Miracles

This is probably totally obvious, but I've been thinking about it today so. . .
Why did Jesus do miracles?  Why do any of the prophets do miracles?  What's the purpose? 

We are shown all through the scriptures examples of people who saw miracles and didn't believe anyway.  We can read that "there is no witness until after the trial of your faith"  so we can see that miracles don't make testimonies and certainly don't bring conversion.

So, what is the purpose of them?  Are they simply to prepare us for the miracle of the atonement?  Are they to give us courage that all is possible?  Why is it so important that miracles haven't ceased other than just that things are the same as before?  What?

This is a question--a real question.
Somebody answer it.