NDSolve is broken up into several basic steps. For advanced usage, it can sometimes be advantageous to access components to carry out each of these steps separately. NDSolve ...

Exact global optimization problems can be solved exactly using Minimize and Maximize. This computes the radius of the circle, centered at the origin, circumscribed about the ...

Throughout Mathematica there is support not only for approximate real numbers, but also for exact numbers represented in algebraic or symbolic form. Functions like Floor, ...

Integers represents the domain of integers, as in x \[Element] Integers.

Complexes represents the domain of complex numbers, as in x \[Element] Complexes.

A Diophantine polynomial system is an expression constructed with polynomial equations and inequalities combined using logical connectives and quantifiers where the variables ...

Power series are in many ways the algebraic analog of limited-precision numbers. Mathematica can generate series approximations to virtually any combination of built-in ...

Factoring a quadratic polynomial in one variable is straightforward. But Mathematica routinely factors degree-100 polynomials in 3 variables—by making use of a tower of ...

The general first-order nonlinear PDE for an unknown function u(x,y) is given by Here F is a function of uu(x,y), p ( ∂u(x,y) ) / ( ∂x ) , and q ( ∂u(x,y) ) / ( ∂y ) . The ...

DiscreteLQRegulatorGains[ss, {q, r}, \[Tau]] gives the optimal discrete-time state feedback gain matrix with sampling period \[Tau] for the continuous-time StateSpaceModel ...