A Second Course in Mathematical Analysis

This book is a truly jewel of analysis, the best book I have found so far in analysis, not for nothing it is the one used for the real analysis course dictated at my University and is the one more asked by mathematics students from the Astronomy, Physics & Mathematics library here also (Pontificia Catholic University of Chile). It has 14 chapters, of which I have only studied the first 9 with exception of chapter 8. In general, I haven't done the exercises but just a few, my approach with books is like peeling an onion on a first reading just read and understand what's being said, on a second reading try the exercises (in this way you can go as quick as you can on covering the material) etc. Also about the exercises I MUST point out that the majority come with answers at the back of the book! I found this awesome and specially suited for self study (which is my case, by the way). The writing is very clear, beautiful and complete. I specially like chapters 1 to 3 where the main concepts addressed are sets, metric spaces, functions and point set topology, chapter 7 where everything related to the concept of the linear derivative for functions of arbitrary domain and range (e.g. f:Rm x Rn-->Rp) are deal with paving the way for the all importants Implicit and Inverse theorem. Chapter 9 (the one I'm currently working on) is about Fourier Series and I must say that I have not found in anywhere else such a complete treatment about Fourier Series and I'm very pleased about this situation. <br />Finally I must tell you that I also have on mathematical analysis the books of T.Apostol, W.Rudin, Courant-John and this is by far the better so if you are thinking about this title my advice is buy it because you will be getting one of those book whose weight is worth on gold, that is, a terrific jewel of analysis.

This is the second volume ot the authors little book A first course in mathematical analysis. This volume is Awell written exposition of the study of functions in several variables. Differentiation , integration and all. Very good reference book.