Im[z] gives the imaginary part of the complex number z.

Re[z] gives the real part of the complex number z.

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 ...

Orthogonal polynomials. Legendre polynomials LegendreP[n,x] arise in studies of systems with three-dimensional spherical symmetry. They satisfy the differential equation ...

Mathematica normally makes as few assumptions as possible about the objects you ask it to manipulate. This means that the results it gives are as general as possible. But ...

InverseZTransform[expr, z, n] gives the inverse Z transform of expr. InverseZTransform[expr, {z_1, z_2, ...}, {n_1, n_2, ...}] gives the multiple inverse Z transform of expr.

This loads packages containing some test problems and utility functions. One of the first and simplest methods for solving initial value problems was proposed by Euler: ...

The control mechanisms set up for NDSolve enable you to define your own numerical integration algorithms and use them as specifications for the Method option of NDSolve. ...

NResidue[expr, {z, z_0}] numerically finds the residue of expr near the point z = z_0.

D[f, x] gives the partial derivative \[PartialD]f/\[PartialD]x. D[f, {x, n}] gives the multiple derivative \[PartialD]^n f/\[PartialD]x^n. D[f, x, y, ...] differentiates f ...