Eigenvalues and eigenvectors. The eigenvalues of a matrix m are the values λ_i for which one can find nonzero vectors v_i such that m.v_i λ_iv_i. The eigenvectors are the ...

When searching for a real simple root of a real valued function, it is possible to take advantage of the special geometry of the problem, where the function crosses the axis ...

The functions accessible with Wolfram LibraryLink make it possible to optimize numerical computations while still keeping the flexibility and generality of Mathematica. If ...

This package contains functions for measuring the performance of Mathematica on your computer and for producing a comparison report that includes benchmark results for other ...

Det[m] gives the determinant of the square matrix m.

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 ( ...

Mathematica's unique symbolic architecture makes it easy to add toolbars with any possible appearance and action to a Mathematica notebook. The ruler is a toolbar used to set ...

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 ...

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 ...

EvaluationMonitor is an option for various numerical computation and plotting functions that gives an expression to evaluate whenever functions derived from the input are ...