# 3 Equations

Laura Greenstreet

## Commands

Latex allows you to quickly write mathematical equations by specifying characters using commands you can type using the keyboard. For example, we can write $ax^2 + bx + c = 0$ using the code

`[‌latex] ax^2 + bx + c = 0 [/latex]`

While some common math symbols like +/- and exponentiation have a single symbol on the keyboard, most commands start with “\” and then describe the command. An example of an equation that requires \ commands is $\cos^2 \theta + \sin^2 \theta = 1$, which requires commands for the sine, cosine, and angle:

`[‌latex] \cos^2 \theta + \sin^2 \theta = 1 [/latex]`

The table below shows some common “\” commands for symbols, in addition to the trigonometric functions and Greek letters used in the previous example.

 Algebra Calculus Logic $\times$ \times $\lim$ \lim $\neg$ \neg $\div$ \div $\int$ \int $\rightarrow$ \rightarrow $\pm$ \pm $\nabla$ \nabla $\exists$ \exists $\approx$ \approx $\partial$ \partial $\forall$ \forall $\equiv$ \equiv $\sum$ \sum $\in$ \in

Commands can also take arguments using curly brackets. For example, the fraction and square root in the quadratic formula both take arguments.

`[‌latex] x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a} [/latex]`

$\displaystyle x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a}$

Superscripts and subscripts are also considered arguments. Use ^{} to create a superscript. If, no brackets are used, only the first character will be part of the superscript.
`[‌latex]e^{i \pi} = -1[/latex]`

$\displaystyle e^{i \pi} = -1$

Use _{} to create a subscript. Again, if no brackets are used only the first character will be part of the subscript.

`[‌latex] x_1 + x_2 = 2x_3[/latex]`

$\displaystyle x_1 + x_2 = 2x_3$

You can add a subscript and a superscript to the same item. The order of the subscript and superscript does not matter. For example:

`[‌latex]\int_{a}^{b} u dv = u(x)v(x)|_a^b - \int^{b}_a v du [/latex]`

$\displaystyle \int_{a}^{b} u dv = u(x)v(x)|_a^b - \int^{b}_a v du$

Latex is generally not sensitive to white space when typesetting math. Outside of Pressbooks, the commands `\;, \:, \,` explicitly add large, medium, and small spaces respectively. However, these commands do not seem to be compatible with the QuickLaTeX plugin. As a workaround, you can use the command `\hspace{}` to add a specific amount of horizontal white space. For example, we can add a space between the functions and the differential variable:

`[‌latex]\int_{a}^{b} u \hspace{2pt} dv = u(x)v(x)|_a^b \int^{b}_a v \hspace{2pt} du[/latex]`

$\displaystyle \int_{a}^{b} u \hspace{2pt} dv = u(x)v(x)|_a^b - \int^{b}_a v \hspace{2pt} du$

### Errors

If a statement is not entered correctly, the equation may not display as expected or QuickLaTeX may display an error. Errors take practice to read. For example, if I were to try to write the quadratic formula as

`[‌latex] x = \frac{-b \pm \sqrt{b^2 + 4ac}{2a} [/latex]`

I would get the error Try to spot what is causing the error. The answer is given in the solutions to the exercises for this section. 