For the most part, it is not possible to run two app simultaneously on the iPad. There are a few exceptions, but they either involve playing music or have time limits and/or other problems you won't want to deal with in the middle of a lecture.
On the other hand there are several apps that do what you want all-in-one; record audio synced with any notes you take on a PDF document. Alas, I don't remember any of their names off the top of my head. However, a search for best college (or student) note taking app (using the custom Google search at the top of this sites webpage) should turn up numerous suggestions and preferences.
You'll have to give up using PDF Expert for note taking. I sympathize. I love that app. But by all reports other students on the forum have been more than pleased by the other apps.
Or, if you get lucky, maybe some of our busy students will stumble across the thread and give you better advice.
