Repeated patterns. Multiple blanks such as x__ allow you to give patterns in which sequences of arbitrary expressions can occur. The Mathematica pattern repetition operators ...

Simplifying expressions. Mathematica does not automatically simplify an algebraic expression like this. Simplify performs the simplification.

In addition to the ordinary characters that appear on a standard keyboard, you can include in Mathematica strings any of the special characters that are supported by ...

Specifying output styles. The second x^2 is here shown in boldface. This shows the word text in font sizes from 10 to 20 points.

Here is a typical palette of modifiers. Mathematica allows you to use any expression as a subscript. Unless you specifically tell it otherwise, Mathematica will interpret a ...

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

The notion of expressions is a crucial unifying principle in Mathematica. It is the fact that every object in Mathematica has the same underlying structure that makes it ...

"Values for Symbols" discussed how you can use transformation rules of the form x->value to replace symbols by values. The notion of transformation rules in Mathematica is, ...

Functions for manipulating trigonometric expressions. This expands out a trigonometric expression. This factors the expression.

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.