<p>I want to make a small app that displays a PDF, presenting zoom-able single pages with a previous-next page function.</p>

The iPhone and iPod touch can view PDFs already, as one of the TV adverts in the UK shows an email with a .pdf attachment (of swimming lessons) being viewed. It can also view .doc, .xls, and so on, so if he is creating a viewer type application then supporting those as well could be a nice feature addition later on.
This means there is a PDF framework on these devices that you will need to access. Presumably Apple can provide support here if he is a paid up developer. Syncing the PDFs to the device is the actual real difficulty, as this isn't supported by iTunes. I assume that you would need to write a network based synchronisation tool, or have an online cloud for holding people's PDFs.
The device doesn't support Flash, so using PDF to Flash conversion tools will not work.