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A Tour of Mathematica | |

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Mathematica as a Calculator | |

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Power Computing with Mathematica | |

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Accessing Algorithms in Mathematica | |

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Mathematical Knowledge in Mathematica | |

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Building Up Computations | |

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Handling Data | |

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Visualization with Mathematica | |

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Mathematica Notebooks | |

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Palettes and Buttons | |

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Mathematical Notation | |

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Mathematica and Your Computing Environment | |

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The Unifying Idea of Mathematica | |

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Mathematica as a Programming Language | |

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Writing Programs in Mathematica | |

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Building Systems with Mathematica | |

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Mathematica as a Software Component | |

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The World of Mathematica | |

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A Practical Introduction to Mathematica | |

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Running Mathematica | |

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Notebook Interfaces | |

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Text-Based Interfaces | |

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Numerical Calculations | |

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Arithmetic | |

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Exact and Approximate Results | |

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Some Mathematical Functions | |

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Arbitrary-Precision Calculations | |

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Complex Numbers | |

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Getting Used to Mathematica | |

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Mathematical Notation in Notebooks | |

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Building Up Calculations | |

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Using Previous Results | |

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Defining Variables | |

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Making Lists of Objects | |

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Manipulating Elements of Lists | |

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The Four Kinds of Bracketing in Mathematica | |

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Sequences of Operations | |

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Using the Mathematica System | |

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The Structure of Mathematica | |

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Differences between Computer Systems | |

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Special Topic: Using a Text-Based Interface | |

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Doing Computations in Notebooks | |

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Notebooks as Documents | |

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Active Elements in Notebooks | |

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Special Topic: Hyperlinks and Active Text | |

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Getting Help in the Notebook Front End | |

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Getting Help with a Text-Based Interface | |

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Mathematica Packages | |

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Warnings and Messages | |

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Interrupting Calculations | |

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Algebraic Calculations | |

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Symbolic Computation | |

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Values for Symbols | |

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Transforming Algebraic Expressions | |

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Simplifying Algebraic Expressions | |

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Advanced Topic: Putting Expressions into Different Forms | |

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Advanced Topic: Simplifying with Assumptions | |

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Picking Out Pieces of Algebraic Expressions | |

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Controlling the Display of Large Expressions | |

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The Limits of Mathematica | |

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Using Symbols to Tag Objects | |

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Symbolic Mathematics | |

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Basic Operations | |

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Differentiation | |

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Integration | |

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Sums and Products | |

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Equations | |

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Relational and Logical Operators | |

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Solving Equations | |

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Differential Equations | |

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Power Series | |

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Limits | |

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Integral Transforms | |

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Packages for Symbolic Mathematics | |

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Advanced Topic: Generic and Non-Generic Cases | |

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Mathematical Notation in Notebooks | |

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Numerical Mathematics | |

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Basic Operations | |

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Numerical Sums, Products and Integrals | |

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Numerical Equation Solving | |

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Numerical Differential Equations | |

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Numerical Optimization | |

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Manipulating Numerical Data | |

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Statistics Packages | |

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Functions and Programs | |

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Defining Functions | |

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Functions as Procedures | |

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Repetitive Operations | |

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Transformation Rules for Functions | |

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Lists | |

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Collecting Objects Together | |

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Making Tables of Values | |

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Vectors and Matrices | |

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Getting Pieces of Lists | |

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Testing and Searching List Elements | |

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Adding, Removing and Modifying List Elements | |

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Combining Lists | |

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Advanced Topic: Lists as Sets | |

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Rearranging Lists | |

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Grouping Together Elements of Lists | |

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Advanced Topic: Alignment and Padding in the Partitioning of Lists | |

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Mathematical Operations on Lists | |

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Advanced Topic: Rearranging Nested Lists | |

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Advanced Topic: Combinatorial Operations | |

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Graphics and Sound | |

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Basic Plotting | |

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Special Topic: How Graphics Are Output | |

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Options | |

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Redrawing and Combining Plots | |

