Conventions for file names. Most files used by Mathematica are completely system independent. .mx and .exe files are however system dependent. For these files, there is a ...

In many kinds of calculations, you may find yourself typing the same input to Mathematica over and over again. You can save yourself a lot of typing by defining a function ...

The replacement operator /. allows you to apply transformation rules to a specific expression. Often, however, you want to have transformation rules automatically applied ...

When you have numerical data, it is often convenient to find a simple formula that approximates it. For example, you can try to "fit" a line or curve through the points in ...

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 ...

Mathematica provides a general mechanism for specifying constraints on patterns. All you need to do is to put /;condition at the end of a pattern to signify that it applies ...

Evaluating sums. Mathematica recognizes this as the power series expansion of e^x. This sum comes out in terms of a Bessel function.

If you have installed Mathematica in a location where multiple users can run it (for example, on a file server or multi-user machine), then you can set up systemwide defaults ...

Basic vector operations. This is a vector in three dimensions. This gives a vector u in the direction opposite to v with twice the magnitude.

SQLExpr[expr] allows a Mathematica expression to be stored in a database.