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Applied Mathematica: Getting Started, Getting it Done

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Applied Mathematica

Getting Started, Getting it Done

By William T. Shaw, Jason Tigg

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Format: Paperback, 448 pages
Other Information: references
Published In: United Kingdom, 31 December 1993
better ways to solve problems. This book shows how Mathematica., the powerful mathematical software system, can be used to solve problems in the applied sciences. Written by two authors who have been teaching Mathematica courses to scientists and engineers for years, this book is a must for anyone who needs to use Mathematica to solve complex problems in the applied sciences. The book tackles complex, practical problems, and shows how to solve them from start to finish. After presenting a 3quick start2 chapter designed to get up and running with Mathematica, the authors show how Mathematica can be used as a data analysis and visualization system. Topics in this section include importing information to Mathematica, organizing information, visualizing data in both 2-D and 3-D, processing information, and exporting results from Mathematica. Next, the authors guide you through programming in Mathematica. Included here are topics such as programming styles, important built-in structures, function definitions, procedural methods, rule-based schemes and iteration, contexts and packages, and increasing efficiency. Also included is a separate section detailing several case studies that explore and apply Mathematica to particular areas. These areas include engineering, finance, environmental modeling, and image processing. The case studies span a wide range of applicationsfrom serious data analysis using robust regression theory and maximum entropy theory, to an enjoyable exploration of the Mandelbrot set using MathLink to create a movie. Features 1. Shows students in the applied sciences how to use Mathematica to solve problems encountered in a variety of applications areas. 2. Explains how to use Mathematica in data analysis, visualization, modeling, programming, or teaching in a wide range of disciplines. 3. Sample applications are included in the form of case studies.

Table of Contents

I. INTRODUCTION TO MATHEMATICA. 1. Getting a Quick Start. Kernels and Front Ends. The Four Pillars of Mathematica. Basic Operations. User-Defined Functions. Pure Functions. The Packages. Summary. II. MANAGING DATA WITH MATHEMATICA. 2. Importing Data into Mathematica. Locating a Data File. Importing the Contents of a Data File. Inspecting a Data File. Searching Directories. Reading Binary Files. Summary. 3. Organizing Information in Mathematica. Organizing Simple Lists. Organizing Lists of Lists. Summary. 4. Visualizing Data in Two Dimensions. Plotting Functions. Plotting Data. Labeling Graphs. Creating Bar Charts and Pie Charts. Including Insets in Graphs. Building your Own Visualization Tools. Exploring an Historic Data Set. Summary. 5. Processing Information in Mathematica. Application of Functions. Linear Regression. Nonlinear Regression. Interpolation. Fourier Analysis. Statistical Analysis. Solution of a PDE. More Numerical Operations. Summary. 6. Visualizing Data in Three or More Dimensions. Plots in Three Dimensions. Plots3 D for Functions. Lists in Three-Dimensional Plotting: A Case Study. Parametric Plots in Three Dimensions. Interpolation and Irregular Grids. Other Constructions with Primitives. Animations. Summary. 7. Exporting Results from Mathematica. Converting and Exporting Entire NoteBooks. Exporting Smaller Elements. FORTRAN Output. Summary. Appendix: FORTRAN Formatting Code. III. MODELING WITH MATHEMATICA. 8. Different Programming Styles. Binned Data. Summary. 9. Important Built-in Structures. List Structures. Mathematica's Perspective on Structures. Deeply Nested Structures. Evaluation Order. Mapping and Similar Operations. Summary. 10. Function Definitions. Simple Function Definitions. Pure Functions. Conditional Evaluation. Blocks of Code and Collision of Variables. Summary. 11. Procedural Methods. Procedural Commands. Disadvantages of the Procedural Approach. Case Study: Printer Tables. Advantages of the Procedural Approach. Summary. 12. Rule-Based Schemes and Iteration. Storage of Results. Pattern Recognition. Iteration. Two-Dimensional Patterns. Summary. 13. Contexts and Packages. Contexts. Packages. Summary. 14. Increased Efficiency. Sources of Inefficiency. Internal Compilation. External Compilation: MathLink. Summary. IV. CASE STUDIES. 15. Robust Regression: An Application of Mathematica to Data Analysis. Fit and Its Problems. Least Median of Squares. Higher Dimensions. Summary. 16. Transform Calculus. The Calculus Packages. Approaches to Solving a Differential Equation. The Solution of Polynomial Equations. Control Theory Graphics. Summary. 17. Time Series Analysis. Working Data. Moving Averages. Fourier Analysis. Spectral Analysis. Summary. Appendix: Spectral Matrix Package. 18. Probabilistic System Assessment. Use of Statistics Packages. An Environmental Example: Migration. A Financial Example: Aggregation. A More Structured Approach to PSA. Expectations and Volume Integration. Wozniakowski's Method and Hammersley Points. Efficient Integration. Summary. Appendix: Prosysas Package. 19. Visualization of the Mandelbrot Set. The Mandelbrot Set. The Mathematica Compiler. Use of MathLink. Further Optimization with MathLink. A Visit to MathMovies. Summary. 20. Maximum Entropy Reconstruction. Singular Value Decomposition. Incomplete Data Sets with Smooth Underlying Image. Maximum Entropy Reconstruction. Summary. 21. Digital Image Processing. Use of Mathematica to View a Digital Image. Removal of Sinusoidal Interference. Image Sharpening. Blurring and Deblurring. Summary. References. Index. 020154217XT04062001

EAN: 9780201542172
ISBN: 020154217X
Publisher: Addison Wesley
Dimensions: 23 x 18 x 1 centimetres (0.68 kg)
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