LaTeX for Publications: Basic Math Equations, Part II

Mathematical expressions use a wide variety of symbols. Some symbols are "built-into" LaTeX. These symbols can be inserted into a math expression by simply typing them in.

+ - = ! / ( ) [ ] , . | ' :

A very complete list of symbols can be found in this document (PDF format):

• Comprehensive List of Math Symbols

To insert a fraction, use the keyword \frac, followed by {numerator}{denominator}.

x=\frac{a}{b}
\frac{a+b}{b-c}
\frac{\frac{1}{a}+\frac{1}{b}}{b-c}

Brackets are essential for clarity in mathematical expressions. The characters ( ) and [ ] are easy to insert, using your keyboard. Here's a simple equation on a single line, using brackets: Such an expression could be inserted into a line of text. We run into trouble, however, when trying to use simple brackets for larger, more complex expressions. The first example below shows standard bracket characters; the second example demonstrates the LaTeX feature for automatically sizing of brackets:
 

(\frac{a^2}{b^3})
\left(\frac{a^2}{b^3}\right)

The second example above uses the command: \left(...\right) to create curved left and right brackets that size themselves to their contents. Alternatively square brackets can be used with the command:\left[...\right]

To create curly brackets above or below all or part of a mathematical expression, use the \overbrace and \underbrace commands, respectively.

\overbrace{a+b}^{6+7}
\underbrace{u'-P(x)u^2-Q(x)u-R(x)}_{\text{=0}}
\frac{\frac{1}{a}+\frac{1}{b}}{b-c}

Powers and indices are common on mathematical expressions. Powers are equivalent to superscripts in normal text, while indices are like subscripts. To add a power, use the carat ( ^ ) symbol, and for an index, use the underscore ( _ ). Remember, though, that if you need to raise (power) or lower (index) more than one character, you need to use curly braces { }.

Power	x^n
	y^{n+1}
Index	b_i
	b_{ac}

The most common use of this feature is to show a square root, which is easy to do with this command: \sqrt{x}, though you can generalize the command to show any magnitude of root, with
\sqrt[n]{x}.

LaTeX will automatically adjust the size of the root notation to fit its contents. As the examples show, the [n] is optional and is needed only when something other than a square root is called for.

x=\sqrt{y+5}
Cube root of a fraction:  \sqrt[3]{\frac{a^2}{9ac + \pi}}
The Quadratic Formula:  x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Although LaTeX does not have a command for creating matrices, we can create a matrix using the array environment. Let's try making a few simple matrices.
 

\left[  \begin{array}{ c c }     a & b \\     c & d  \end{array}  \right]
\left|  \begin{array}{ c c c c }     V_1 & V_2 & V_3 & V_4 \\     0 & 0 & 0 & 0 \\     0 & 0 & 0 & 0 \\     0 & 0 & 9 & 0 \\     5 & 7 & 8 & 0 \\     a & n & x & ax^n  \end{array}  \right|