book

Mathematica Cookbook

Name: Mathematica Cookbook
Author: Sal Mangano
ISBN: 9780596520991

by Sal Mangano

May 2010

Intermediate to advanced

830 pages

17h 52m

English

O'Reilly Media, Inc.

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Dedication
Special Upgrade Offer
Preface
IntroductionMathematicaCookbook.comStructure of This BookAcknowledgmentsConventions Used in This BookUsing Code ExamplesSafari® EnabledHow to Contact Us
1. Numerics
1.0 Introduction1.1 Controlling Precision and Accuracy1.2 Mixing Different Numerical Types1.3 Representing Numbers in Other Bases1.4 Extracting the Digits of a Number1.5 Working with Intervals1.6 Converting Between Numerical Types1.7 Displaying Numbers in Alternate Forms
2. Functional Programming
2.0 Introduction2.1 Mapping Functions with More Than One Argument2.2 Holding Arbitrary Arguments2.3 Creating Functions That Automatically Map Over Lists2.4 Mapping Multiple Functions in a Single Pass2.5 Keeping Track of the Index of Each Item As You Map2.6 Mapping a Function over a Moving Sublist2.7 Using Prefix and Postfix Notation to Produce More Readable Code2.8 Defining Indexed Functions2.9 Understanding the Use of Fold As an Alternative to Recursion2.10 Incremental Construction of Lists2.11 Computing Through Repeated Function Application2.12 Building a Function Through Iteration2.13 Exploiting Function Composition and Inverse Functions2.14 Implementing Closures2.15 Currying in Mathematica2.16 Creating Functions with Default Values2.17 Creating Functions That Accept Options
3. Data Structures
3.0 Introduction3.1 Ensuring the Most Efficient Representation of Numerical Lists3.2 Sorting Lists3.3 Determining Order Without Sorting3.4 Extracting the Diagonals of a Matrix3.5 Constructing Matrices of Specific Structure3.6 Constructing Permutation and Shift Matrices3.7 Manipulating Rows and Columns of Matrices3.8 Using Sparse Arrays to Conserve Memory3.9 Manipulating Deeply Nested Lists Using Functions with Level Specifications3.10 Implementing Bit Vectors and Using Format to Customize Their Presentation3.11 Implementing Trees and Traversals Using Lists3.12 Implementing Ordered Associative Lookup Using a Red-Black Tree3.13 Exploiting Mathematica’s Built-In Associative Lookup3.14 Constructing Graphs Using the Combinatorica’ Package3.15 Using Graph Algorithms to Extract Information from Graphs
4. Patterns and Rule-Based Programming
4.0 Introduction4.1 Collecting Items That Match (or Don’t Match) a Pattern4.2 Excluding Items That Match (or Don’t Match) a Pattern4.3 Counting Items That Match a Pattern4.4 Replacing Parts of an Expression4.5 Finding the Longest (or Shortest) Match for a Pattern4.6 Implementing Algorithms in Terms of Rules4.7 Debugging Infinite Loops When Using ReplaceRepeated4.8 Preventing Evaluation Until Replace Is Complete4.9 Manipulating Patterns with Patterns4.10 Optimizing Rules4.11 Using Patterns As a Query Language4.12 Semantic Pattern Matching4.13 Unification Pattern Matching
5. String and Text Processing
5.0 Introduction5.1 Comparing Strings5.2 Removing and Replacing Characters from Strings5.3 Extracting Characters and Substrings5.4 Duplicating a String5.5 Matching and Searching Text5.6 Tokenizing Text5.7 Working with Natural Language Dictionaries5.8 Importing XML5.9 Transforming XML Using Patterns and Rules5.10 Transforming XML Using Recursive Functions (à la XSLT)5.11 Writing Parsers and Grammars in Mathematica
6. Two-Dimensional Graphics and Plots
6.0 Introduction6.1 Plotting Functions in Cartesian Coordinates6.2 Plotting in Polar Coordinates6.3 Creating Plots Parametrically6.4 Plotting Data6.5 Mixing Two or More Graphs into a Single Graph6.6 Displaying Multiple Graphs in a Grid6.7 Creating Plots with Legends6.8 Displaying 2D Geometric Shapes6.9 Annotating Graphics with Text6.10 Creating Custom Arrows
7. Three-Dimensional Graphics and Plots
7.0 Introduction7.1 Plotting Functions of Two Variables in Cartesian Coordinates7.2 Plotting Functions in Spherical Coordinates7.3 Plotting Surfaces in Cylindrical Coordinates7.4 Plotting 3D Surfaces Parametrically7.5 Creating 3D Contour Plots7.6 Combining 2D Contours with 3D Plots7.7 Constraining Plots to Specified Regions7.8 Plotting Data in 3D7.9 Plotting 3D Regions Where a Predicate Is Satisfied7.10 Displaying 3D Geometrical Shapes7.11 Constructing Wireframe Models from Mesh7.12 Controlling Viewing Geometry7.13 Controlling Lighting and Surface Properties7.14 Transforming 3D Graphics7.15 Exploring Polyhedra7.16 Importing 3D Graphics from CAD and Other 3D Software

