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 Documentation / Mathematica / The Mathematica Book / Practical Introduction  /
A Practical Introduction to Mathematica
1.0 Running Mathematica
1.0.1 Notebook Interfaces
1.0.2 Text-Based Interfaces

1.1 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

1.2 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

1.3 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

1.4 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 Picking Out Pieces of Algebraic Expressions
1.4.7 Controlling the Display of Large Expressions
1.4.8 The Limits of Mathematica
1.4.9 Using Symbols to Tag Objects

1.5 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 Differential Equations
1.5.9 Power Series
1.5.10 Limits
1.5.11 Packages for Symbolic Mathematics
1.5.12 Advanced Topic: Generic and Non-Generic Cases
1.5.13 Mathematical Notation in Notebooks

1.6 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 Packages

1.7 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

1.8 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 Mathematical Operations on Lists
1.8.12 Advanced Topic: Rearranging Nested Lists
1.8.13 Advanced Topic: Combinatorial Operations

1.9 Graphics and Sound
1.9.1 Basic Plotting
1.9.2 Special Topic: How Graphics Are Output
1.9.3 Options
1.9.4 Redrawing and Combining Plots
1.9.5 Advanced Topic: Manipulating Options
1.9.6 Contour and Density Plots
1.9.7 Three-Dimensional Surface Plots
1.9.8 Converting between Types of Graphics
1.9.9 Plotting Lists of Data
1.9.10 Parametric Plots
1.9.11 Some Special Plots
1.9.12 Special Topic: Animated Graphics
1.9.13 Sound

1.10 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

1.11 Files and External Operations
1.11.1 Reading and Writing Mathematica Files
1.11.2 Advanced Topic: Finding and Manipulating Files
1.11.3 Reading Data Files
1.11.4 Generating C and Fortran Expressions
1.11.5 Exporting Graphics
1.11.6 Exporting Formulas from Notebooks
1.11.7 Generating TeX
1.11.8 Converting Notebooks to HTML
1.11.9 Splicing Mathematica Output into External Files
1.11.10 Running External Programs
1.11.11 MathLink

1.12 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