Indeholder "What Is Mathematica? ", " Numerical Computation", " Symbolic Computation", " Graphics", " The Mathematica Language", " Mathematica Interfaces", "About This Book", " The Scope of This Book", " The Mathematica System Described in This Book", " The Parts of This Book", " How to Read This Book", " About the Examples in This Book", " Suggestions about Learning Mathematica", " What Else to Read", " Changes since the First Edition", " About the Production of This Book", " Acknowledgments", "Tour of Mathematica", " 1. Numerical Calculations", " 2. Graphics", " 3. Algebra and Calculus", " 4. Solving Equations", " 5. Lists", " 6. Matrices", " 7. Transformation Rules and Definitions", " 8. Advanced Topic: Symbolic Computation", " 9. Programming", " 10. Mathematica Packages", " 11. Interfacing with Mathematica", " 12. Front Ends and Notebooks", "Mathematica Graphics Gallery", "Part 1. A Practical Introduction to Mathematica", "1.0 Running Mathematica", " Text-Based Interfaces", " Notebook Interfaces", "1.1 Numerical Calculations", " Arithmetic", " Exact and Approximate Results", " Some Mathematical Functions", " Arbitrary-Precision Calculations", " Complex Numbers", " Getting Used to Mathematica", "1.2 Building Up Calculations", " Using Previous Results", " Defining Variables", " Making Lists of Objects", " Manipulating Elements of Lists", " The Four Kinds of Bracketing in Mathematica", " Sequences of Operations", "1.3 Using the Mathematica System", " Interfaces to Mathematica", " Entering Input", " Special Topic: Notebooks", " Mathematica Packages", " Getting Information from Mathematica", " Warnings and Messages", " Interrupting Calculations", "1.4 Algebraic Calculations", " Symbolic Computation", " Values for Symbols", " Transforming Algebraic Expressions", " Simplifying Algebraic Expressions", " Advanced Topic: Putting Expressions into Different Forms", " Picking Out Pieces of Algebraic Expressions", " Controlling the Display of Large Expressions", " The Limits of Mathematica", " Using Symbols to Tag Objects", "1.5 Symbolic Mathematics", " Basic Operations", " Differentiation", " Integration", " Sums and Products", " Equations", " Relational and Logical Operators", " Solving Equations", " Differential Equations", " Power Series", " Limits", " Packages for Symbolic Mathematics ", "1.6 Numerical Mathematics", " Basic Operations", " Numerical Sums, Products and Integrals", " Numerical Equation Solving", " Numerical Differential Equations", " Numerical Optimization", " Manipulating Numerical Data", " Statistics Packages", "1.7 Functions and Programs", " Defining Functions", " Functions as Procedures", " Repetitive Operations", " Transformation Rules for Functions ", "1.8 Lists", " Collecting Objects Together", " Making Tables of Values", " Vectors and Matrices", " Getting Pieces of Lists", " Testing and Searching List Elements", " Adding, Removing and Modifying List Elements", " Combining Lists", " Advanced Topic: Lists as Sets", " Rearranging Lists", " Grouping Together Elements of Lists", " Mathematical Operations on Lists", " Advanced Topic: Rearranging Nested Lists", " Advanced Topic: Combinatorial Operations", "1.9 Graphics and Sound", " Basic Plotting", " Special Topic: How Graphics Are Output", " Options", " Redrawing and Combining Plots", " Advanced Topic: Manipulating Options", " Contour and Density Plots", " Three-Dimensional Surface Plots", " Converting between Types of Graphics", " Plotting Lists of Data", " Parametric Plots", " Some Special Plots", " Special Topic: Animated Graphics", " Special Topic: Sound", "1.10 Files and External Operations", " Reading and Writing Mathematica Files", " Advanced Topic: Finding and Manipulating Files", " Reading Data Files", " Generating C and Fortran Expressions", " Generating TEX Input", " Splicing Mathematica Output into External Files", " Running External Programs", " MathLink", "Part 2. Principles of Mathematica", "2.1 Expressions", " Everything Is an Expression", " The Meaning of Expressions", " Special Ways to Input Expressions", " Parts of Expressions", " Manipulating