Mathematical Analysis

The purpose is to provide development of the subject-matter which is well motivated, rigorous and at the same time not too pedantic. Most of the hard theorems which are either omitted or treated rather skimply in many texts in advanced analysis have been proved with care. Some of them are ordinarily considered too difficult for a standard course in calculus but too elementary for a course of analysis. With the inclusion of those theorems, the book attempts to fill the gap and to make the transfer from elementary calculus to advanced course in analysis as smooth as possible.