By default, you are only meant to sync your iPad (or any other iOS device) with one computer. This is Apple's way of doing it's best to prevent piracy. If you could simply plug you iPad into someone elses computer and 'give' them all of your music and purchased media, then why would anyone buy anything ever again???
If you are using the same iTunes or Apple ID on both computers, use the 'Transfer Purchases' option on that window that pops up when you are trying to sync your iPad on a new computer. This will take any items purchased on your iPad and save it to the new computer.
There is a work-around. To sync to multiple computers, you need to set your iPad to the 'manual' syncing mode. Instead of automatically adding any new song, video and app when you plug it in, you'll have to drag-n-drop the new stuff onto your device. Here's how to do this:
There is one more option if you are only concerned about synching apps. On the iPad if you open the 'App Store' app, there is a 'Purchased' option on the bottom black menu. As long as an app was downloaded or purchased using your Apple ID, then you can head to this spot and download an app purchased on another computer (work or home) without the need to sync or re-purchase the item.
After the very first sync to get you up and running, you only REALLY need to sync your iPad once a month or so to back it up, and that should be done on the same computer all the time.
However, if you have two separate Apple or iTunes ID's (one for home purchases and a school account), then the management becomes really hard. I??have always just used my own Apple ID, so I have not had to muddle through this situation. It's best to pick one, and stick??with it.