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, ...

There are many situations where one wants to find a formula that best fits a given set of data. One way to do this in Mathematica is to use Fit. Basic linear fitting. Here is ...

Integration functions. Here is the integral ∫_a^bx^2 dx. This gives the multiple integral ∫_0^adx ∫_0^bd y(x^2+y^2).

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

The functions described here are among the most commonly used discrete univariate statistical distributions. You can compute their densities, means, variances, and other ...

A common operation in analyzing various kinds of data is to find the discrete Fourier transform (or spectrum) of a list of values. The idea is typically to pick out ...

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 ( ...

A Mathematica script is simply a file containing Mathematica commands that you would normally evaluate sequentially in a Mathematica session. Writing a script is useful if ...

Implicit Runge–Kutta methods have a number of desirable properties. The Gauss–Legendre methods, for example, are self-adjoint, meaning that they provide the same solution ...

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 ...