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
