If you have a list of elements, it is often important to be able to apply a function separately to each of the elements. You can do this in Mathematica using Map. This ...

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

When you make a definition in the form f[args]=rhs or f[args]:=rhs, Mathematica associates your definition with the object f. This means, for example, that such definitions ...

Definitions such as f[x_]=x^2 specify values for functions. Sometimes, however, you need to specify general properties of functions, without necessarily giving explicit ...

Expressions are the main type of data in Mathematica. Expressions can be written in the form h[e_1,e_2,…]. The object h is known generically as the head of the expression. ...

Mathematica provides various ways to set up conditionals, which specify that particular expressions should be evaluated only if certain conditions hold. Conditional ...

It is always a good idea to give variables and functions names that are as explicit as possible. Sometimes, however, such names may get inconveniently long. In Mathematica, ...

Convolution and correlation are central to many kinds of operations on lists of data. They are used in such areas as signal and image processing, statistical data analysis, ...

There are many situations where one wants to find a formula that best fits a given set of data. One way to do this in Mathematica is to use Fit. Basic linear fitting. Here is ...

Integration functions. Here is the integral ∫_a^bx^2 dx. This gives the multiple integral ∫_0^adx ∫_0^bd y(x^2+y^2).