Real and Complex Analysis

1. Front Matter

   Pages i-xi

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2. Holomorphic and Harmonic Functions

   • Rajnikant Sinha

   Pages 1-188

3. Conformal Mapping

   • Rajnikant Sinha

   Pages 189-308

4. Analytic Continuation

   • Rajnikant Sinha

   Pages 309-427

5. Special Functions

   • Rajnikant Sinha

   Pages 429-678

6. Back Matter

   Pages 679-679

   PDF

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

“I think that this book will be useful for students who could, for example, practice restoring the traditional order: theorems followed by their proofs. As always, mathematical knowledge needs to be rethought.” (Richard Becker, Mathematical Reviews, May, 2023)

• Varanasi, India

  Rajnikant Sinha

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.

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