Introduction to Real Analysis

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 constituted thus 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.