i am having the same issue with the battery of my new i Phone. it does die out quit quickly. There is a trick that you should always bear in mind though. Make sure you dont have many applications open all the time. Make it a habit to double clik on the round button (at the center bottom of the phone), and close the applications that you are not using. YOu may close by hold-pressing on one of the icons, then when they start shaking, close them by clicking on the red thing (top left corner of the icon).
Hope that helps,
Thanks