## Mathematical Solvers

There are several specialized mathematical packages designed to help solve mathematical problems. As such they can be useful for modeling, since after all models are mathematical entities, which need to be solved. These packages are not very helpful in formulating models. In this regard, they are as universal as spreadsheets. But unlike spreadsheets, which are quite well known and intuitive to use, the mathematical packages have a steep learning curve, and require learning specialized programming languages. On the benefit side, the computing power and versatility of mathematical methods you get is unsurpassed.

• MATLAB - The MathWorks, http://www. mathworks.com/ - free trial version, Mac/Win/UNIX

This is a high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis, and numeric computation. It is faster to master MATLAB than C or Fortran, but it certainly requires a major investment of time. Includes mathematical functions for linear algebra, statistics, Fourier analysis, filtering, optimization, and numerical integration, two-dimensional (2-D) and 3-D graphics functions for visualizing data, tools for building custom GUIs, functions for integrating with external applications and languages, such as C, C++, Fortran, Java, COM, and Microsoft Excel. May be a great tool to analyze models, but offers little help in conceptualizing and building them. There are sister products, such as Simulink (see above) or Simscape that are designed to handle the modeling process.

• Mathematica - Wolfram Research, Inc., http:// www.wolfram.com/ - free web seminars and demos, Mac/Win/Linux/UNIX

Integrates numeric and, most importantly, symbolic computations. Provides automation in algorithmic computation, interactive document capabilities, powerful connectivity, and rich graphical interfaces in 2-D and 3-D. It is based on its own advanced programming language, which takes time and effort to master. Has no specific tools to support modeling per se, but can be very useful to solve, run, and analyze already-built models. Can be very useful to study individual functions that are used in your model, for example, to test how parameters impact the functional response (e.g., see http:// www.wolfram.com/products/mathematica/newin6/con-tent/DynamicInteractivity/FindSampleCodeInThe WolframDemonstrationsProject.html).

Pros. Mathematical power that is hard to match.

Cons. Steep learning curve, require a solid mathematical background.

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