Whenever machine-precision numbers appear in a calculation, the whole calculation is typically done in machine precision. Mathematica will then give machine-precision numbers ...

Finding memory usage. Particularly for symbolic computations, memory is usually the primary resource which limits the size of computations you can do. If a computation runs ...

Pure functions. When you use functional operations such as Nest and Map, you always have to specify a function to apply. In all the examples above, we have used the "name" of ...

When Mathematica transforms an expression such as x+x into 2x, it is treating the variable x in a purely symbolic or formal fashion. In such cases, x is a symbol which can ...

SQLBinary[data] represents raw binary data that can be stored in a database.

Many SQL databases can be configured to require a username and password when a connection is made. This is useful for preventing unwanted access and restricting the range of ...

"Calling .NET from Mathematica" describes using .NET/Link to allow you to call from Mathematica into .NET, thereby extending the Mathematica environment to include the ...

"Introduction to Manipulate" and "Introduction to Dynamic" provide most of the information you need to use Mathematica's interactive features accessible through the functions ...

Extrapolation methods are a class of arbitrary-order methods with automatic order and step-size control. The error estimate comes from computing a solution over an interval ...

The Mathematica compiler provides an important way both to speed up and also to work with Mathematica computations. It does this by taking assumptions about the computations ...