Modern Real and Complex Analysis 1st Edition by Bernard R. Gelbaum (PDF)

Description

Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this textoffers a lucid presentation of all the topics essential to graduatestudy in analysis. While maintaining the strictest standards ofrigor, Professor Gelbaum’s approach is designed to appeal tointuition whenever possible. Modern Real and Complex Analysisprovides up-to-date treatment of such subjects as the Daniellintegration, differentiation, functional analysis and Banachalgebras, conformal mapping and Bergman’s kernels, defectivefunctions, Riemann surfaces and uniformization, and the role ofconvexity in analysis. The text supplies an abundance of exercisesand illustrative examples to reinforce learning, and extensivenotes and remarks to help clarify important points.

User’s Reviews

Editorial Reviews: From the Publisher Using a contemporary approach and a lively style, Gelbaum combines real and complex analysis, covering all major topics. He discusses topology in three ways: via open sets, nets and filters. Features a detailed exploration of the link between measure as derived from a Daniell functional and classical Lebesgue-Caratheodory measure. Includes complete definitions of all mathematical concepts as well as numerous exercises and illustrations. From the Inside Flap Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum’s approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman’s kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points. From the Back Cover Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum’s approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman’s kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points. About the Author BERNARD R. GELBAUM is Professor of Mathematics at the State University of New York at Buffalo. He has previously served on the faculties of the University of Minnesota, the University of California, Irvine, and as a Fulbright Senior Scholar at University College, Galway, Ireland. He has published research in analysis and probability theory and is the author of Theorems and Counterexamples in Mathematics; Problems in Real and Complex Analysis; and Linear Algebra: Basics, Practice and Theory. Read more

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