Classical Analysis in the Complex Plane e-bog

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.Key features:* Offers over 70 pages of rich historical notes that are scattered throughout the text to enhance the mathematics presented* Features challenging exercises along with hints on how to solve them* Includes numerous helpful remarks after definitions and examples* Provides an extensive bibliography with over 2,000 entriesThis 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.