Concepts in Real Analysis

Real analysis is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real numbers, and continuity, smoothness and related properties of real-valued functions. Real analysis is an area of analysis that studies concepts such as sequences and their limits, continuity, differentiation, integration and sequences of functions. By definition, real analysis focuses on the real numbers, often including positive or negative infinity. The real numbers have several important lattice-theoretic properties that are absent in the complex numbers. Most importantly, the real numbers form an ordered field, in which addition and multiplication preserve positivity. Moreover, the ordering of the real numbers is total, and the real numbers have the least upper bound property. The present publication has been written by keeping in view the basic concepts of the subject.