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Advanced Topic: Manipulating Options | |

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Contour and Density Plots | |

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Three-Dimensional Surface Plots | |

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Converting between Types of Graphics | |

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Plotting Lists of Data | |

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Parametric Plots | |

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Some Special Plots | |

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Special Topic: Animated Graphics | |

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Sound | |

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Input and Output in Notebooks | |

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Entering Greek Letters | |

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Entering Two-Dimensional Input | |

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Editing and Evaluating Two-Dimensional Expressions | |

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Entering Formulas | |

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Entering Tables and Matrices | |

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Subscripts, Bars and Other Modifiers | |

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Special Topic: Non-English Characters and Keyboards | |

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Other Mathematical Notation | |

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Forms of Input and Output | |

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Mixing Text and Formulas | |

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Displaying and Printing Mathematica Notebooks | |

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Creating Your Own Palettes | |

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Setting Up Hyperlinks | |

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Automatic Numbering | |

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Exposition in Mathematica Notebooks | |

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Files and External Operations | |

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Reading and Writing Mathematica Files | |

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Advanced Topic: Finding and Manipulating Files | |

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Importing and Exporting Data | |

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Exporting Graphics and Sounds | |

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Exporting Formulas from Notebooks | |

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Generating TEX | |

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Converting Notebooks to HTML | |

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Generating C and Fortran Expressions | |

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Splicing Mathematica Output into External Files | |

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Running External Programs | |

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MathLink | |

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Special Topic: The Internals of Mathematica | |

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Why You Do Not Usually Need to Know about Internals | |

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Basic Internal Architecture | |

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The Algorithms of Mathematica | |

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The Software Engineering of Mathematica | |

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Testing and Verification | |

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Principles of Mathematica | |

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Expressions | |

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Everything Is an Expression | |

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The Meaning of Expressions | |

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Special Ways to Input Expressions | |

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Parts of Expressions | |

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Manipulating Expressions like Lists | |

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Expressions as Trees | |

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Levels in Expressions | |

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Functional Operations | |

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Function Names as Expressions | |

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Applying Functions Repeatedly | |

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Applying Functions to Lists and Other Expressions | |

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Applying Functions to Parts of Expressions | |

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Pure Functions | |

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Building Lists from Functions | |

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Selecting Parts of Expressions with Functions | |

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Expressions with Heads That Are Not Symbols | |

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Advanced Topic: Working with Operators | |

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Structural Operations | |

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Sequences | |

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Patterns | |

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Introduction | |

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Finding Expressions That Match a Pattern | |

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Naming Pieces of Patterns | |

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Specifying Types of Expression in Patterns | |

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Putting Constraints on Patterns | |

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Patterns Involving Alternatives | |

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Flat and Orderless Functions | |

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Functions with Variable Numbers of Arguments | |

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Optional and Default Arguments | |

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Setting Up Functions with Optional Arguments | |

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Repeated Patterns | |

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Verbatim Patterns | |

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Patterns for Some Common Types of Expression | |

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An Example: Defining Your Own Integration Function | |

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Transformation Rules and Definitions | |

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Applying Transformation Rules | |

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Manipulating Sets of Transformation Rules | |

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Making Definitions | |

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Special Forms of Assignment | |

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Making Definitions for Indexed Objects | |

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Making Definitions for Functions | |

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The Ordering of Definitions | |

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Immediate and Delayed Definitions | |

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Functions That Remember Values They Have Found | |

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Associating Definitions with Different Symbols | |

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Defining Numerical Values | |

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Modifying Built-in Functions | |

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Advanced Topic: Manipulating Value Lists | |

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Evaluation of Expressions | |

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Principles of Evaluation | |

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Reducing Expressions to Their Standard Form | |

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Attributes | |

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The Standard Evaluation Procedure | |

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Non-Standard Evaluation | |

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Evaluation in Patterns, Rules and Definitions | |

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Evaluation in Iteration Functions | |

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Conditionals | |

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Loops and Control Structures | |

