I'm taking Calculus 3 at the moment often I like to look at the courses I am going to be taking in the coming semester. At my school, they only list Math Analysis and there are no courses for Real Analysis or Advanced Calculus. Some professors have mentioned they are different while others say they cover the same thing, so I'm a bit confused. I looked at the books at the library and it seems that the three subject cover very similar topics. I have three questions:
1. Are they the same subjects just branded differently or are there differences such as the style with which they approach the material and even the material itself covered?
2. If so which is the best of the three to tackle first? Since I cannot take the Math Analysis course at my school for another year and half( course if taught in the spring of even number years only) I may as well self study til then.
3. What is a recommended set of best books to buy for each (if they're different) or if they are more or less the same what are some recommended books that cover the topics most concisely and give the material a "modern treatment"?
Thanks for the help in advance!