ListInterpolation[array] constructs an InterpolatingFunction object that represents an approximate function that interpolates the array of values given. ...

Identity[expr] gives expr (the identity operation).

Newton's method for nonlinear equations is based on a linear approximation so the Newton step is found simply by setting M_k(p)=0, Near a root of the equations, Newton's ...

The equations of motion for a free rigid body whose center of mass is at the origin are given by the following Euler equations (see [MR99]). Two quadratic first integrals of ...

The symbolic character of Mathematica makes possible a uniquely coherent approach to integer sequences, integrating functional forms, equations, generating functions, and ...

ModularLambda[\[Tau]] gives the modular lambda elliptic function \[Lambda](\[Tau]).

To begin, consider an initial value problem for a linear first-order ODE. This is a linear first-order ODE. Notice that the general solution is a linear function of the ...

PossibleZeroQ[expr] gives True if basic symbolic and numerical methods suggest that expr has value zero, and gives False otherwise.

The differential equations that arise in practice are of two types. Here is an example of the first type. Here is an example of the second type. This equation has a symbolic ...

Exponent[expr, form] gives the maximum power with which form appears in the expanded form of expr. Exponent[expr, form, h] applies h to the set of exponents with which form ...