$ModuleNumber gives the current serial number to be used for local variables that are created.

$PreRead is a global variable whose value, if set, is applied to the text or box form of every input expression before it is fed to Mathematica.

You can define the derivative in Mathematica of a function f of one argument simply by an assignment like f'[x_]=fp[x]. This defines the derivative of f(x) to be fp(x). In ...

Here is a homogeneous equation in which the total degree of both the numerator and the denominator of the right-hand side is 2. The two parts of the solution list give ...

Special forms for some common symbols. This is equivalent to Sin[60Degree]. Here is the long form of the input.

In an expression like f[x], the 'function name' f is itself an expression, and you can treat it as you would any other expression. You can replace names of functions using ...

You can rotate 3D graphics with your mouse. Move the pointer over the 3D graphic. The pointer changes to the 3D rotate pointer GraphicsBox[RasterBox[CompressedData[ ]], ...

Turning conditions into numbers. Boole[expr] is a basic function that turns True and False into 1 and 0. It is sometimes known as the characteristic function or indicator ...

Functions for rearranging lists. This sorts the elements of a list into a standard order. In simple cases like this, the order is alphabetical or numerical. This sorts the ...

Solving equations involving power series. Here is a power series. This gives an equation involving the power series.