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Contents Preface 1 Natural Number 2 Real and Complex Numbers 3 Sequences 4 Infinite Series 5 Harmonic Series 6 Power Series 7 Fourier Series 8 Cauchy Convergence 9 Limits and Continuity 10 Differential Calculus 11 Differentiability 12 Techniques of Integration 13 Improper Integrals 14 Multivariable Calculus 15 Laplace Transforms Bibliography IndexReal Analysis or theory of functions of a real variable is a significant branch dealing with the set of real numbers 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 which studies concepts such as sequences and their limits continuity differentiation integration and sequences of functions By definition real analysis of 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 filed in which addition and multiplication preserve positivityPresent book covers all dimensions of the subject particularly aimed at the students who intend to master in this field of Mathematics This book is an asset for all scholars researchers and students Jacket 378 pp.