$TimeZone gives the current time zone to assume for dates and times.

$UserBaseDirectory gives the base directory in which user-specific files to be loaded by Mathematica are conventionally placed.

You can do arithmetic with Mathematica just as you would on an electronic calculator. This is the sum of two numbers. Here the / stands for division, and the ^ stands for ...

Basic plotting functions. This plots a graph of sin(x) as a function of x from 0 to 2π. You can plot functions that have singularities. Mathematica will try to choose ...

We first encountered lists in "Making Lists of Objects" as a way of collecting numbers together. Here, we shall see many different ways to use lists. You will find that lists ...

Converting power series to normal expressions. Power series in Mathematica are represented in a special internal form, which keeps track of such attributes as their expansion ...

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 ...

Differentiating a known function gives an explicit result. Differentiating an unknown function f gives a result in terms of f'. Mathematica applies the chain rule for ...

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

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 ...