Okay, so it's not free like your local library, but for $20 you can have library privileges at UCLA. You have to present proof of current enrollment (every quarter) and a photo ID at either Young Research Library or Louise M. Darling Biomedical Library to get a library card. This could be well worth it when you're enrolled in say, Design History and Context.
Here is a link to the UCLA Arts Library: http://www.library.ucla.edu/libraries/arts/index.cfm
Here is a link about researching design and media arts topics specifically:
Also, here is a link to design topic bibliographies at AIGA:
Also, in terms of resources, if you haven't spent a lot of time browsing the back pages of the UCLA Extension catalog (General Information), may I suggest you do so. It's a good orientation into what resources are available and how to go about certain administrative tasks. It's a reference I use often!
[Thanks to graduate Karen Ng and new student Aileen Tu.]