.

0 (hodnocen0 x )

(2) Půjčeno:4x 

BK

Redwood City ; Menlo Park ; Reading ; New York ; Don Mills ; Wokingham ; Amsterdam ; Bonn ; Sydney ; Singapore ; Tokyo ; Madrid ; San Juan : Addison-Wesley, 1991

xxii, 961 s. : il. ; 23 cm

ISBN 0-201-51507-5 (brožováno)

000058615

What Is Mathematics? ...vii // Numerical Computation - Symbolic Computation - Graphics - The Mathematica Language - Mathematica Interfaces // About This Book ...xii // 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 // 2. Graphics ...3 // 3. Algebra and Calculus ...6 // 4. Solving Equations ...7 // 5. Lists ...8 // 6. Matrices ...9 // 7. Transformation Rules and Definitions ...10 // 8. Advanced Topic: Symbolic Computation ...11 // 9. Programming ...12 // 10. Mathematica Packages ...14 // 11. Interfacing with Mathematica ...16 // 12. Front Ends and Notebooks ...17 // Mathematica Graphics Gallery // 1.0 Running Mathematica // Text-Based Interfaces - Notebook Interfaces // 1.1 Numerical Calculations ...47 // Arithmetic - Exact and Approximate Results - Some Mathematical Functions - Arbitrary-Precision Calculations - Complex Numbers - Getting Used to Mathematica // 1.2 Building Up Calculations ...54 // 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 ...60 // Interfaces to Mathematica - Entering Input - Special Topic: Notebooks - Mathematica Packages - Getting Information from Mathematica - Warnings and Messages - Interrupting Calculations //

1.4 Algebraic Calculations ...72 // 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 ...87 // 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 ...105 // 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 ...113 // Defining Functions - Functions as Procedures - Repetitive Operations - Transformation Rules for Functions // 1.8 Lists ...118 // 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 ...134 // 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 ...178 // Reading and Writing Mathematica Files - Advanced Topic: Finding and Manipulating Files - Reading Data Files - Generating ? and Fortran Expressions - Generating TpX Input - Splicing Mathematica Output into External Files - Running // External Programs - MathLink // Part 2. Principles of Mathematica // 2.1 Expressions ...190 // 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 ...200 // 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 ...219 // 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 ...243 // 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 ...267 // 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 ...318 // 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 ...343 // 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 ...365 // 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 ...394 // 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 // 477 // 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 Mathematics Sessions ...513 // 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 ...534 // 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 ...550 // 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 ...591 // 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 ...606 // 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 ...624 // 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 ...639 // 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 ...649 // 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 ...672 // Curve Fitting - Approximate Functions and Interpolation - Fourier Transforms // 3.9 Numerical Operations on Functions ...683 // 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 ...710 // A.2 Input Syntax ...714 // A.3 Some General Notations and Conventions ...723 // A.4 Evaluation ...729 // A.5 Patterns and Transformation Rules ...733 // A.6 Input and Output ...738 // A.7 Mathematica Sessions and Global Objects ...741 // A.8 Listing of Built-in Mathematica Objects ...749 // Index ...907