Mathematica beyond mathematics: the Wolfram language in the real world

Front Matter....1

Half Title....1

Title Page....3

Copyright Page....4

Contents....5

Preface....9

1 Getting Started....-1

1. Getting Started....13

1.1 Mathematica, an Integrated Technical Computing System....13

1.2 First Steps....16

1.3 The Help System....23

1.4 Basic Ideas....25

1.5 Computational Capabilities....40

1.6 Utilities....46

1.7 Editing Notebooks....50

1.8 Sharing Notebooks....54

1.9 The Wolfram Cloud....55

1.10 Additional Resources....56

2 Data Analysis and Manipulation....-1

2. Data Analysis and Manipulation....57

2.1 Lists....57

2.2 Importing/Exporting....60

2.3 Descriptive Statistics....69

2.4 Application: Analysis of the Evolution of Two Cell Populations....73

2.5 Application: Global Energy Consumption Analysis....74

2.6 Database Access with Open Database Connectivity (ODBC)....81

2.7 Additional Resources....86

3 Programming The Beauty and Power of the Wolfram Language....-1

3. Programming: The Beauty and Power of the Wolfram Language....87

3.1 Mathematica’s Programming Language: The Wolfram Language....87

3.2 Functional vs. Procedural Programming....89

3.3 Set vs. SetDelayed....91

3.4 Matrices and Lists Operations....93

3.5 How Mathematica Works Internally....96

3.6 Apply, Map and Other Related Functions....98

3.7 Iterative Functions....101

3.8 Pure Functions....101

3.9 Global and Local Variables....105

3.10 Conditional Expressions....107

3.11 Accuracy and Precision....112

3.12 Choosing the Method of Computation....115

3.13 Optimizing the Computation Time....117

3.14 Cloud Deployment....119

3.15 Package Development....120

3.16 Advanced Programming Tools....125

3.17 Additional Resources....126

4 Interactive Applications Image Processing and More....-1

4. Interactive Applications, Image Processing, and More....127

4.1 Manipulate....127

4.2 Creating Demonstrations....137

4.3 Image Processing....143

4.4 Graphs and Networks....153

4.5 Mazes....156

4.6 Application: Finding the Period of a Pendulum....157

4.7 Advanced Calculus....160

4.8 Additional Resources....164

5 Accessing Scientific and Technical Information....-1

5. Accessing Scientific and Technical Information....165

5.1 Computable Data: Doing Computations with Data from Different Fields....165

5.2 Astronomy....171

5.3 Nuclear and Particle Physics....172

5.4 Engineering....173

5.5 Chemical and Physical Properties of Elements and Compounds....174

5.6 Genomics and Proteomics....178

5.7 Meteorology....181

5.8 Combining Data and Graphics....184

5.9 Geodata....185

5.10 Some Recommendations....194

5.11 Additional Resources....194

6 Probability and Statistics....-1

6. Probability and Statistics....195

6.1 The Latest Features....195

6.2 Statistics Data....196

6.3 Probability Distributions....199

6.4 Application: Fitting Experimental Data....219

6.5 Time Series Analysis....222

6.6 Cluster Analysis....224

6.7 Stochastic Processes....232

6.8 Reliability and Survival Analysis....232

6.9 R Integration with Rlink....234

6.10 Application: Predicting Outputs Using Machine Learning Methods....234

6.11 Application: Development of a Package for Quality Control....235

6.12 Additional Resources....240

7 Calculating and Other Mathematical Tales....-1

7. Calculating π and Other Mathematical Tales....241

7.1 The Origins of π....241

7.2 Archimedes’ Approximation....242

7.3 π with More Than One Billion Decimals....246

7.4 Buffon’s Method....250

7.5 Application: Are the Decimal Digits of π Random?....252

7.6 The Strange Connection....256

7.7 The Riemann Hypothesis....258

7.8 Additional Resources....264

8 Looking at the Sky....-1

8. Looking at the Sky....265

8.1 A Short Astronomical Walk....265

8.2 Stargazing....268

8.3 Application: Determining the Color of the Stars....285

8.4 The Measurement of Distances Across the Universe....288

8.5 Application: Binary Systems and the Search for Extrasolar Planets....292

8.6 Light Curves....295

8.7 Additional Resources....304

9 Nuclei and Radiations....-1

9. Nuclei and Radiations....305

9.1 What are Isotopes?....305

9.2 Decay Constants, Decay Periods and Half-Lives....307

9.3 Decay Chains....311

9.4 Application: Modeling the Evolution of a Chain of Isotopes Over Time....315

9.5 Application: Dating the History of Humankind....318

9.6 Application: Calculating Binding Energies....323

9.7 Additional Resources....328

10 Modeling Applications in Biokinetics....-1

10. Modeling: Applications in Biokinetics....329

10.1 Compartmental and Physiological Modeling....329

10.2 Application: Fitting a Model....345

10.3 Optimal Experimental Designs (OED)....349

10.4 Biokmod: Applications to ICRP Models....354

10.5 Radiation Attenuation....364

10.6 Additional Resources....365

11 Economic and Financial Applications....-1

11. Economic and Financial Applications....367

11.1 Financial Information....367

11.2 Financial Functions....374

11.3 Optimization....385

11.4 The Shortest Path Problem....399

11.5 Optimum Flows....404

11.6 Additional Resources....406

12 Faster Further....-1

12. Faster, Further....407

12.1 Parallel Computing....407

12.2 Parallel Programming....408

12.3 Application: The Mandelbrot Set....415

12.4 Application: Comparing Organisms Genetically....420

12.5 Grid Computing with Wolfram Lightweight Grid Manager (WLGM)....423

12.6 Compute Unified Device Architecture (CUDA)....430

12.7 Mathematica for the Web: webMathematica....431

12.8 Software Development with Wolfram Workbench....439

12.9 New Applications and Functionality Integrated in Mathematica....444

12.10 Additional Resources....445

Although many books have been written about Mathematica, very few of them cover the new functionality added to the most recent versions of the program. Mathematica Beyond Mathematics: The Wolfram Language in the Real World introduces the new features using real-world examples, based on the experience of the author as a consultant. In the process, you will also learn more about the Wolfram Language and how you can use it to solve a wide variety of problems. The author raises questions from a wide range of topics and answers them by taking full advantage of Mathematica's latest features. For example; What sources of energy does the world really use? How can we calculate tolerance limits in manufacturing processes? Are our cities getting warmer? Is the novel El Quijote written in Pi? How can we find planets outside our solar system?