaluation

Overriding Non-Standard Argument Evaluation

Preventing Evaluation

Global Control of Evaluation

Aborts

A.5 Patterns and Transformation Rules 1038

Patterns

Assignments

Types of Values

Clearing and Removing Objects

Transformation Rules

A.6 Files and Streams 1043

File Names

Streams

A.7 Mathematica Sessions 1045

Command-Line Options and Environment Variables

Initialization

Termination

Network License Management

A.8 Installation and Organization of System Files 1050

Running and Installing Mathematica

Overall Organization of the CD-ROM

Running the Executable Programs

The Installation Process

File Organization after Installation

Configuration Files

Documentation Files

Add-ons

A.9 Some Notes on Internal Implementation 1059

Data Structures and Memory Management

Basic System Features

Numerical and Related Functions

Algebra and Calculus

Output and Interfacing

A.10 Listing of Major Built-in Mathematica Objects 1065

A.11 Listing of C Functions in the MathLink Library 1317

A.12 Listing of Named Characters 1328.

Notes:

Includes index.

ISBN:

1579550045

0521643147

OCLC:

39890336

Online:

Publisher description