May 2024
Intermediate to advanced
585 pages
15h 38m
English
Overview
This text book is designed for an undergraduate course on mathematics. It covers the basic material that every graduate student should know in the classical theory of functions of real variables, measures, limits and continuity. This text book offers readability, practicality and flexibility. It presents fundamental theorems and ideas from a practical viewpoint, showing students the motivation behind mathematics and enabling them to construct their own proofs.
About The Author –
The author completed his Ph.D. in mathematics from Ramanujan Institute for Advanced Study, University of Madras, in 1977. He joined Madurai Kamaraj University as a lecturer in 1978, became a senior professor in 2007 and was the chair person, School of Mathematics, during 2006–2008. He received a Young Scientist Career Award from the University Grant Commission, India, in 1985 and was a recipient of the C. L. Chandna Award from Canada in recognition of his “Distinguished and Outstanding Contributions to Mathematics Teaching and Research” in 1998. He has published about sixty research papers in refereed international journals. His topics of interest include Real and Complex Analysis and Generalized Integral Transforms. After retirement from Madurai Kamaraj University in 2010, he also served as a guest faculty at the Central University of Tamil Nadu, Thiruvarur, during 2010–2011.
Book Contents –
Chapter 1: Basic Properties of the Real Number System
Chapter 2: Some Finer Aspects of Set Theory
Chapter 3: Sequences and Series
Chapter 4: Topological Aspects of the Real Line
Chapter 5: Limits and Continuity
Chapter 6: Differentiation
Chapter 7: Functions of Bounded Variation
Chapter 8: Riemann Integration
Chapter 9: Sequences and Series of Functions
Chapter 10: Power Series and Special Functions
Chapter 11: Fourier Series
Chapter 12: Real-Valued Functions of Two Real Variables
Chapter 13: Lebesgue Measure Andintegration
Chapter 14: Lp-Spaces
Bibliography
Index
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