TITLE: What does "test function" mean?
QUESTION [22 upvotes]: I am trying to learn weak derivatives. In that, we call $\mathbb{C}^{\infty}_{c}$ functions as test functions and we use these functions in weak derivatives. I want to understand why these are called test functions and why the functions with these properties are needed. I have some idea about these but couldn't understand them properly.
Also, I'll be happy if any one can suggest some good reference on this topic and Sobolev spaces.

REPLY [2 votes]: Specifically why it is called test function. (Essentially not different from another answer.)
Strichartz liked to introduce the concept with physical intuition. 
https://books.google.com/books?id=T7vEOGGDCh4C&lpg=PP1&dq=strichartz%20distribution&pg=PA1#v=onepage&q=temperature&f=false
Suppose you want to measure the temperature at a point in the room. You hold out your thermometer, but the tip of it is actually a blob of glass with some liquid inside, so are you really measuring the temperature at any actual point? At best it is a weighted average in a neighborhood of the point.