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 ...

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 ...

In a statement like x^4+x^2>0, Mathematica treats the variable x as having a definite, though unspecified, value. Sometimes, however, it is useful to be able to make ...

When you generate a very large output expression in Mathematica, you often do not want to see the whole expression at once. Rather, you would first like to get an idea of the ...

Lists are normally specified in Mathematica just by giving explicit lists of their elements. But particularly in working with large arrays, it is often useful instead to be ...

Even with "Newton methods" where the local model is based on the actual Hessian, unless you are close to a root or minimum, the model step may not bring you any closer to the ...

LogPlot[f, {x, x_min, x_max}] generates a log plot of f as a function of x from x_min to x_max. LogPlot[{f_1, f_2, ...}, {x, x_min, x_max}] generates log plots of several ...

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

Mathematica provides functions that allow users to write their own file format converters and integrate them with the Mathematica Import and Export framework. You can ...