8. Image Processing
8.0 Introduction8.1 Extracting Image Information8.2 Converting Images from RGB Color Space to HSV Color Space8.3 Enhancing Images Using Histogram Equalization8.4 Correcting Images Using Histogram Specification8.5 Sharpening Images Using Laplacian Transforms8.6 Sharpening and Smoothing with Fourier Transforms8.7 Detecting Edges in Images8.8 Image Recognition Using Eigenvectors (Eigenimages)
9. Audio and Music Processing
9.0 Introduction9.1 Creating Musical Notes9.2 Creating a Scale or a Melody9.3 Adding Rhythm to a Melody9.4 Controlling the Volume9.5 Creating Chords9.6 Playing a Chord Progression9.7 Writing Music with Traditional Chord Notation9.8 Creating Percussion Grooves9.9 Creating More Complex Percussion Grooves9.10 Exporting MIDI files9.11 Playing Functions As Sound9.12 Adding Tremolo9.13 Adding Vibrato9.14 Applying an Envelope to a Signal9.15 Exploring Alternate Tunings9.16 Importing Digital Sound Files9.17 Analyzing Digital Sound Files9.18 Slicing a Sample
10. Algebra
10.0 Introduction10.1 Solving Algebraic Equations10.2 Finding a Polynomial from a Given Root10.3 Transforming Expressions to Other Forms10.4 Generating Polynomials10.5 Decomposing Polynomials into Their Constituent Parts10.6 Dividing Polynomials by Other Polynomials
11. Calculus: Continuous and Discrete
11.0 Introduction11.1 Computing Limits11.2 Working with Piecewise Functions11.3 Using Power Series Representations11.4 Differentiating Functions11.5 Integration11.6 Solving Differential Equations11.7 Solving Minima and Maxima Problems11.8 Solving Vector Calculus Problems11.9 Solving Problems Involving Sums and Products11.10 Solving Difference Equations11.11 Generating Functions and Sequence Recognition
12. Statistics and Data Analysis
12.0 Introduction12.1 Computing Common Statistical Metrics of Numerical and Symbolic Data12.2 Generating Pseudorandom Numbers with a Given Distribution12.3 Working with Probability Distributions12.4 Demonstrating the Central Limit Theorem12.5 Computing Covariance and Correlation of Vectors and Matrices12.6 Measuring the Shape of Data12.7 Finding and Adjusting for Outliers12.8 Fitting Data Using a Linear Model12.9 Fitting Data Using a Nonlinear Model12.10 Creating Interpolation Functions from Data12.11 Testing for Statistically Significant Difference Between Groups Using ANOVA12.12 Hypothesis Testing with Categorical Data12.13 Grouping Data into Clusters12.14 Creating Common Statistical Plots12.15 Quasi-Random Number Generation12.16 Creating Stochastic Simulations
13. Science and Engineering
13.0 Introduction13.1 Working with Element Data13.2 Working with Chemical Data13.3 Working with Particle Data13.4 Working with Genetic Data and Protein Data13.5 Modeling Predator-Prey Dynamics13.6 Solving Basic Rigid Bodies Problems13.7 Solving Problems in Kinematics13.8 Computing Normal Modes for Coupled Mass Problems13.9 Modeling a Vibrating String13.10 Modeling Electrical Circuits13.11 Modeling Truss Structures Using the Finite Element Method
14. Financial Engineering
14.0 Introduction14.1 Leveraging Mathematica’s Bundled Financial Data14.2 Importing Financial Data from Websites14.3 Present Value of Future Cash Flows14.4 Interest Rate Sensitivity of Bonds14.5 Constructing and Manipulating Yield Curves14.6 Black-Scholes for European Option Pricing14.7 Computing the Implied Volatility of Financial Derivatives14.8 Speeding Up NDSolve When Solving Black-Scholes and Other PDEs14.9 Developing an Explicit Finite Difference Method for the Black-Scholes Formula14.10 Compiling an Implementation of Explicit Trinomial for Fast Pricing of American Options14.11 Modeling the Value-at-Risk of a Portfolio Using Monte Carlo and Other Methods14.12 Visualizing Trees for Interest-Rate Sensitive Instruments
15. Interactivity
15.0 Introduction15.1 Manipulating a Variable15.2 Manipulating a Symbolic Expression15.3 Manipulating a Plot15.4 Creating Expressions for Which Value Dynamically Updates15.5 Intercepting the Values of a Control Attached to a Dynamic Expression15.6 Controlling Updates of Dynamic Values15.7 Using DynamicModule As a Scoping Construct in Interactive Notebooks15.8 Using Scratch Variables with DynamicModule to Balance Speed Versus Space15.9 Making a Manipulate Self-Contained15.10 Remembering the Values Found Using Manipulate15.11 Improving Performance of Manipulate by Segregating Fast and Slow Operations15.12 Localizing a Function in a Manipulate15.13 Sharing DynamicModule Variables across Cell or Window Boundaries15.14 Creating Your Own Custom Controls15.15 Animating an Expression15.16 Creating Custom Interfaces15.17 Managing a Large Number of Controls in Limited Screen Real Estate
