Math with Latex

Let’s switch gears for a second and learn a little about a tool that is incredibly helpful for writing mathematical expressions and formulae: Latex math mode. Latex (pronounced lah-teck) is a document preparation system that differs from software like Microsoft Word in that it is not a what-you-see-is-what-you-get program. Instead, Latex uses, for lack of a better word, commands to help you build and format your documents. It is used extensively in the academic and scientific fields because Latex makes creating complex documents significantly easier than typical word processing software.

Here, we are only going to learn about one aspect of Latex: math mode. Latex math mode makes writing math expressions very straightforward. Instead of relying on a mouse-driven equation editor, which can be quite cumbersome, math mode uses specific keystrokes to help create beautifully formatted equations.

In order to get access to Latex math mode, you need to download and install a complete Latex distriubtion such as MacTex (for Max) or MikTex (for Windows). Then, there are packages available that allow you to run just math mode to produce equations that can be dragged and dropped (copied and pasted) into another document (e.g. Word, Powerpoint, etc.). For example, MacTex comes with one such package called LatexIt. Windows (and Mac) users can install kLatexFormula.

Latex Math Mode in the browser

Maybe even better, there are several websites that allow you to run Latex math mode from the browser, and I recommend going in that direction for now as installing a full Latex distribution is more than we need at this point. To get started, head over to https://www.latex4technics.com/ which does everything we need it to.

latex4technics landing page.

Once there, you should be greeted with a simple interface that has 3 main panes: the sidebar “catalogue” which gives you mouse access to a subset of the math mode “commands”, the main latex math text entry pane in the middle, and the output pane on the right (there are two, but for all intents and purposes, they do the same thing). There is also a header bar at the top of the window with compile, save and export image options. The text entry pane may even already have a sample equation written for you.

This website works pretty simply. First you add text to the text entry pane. When you are finished, you hit the compile button. Then, your lovely equation should show up in the output window, assuming everything was entered correctly. Finally, you can either right click on the equation that is output and copy the image, or click the export button to save the image in a format of your choice (and the resolution of your choice). The hard part, if you can call it hard, is figuring out what to enter in the text entry pane.

Latex syntax

The wonderful thing about Latex math mode is that the syntax is meant to be extremely simple and intuitive. Still, there is a lot that you can do and it can be difficult to remember some of the descriptions for different mathematical operations. For that reason, the best resource that I’ve found for everything math mode related is this wikibooks site: https://en.wikibooks.org/wiki/LaTeX/Mathematics. This should be your go to resource for getting up and running. For this reason, I will touch on just a few things here.

As you can see from the example, anything special that you want to do needs to start with a backslash \. Think of the backslash as a special character that initiates a command. After the backslash is the command name. Again, these are meant to be intuitive. Let’s go ahead and try a few in the text window in the browser.

For greek letters, it’s simply the backslash and the letter name: \rho, \Delta, \theta, etc. As you should find, if you start the greek word with a capital letter, you get the capital greek letter. If you want to do exponents, you use ^, as in x^n. If the exponent has more than 1 character, use {}: x^{n+1}. Similarly, subscripts are done with the underscore: y_{i-1}.

Fractions are easy! Use the \frac command with two sets of {}: 1 for the numerator and 1 for the denominator: \frac{x^5}{5!}. Many special functions and symbols use a shorthand notation. Examples include square root: \sqrt{1+x}, integrals and the infinity symbol: \int_0^\infty x^2 dx. Derivatives can be written in a couple forms: \frac{\partial E}{\partial x} gives us partials and we can use \nabla\cdot E to use the del operator (here with a dot product to give us the divergence of E!).

Note that the catalogue (left window) gives you quick access to some of the math mode functionality. However, I highly recommend learning the keystrokes as it is much faster and more efficient then messing around in those menus. Use the catalogue as a way to get a quick reminder on the math mode syntax if you forget something. Also, not all of the functionality of math mode is within the catalogue.

Again, I’m not going to go into a ton of detail here. My goal here is to introduce this tool and direct you to resources that can help you use it, including the wikibooks site. You will get some experience with math mode in an upcoming exercise set. Beyond that, I hope that you will find this useful when preparing documents for your physics and math courses.