The Lotka–Volterra system arises in mathematical biology and models the growth of animal species. Consider two species where Y_1(T) denotes the number of predators and Y_2(T) ...

RootIntervals[{poly_1, poly_2, ...}] gives a list of isolating intervals for the real roots of any of the poly_i, together with a list of which polynomials actually have each ...

The solutions to many second-order ODEs can be expressed in terms of special functions. Solutions to certain higher-order ODEs can also be expressed using AiryAi, BesselJ, ...

DSolve can find solutions for most of the standard linear second-order ODEs that occur in applied mathematics. Here is the solution for Airy's equation. Here is a plot that ...

AlgebraicIntegerQ[a] yields True if a is an algebraic integer, and yields False otherwise.

 

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

Built into Mathematica are state-of-the-art constrained nonlinear fitting capabilities, conveniently accessed with models given directly in symbolic form. Mathematica also ...

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 a flexible system for specifying arbitrary symbolic assumptions about variables. It uses a wide range of sophisticated algorithms to infer the consequences of ...