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 ...

Functions that are specified by simple algebraic formulas tend to be such that when their input is changed only slightly, their output also changes only slightly. But ...

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 ( ...

Patterns are used throughout Mathematica to represent classes of expressions. A simple example of a pattern is the expression f[x_]. This pattern represents the class of ...

With the default option setting Lighting->Automatic, Mathematica uses a simulated lighting model to determine how to color polygons in three-dimensional graphics. Mathematica ...

Functions for creating power series. Here is the power series expansion for exp(x) about the point x0 to order x^4. Here is the series expansion of exp(x) about the point ...

You can use lists as tables of values. You can generate the tables, for example, by evaluating an expression for a sequence of different parameter values. This gives a table ...

Mathematica expressions provide a very general way to handle all kinds of data, and you may sometimes want to use such expressions inside your external programs. A language ...

A full Mathematica installation consists of thousands of separate files, arranged in several hundred directories under the main installation directory. The location of the ...

Ways to construct nested lists. This generates a table corresponding to a 2×3 nested list. This generates an array corresponding to the same nested list.