RiccatiSolve[{a, b}, {q, r}] gives the matrix x that is the stabilizing solution of the continuous algebraic Riccati equation ConjugateTranspose[a].x + x.a - ...

Mathematica is widely used throughout the world for precollege education, in mathematics and many other fields. This page lists a few Mathematica functions used particularly ...

Mathematica has special sparse-array technology for efficiently handling arrays with literally astronomical numbers of elements when only a small fraction of the elements are ...

SolveAlways[eqns, vars] gives the values of parameters that make the equations eqns valid for all values of the variables vars.

Important for elliptical shapes and periodic potentials, Mathematica achieves a new level of implementation for Mathieu-related functions, supporting arbitrary-precision ...

Basic plotting functions. This plots a graph of sin(x) as a function of x from 0 to 2π. You can plot functions that have singularities. Mathematica will try to choose ...

An Euler equation is an ODE of the form The following is an example of an Euler equation. The Legendre linear equation is a generalization of the Euler equation. It has the ...

Polynomial algorithms are at the core of classical "computer algebra". Incorporating methods that span from antiquity to the latest cutting-edge research at Wolfram Research, ...

NDSolve solves a differential equation numerically. It returns solutions in a form that can be readily used in many different ways. One typical use would be to produce a plot ...

In calculus even more than other areas, Mathematica packs centuries of mathematical development into a small number of exceptionally powerful functions. Continually enhanced ...