Representations of real intervals. This represents all numbers between -2 and +5. The square of any number between -2 and +5 is always between 0 and 25.

Numerical solution of differential equations. This generates a numerical solution to the equation y^′(x)y(x) with 0<x<2. The result is given in terms of an ...

Basic Objects Input Syntax Some General Notations and Conventions

You can manipulate lists of transformation rules in Mathematica just like other symbolic expressions. It is common to assign a name to a rule or set of rules. This assigns ...

Manipulating global options in the front end. Just like cells and notebooks, the complete Mathematica front end has various options, which you can look at and manipulate from ...

Finding and setting values of symbols. Mathematica effectively stores all definitions you give as lists of transformation rules. When a particular symbol is encountered, the ...

Mathieu and related functions. The Mathieu functions MathieuC[a,q,z] and MathieuS[a,q,z] are solutions to the equation y^′′+[a-2qcos(2z)]y0. This equation appears in many ...

Mathematica allows you to define transformation rules for any expression. You can define such rules not only for functions that you add to Mathematica, but also for intrinsic ...

Particularly when you use transformation rules, you often need to name pieces of patterns. An object like x_ stands for any expression, but gives the expression the name x. ...

It is often useful to carry out a numerical integration using fixed step sizes. For example, certain methods such as "DoubleStep" and "Extrapolation" carry out a sequence of ...