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From simple calculator operations to large-scale programming and interactive-document preparation, Mathematica is the tool of choice at the frontiers of scientific research, engineering analysis and modeling. It is also being increasingly used in high school and university teaching, and has application in a vast array of industries -- even computer gaming and art design.

Wolfram Demonstrations Project

Choose from thousands of fully functional, interactive videos with full source code ranging from math/science to geography/music.

Experimental Data Analyst

Exp Data

From extensive data fitting capabilities to data visualization and transformation, Experimental Data Analyst provides you with an impressive set of detailed programs and packages that help you get the most out of your experimental data. A wide array of examples that include real experimental data quickly gets you up and running on your own projects and helps you harness the power and flexibility of Mathematica.

Extensive error-analysis capabilities in Experimental Data Analyst easily handle errors in both coordinates of the data, obtain estimated errors in the fit parameters, and examine graphical information about the fit, including residuals of the fit.

Experimental Data Analyst allows you to fit data to linear or arbitrary models. You can fit data to lines or curves when one or more of the data points may be "wild" and the least-squares technique cannot be used. For advanced problems, it's easy to customize the behavior of the fitting routines by selecting from numerous options. For less complex cases, you can simply rely on the defaults for quick, accurate solutions.

Various data transformation techniques such as data smoothing and noise elimination as well as routines that automatically propagate errors of precision are available.

Impressive graphics capabilities provide a rich environment for visualizing your experimental data. An extension of Mathematica's function ListPlot visualizes errors in your data coordinates with error bars. The distribution of your data values can be viewed pictorially using histograms or box plots. You can fully control the display based on the data, the number of bins, the min, and the max.

The package comes with electronic documentation, which is fully integrated with the Mathematica Help Browser.


Fuzzy Logic

Fuzzy Logic brings you an essential set of tools for creating, modifying, and visualizing fuzzy sets and fuzzy logic-based systems. Ideal for engineers, researchers, and educators, Fuzzy Logic provides practical examples that introduce you to basic concepts of fuzzy logic and demonstrate how to effectively apply the tools in the package to a wide variety of fuzzy system design tasks. Experienced fuzzy logic designers will find it easy to use the package to research, model, test, and visualize highly complex systems.
The package's built-in functions help you at every stage of the fuzzy logic design process as you define inputs and outputs, create fuzzy set membership functions, manipulate and combine fuzzy sets and relations, apply inferencing functions to system models, and incorporate defuzzification routines. Ready-to-use graphics routines make it easy to visualize defuzzification strategies, fuzzy sets, and fuzzy relations.

"This is the most useful computational package for the use and study of fuzzy logic by practicing professionals and students."
Timothy J. Ross, author of Fuzzy Logic with Engineering Applications and editor-in-chief of Journal of Intelligent and Fuzzy Systems

Fuzzy Logic also takes advantage of Mathematica notebooks, letting you combine fuzzy design settings, computations, 2D and 3D graphics, and even text in a single document on screen. This interactive document format not only is useful to professionals working on a complex fuzzy model but also is ideal for presenting concepts to students and allows them to turn in completed homework assignments and lab reports either electronically or on paper as a printed notebook.
The package comes with electronic documentation, which is fully integrated with the Mathematica Help Browser.
Fuzzy Logic 2.0.2 requires Mathematica 5.0-5.2 and is available for all Mathematica platforms.


MathOptimizer

MathOptimizer enables the global and local numerical solution of a very general class of optimization problems defined by a finite number of real-valued, continuous functions over a finite n-dimensional interval region.

Special emphasis is placed on nonlinear models, including those that typically have an unknown number of local optima. Nonlinear and global optimization problems are ubiquitous in the sciences, engineering, and economics. Several prominent examples are systems of nonlinear equations and inequalities, nonlinear regression, forecasting models, data classification, minimal-energy models, various packing problems, risk management and other stochastic decision problems, and the design and operation of "black box" engineering systems (which are often defined by a complicated, numerically intensive procedure).

MathOptimizer consists of two core solver packages and a solver integrator package. The first core solver package is used for approximate global optimization of an aggregated merit (exact penalty) function on a given interval range. This package is based on a globally convergent adaptive stochastic search procedure, and it also incorporates statistical estimation techniques.

The second core solver package is meant for precise local optimization. It is based on the standard nonlinear (convex) programming approach and refines a given initial solution. The solver integrator package supports the individual or combined use of the core solver packages, but both of the core packages can also be used in standalone mode.

The MathOptimizer User Guide includes concise mathematical background notes and useful modeling tips. It also discusses a number of test problems and several nontrivial application examples. The guide can be accessed directly through Mathematica's online help system.

MathOptimizer 2 requires Mathematica 6, 7, or 8 and is available for Windows, Linux, and Mac OS X.


MathOptimizer Professional

MathOptimizer Professional combines the power of Mathematica with the established LGO (Lipschitz Global Optimizer) solver suite, offering sophisticated application development tools and a solver-based functionality comparable to other compiler-based or optimization modeling language-related implementations.

