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Front Matter
Copyright Information
About the Author
About the Mathematica Teacher's Edition
What Is Mathematica TE?
What Is TE?
Numerical Computation
Symbolic Computation
Example: Factor the polynomial 
Graphics
The Mathematica Language
TE Interfaces
About This Book
The Parts of This Book
About the Examples in This Book
Suggestions about Learning TE
Tour of TE
Introduction
Numerical Calculations
Graphics
Algebra
Calculus
Solving Equations
Lists
Vectors and Matrices
Transformation Rules and Definitions
Advanced Topic: Symbolic Computation
Programming
Front Ends and Notebooks
Basic Calculations
Running Mathematica TE
Introduction
1.1 Notebooks
1.2 Starting and Quitting
1.3 Entering Input
1.4 Getting Information from Mathematica
1.5 Getting Help in the Notebook Front End
1.6 Interrupting Calculations
1.7 Warnings and Messages
Numerical Calculations
2.1 Arithmetic
2.2 Exact and Approximate Results
2.3 Some Mathematical Functions
2.4 Arbitrary-Precision Calculations
2.5 Getting Used to Mathematica
2.6 Mathematical Notation in Notebooks
One Thing after Another
3.1 Defining Variables
3.2 Using Previous Results
3.3 Sequences of Operations
3.4 Making Lists of Objects
3.5 Manipulating Elements of Lists
3.6 The Four Kinds of Bracketing in Mathematica
3.7 Doing Computations in Notebooks
3.8 Notebooks as Documents
3.9 Active Elements in Notebooks
3.10 Special Topic: Hyperlinks and Active Text
3.11 Getting Help in the Notebook Front End
Real and Complex Numbers
4.1 Types of Numbers
4.2 Numerical Functions
4.3 Elementary Transcendental Functions
4.4 Complex Numbers
4.5 Defining Mathematica Functions
4.6 The Problem of Inverse Functions
4.7 Numerical Precision
4.8 Advanced Topic: A Few Examples of Special Functions
Integers
5.1 Digits and Number Bases
5.2 Division of Integers
5.3 Factoring Integers
Algebra
6.1 Symbolic Computation
6.2 Using Symbols for Units
6.3 Values for Symbols
6.4 Transforming Algebraic Expressions
6.5 Simplifying Algebraic Expressions
6.6 Sums and Products
6.7 Advanced Topic: Putting Expressions into Different Forms
6.8 Advanced Topic: Transforming Trigonometric Expressions
Solving Equations
7.1 Equations
7.2 Solving Algebraic Equations
7.3 Solving Simultaneous Equations
7.4 Numerical Solution of Polynomial Equations
7.5 Solving Nonalgebraic Equations
7.6 Eliminating Variables
Plotting Curves
8.1 Plotting Functions
8.2 Parametric Plots
8.3 Plotting Lists of Data
8.4 Options for Plot
8.5 Plotting Lists of Functions
Two-Dimensional Graphics
9.1 Two-Dimensional Graphics Elements
9.2 Graphics Directives and Options
Three-Dimensional Graphics
10.1 Three-Dimensional Graphics Primitives
10.2 Three-Dimensional Graphics Directives
10.3 Importing and Exporting Data
10.4 Exporting Graphics and Sounds
10.5 Exporting Formulas from Notebooks
10.6 Exchanging Material with the Web
Input and Output in Notebooks
11.1 Entering Greek Letters
11.2 Entering Two-Dimensional Input
11.3 Editing and Evaluating Two-Dimensional Expressions
11.4 Entering Formulas
11.5 Entering Tables and Matrices
11.6 Subscripts, Bars and Other Modifiers
11.7 Special Topic: Non-English Characters and Keyboards
11.8 Other Mathematical Notation
11.9 Forms of Input and Output
11.10 Mixing Text and Formulas
11.11 Displaying and Printing TE Notebooks
11.12 Creating Your Own Palettes
11.13 Setting Up Hyperlinks
11.14 Automatic Numbering
11.15 Exposition in TE Notebooks
Interlude 1
Lists
12.1 Collecting Objects Together
12.2 Making Tables of Values
12.3 Getting Pieces of Lists
12.4 Testing and Searching List Elements
12.5 Adding, Removing and Modifying List Elements
12.6 Combining Lists
12.7 Lists as Sets
12.8 Rearranging Lists
12.9 Grouping and Ungrouping Elements of Lists
More Mathematics
Differentiation and Limits
13.1 Differentiation
13.2 Total Derivatives
13.3 Derivatives of Unknown Functions
13.4 Advanced Topic: Indeterminate and Infinite Results
13.5 Finding Limits
Roots and Minimization
14.1 Numerical Root Finding
14.2 Numerical Minimization
14.3 Linear Programming
Integration and Sums
15.1 Indefinite Integrals
15.2 Integrals That Can and Cannot Be Done
15.3 Definite Integrals
15.4 Numerical Mathematics in TE
15.5 The Uncertainties of Numerical Mathematics
15.6 Numerical Integration
15.7 Numerical Evaluation of Sums and Products
Power Series
16.1 Overview
16.2 Operations on Power Series
Vectors and Matrices
17.1 Vectors
17.2 Matrices
17.3 Getting Pieces of Matrices
17.4 Multiplying Vectors and Matrices
17.5 Matrix Inversion
17.6 Basic Matrix Operations
Linear Algebra
18.1 Solving Linear Systems
18.2 Eigenvalues and Eigenvectors
Approximating Functions
19.1 Curve Fitting
19.2 Approximate Functions and Interpolation
