I'm enrolling in my first real analysis course this fall called "basic real analysis" that uses Wade as the text. Amazon makes it clear that this is one of the worst analysis texts out there, but there's also another course called "Intro to Real Analysis" that uses Rudin's Principles of Analysis. Technically, one should take basic analysis first, but it seems to be that some students at my school just skip basic and take Intro Analysis. I've taken multivariable calculus and basic linear algebra, so do you think I can handle Rudin?
Yes, you will be able to handle Rudin, but you'll have to work hard. Real analysis is not a joke, so better be prepared. Also, I very much suggest that you buy another book to complement Rudin. Rudin sucks at explaining intuition at times, and another book might bring a breeze of fresh air to the topic.
I was thinking about the exact same thing, since we go to the same school. Thing is, Imbrie's reviews aren't all that fantastic either, and this is supposed to be a pretty damn tough class. Plus it conflicts with Math 5210 which is required for a Physics BS, so I'll probably be putting it off til next year.
A not so known textbook on Analysis is Mathematical Analysis by Ken Bimore. It'll be helpful if this is your first time taking Real Analysis.
Having a second Analysis textbook is a god-send at times, so I would highly recommend it. The two textbooks I used were: "Analysis: with an introduction to proof" by Stephen R. Lay and "Understanding Analysis" by Stephen Abbott Both were pretty comprehensive, and it helped to switch between the two whenever I felt the other failed at explaining the concepts I was covering. Hope this helps.