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Complex Variables (Dover Books on Mathematics)

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Book Details

  • Author: Robert B. Ash

  • Publisher: Dover

  • Edition: 2

  • Binding: Paperback

  • Number of Pages: 214

  • Release Date: 19-10-2007

  • ISBN: 9780486462509

  • Package Dimensions: 9.1 x 6.1 x 0.5 inches

  • Languages: English

About The Book
"Complex Variables" by Robert B. Ash offers a concise yet comprehensive exploration of complex analysis, tailored for graduate and advanced undergraduate students who have completed an introductory course in real analysis. This revised and updated edition of Ash’s popular text provides thorough and clear explanations of essential concepts in the field, complemented by a wide range of problems and solutions to deepen students’ understanding.

The book begins with an introduction to basic definitions, including the topology of the complex plane, analytic functions, and the Cauchy-Riemann equations, before moving on to more advanced topics. The early chapters focus on core theories such as the general Cauchy theorem, its applications to singularities, residue theory, and the open mapping theorem for analytic functions. It also explores linear fractional transformations and conformal mappings in great detail, offering students a solid grounding in these key concepts.

One of the highlights of this text is the thorough treatment of the Riemann mapping theorem, a central result in complex analysis. The book also delves into the factorization of analytic functions, which is an important topic for those seeking to apply complex analysis in various mathematical contexts. To conclude, the text provides a proof of the prime number theorem, applying many of the ideas and results developed throughout the book.

With its blend of theory and application, this text is ideal for students seeking a deeper understanding of complex analysis. The clear writing style, well-structured chapters, and an abundance of exercises make this book a valuable resource for those looking to master the essential techniques of complex variables.