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Tracing Evaluation | |

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Advanced Topic: The Evaluation Stack | |

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Advanced Topic: Controlling Infinite Evaluation | |

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Advanced Topic: Interrupts and Aborts | |

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Compiling Mathematica Expressions | |

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Advanced Topic: Manipulating Compiled Code | |

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Modularity and the Naming of Things | |

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Modules and Local Variables | |

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Local Constants | |

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How Modules Work | |

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Advanced Topic: Variables in Pure Functions and Rules | |

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Dummy Variables in Mathematics | |

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Blocks and Local Values | |

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Blocks Compared with Modules | |

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Contexts | |

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Contexts and Packages | |

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Setting Up Mathematica Packages | |

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Automatic Loading of Packages | |

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Manipulating Symbols and Contexts by Name | |

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Advanced Topic: Intercepting the Creation of New Symbols | |

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Strings and Characters | |

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Properties of Strings | |

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Operations on Strings | |

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String Patterns | |

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Characters in Strings | |

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Special Characters | |

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Advanced Topic: Newlines and Tabs in Strings | |

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Advanced Topic: Character Codes | |

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Advanced Topic: Raw Character Encodings | |

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Textual Input and Output | |

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Forms of Input and Output | |

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How Input and Output Work | |

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The Representation of Textual Forms | |

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The Interpretation of Textual Forms | |

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Short and Shallow Output | |

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String-Oriented Output Formats | |

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Output Formats for Numbers | |

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Tables and Matrices | |

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Styles and Fonts in Output | |

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Representing Textual Forms by Boxes | |

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Adjusting Details of Formatting | |

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String Representation of Boxes | |

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Converting between Strings, Boxes and Expressions | |

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The Syntax of the Mathematica Language | |

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Operators without Built-in Meanings | |

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Defining Output Formats | |

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Advanced Topic: Low-Level Input and Output Rules | |

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Generating Unstructured Output | |

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Generating Styled Output in Notebooks | |

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Requesting Input | |

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Messages | |

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International Messages | |

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Documentation Constructs | |

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The Structure of Graphics and Sound | |

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The Structure of Graphics | |

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Two-Dimensional Graphics Elements | |

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Graphics Directives and Options | |

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Coordinate Systems for Two-Dimensional Graphics | |

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Labeling Two-Dimensional Graphics | |

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Making Plots within Plots | |

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Density and Contour Plots | |

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Three-Dimensional Graphics Primitives | |

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Three-Dimensional Graphics Directives | |

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Coordinate Systems for Three-Dimensional Graphics | |

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Plotting Three-Dimensional Surfaces | |

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Lighting and Surface Properties | |

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Labeling Three-Dimensional Graphics | |

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Advanced Topic: Low-Level Graphics Rendering | |

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Formats for Text in Graphics | |

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Graphics Primitives for Text | |

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Advanced Topic: Color Output | |

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The Representation of Sound | |

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Exporting Graphics and Sounds | |

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Importing Graphics and Sounds | |

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Manipulating Notebooks | |

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Cells as Mathematica Expressions | |

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Notebooks as Mathematica Expressions | |

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Manipulating Notebooks from the Kernel | |

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Manipulating the Front End from the Kernel | |

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Advanced Topic: Executing Notebook Commands Directly in the Front End | |

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Button Boxes and Active Elements in Notebooks | |

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Advanced Topic: The Structure of Cells | |

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Styles and the Inheritance of Option Settings | |

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Options for Cells | |

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Text and Font Options | |

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Advanced Topic: Options for Expression Input and Output | |

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Options for Graphics Cells | |

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Options for Notebooks | |

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Advanced Topic: Global Options for the Front End | |

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Files and Streams | |

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Reading and Writing Mathematica Files | |

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External Programs | |

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Advanced Topic: Streams and Low-Level Input and Output | |

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Naming and Finding Files | |

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Files for Packages | |

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Manipulating Files and Directories | |

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Importing and Exporting Files | |

