Mathematica usually pays no attention to whether variables like x stand for real or complex numbers. Sometimes, however, you may want to make transformations which are ...

In most cases, you want the head f of a Mathematica expression like f[x] to be a single symbol. There are, however, some important applications of heads that are not symbols. ...

Finding elements that match a pattern. This gives the elements of the list which match the pattern x^_. Here is the total number of elements which match the pattern.

In doing many kinds of calculations, you need to evaluate expressions when variables take on particular values. In many cases, you can do this simply by applying ...

Finding the structure of polynomials written in expanded form. Here is a polynomial in two variables. This is the polynomial in expanded form.

Here is one way to enter a particular expression. Here is another way to enter the same expression. With a notebook front end, you can also enter the expression directly in ...

When you make a function definition using :=, the value of the function is recomputed every time you ask for it. In some kinds of calculations, you may end up asking for the ...

Unless f is a flat function, a pattern like f[x_,y_] stands only for instances of the function with exactly two arguments. Sometimes you need to set up patterns that can ...

In many practical situations it is convenient to consider limits in which a fixed amount of something is concentrated into an infinitesimal region. Ordinary mathematical ...

Picking out elements of lists. We will use this list for the examples. Here is the last element of t.