In use since 1990, the LGO solver engine is currently available for professional C and Fortran compiler platforms, with links to Excel and several prominent optimization modeling languages.

MathOptimizer Professional enables the global and local solution of a general class of continuous optimization problems.

These key analytical assumptions guarantee that the model considered has a globally optimal solution. At the same time--without further specific structural assumptions--this model can represent a very difficult numerical challenge because of the possibility of having a disconnected, nonconvex, feasible region and a multitude of local optima. For illustration, please see the graphic above, which shows the squared error function related to solving a given pair of transcendental equations as a function of the two unknown arguments.

The current version of MathOptimizer Professional enables users to solve models of up to one thousand variables and one thousand constraints. These limitations should accommodate most applications because, in global and nonlinear optimization, these rather sizable models result in very difficult and processor-intensive calculations (with corresponding run times on state-of-the-art personal computers varying from a few minutes to several hours). Users can contact the developers directly to relax these limitations at no cost.

MathOptimizer Professional 3 requires Mathematica 6, 7, or 8 and a C or Fortran compiler (specified at time of purchase), and is available for Windows.


Mechanical Systems

Minimize your rigid-body-system design time and explore more design options with MechanicalSystems. This powerful package speeds up your prototyping and simulation tasks, helping you develop and modify complex models as well as instantly visualize and analyze your design changes.

Using the complete library of over 50 two- and three-dimensional geometric constraints in MechanicalSystems, you can easily model complex mechanical relationships and define custom algebraic constraints to model nongeometric or control relationships. The object-oriented, model-building commands let you assemble constraints into a complete mechanism that can be solved for component position, velocity, and acceleration. By applying loads to the model, you can quickly solve for static reaction forces at mechanism joints or for dynamic forces when inertia properties are defined. The special Adams-Bashforth integrator, highly optimized for 3D motion problems, provides efficient forward dynamics simulations for underconstrained systems.

MechanicalSystems can also return mathematical components of a model in symbolic form, including equations of motion, algebraic constraints, inertia matrices, and Coriolis forces. To visualize mechanism motion, extensive graphics functions let you locate and animate complex images.

The package comes with electronic documentation.

MechanicalSystems 2.1.1 requires Mathematica 7 or 8 and is available for all Mathematica platforms.


Neural Networks

Artificial neural networks have revolutionized the way researchers solve many complex and real-world problems in engineering, science, economics, and finance. Neural Networks capitalizes on the computational power and flexibility of Mathematica to help you utilize this cutting-edge technology.

Neural Networks gives professionals and students the tools to train, visualize, and validate neural network models. It supports a comprehensive set of neural network structures—including radial basis function, feedforward, dynamic, Hopfield, perceptron, vector quantization, unsupervised, and Kohonen networks. It implements state-of-the-art training algorithms like Levenberg-Marquardt, Gauss-Newton, and steepest descent. Neural Networks also includes special functions to address typical problems in data analysis, such as function approximation, classification and detection, clustering, nonlinear time series, and nonlinear system identification problems.

Neural Networks is equally suited for advanced and inexperienced users. The built-in palettes facilitate the input of any parameter for the analysis, evaluation, and training of your data. The online documentation contains a number of detailed examples that demonstrate different neural network models. You can solve many problems simply by applying the example commands to your own data. Neural Networks also provides numerous options to modify the training algorithms. The default values have been set to give good results for a large variety of problems, allowing you to get started quickly using only a few commands. As you gain experience, you will be able to customize the algorithms to improve the performance, speed, and accuracy of your neural network models.

With Neural Networks and Mathematica, you will have access to a robust modeling environment that lets you test and explore neural network models faster and easier than ever before.

The package comes with electronic documentation.

Neural Networks 1.1.2 requires Mathematica 7 or 8 and is available for all Mathematica platforms.


Optica

Optica is a new generation of optical design software. It offers unprecedented flexibility and builds upon the enormous repertoire of symbolic, numeric, and graphic capabilities in Mathematica. With its searchable component database of more than 6800 commercial optical parts, you can design optical systems faster than ever before. Yet Optica does not limit you to predefined components, nor constrain you by limited script languages.

Optica has a modular building-block architecture that makes addition of custom components a snap. Aspheric lenses, custom surfaces, resonating cavities, and optical fibers represent just a few of the possibilities, from mundane to exotic.Optica is limited only by your imagination and the vast possibilities of Mathematica. If a component or analysis function doesn't exist in Optica, you have the tools to build it yourself. The simple building-block architecture of Optica also makes it easy to learn.

The power of Optica lies not only in the components of optical systems, but also in the rays themselves. These are full-fledged system objects in their own right. You can tag specific rays with descriptive labels and follow them through a complex system. Optical ray tracing can be sequential or non-sequential. The ray-tracing engine can even perform traces with arbitrary precision, beyond standard machine precision.

Here is just a bit of what you'll find in Optica's vast library of predefined elements:

  • 122 optical components

  • 38 lenses

  • 23 mirrors

  • 22 prisms

  • 12 light sources

  • 22 high-level functions

Optica 3 requires Mathematica 6, 7, or 8 and is compatible with all supported Mathematica platforms.


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