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Reading Textual Data | |

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Searching Files | |

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Searching and Reading Strings | |

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MathLink and External Program Communication | |

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How MathLink Is Used | |

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Installing Existing MathLink-Compatible Programs | |

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Setting Up External Functions to Be Called from Mathematica | |

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Handling Lists, Arrays and Other Expressions | |

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Special Topic: Portability of MathLink Programs | |

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Using MathLink to Communicate between Mathematica Sessions | |

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Calling Subsidiary Mathematica Processes | |

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Special Topic: Communication with Mathematica Front Ends | |

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Two-Way Communication with External Programs | |

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Special Topic: Running Programs on Remote Computers | |

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Special Topic: Running External Programs under a Debugger | |

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Manipulating Expressions in External Programs | |

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Advanced Topic: Error and Interrupt Handling | |

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Running Mathematica from Within an External Program | |

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Global Aspects of Mathematica Sessions | |

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The Main Loop | |

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Dialogs | |

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Date and Time Functions | |

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Memory Management | |

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Advanced Topic: Global System Information | |

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Advanced Topic: Customizing Your Mathematica Configuration | |

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Advanced Mathematics in Mathematica | |

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Numbers | |

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Types of Numbers | |

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Numeric Quantities | |

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Converting between Different Forms of Numbers | |

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Numerical Precision | |

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Arbitrary-Precision Numbers | |

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Machine-Precision Numbers | |

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Advanced Topic: Interval Arithmetic | |

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Advanced Topic: Indeterminate and Infinite Results | |

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Advanced Topic: Controlling Numerical Evaluation | |

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Mathematical Functions | |

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Naming Conventions | |

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Numerical Functions | |

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Pseudorandom Numbers | |

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Integer and Number-Theoretical Functions | |

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Combinatorial Functions | |

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Elementary Transcendental Functions | |

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Functions That Do Not Have Unique Values | |

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Mathematical Constants | |

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Orthogonal Polynomials | |

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Special Functions | |

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Elliptic Integrals and Elliptic Functions | |

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Mathieu and Related Functions | |

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Working with Special Functions | |

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Statistical Distributions and Related Functions | |

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Algebraic Manipulation | |

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Structural Operations on Polynomials | |

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Finding the Structure of a Polynomial | |

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Structural Operations on Rational Expressions | |

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Algebraic Operations on Polynomials | |

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Polynomials Modulo Primes | |

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Advanced Topic: Polynomials over Algebraic Number Fields | |

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Trigonometric Expressions | |

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Expressions Involving Complex Variables | |

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Simplification | |

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Using Assumptions | |

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Manipulating Equations | |

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The Representation of Equations and Solutions | |

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Equations in One Variable | |

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Advanced Topic: Algebraic Numbers | |

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Simultaneous Equations | |

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Equations Involving Functions | |

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Getting Full Solutions | |

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Advanced Topic: Existence of Solutions | |

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Eliminating Variables | |

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Solving Equations with Subsidiary Conditions | |

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Advanced Topic: Solving Logical Combinations of Equations | |

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Advanced Topic: Equations Modulo Integers | |

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Calculus | |

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Differentiation | |

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Total Derivatives | |

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Derivatives of Unknown Functions | |

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Advanced Topic: The Representation of Derivatives | |

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Defining Derivatives | |

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Indefinite Integrals | |

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Integrals That Can and Cannot Be Done | |

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Definite Integrals | |

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Manipulating Integrals in Symbolic Form | |

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Differential Equations | |

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Integral Transforms and Related Operations | |

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Generalized Functions and Related Objects | |

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Series, Limits and Residues | |

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Making Power Series Expansions | |

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Advanced Topic: The Representation of Power Series | |

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Operations on Power Series | |

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Advanced Topic: Composition and Inversion of Power Series | |

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Converting Power Series to Normal Expressions | |

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Solving Equations Involving Power Series | |

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Summation of Series | |

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Finding Limits | |

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Residues | |

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Linear Algebra | |

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Constructing Matrices | |

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Getting Pieces of Matrices | |

