Question: What program or system utility can I use to convert my desktop into two work areas using a single monitor?

*Some recommendations for an easy to use application?*

Answer: 
I agree with the posted answers; they're the right answers. But there's another option in stock Ubuntu that runs Unity (e.g. 14.04, but not 16.04+) that satisfies one interpretation of the question, and can generally be handy to know

You can easily resize windows to take up half or a quarter of the screen. You can do this with `Ctrl`+`Alt`+**any number on the num pad** (in number mode). This will resize the current window as follows:

* `ctrl`+`alt` + ...
* `1`: top left
* `2`: bottom half, full-width
* `3`: bottom left
* `4`: left half, full-height
* `5`: full screen
* `6`: right half, full-height
* `7`: top left quarter
* `8`: top half, full-width
* `9`: top right quarter
* `0`: minimize window (I've remapped this to make windows take the full vertical screen height, keeping the current width)

So with one window do `Ctrl`+`Alt`+`4`, and with the other `Ctrl`+`Alt`+`6`, you'll have the screen split into two halves temporarily.
Tilers are excellent choices.

[![enter image description here](https://i.stack.imgur.com/ZBc5v.jpg)](https://i.stack.imgur.com/ZBc5v.jpg)

You can install it the following way:

To install awesome on Ubuntu 16.04 (Xenial Xerus) run the following commands:

```
sudo apt-get install awesome

```

You can read more about the tilers in [this article](https://freedompenguin.com/articles/desktop/exploring-tiling-window-managers/) and on the [AWESOME website](https://awesomewm.org/) itself.