Module[{x, y, ...}, expr] specifies that occurrences of the symbols x, y, ... in expr should be treated as local. Module[{x = x_0, ...}, expr] defines initial values for x, ...

Plot3D[f, {x, x_min, x_max}, {y, y_min, y_max}] generates a three-dimensional plot of f as a function of x and y. Plot3D[{f_1, f_2, ...}, {x, x_min, x_max}, {y, y_min, ...

Throughout any computation, Mathematica maintains an evaluation stack containing the expressions it is currently evaluating. You can use the function Stack to look at the ...

ArrayQ[expr] gives True if expr is a full array or a SparseArray object, and gives False otherwise. ArrayQ[expr, patt] requires expr to be a full array with a depth that ...

Mathematica provides convenient and efficient system-independent functions for handling file-related constructs at all levels.

lhs :> rhs or lhs :> rhs represents a rule that transforms lhs to rhs, evaluating rhs only after the rule is used.

GatherBy[list, f] gathers into sublists each set of elements in list that gives the same value when f is applied.GatherBy[list, {f_1, f_2, ...}] gathers list into nested ...

The general form of a nonlinear second-order ODE is For simplicity, assume that the equation can be solved for the highest-order derivative y^ ′′(x) to give There are a few ...

The introduction of Mathematica 6 in 2007 represented a revolutionary redefinition of Mathematica. Arriving only 18 months after Mathematica 6, Mathematica 7 represents ...

Mathematica provides hundreds of options to control every aspect of the construction and styling of graphics. The options are carefully designed to be both flexible and ...