Module (Built-in Mathematica Symbol)

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, ...

StirlingS2 (Built-in Mathematica Symbol)

StirlingS2[n, m] gives the Stirling number of the second kind \[ScriptCapitalS]_n^(m).

TautologyQ (Built-in Mathematica Symbol)

TautologyQ[bf] gives True if all combinations of values of variables make the Boolean function bf yield True.TautologyQ[expr, {a_1, a_2, ...}] gives True if all combinations ...

Algebraic Number Fields (Mathematica Tutorial)

Mathematica provides representation of algebraic numbers as Root objects. A Root object contains the minimal polynomial of the algebraic number and the root number—an integer ...

Character Codes (Mathematica Tutorial)

Converting to and from character codes. Mathematica assigns every character that can appear in a string a unique character code. This code is used internally as a way to ...

Second-Order PDEs (Mathematica Tutorial)

The general form of a linear second-order PDE is Here uu(x,y), and a, b, c, d, e, f, and g are functions of x and y only—they do not depend on u. If g0, the equation is ...

Is the Problem Well-Posed? (Mathematica Tutorial)

DSolve returns a general solution for a problem if no initial or boundary conditions are specified. The general solution to this equation is returned. However, if initial or ...

Machine-Precision Numbers (Mathematica Tutorial)

Whenever machine-precision numbers appear in a calculation, the whole calculation is typically done in machine precision. Mathematica will then give machine-precision numbers ...

Numerical Methods for Solving the ... (Mathematica Tutorial)

The Lotka–Volterra system arises in mathematical biology and models the growth of animal species. Consider two species where Y_1(T) denotes the number of predators and Y_2(T) ...

Deleting Data (DatabaseLink Tutorial)

SQLDelete deletes data from a database. An alternative, using raw SQL, is described in "Deleting Data with Raw SQL". If you find that the examples in this tutorial do not ...