Expressions Like Lists", " Expressions as Trees", " Advanced Topic: Levels in Expressions ", "2.2 Functional Operations", " Function Names as Expressions", " Applying Functions Repeatedly", " Applying Functions to Lists and Other Expressions", " Applying Functions to Parts of Expressions", " Pure Functions", " Building Lists from Functions", " Selecting Parts of Expressions with Functions", " Expressions with Heads That Are Not Symbols", " Advanced Topic: Working with Operators", " Structural Operations ", "2.3 Patterns", " Introduction", " Finding Expressions That Match a Pattern", " Naming Pieces of Patterns", " Specifying Types of Expression in Patterns", " Putting Constraints on Patterns", " Patterns Involving Alternatives", " Flat and Orderless Functions", " Functions with Variable Numbers of Arguments", " Optional and Default Arguments", " Setting Up Functions with Optional Arguments", " Repeated Patterns", " Patterns for Some Common Types of Expression", " An Example: Defining Your Own Integration Function", "2.4 Transformation Rules and Definitions", " Applying Transformation Rules", " Manipulating Sets of Transformation Rules", " Making Definitions", " Special Forms of Assignment", " Making Definitions for Indexed Objects", " Making Definitions for Functions", " The Ordering of Definitions", " Immediate and Delayed Definitions", " Functions That Remember Values They Have Found", " Associating Definitions with Different Symbols", " Defining Numerical Values", " Modifying Built-in Functions", " Advanced Topic: Manipulating Value Lists", "2.5 Evaluation of Expressions", " Principles of Evaluation", " Reducing Expressions to Standard Form", " Attributes", " The Standard Evaluation Procedure", " Non-Standard Evaluation", " Evaluation in Patterns, Rules and Definitions", " Evaluation in Iteration Functions", " Conditionals", " Loops and Control Structures", " Tracing Evaluation", " Advanced Topic: The Evaluation Stack", " Advanced Topic: Controlling Infinite Evaluation", " Advanced Topic: Interrupts and Aborts", " Compiling Mathematica Expressions", " Advanced Topic: Manipulating Compiled Code", "2.6 Modularity and the Naming of Things", " Modules and Local Variables", " Local Constants", " How Modules Work", " Advanced Topic: Variables in Pure Functions and Rules", " Dummy Variables in Mathematics", " Blocks and Local Values", " Blocks Compared with Modules", " Contexts", " Contexts and Packages", " Setting Up Mathematica Packages", " Automatic Loading of Packages", "2.7 Textual Output", " Output Formats", " How Output Formats Work", " Short and Shallow Output", " Textual Output Formats", " Output Formats for Numbers", " Tables and Matrices", " Defining Your Own Output Forms", " Mimicking Mathematical Notation", " Generating Output", "2.8 Strings, Names and Messages", " Text Strings", " Advanced Topic: Special and International Characters", " Operations on Strings", " Converting between Strings and Expressions", " String Patterns", " Symbol Names", " Advanced Topic: Intercepting the Creation of New Symbols", " Messages", " International Messages", " Documentation Constructs", "2.9 The Structure of Graphics and Sound", " The Structure of Graphics", " Two-Dimensional Graphics Elements", " Graphics Directives and Options", " Coordinate Systems for Two-Dimensional Graphics", " Labeling Two-Dimensional Graphics", " Making Plots within Plots", " Density and Contour Plots", " Three-Dimensional Graphics Primitives", " Three-Dimensional Graphics Directives", " Coordinate Systems for Three-Dimensional Graphics", " Plotting Three-Dimensional Surfaces", " Lighting and Surface Properties", " Labeling Three-Dimensional Graphics", " Advanced Topic: Low-Level Graphics Rendering", " Fonts for Text in Graphics", " Graphics Primitives for Text", " Advanced Topic: Color Output", " The Representation of Sound", "2.10 Input and Output", " Reading and Writing Mathematica Files", " External Programs", " Advanced Topic: Streams and Low-Level Input and Output", " Naming and Finding Files", " Manipulating Files and Directories", " Reading