Introduction to Real Analysis: 0 - Softcover

Introduction to Real Analysis is designed as a course of real analysis of functions of a single variable and thus it is suitable for any student who desires to study real analysis for the first time. Therefore it meets the requirement of the contents of syllabi of all Indian universities designed for undergraduate classes. Each chapter begins with an analytical treatment of the subject matter by assigning the conditions necessary for its growth by inferring the properties of a mathematical system and then analysing the system by means of the resolution into the fundamental properties of which it is constitutedthus the theory demands three main steps, namely, assumptions, inference and resolution. An attempt has always been made to present the subject matter in a clear and lucid manner. The collection of examples and problems is the result of many years of teaching analysis at the college level.1 sets and functions. 2 real number system. 3 countable sets. 4 open sets and closed sets. 5 sequences of real numbers. 6 infinite series. 7 limits and continuity of functions. 8 differentiation. 9 the riemann tntegral. 10 the riemann stietljes integral. 11 improper integrals. 12 sequence and series of functions.

Dr. B.S.Vatsa is the Head of the Department of Mathematics at St. Johns College, Agra for the last ten years. He did his Ph.D. in Coding Theory with the application of linear algebra and Galois theory. He has published several papers in international journals in Coding Theory, Modern Algebra and Analysis. He is the Dean of Science Faculty of Agra University; the Convenor of Board of Studies of Mathematics; and also the Convenor of Research Degree Committee of Agra University. He is the author of more than 20 books in Hindi as well as in English.