When you make a definition in the form f[args]=rhs or f[args]:=rhs, Mathematica associates your definition with the object f. This means, for example, that such definitions ...

Convolution and correlation are central to many kinds of operations on lists of data. They are used in such areas as signal and image processing, statistical data analysis, ...

Descriptive statistics refers to properties of distributions, such as location, dispersion, and shape. The functions described here compute descriptive statistics of lists of ...

First-order PDEs are usually classified as linear, quasi-linear, or nonlinear. The first two types are discussed in this tutorial. A first-order PDE for an unknown function ...

Many real-world applications require the solution of IVPs and BVPs for nonlinear ODEs. For example, consider the logistic equation, which occurs in population dynamics. This ...

One-dimensional Laplace transforms. The Laplace transform of a function f(t) is given by ∫_0^∞f(t)e^-stt. The inverse Laplace transform of F(s) is given for suitable γ by ( ...

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 ...

Here the standard procedure used by Mathematica to evaluate expressions is described. This procedure is the one followed for most kinds of expression. There are, however, ...

Most of the documentation provided for Mathematica is concerned with explaining what Mathematica does, not how it does it. But the purpose of this is to say at least a little ...