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Scalars, Vectors and Matrices | |

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Operations on Scalars, Vectors and Matrices | |

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Multiplying Vectors and Matrices | |

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Matrix Inversion | |

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Basic Matrix Operations | |

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Solving Linear Systems | |

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Eigenvalues and Eigenvectors | |

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Advanced Topic: Matrix Decompositions | |

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Advanced Topic: Tensors | |

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Numerical Operations on Data | |

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Curve Fitting | |

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Approximate Functions and Interpolation | |

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Fourier Transforms | |

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Convolutions and Correlations | |

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Numerical Operations on Functions | |

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Numerical Mathematics in Mathematica | |

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The Uncertainties of Numerical Mathematics | |

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Numerical Integration | |

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Numerical Evaluation of Sums and Products | |

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Numerical Solution of Polynomial Equations | |

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Numerical Root Finding | |

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Numerical Solution of Differential Equations | |

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Numerical Minimization | |

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Linear Programming | |

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Advanced Topic: Functions with Sensitive Dependence on Their Input | |

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Mathematical and Other Notation | |

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Special Characters | |

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Names of Symbols and Mathematical Objects | |

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Letters and Letter-like Forms | |

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Operators | |

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Structural Elements and Keyboard Characters | |

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Formula Gallery | |

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Graphics Gallery | |

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Mathematica Reference Guide | |

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Basic Objects | |

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Expressions | |

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Symbols | |

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Contexts | |

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Atomic Objects | |

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Numbers | |

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Character Strings | |

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Input Syntax | |

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Entering Characters | |

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Types of Input Syntax | |

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Character Strings | |

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Symbol Names and Contexts | |

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Numbers | |

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Bracketed Objects | |

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Operator Input Forms | |

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Two-Dimensional Input Forms | |

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Input of Boxes | |

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The Extent of Input Expressions | |

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Special Input | |

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Front End Files | |

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Some General Notations and Conventions | |

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Function Names | |

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Function Arguments | |

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Options | |

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Part Numbering | |

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Sequence Specifications | |

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Level Specifications | |

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Iterators | |

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Scoping Constructs | |

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Ordering of Expressions | |

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Mathematical Functions | |

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Mathematical Constants | |

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Protection | |

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String Patterns | |

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Evaluation | |

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The Standard Evaluation Sequence | |

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Non-Standard Argument Evaluation | |

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Overriding Non-Standard Argument Evaluation | |

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Preventing Evaluation | |

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Global Control of Evaluation | |

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Aborts | |

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Patterns and Transformation Rules | |

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Patterns | |

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Assignments | |

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Types of Values | |

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Clearing and Removing Objects | |

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Transformation Rules | |

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Files and Streams | |

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File Names | |

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Streams | |

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Mathematica Sessions | |

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Command-Line Options and Environment Variables | |

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Initialization | |

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The Main Loop | |

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Messages | |

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Termination | |

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Network License Management | |

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Installation and Organization of System Files | |

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Running and Installing Mathematica | |

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Overall Organization of the CD-ROM | |

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Running the Executable Programs | |

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The Installation Process | |

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File Organization after Installation | |

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Configuration Files | |

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Documentation Files | |

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Add-ons | |

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Some Notes on Internal Implementation | |

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Introduction | |

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Data Structures and Memory Management | |

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Basic System Features | |

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Numerical and Related Functions | |

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Algebra and Calculus | |

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Output and Interfacing | |

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Listing of Major Built-in Mathematica Objects | |

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Introduction | |

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Conventions in This Listing | |

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Listing | |

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Listing of C Functions in the MathLink Library | |

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Introduction | |

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Listing | |

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Listing of Named Characters | |

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Introduction | |

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Listing | |

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Incompatible Changes since Mathematica Version 1 | |

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Incompatible Changes between Version 1 and Version 2 | |

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Incompatible Changes between Version 2 and Version 3 | |

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Incompatible Changes between Version 3 and Version 4 | |

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Index | |