Exists[x, expr] represents the statement that there exists a value of x for which expr is True. Exists[x, cond, expr] states that there exists an x satisfying the condition ...

ForAll[x, expr] represents the statement that expr is True for all values of x. ForAll[x, cond, expr] states that expr is True for all x satisfying the condition cond. ...

Probability[pred, x \[Distributed] dist] gives the probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution ...

This package provides an interactive tool for investigating the solutions of differential equations as well as other types of equations that have solutions that can be viewed ...

Wolfram LibraryLink allows dynamic libraries to be directly loaded into the Mathematica kernel so that functions in the libraries can be immediately called from Mathematica. ...

Benchmark[] runs the MathematicaMark8 benchmark.

Transparency is useful in plots when you need an unobstructed view of multiple components of one plot, or simply want to lighten a single plot component against a white ...

Functions in Mathematica are carefully set up so that you normally do not have to know how they work inside. But particularly for numerical functions that use iterative ...

Consider the matrix differential equation where the initial value y_0 y(0)∈^m×p is given. Assume that y_0^Ty_0I, that the solution has the property of preserving ...

The basic idea behind the "StiffnessSwitching" method is to provide an automatic means of switching between a nonstiff and a stiff solver. The "StiffnessTest" and ...