Introduction to Mathematical Analysis

This book is a straightforward and comprehensive presentation of the concepts and methodology of elementary real analysis. Targeted to undergraduate students of mathematics and engineering, it serves as the foundation for mathematical reasoning and proofs. The topics discussed are logic, methods of proof, functions, real number properties, sequences and series, limits and continuity and differentiation and integration (Riemann integral and Lebesgue integral). The book explains the concepts and theorems through geometrical and pictorial representation. Limits of sequences and functions, topology of metric spaces, continuity of functions and the Cauchy sequence have been thoroughly discussed in the book.

Chapter 1 The System of Real Numbers.- Chapter 2 Real Sequences.- Chapter 3 Infinite Series of Numbers.- Chapter 4 Limits, Continuity and Differentiability.- Chapter 5 Metric Spaces.

Naokant Deo is a professor at the Department of Applied Mathematics, Delhi Technological University, New Delhi, India. He completed his Ph.D. in Mathematics from Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh, India. His areas of interest include real analysis and approximation theory with a focus on positive linear operators. Professor Deo is a recipient of the CAS-TWAS Fellowship awarded by the Chinese Academy of Sciences, Beijing, China, and the International Centre for Theoretical Physics, Trieste, Italy. He is an active member of the Indian Mathematical Society, India, and Research Group in Mathematical Inequalities and Applications, Australia. His research works have appeared in prestigious national and international journals.

Ryozi Sakai is a renowned researcher at the Department of Mathematics at Meijo University, Aichi, Japan, since 2009. Earlier, he had been enjoying a successful career as a senior high school teacher from 1968–2003. His main research area is polynomial approximation theory. Born in 1943, in Miyazaki, Japan, he received a Doctor of Science (Mathematics) degree from Kanazawa University in Japan, in 1992. Dr. Sakai has published numerous research papers in esteemed journals throughout his career.