Purdue's campus is situated in the small city of West Lafayette, near the western bank of the Wabash River, across which sits the larger city of Lafayette. State Street, which is concurrent with State Road 26, divides the northern and southern portions of campus.
People who have sent you friend requests are visible by clicking the friend request icon in the menu bar. Friend requests you have sent are visible in your Activity Log, using filter Friends: (you may have to click more to see it).
Doing so will remove the request from your Requests list. They will not be notified that their friend request was declined, but they will be able to send you another friend request in the future. The only solution I can think of is that you keep a list of people you have sent friend requests to.