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 (4 chapters)
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About this book
This is the second volume of the two-volume book on real and complex analysis. This volume is an introduction to the theory of holomorphic functions. Multivalued functions and branches have been dealt carefully with the application of the machinery of complex measures and power series. 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 four chapters, it discusses holomorphic functions and harmonic functions, Schwarz reflection principle, infinite product and the Riemann mapping theorem, analytic continuation, monodromy theorem, prime number theorem, and Picard’s little theorem. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complexanalysis, most of which are the work of great mathematicians of the 19th and 20th centuries.
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Bibliographic Information
Book Title: Real and Complex Analysis
Book Subtitle: Volume 2
Authors: Rajnikant Sinha
DOI: https://doi.org/10.1007/978-981-13-2886-2
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Hardcover ISBN: 978-981-13-2885-5Published: 10 December 2018
eBook ISBN: 978-981-13-2886-2Published: 22 November 2018
Edition Number: 1
Number of Pages: XI, 679
Number of Illustrations: 9 b/w illustrations
Topics: Analysis