Q: I have iBook on my iPad and iPhone, while I can sync the books that I've downloaded I'm having trouble syncing PDFs. Does iBooks allow syncing of PDFs?

It doesn't allow syncing, but even though they aren't iTunes purchases you should be able to copy them from your iPad to your computer's iTunes via File > Devices > Transfer Purchases (they should copy over to the Books part of your library) and you can then sync them to your iPhone

Huh? I don't understand. My pdfs (which consist of things like my friend's dissertation) are on my iPad in i

Books. How am I supposed to get to File>Devices>Transfer Purchases on my iPad?

You need to connect the iPad to your computer's iTunes and do File > Devices > Transfer Purchases on your computer's iTunes to copy them over to the Books part of your computer's iTunes library