Classical Analysis in the Complex Plane - (Cornerstones) by Robert B Burckel (Hardcover)
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<p/><br></br><p><b> Book Synopsis </b></p></br></br><p>This volume is a comprehensive guide to a single complex variable that goes above and beyond any introductory course. In developing the tools necessary for the study of the complex plane, the author's well-organized treatment in the first chapters provide all the essential elements for subsequent chapters. The book explores such topics as plane topology, holomorphic functions, the Cauchy--Gourset theorem, local theory, the Schwarz lemma, the Riemann mapping theorem, and many more.</p> <p>Key features: </p> <p>* Offers over 70 pages of rich historical notes that are scattered throughout the text to enhance the mathematics presented</p> <p>* Features challenging exercises along with hints on how to solve them</p> <p>* Includes numerous helpful remarks after definitions and examples</p> <p>* Provides an extensive bibliography with over 2,000 entries</p> <p>This book may be used in the classroom or as a self-study resource for students. In addition, because of the expansive nature of the material covered, the work may also serve as an excellent reference for researchers in the field. The only prerequisites are differential and integral calculus; however, a familiarity with metric spaces and set theory is also useful.</p><p/><br></br><p><b> From the Back Cover </b></p></br></br><p>This authoritative text presents the classical theory of functions of a single complex variable in complete mathematical and historical detail. Requiring only minimal, undergraduate-level prerequisites, it covers the fundamental areas of the subject with depth, precision, and rigor. Standard and novel proofs are explored in unusual detail, and exercises - many with helpful hints - provide ample opportunities for practice and a deeper understanding of the material.</p><p>In addition to the mathematical theory, the author also explores how key ideas in complex analysis have evolved over many centuries, allowing readers to acquire an extensive view of the subject's development. Historical notes are incorporated throughout, and a bibliography containing more than 2,000 entries provides an exhaustive list of both important and overlooked works. <br></p><p><i>Classical Analysis in the Complex Plane</i> will be a definitive reference for both graduate students and experienced mathematicians alike, as well as an exemplary resource for anyone doing scholarly work in complex analysis. The author's expansive knowledge of and passion for the material is evident on every page, as is his desire to impart a lasting appreciation for the subject.<br></p><p><br></p><p><i>"I can honestly say that Robert Burckel's book has profoundly influenced my view of the subject of complex analysis. It has given me a sense of the historical flow of ideas, and has acquainted me with byways and ancillary results that I never would have encountered in the ordinary course of my work. The care exercised in each of his proofs is a model of clarity in mathematical writing...Anyone in the field should have this book on [their bookshelves] as a resource and an inspiration."</i><br></p>- From the Foreword by Steven G. Krantz<p/><br></br><p><b> About the Author </b></p></br></br>Robert B. Burckel is Professor Emeritus of Mathematics at Kansas State University.
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