# 3 Equations

## 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 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 , 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 \lim \neg \div \int \rightarrow \pm \nabla \exists \approx \partial \forall \equiv \sum \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]

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]

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]

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]

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]

### 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.