Data", " Searching Files", " Searching and Reading Strings", " Special Topic: Calling External Functions", " Advanced Topic: The Structure of MathLink", "2.11 Global Aspects of Mathematica Sessions", " The Main Loop", " Dialogs", " Interactive Input", " Date and Time Functions", " Memory Management", " Advanced Topic: System Parameters", " Special Topic: Saving the State of a Mathematica Session", "Part 3. Advanced Mathematics in Mathematica", "3.1 Numbers", " Types of Numbers", " Converting between Different Forms of Numbers", " Numerical Precision", " Arbitrary-Precision Numbers", " Machine-Precision Numbers", " Advanced Topic: Indeterminate and Infinite Results ", "3.2 Mathematical Functions", " Naming Conventions", " Numerical Functions", " Pseudorandom Numbers", " Integer and Number-Theoretical Functions", " Combinatorial Functions", " Elementary Transcendental Functions", " Functions That Do Not Have Unique Values", " Mathematical Constants", " Orthogonal Polynomials", " Special Functions", " Elliptic Integrals and Elliptic Functions", " Statistical Distributions and Related Functions ", "3.3 Algebraic Manipulation", " Structural Operations on Polynomials", " Finding the Structure of a Polynomial", " Structural Operations on Rational Expressions", " Algebraic Operations on Polynomials", " Polynomials Modulo Primes", " Trigonometric Expressions", " Expressions Involving Complex Variables ", "3.4 Manipulating Equations", " The Representation of Equations and Solutions", " Equations in One Variable", " Simultaneous Equations", " Equations Involving Functions", " Getting Full Solutions", " Advanced Topic: Existence of Solutions", " Eliminating Variables", " Solving Equations with Subsidiary Conditions", " Advanced Topic: Solving Logical Combinations of Equations", " Advanced Topic: Equations Modulo Integers", " Setting Up Algebraic Transformation Rules", "3.5 Calculus", " Differentiation", " Total Derivatives", " Derivatives of Unknown Functions", " Advanced Topic: The Representation of Derivatives", " Defining Derivatives", " Indefinite Integrals", " Integrals That Mathematica Can and Cannot Do", " Definite Integrals", " Defining Integrals", " Manipulating Integrals in Symbolic Form", " Differential Equations ", "3.6 Power Series, Limits and Residues", " Making Power Series Expansions", " Advanced Topic: The Representation of Power Series", " Operations on Power Series", " Advanced Topic: Composition and Inversion of Power Series", " Converting Power Series to Normal Expressions", " Solving Equations Involving Power Series", " Finding Limits", " Residues ", "3.7 Linear Algebra", " Constructing Matrices", " Getting Pieces of Matrices", " Scalars, Vectors and Matrices", " Operations on Scalars, Vectors and Matrices", " Multiplying Vectors and Matrices", " Matrix Inversion", " Basic Matrix Operations", " Solving Linear Systems", " Advanced Topic: Generalized Linear Algebra", " Eigenvalues and Eigenvectors", " Advanced Topic: Matrix Decompositions", " Advanced Topic: Tensors", "3.8 Numerical Operations on Data", " Curve Fitting", " Approximate Functions and Interpolation", " Fourier Transforms ", "3.9 Numerical Operations on Functions", " Numerical Mathematics in Mathematica", " The Uncertainties of Numerical Mathematics", " Numerical Integration", " Numerical Evaluation of Sums and Products", " Numerical Solution of Polynomial Equations", " Numerical Root Finding", " Numerical Solution of Differential Equations", " Numerical Minimization", " Linear Programming", "Appendix. Mathematica Reference Guide", " A.1 Basic Objects", " A.2 Input Syntax", " A.3 Some General Notations and Conventions", " A.4 Evaluation", " A.5 Patterns and Transformation Rules", " A.6 Input and Output", " A.7 Mathematica Sessions and Global Objects", " A.8 Listing of Built-in Mathematica Objects".

Mathematica er et helt fantastisk omfattende system til at lave matematik med. Denne mammutbog er bare en lille appetitvækker til version 2. I skrivende stund er vi nået til version 9 og der er pakker og notes til alt, hvad hjertet kan begære. ( )