Also check your battery. An older or pour condition battery will lose it charge at rest faster which means that every morning you start your car with just barely enough juice and then your alternater has to work hard to charge it. An alternator is designed to keep a fully charged battery charged up, they are not designed to recharge a dead battery. One of the fastest ways to kill an alternator is using it to charge your dead battery when you left the lights on or something.

Good Luck