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 ...

Numerical sums and products. This gives a numerical approximation to ∑_(i=1)^∞((1)/(i^3+i!)). There is no exact result for this sum, so Mathematica leaves it in a symbolic ...

Functions relating real numbers and integers. Extracting integer and fractional parts. IntegerPart[x] and FractionalPart[x] can be thought of as extracting digits to the left ...

When Solve cannot find solutions in terms of radicals to polynomial equations, it returns a symbolic form of the result in terms of Root objects. You can get numerical ...

Most mathematical functions in Mathematica are set up to apply themselves separately to each element in a list. This is true in particular of all functions that carry the ...

Mathematica supports an extremely wide range of mathematical notation, although often it does not assign a predefined meaning to it. Thus, for example, you can enter an ...

Mathematica can be used to make plots of functions. You give Mathematica a function, and it builds up a curve or surface by evaluating the function at many different points. ...

Much of what Mathematica does revolves around manipulating structured expressions. But you can also use Mathematica as a system for handling unstructured strings of text. ...