Functions for creating power series. Here is the power series expansion for exp(x) about the point x0 to order x^4. Here is the series expansion of exp(x) about the point ...

Mathematica expressions provide a very general way to handle all kinds of data, and you may sometimes want to use such expressions inside your external programs. A language ...

The library now fully supports the Unicode character encoding forms UTF-8, UTF-16, and UTF-32. Use the following new API functions to put or get Unicode characters to or from ...

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

Supporting a large number of numerical integration methods for differential equations is a lot of work. In order to cut down on maintenance and duplication of code, common ...

Implicit Runge–Kutta methods have a number of desirable properties. The Gauss–Legendre methods, for example, are self-adjoint, meaning that they provide the same solution ...

When a differential system has a certain structure, it is advantageous if a numerical integration method preserves the structure. In certain situations it is useful to solve ...

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 ...

NDSolve uses norms of error estimates to determine when solutions satisfy error tolerances. In nearly all cases the norm has been weighted, or scaled, such that it is less ...

Ways to construct nested lists. This generates a table corresponding to a 2×3 nested list. This generates an array corresponding to the same nested list.