I have just completed my undergraduate course in mathematics but I don't feel better in analysis, there is a mugup of books in my book collection But don't know what to choose who will help me to teach me analysis I have the options of Battle, Apostol and Rudin and some other local book so will u plz suggest me which book will provide me a rigour course at elementary level so that I could understand Rudin well in my master,
P. M. Fitzpatrick - Advanced Calculus. Here is the reviews.
As a next advanced book after that, is H. L. Royden and P. Fitzpatrick - Real Analysis.
Just Fitzpatrick's Advanced Calculus is enough to cover Rudin's Real Analysis, and it includes also many exercises as well as it's a rigorous text and very readable for self-learning as well.
Well I have quite a collection of analysis books myself. Here are my favorites.
"Introduction to real analysis - Bartle and Sherbert" Is my favorite book on the subject. Everything is well laid out and easy to understand. Unfortunately the treatment very elementary in nature. For example there is no treatment of improper integrals or a thorough treatment of power series. If you are weak in this subject I suggest you do a thorough study of this book. Solve all the exercises.
"Mathematical analysis - Apostol" Is a exhaustive book on the subject. Every course I have ever done in real analysis is covered in this book. The exercises are very well laid out. This is the book I would pick if I had to brush up my analysis.