The following is the sequence of steps that Mathematica follows in evaluating an expression like h[e_1,e_2…]. Every time the expression changes, Mathematica effectively ...

You may have noticed that there are two different ways to make assignments in Mathematica: lhs=rhs and lhs:=rhs. The basic difference between these forms is when the ...

Evaluating integrals is much more difficult than evaluating derivatives. For derivatives, there is a systematic procedure based on the chain rule that effectively allows any ...

Mathematica's unique symbolic architecture makes it easy to add toolbars with any possible appearance and action to a Mathematica notebook. The ruler is a toolbar used to set ...

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 ...

ParametricPlot3D[{f_x, f_y, f_z}, {u, u_min, u_max}] produces a three-dimensional space curve parametrized by a variable u which runs from u_min to u_max. ...

All is a setting used for certain options. In Part and related functions, All specifies all parts at a particular level.

The NumericalDifferentialEquationAnalysis package combines functionality for analyzing differential equations using Butcher trees, Gaussian quadrature, and Newton-Cotes ...

Beta[a, b] gives the Euler beta function \[CapitalBeta](a, b). Beta[z, a, b] gives the incomplete beta function \[CapitalBeta]_z (a, b).