Real and Complex Analysis

Volume 2

  • Rajnikant Sinha

Table of contents

  1. Front Matter
    Pages i-xi
  2. Rajnikant Sinha
    Pages 1-188
  3. Rajnikant Sinha
    Pages 189-308
  4. Rajnikant Sinha
    Pages 309-427
  5. Rajnikant Sinha
    Pages 429-678
  6. Back Matter
    Pages 679-679

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 complex analysis, most of which are the work of great mathematicians of the 19th and 20th centuries.


Holomorphic functions Harmonic Functions Conformal Mapping Analytic Continuation Laurent Series Euler’s Constant Riemann Hypothesis

Authors and affiliations

  • Rajnikant Sinha
    • 1
  1. 1.VaranasiIndia

Bibliographic information