Overview
Discusses major topics in real and complex analysis
Includes the essential analysis that is needed for the study of functional analysis
Presents applications of complex analysis to analytic number theory
Features over 800 step-by-step, fully solved examples
Is useful to undergraduate students of mathematics and engineering
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Table of contents(3 chapters)
About this book
This is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. Intended for undergraduate students of mathematics and engineering, it covers the essential analysis that is needed for the study of functional analysis, developing the concepts rigorously with sufficient detail and with minimum prior knowledge of the fundamentals of advanced calculus required. Divided into three chapters, it discusses exponential and measurable functions, Riesz representation theorem, Borel and Lebesgue measure, -spaces, Riesz–Fischer theorem, Vitali–Caratheodory theorem, the Fubini theorem, and Fourier transforms. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complex analysis, most of which are the work of great mathematicians of the 19th and 20th centuries.
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Authors and Affiliations
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Varanasi, India
Rajnikant Sinha
About the author
RAJNIKANT SINHA is former professor of mathematics at Magadh University, Bodh Gaya, India. A passionate mathematician, Prof. Sinha has published numerous interesting research findings in international journals and books, including Smooth Manifolds (Springer) and the contributed book Solutions to Weatherburn’s Elementary Vector Analysis. His research focuses on topological vector spaces, differential geometry and manifolds.
Bibliographic Information
Book Title: Real and Complex Analysis
Book Subtitle: Volume 1
Authors: Rajnikant Sinha
DOI: https://doi.org/10.1007/978-981-13-0938-0
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Hardcover ISBN: 978-981-13-0937-3Published: 15 November 2018
eBook ISBN: 978-981-13-0938-0Published: 04 November 2018
Edition Number: 1
Number of Pages: IX, 637
Topics: Analysis