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A Practical Introduction to Mathematica

Introduction

Running Mathematica

Introduction

1.0.1 Notebook Interfaces

1.0.2 Text-Based Interfaces

Numerical Calculations

1.1.1 Arithmetic

1.1.2 Exact and Approximate Results

1.1.3 Some Mathematical Functions

1.1.4 Arbitrary-Precision Calculations

1.1.5 Complex Numbers

1.1.6 Getting Used to Mathematica

1.1.7 Mathematical Notation in Notebooks

Building Up Calculations

1.2.1 Using Previous Results

1.2.2 Defining Variables

1.2.3 Making Lists of Objects

1.2.4 Manipulating Elements of Lists

1.2.5 The Four Kinds of Bracketing in Mathematica

1.2.6 Sequences of Operations

Using the Mathematica System

1.3.1 The Structure of Mathematica

1.3.2 Differences between Computer Systems

1.3.3 Special Topic: Using a Text-Based Interface

1.3.4 Doing Computations in Notebooks

1.3.5 Notebooks as Documents

1.3.6 Active Elements in Notebooks

1.3.7 Special Topic: Hyperlinks and Active Text

1.3.8 Getting Help in the Notebook Front End

1.3.9 Getting Help with a Text-Based Interface

1.3.10 Mathematica Packages

1.3.11 Warnings and Messages

1.3.12 Interrupting Calculations

Algebraic Calculations

1.4.1 Symbolic Computation

1.4.2 Values for Symbols

1.4.3 Transforming Algebraic Expressions

1.4.4 Simplifying Algebraic Expressions

1.4.5 Advanced Topic: Putting Expressions into Different Forms

1.4.6 Advanced Topic: Simplifying with Assumptions

1.4.7 Picking Out Pieces of Algebraic Expressions

1.4.8 Controlling the Display of Large Expressions

1.4.9 The Limits of Mathematica

1.4.10 Using Symbols to Tag Objects

Symbolic Mathematics

1.5.1 Basic Operations

1.5.2 Differentiation

1.5.3 Integration

1.5.4 Sums and Products

1.5.5 Equations

1.5.6 Relational and Logical Operators

1.5.7 Solving Equations

1.5.8 Inequalities

1.5.9 Differential Equations

1.5.10 Power Series

1.5.11 Limits

1.5.12 Integral Transforms

1.5.13 Recurrence Equations

1.5.14 Packages for Symbolic Mathematics

1.5.15 Advanced Topic: Generic and Non-Generic Cases

1.5.16 Mathematical Notation in Notebooks

Numerical Mathematics

1.6.1 Basic Operations

1.6.2 Numerical Sums, Products and Integrals

1.6.3 Numerical Equation Solving

1.6.4 Numerical Differential Equations

1.6.5 Numerical Optimization

1.6.6 Manipulating Numerical Data

1.6.7 Statistics

Functions and Programs

1.7.1 Defining Functions

1.7.2 Functions as Procedures

1.7.3 Repetitive Operations

1.7.4 Transformation Rules for Functions

Lists

1.8.1 Collecting Objects Together

1.8.2 Making Tables of Values

1.8.3 Vectors and Matrices

1.8.4 Getting Pieces of Lists

1.8.5 Testing and Searching List Elements

1.8.6 Adding, Removing and Modifying List Elements

1.8.7 Combining Lists

1.8.8 Advanced Topic: Lists as Sets

1.8.9 Rearranging Lists

1.8.10 Grouping Together Elements of Lists

1.8.11 Ordering in Lists

1.8.12 Advanced Topic: Rearranging Nested Lists

Graphics and Sound

1.9.1 Basic Plotting

1.9.2 Options

1.9.3 Redrawing and Combining Plots

1.9.4 Advanced Topic: Manipulating Options

1.9.5 Contour and Density Plots

1.9.6 Three-Dimensional Surface Plots

1.9.7 Converting between Types of Graphics

1.9.8 Plotting Lists of Data

1.9.9 Parametric Plots

1.9.10 Some Special Plots

1.9.11 Special Topic: Animated Graphics

1.9.12 Sound

Input and Output in Notebooks

1.10.1 Entering Greek Letters

1.10.2 Entering Two-Dimensional Input

1.10.3 Editing and Evaluating Two-Dimensional Expressions

1.10.4 Entering Formulas

1.10.5 Entering Tables and Matrices

1.10.6 Subscripts, Bars and Other Modifiers

1.10.7 Special Topic: Non-English Characters and Keyboards

1.10.8 Other Mathematical Notation

1.10.9 Forms of Input and Output

1.10.10 Mixing Text and Formulas

1.10.11 Displaying and Printing Mathematica Notebooks

1.10.12 Creating Your Own Palettes

1.10.13 Setting Up Hyperlinks

1.10.14 Automatic Numbering

1.10.15 Exposition in Mathematica Notebooks

Files and External Operations

1.11.1 Reading and Writing Mathematica Files

1.11.2 Advanced Topic: Finding and Manipulating Files

1.11.3 Importing and Exporting Data

1.11.4 Exporting Graphics and Sounds

1.11.5 Exporting Formulas from Notebooks

1.11.6 Generating TeX

1.11.7 Exchanging Material with the Web

1.11.8 Generating C and Fortran Expressions

1.11.9 Splicing Mathematica Output into External Files

1.11.10 Running External Programs

1.11.11 MathLink

Special Topic: The Internals of Mathematica

1.12.1 Why You Do Not Usually Need to Know about Internals

1.12.2 Basic Internal Architecture

1.12.3 The Algorithms of Mathematica

1.12.4 The Software Engineering of Mathematica

1.12.5 Testing and Verification