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

Here is a system of two ODEs whose coefficient matrix has real and distinct eigenvalues. This solves the system. Note that the general solution depends on two arbitrary ...

ComplexInfinity represents a quantity with infinite magnitude, but undetermined complex phase.

An Abel ODE is a first-order equation of the form This equation arose in the context of the studies of Niels Henrik Abel on the theory of elliptic functions, and represents a ...

Wronskian[{y_1, y_2, ...}, x] gives the Wronskian determinant for the functions y_1, y_2, ... depending on x.Wronskian[eqn, y, x] gives the Wronskian determinant for the ...

Grad[f] gives the gradient, \[Del]f, of the scalar function f in the default coordinate system. Grad[f, coordsys] gives the gradient of f in the coordinate system coordsys.

Mathematica 6.0 represented a major new level in Mathematica's distinguished twenty-year history of broad cutting-edge algorithm development. Mathematica's unified ...

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) ...

If you represent the n^th term in a sequence as a[n], you can use a recurrence equation to specify how it is related to other terms in the sequence. RSolve takes recurrence ...

In many practical situations it is convenient to consider limits in which a fixed amount of something is concentrated into an infinitesimal region. Ordinary mathematical ...