19.3 Fourier Transforms
Differential Equations
20.1 Symbolic Solution of Differential Equations
Surfaces and Space Curves
21.1 Three-Dimensional Surface Plots
21.2 Parametric Plots
Other Plots
22.1 Contour Plots
22.2 Density Plots
22.3 Plotting Lists of Data
22.4 Some Special Plots
Interlude 2
Packages
23.1 TE Packages
Statistics
24.1 Pseudorandom Numbers
24.2 Statistics Packages
24.3 Statistics`DataManipulation`
24.4 Statistics`DescriptiveStatistics`
24.5 Statistics`DiscreteDistributions`
24.6 Statistics`LinearRegression`
The Mathematica Language
Expressions
25.1 Everything Is an Expression
25.2 The Meaning of Expressions
25.3 Special Ways to Input Expressions
Functional Operations
26.1 Function Names as Expressions
26.2 Applying Functions Repeatedly
26.3 Applying Functions to Lists
26.4 Applying Functions to Parts of Expressions
26.5 Pure Functions
26.6 Selecting Parts of Expressions with Functions
Patterns
27.1 Classes of Expressions
27.2 Finding Expressions That Match a Pattern
27.3 Naming Pieces of Patterns
27.4 Specifying Types of Expression in Patterns
27.5 Putting Constraints on Patterns
27.6 Patterns Involving Alternatives
27.7 Functions with Variable Numbers of Arguments
Transformation Rules and Definitions
28.1 Applying Transformation Rules
28.2 Making Definitions
28.3 Making Definitions for Functions
28.4 The Ordering of Definitions
28.5 Immediate and Delayed Definitions
28.6 Functions That Remember Values They Have Found
Programming
29.1 Principles of Evaluation
29.2 Reducing Expressions to Standard Form
29.3 The Standard Evaluation Procedure
29.4 Relational and Logical Operators
29.5 Conditionals
29.6 Loops and Control Structures
29.7 Modules and Local Variables
29.8 Generating Output
Interlude 3
Other Capabilities
30.1 Reading and Writing Mathematica Files
30.2 Reading Data
30.3 Strings
30.4 Some Other Groups of Functions
Graphics and Sound
Manipulating Plots
31.1 Redrawing Plots
31.2 Multiple Plots
31.3 Making Plots within Plots
Animation and Sound
32.1 Animated Graphics
32.2 Sound
The Structure of Graphics
33.1 How Graphics Are Represented
33.2 Style Options
33.3 Advanced Topic: Manipulating Options
33.4 Converting between Types of Graphics
33.5 Representing Three-Dimensional Surfaces
Coordinate Systems for Graphics
34.1 Coordinate Systems for Two-Dimensional Graphics
34.2 Coordinate Systems for Three-Dimensional Graphics
Color and Lighting
35.1 Coloring Surfaces
35.2 Lighting
Labeling Graphics
36.1 Labeling Two-Dimensional Graphics
36.2 Labeling Three-Dimensional Graphics
Text in Graphics
37.1 Graphics Primitives for Text
Appendix
Introduction
Basic Objects
A.1.1 Expressions
A.1.2 Symbols
A.1.3 Contexts
A.1.4 Atomic Objects
A.1.5 Numbers
A.1.6 Character Strings
Input Syntax
A.2.1 Entering Characters
A.2.2 Types of Input Syntax
A.2.3 Character Strings
A.2.4 Symbol Names and Contexts
A.2.5 Numbers
A.2.6 Bracketed Objects
A.2.7 Operator Input Forms
A.2.8 Two-Dimensional Input Forms
A.2.9 Input of Boxes
A.2.10 The Extent of Input Expressions
A.2.11 Special Input
A.2.12 Front End Files
Some General Notations and Conventions
A.3.1 Function Names
A.3.2 Function Arguments
A.3.3 Options
A.3.4 Part Numbering
A.3.5 Sequence Specifications
A.3.6 Level Specifications
A.3.7 Iterators
A.3.8 Scoping Constructs
A.3.9 Ordering of Expressions
A.3.10 Mathematical Functions
A.3.11 Mathematical Constants
A.3.12 Protection
A.3.13 String Patterns
Evaluation
A.4.1 The Standard Evaluation Sequence
A.4.2 Non-Standard Argument Evaluation
A.4.3 Overriding Non-Standard Argument Evaluation
A.4.4 Preventing Evaluation
A.4.5 Global Control of Evaluation
A.4.6 Aborts
Patterns and Transformation Rules
A.5.1 Patterns
A.5.2 Assignments
A.5.3 Types of Values
A.5.4 Clearing and Removing Objects
A.5.5 Transformation Rules
Files and Streams
A.6.1 File Names
A.6.2 Streams
Mathematica Sessions
A.7.1 Command-Line Options and Environment Variables
A.7.2 Initialization
A.7.3 The Main Loop
A.7.4 Messages
A.7.5 Termination
A.7.6 Network License Management
Installation and Organization of System Files
A.8.1 Overall Organization of the CD-ROM
A.8.2 Running the Executable Programs
A.8.3 The Installation Process
A.8.4 File Organization after Installation
A.8.5 Configuration Files
A.8.6 Documentation Files
A.8.7 Add-ons
Some Notes on Internal Implementation
A.9.1 Introduction
A.9.2 Data Structures and Memory Management
A.9.3 Basic System Features
A.9.4 Numerical and Related Functions
A.9.5 Algebra and Calculus
A.9.6 Output and Interfacing
Listing of Major Built-in Mathematica Objects
A.10.1 Introduction
A.10.2 Conventions in This Listing
A.10.3 Listing
Listing of Named Characters
A.11.1 Introduction
    
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