» Thu May 31, 2012 6:53 pm
You can indeed get free spells at the college, at certain points, but they aren't spellbooks, they are directly added to you during dialogue. Before entrance to the college, you are given a test to see if you are worthy to proceed. The "gatekeeper" chooses an apprentice spell at random from one of the various schools and asks you if you can cast it. If you don't already have the spell she will teach it to you for 30 gold, although I'm pretty sure that if you have less than 30 gold, she'll teach it to you anyway, as that has happened to me once (I think). Anyway, one of the spells she can teach you is the firebolt you're looking for. Also, after entrance to the college, you can get one of the masters to teach you the Lesser Ward spell for free... in fact, you pretty much have to learn it if you don't already know it, because the only way to keep the questline going in the college is to cast the ward spell.
-Loth
Edit: I forgot to mention that you should save right before talking to the college gatekeeper, assuming you are trying to get the firebolt for free. If she asks you to try a different spell than firebolt, just reload your game until she does.