16. Parallel Mathematica
16.0 Introduction16.1 Configuring Local Kernels16.2 Configuring Remote Services Kernels16.3 Sending a Command to Multiple Kernels for Parallel Evaluation16.4 Automatically Parallelizing Existing Serial Expressions16.5 Distributing Data Segments in Parallel and Combining the Results16.6 Implementing Data-Parallel Algorithms by Using ParallelMap16.7 Decomposing a Problem into Parallel Data Sets16.8 Choosing an Appropriate Distribution Method16.9 Running Different Algorithms in Parallel and Accepting the First to Complete16.10 Sharing Data Between Parallel Kernels16.11 Preventing Race Conditions When Multiple Kernels Access a Shared Resource16.12 Organizing Parallel Processing Operations Using a Pipeline Approach16.13 Processing a Massive Number of Files Using the Map-Reduce Technique16.14 Diagnosing Parallel Processing Performance16.15 Measuring the Overhead of Parallelization in Your Environment
17. Interfacing Mathematica
17.0 Introduction17.1 Calling External Command Line Programs from Mathematica17.2 Launching Windows Programs from Mathematica17.3 Connecting the Frontend to a Remote Kernel17.4 Using Mathematica with C and C++17.5 Using Mathematica with Java17.6 Using Mathematica to Interact with Microsoft’s .NET Framework17.7 Using the Mathematica Kernel from a .NET Application17.8 Querying a Database17.9 Updating a Database17.10 Introspection of Databases
18. Tricks of the Trade
18.0 Introduction18.1 Cleaning Up During Incremental Development18.2 Modifying Built-in Functions and Constants18.3 Locating Undocumented Functions18.4 Packaging Your Mathematica Solutions into Libraries for Others to Use18.5 Compiling Functions to Improve Performance18.6 Automating and Standardizing the Appearance of Notebooks Using Stylesheets18.7 Transforming Notebooks into Other Forms18.8 Calling into the Mathematica Frontend18.9 Initializing and Cleaning Up Automatically18.10 Customizing Frontend User Interaction
19. Debugging and Testing
19.0 Introduction19.1 Printing as the First Recourse to Debugging19.2 Debugging Functions Called Many Times19.3 Stack Tracing to Debug Recursive Functions19.4 Taming Trace to Extract Useful Debugging Information19.5 Creating a Poor Man’s Mathematica Debugger19.6 Debugging Built-In Functions with Evaluation and Step Monitors19.7 Visual Debugging with Wolfram Workbench19.8 Writing Unit Tests to Help Ensure Correctness of Your Code19.9 Creating MUnit Tests Where Success Is Not Based on Equality Testing19.10 Organizing and Controlling MUnit Tests and Test Suites19.11 Integrating Wolfram Workbench’s MUnit Package into the Frontend
A. About the Author
Index
About the Author
Colophon
Special Upgrade Offer
Copyright

Overview

Mathematica Cookbook helps you master the application's core principles by walking you through real-world problems. Ideal for browsing, this book includes recipes for working with numerics, data structures, algebraic equations, calculus, and statistics. You'll also venture into exotic territory with recipes for data visualization using 2D and 3D graphic tools, image processing, and music.

Although Mathematica 7 is a highly advanced computational platform, the recipes in this book make it accessible to everyone -- whether you're working on high school algebra, simple graphs, PhD-level computation, financial analysis, or advanced engineering models.

Learn how to use Mathematica at a higher level with functional programming and pattern matching
Delve into the rich library of functions for string and structured text manipulation
Learn how to apply the tools to physics and engineering problems
Draw on Mathematica's access to physics, chemistry, and biology data
Get techniques for solving equations in computational finance
Learn how to use Mathematica for sophisticated image processing
Process music and audio as musical notes, analog waveforms, or digital sound samples

Visit the catalog page for Mathematica CookbookVisit the errata page for Mathematica Cookbook

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