NDSolve uses norms of error estimates to determine when solutions satisfy error tolerances. In nearly all cases the norm has been weighted, or scaled, such that it is less ...

While most built-in Mathematica functions follow the standard evaluation procedure, some important ones do not. For example, most of the Mathematica functions associated with ...

Mathematica provides users with access to their computer's file system (Files), interprocess communication (MathLink Mathematica Functions), evaluation of data as code ...

Numerical integration functions. This finds a numerical approximation to the integral ∫_(0)^∞ e^-x^3 x. Here is the numerical value of the double integral ∫_(-1)^1 dx ...

As discussed in "Exact and Approximate Results", Mathematica can handle approximate real numbers with any number of digits. In general, the precision of an approximate real ...

Mathematica provides a variety of functions for manipulating strings. Most of these functions are based on viewing strings as a sequence of characters, and many of the ...

Orthogonal polynomials. Legendre polynomials LegendreP[n,x] arise in studies of systems with three-dimensional spherical symmetry. They satisfy the differential equation ...

Partitioning elements in a list. This partitions in blocks of 3. This partitions in blocks of 3 with offset 1.

The Mathematica side of a MathLink connection is set up to work exactly the same on all computer systems. But inevitably there are differences between external programs on ...

Finding lines that contain specified text. Here is a file containing some text. This returns a list of all the lines in the file containing the text is.