An Introduction to Real Analysis

This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.

Logic and Proof Techniques. Sets and Functions. Real Numbers. Open and Closed Sets. Cardinality. Real-valued Functions. Real Sequences. Real Sequences (Contd.). Infinite Series. Infinite Series (Contd.). Limits of Functions. Continuous Functions. Discontinuous Functions. Uniform and Absolute Continuities and Functions of Bounded Variation. Differentiable Functions. Higher Order Differentiable Functions. Convex Functions. Indeterminate Forms. Riemann Integration. Properties of the Riemann Integral. Improper Integrals. Riemann-Lebesgue Theorem. Riemann-Stieltjes Integral. Sequences of Functions. Sequences of Functions (Contd.). Series of Functions. Power and Taylor Series. Power and Taylor Series (Contd.). Metric Spaces. Metric Spaces (Contd.).Bibliography. Index.

Dr. Ravi P Agarwal was born in Moradabad (India) on July 10, 1947. After completing his schooling, he earned his Master’s degree from Agra University in 1969 and Ph. D. in Mathematics (1973) at the Indian Institute of Technology in Madras, India. Dr. Agarwal has been actively involved in research as well as pedagogical activities for the last 45 years. His major research interests include Numerical Analysis, Differential and Difference Equations, Inequalities, and Fixed Point Theorems. He has published 40 research monographs and more than 1,400 publications in prestigious national and international mathematics journals. He has been recognized as one of the “World’s Most Influential Scientific Minds” in 2014 by Thomas Reuters. He serves as a co-Editor-in-Chief of four prestigious scientific Journals published by SpringerOpen. He has served over 40 journals in the capacity of an Editor or Associate Editor, and published 24 books as an editor. Cristina Flaut is a professor in the Department of Mathematics and Computer Science at Ovidius University, Romania. Dr Flaut is the co-author of more than two dozen papers and monographs. Her research interests include linear algebra, non-associative algebras, coding theory. Donal O’Regan is a professor in the School of Mathematics, Statistics and Applied Mathematics at National University of Ireland, Galway. He is the author of 25 books and over 1200 papers. His research interest is in nonlinear analysis. He alsoserves on many editorial boards.