### Linearly independency for exponential functions

Written by Changhui TanThis is a supplementary notes for MATH211 ODE and Linear Algebra.

### Display the part of the graph beyond the axis limit in Matlab

Written by Changhui TanWhen I tried to manually adjust the axis limits of a graph, Matlab will automatically cut off the part of the graph that is beyond the axis limits. This didn't happen before (and before means 2014a or earlier versions). I took a little while to find the cure. Just try the following scripts.

```
ax = gca;
ax.Clipping = 'off';
```

Here is the steps to change default mail app in OS X:

- Open
**Mail**app. - Select Preferences -> General. Under "Default email reader", select your preferred mail app.

I am running into a problem by following the steps: the default email reader changes back to the original mail app seconds after I made the change. Here is the solution that works for me. Open terminal. Copy and paste the following script.

`/System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/LaunchServices.framework/Versions/A/Support/lsregister -kill -r -all local,system,user`

Then try step 1-2 again, and it won't change back again!

The purpose of this note is to clarify questions and statements in class, and to provide detailed procedures to find polynomial interpolations.

This note is taken in the PDE discussion group in 2012, on the topic of important spaces in fluid dynamics.

Lecture 2: Carleson measure