Apple has set the stage for a textbook revolution with the new iBooks 2 and free iBooks Author software, but as it turns out, that was only the first of the company’s plans to unveil in New York City today -- Cupertino is also introducing a new iTunes U app for allowing colleges and universities to share their knowledge with the world.

Apple’s senior vice president of internet software and services Eddy Cue followed up the announcement of iBooks 2 and iBooks Author in New York City this morning with the introduction of a new iTunes U app. "iTunes U lets colleges and universities around the world deliver content... around the world to anyone using an iPhone, iPod touch or an iPad,” Cue explained.

Touting more than 1,000 colleges and universities that are already using iTunes U with 700 million downloads since launching four years ago, Cue calls it the number one catalog for educational content, but notes that it’s currently only used for delivering lectures. "We want to let teachers do a lot more,” Cue teased. “We want to create full online courses."

Cue introduced Apple vice president of consumer applications Jeff Robbin to demonstrate the new iTunes U app with an online course from Duke: Core Concepts in Chemistry. The app features an overview of the course, details on the teacher (including office hours), a complete syllabus and information on credits.

Tabs on the right side of the page include Posts, Notes and Materials. Posts are updates from the teachers that can be pushed out to students, such as assignments and to-do lists -- assignments, for example, will appear right in iBooks for quick and easy homework (but you’ll still have to do the hard part yourself, sorry). The Materials tab includes a list of everything you’ll need for completing the course, including books, videos, audio and documents, with the ability to buy them with a tap if you don’t already have them.

But what about signing up for courses in the first place? Yes, the iTunes U app offers this ability as well with a single tap. Cue returned to the stage to hail the long list of schools currently using the previous iTunes U, along with six who have had early access to the new app: Duke, Yale, HACC, MIT and The Open University.

The new iTunes U app isn’t just about higher education, either: K-12 schools can now join in the fun. "This means that teachers in these schools will now be able to deliver full online courses to anyone for free,” Cue explained. The new universal app is free and available now from the iOS App Store in 123 countries.

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