Introduction to Real Analysis by Robert G Bartle HB 1992 Wiley Pub Used

Description: Separating from the spine highlights throughout PREFACE The study of real analysis has great value for any student who wishes to go beyond the routine manipulations of formulas to solve standard problems, for the ability to think deductively and analyze complicated examples is essential to modifying and extending concepts to new contexts. Furthermore, the central concepts of limit and continuity in real analysis play a vital role in a great many areas of mathematics and its applications. Indeed, mathematics has become an indispensable tool in many areas, including economics and management science as well as the physical sciences, engineering, and computer science, and real analysis is one of the main pillars of mathematics. Our goal is to provide an accessible, reasonably paced textbook in the fundamental concepts and techniques of real analysis for students in these areas. Though very challenging, the study of real analysis proves to be rewarding in later work in mathematics and its applications. We restrict our attention here to functions of one variable; readers who wish to study functions of several variables are referred to the book The Elements of Real Analysis (cited in this book as ERA) by the first-named author. The first edition of this book was very well received, and we have kept its spirit and user-friendly approach in this edition. For the second edition, we examined every section, moved certain topics to new locations, and added a few new topics; these changes are described below. The problem sets were all reviewed, with some exercises revised and a considerable number of new ones added. There is more material in the book than is needed for a semester, and we have noted that a number of sections can be partially, or entirely, omitted. To provide some help for the students in their analyzing proofs of theorems, we have included an appendix on "Logic and Proofs" that discusses topics such as implications, quantifiers, negations, contrapositives, and different types of proofs. We have kept the discussion informal to avoid becoming mired in the technical details of formal logic. Its location in an appendix indicates that it is optional reading and can be examined at any time and as needed. We feel that it is a more useful experience to analyze and construct proofs of theorems than simply to read about proofs. One significant change in this edition is that topological concepts, such as open set, closed set, and compactness, have been gathered together and put into a new chapter: Chapter 10, The Topology of R. In the first edition, these topics were

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