# Real Analysis

### A sample presentation

This is the title slide for this short presentation that's just meant to illustrate what presentations look like.

## Top of first real column

This is the first slide in the top of the first column of content.

You can use your arrow keys navigate down to the next slide or to the right to get to the next column. You can also use the arrow controller at the bottom right of your screen.

### Second content slide

This is the second and final slide of the first column of content.

## Mathematical content

Naturally, we can type mathematical content, like $$ \int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}. $$

### Real content

For this class, the following might be a more appropriate example:

If for every $\varepsilon > 0$, there is a $\delta > 0$, such that $$ |f(x) - L| < \varepsilon \: \text{ whenever } \: |x-a| < \delta, $$ then we say that $$\lim_{x\to a} f(x) = L.$$

### Graphing a function

We can include interactive images, as well, like the graph of $$ f_{a,b}(x) = \sum_{n=0}^{\infty} a^n \cos(b^n x). $$

## Keyboard commands

Here are a few useful keyboard commands:

- O: Toggle overview
- F: Enter fullscreen
- Esc: Get out of fullscreen
- C: Pull up a marker to draw comment on a slide
- B: Enter blackboard mode.

The marker and blackboard modes are particularly nice when teaching via Zoom. The marker and chalk are only positioned properly when in fullscreen mode, though.