Mathematica Book, Version 4

ISBN-10: 0521643147
ISBN-13: 9780521643146
Edition: 4th 1999 (Revised)
Authors: Stephen Wolfram
List price: $165.00
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Description: With over a million users around the world, the Mathematica software system created by Stephen Wolfram has defined the direction of technical computing for the past decade. The enhanced text and hypertext processing and state-of-the-art numerical  More...

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Book details

List price: $165.00
Edition: 4th
Copyright year: 1999
Publisher: Cambridge University Press
Publication date: 2/28/1999
Binding: Hardcover
Pages: 1496
Size: 9.00" wide x 9.50" long x 3.00" tall
Weight: 7.304
Language: English

With over a million users around the world, the Mathematica software system created by Stephen Wolfram has defined the direction of technical computing for the past decade. The enhanced text and hypertext processing and state-of-the-art numerical computation features ensure that Mathematica 4 takes scientific computing into the next century. New to this version: visual tour of key features, practical tutorial introduction, full descriptions of 1100 built-in functions, a thousand illustrative examples, easy-to-follow descriptive tables, essays highlighting key concepts, examples of data import and export, award-winning gallery of Mathematica graphics, gallery of mathematical typesetting, dictionary of 700 special characters, a complete guide to the MathLink API, notes on internal implementation, and an index with over 10,000 entries copublished with Wolfram Media.

A Tour of Mathematica
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
A Practical Introduction to Mathematica
Running Mathematica
Notebook Interfaces
Text-Based Interfaces
Numerical Calculations
Arithmetic
Exact and Approximate Results
Some Mathematical Functions
Arbitrary-Precision Calculations
Complex Numbers
Getting Used to Mathematica
Mathematical Notation in Notebooks
Building Up Calculations
Using Previous Results
Defining Variables
Making Lists of Objects
Manipulating Elements of Lists
The Four Kinds of Bracketing in Mathematica
Sequences of Operations
Using the Mathematica System
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
Algebraic Calculations
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
Symbolic Mathematics
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
Mathematical Notation in Notebooks
Numerical Mathematics
Basic Operations
Numerical Sums, Products and Integrals
Numerical Equation Solving
Numerical Differential Equations
Numerical Optimization
Manipulating Numerical Data
Statistics Packages
Functions and Programs
Defining Functions
Functions as Procedures
Repetitive Operations
Transformation Rules for Functions
Lists
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
Graphics and Sound
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
Input and Output in Notebooks
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
Files and External Operations
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
Special Topic: The Internals of Mathematica
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
Principles of Mathematica
Expressions
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
Functional Operations
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
Patterns
Introduction
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
Transformation Rules and Definitions
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
Evaluation of Expressions
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
Modularity and the Naming of Things
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
Strings and Characters
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
Textual Input and Output
Forms of Input and Output
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
The Structure of Graphics and Sound
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
Exporting Graphics and Sounds
Importing Graphics and Sounds
Manipulating Notebooks
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
Files and Streams
Reading and Writing Mathematica Files
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
MathLink and External Program Communication
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
Global Aspects of Mathematica Sessions
The Main Loop
Dialogs
Date and Time Functions
Memory Management
Advanced Topic: Global System Information
Advanced Topic: Customizing Your Mathematica Configuration
Advanced Mathematics in Mathematica
Numbers
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
Mathematical Functions
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
Algebraic Manipulation
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
Manipulating Equations
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
Calculus
Differentiation
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
Differential Equations
Integral Transforms and Related Operations
Generalized Functions and Related Objects
Series, Limits and Residues
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
Linear Algebra
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
Numerical Operations on Data
Curve Fitting
Approximate Functions and Interpolation
Fourier Transforms
Convolutions and Correlations
Numerical Operations on Functions
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
Mathematical and Other Notation
Special Characters
Names of Symbols and Mathematical Objects
Letters and Letter-like Forms
Operators
Structural Elements and Keyboard Characters
Formula Gallery
Graphics Gallery
Mathematica Reference Guide
Basic Objects
Expressions
Symbols
Contexts
Atomic Objects
Numbers
Character Strings
Input Syntax
Entering Characters
Types of Input Syntax
Character Strings
Symbol Names and Contexts
Numbers
Bracketed Objects
Operator Input Forms
Two-Dimensional Input Forms
Input of Boxes
The Extent of Input Expressions
Special Input
Front End Files
Some General Notations and Conventions
Function Names
Function Arguments
Options
Part Numbering
Sequence Specifications
Level Specifications
Iterators
Scoping Constructs
Ordering of Expressions
Mathematical Functions
Mathematical Constants
Protection
String Patterns
Evaluation
The Standard Evaluation Sequence
Non-Standard Argument Evaluation
Overriding Non-Standard Argument Evaluation
Preventing Evaluation
Global Control of Evaluation
Aborts
Patterns and Transformation Rules
Patterns
Assignments
Types of Values
Clearing and Removing Objects
Transformation Rules
Files and Streams
File Names
Streams
Mathematica Sessions
Command-Line Options and Environment Variables
Initialization
The Main Loop
Messages
Termination
Network License Management
Installation and Organization of System Files
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
Some Notes on Internal Implementation
Introduction
Data Structures and Memory Management
Basic System Features
Numerical and Related Functions
Algebra and Calculus
Output and Interfacing
Listing of Major Built-in Mathematica Objects
Introduction
Conventions in This Listing
Listing
Listing of C Functions in the MathLink Library
Introduction
Listing
Listing of Named Characters
Introduction
Listing
Incompatible Changes since Mathematica Version 1
Incompatible Changes between Version 1 and Version 2
Incompatible Changes between Version 2 and Version 3
Incompatible Changes between Version 3 and Version 4
Index

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