Bernard R. Gelbaum
Problems in real and complex analysis - New York, Springer-Verlag: [c1992] - 488 p. - Problem book in mathematics .
Real Analysis: Problems
Chapter 1. Set Algebra and Function Lattices
Chapter 2. Topology, Limits, and Continuity
Chapter 3. Real- and Complex-valued Functions
Chapter 5. Measure and Topology
Chapter 6. Measure Theory
Chapter 7. Topological Vector Spaces
Complex Analysis: Problems
Chapter 1. Elementary Theory
Chapter 2. Functions Holomorphic in a Disc
Chapter 3. Functions Holomorphic in a Region
Chapter 5. Entire Functions
Chapter 6. Analytic Continuation
Chapter 7. Singularities
Chapter 8. Harmonic Functions
Chapter 9. Families of Functions
Chapter 10. Convexity Theorems
In the pages that follow there are: A. A revised and enlarged version of Problems in analysis (PIA) . (All typographical, stylistic, and mathematical errors in PIA and known to the writer have been corrected.) B. A new section COMPLEX ANALYSIS containing problems distributed among many of the principal topics in the theory of functions of a complex variable. C. A total of 878 problems and their solutions. D. An enlarged Index/Glossary and an enlarged Symbol List. Notational and terminological conventions are to be found for the most part under Conventions at the beginnings of the chapters. Spe cial items not included in Conventions are completely explained in the Index/Glossary. The audience to which the current book is addressed differs little from the audience for PIA. The background of the reader is assumed to include a knowledge of the basic principles and theorems in real and complex analysis as those subjects are currently viewed. The aim of the problems is to sharpen and deepenthe understanding of the mechanisms that underlie modern analysis. I thank Springer-Verlag for its interest in and support of this project. State University of New York at Buffalo B. R. G. v Contents The symbol alb under Pages below indicates that the Problems for the section begin on page a and the corresponding Solutions begin on page b. Thus 3/139 on the line for Set Algebra indicates that the Problems in Set Algebra begin on page 3 and the corresponding Solutions begin on page 139.---Summary provided by publisher
9788184896275
Mathematics
QA301
Problems in real and complex analysis - New York, Springer-Verlag: [c1992] - 488 p. - Problem book in mathematics .
Real Analysis: Problems
Chapter 1. Set Algebra and Function Lattices
Chapter 2. Topology, Limits, and Continuity
Chapter 3. Real- and Complex-valued Functions
Chapter 5. Measure and Topology
Chapter 6. Measure Theory
Chapter 7. Topological Vector Spaces
Complex Analysis: Problems
Chapter 1. Elementary Theory
Chapter 2. Functions Holomorphic in a Disc
Chapter 3. Functions Holomorphic in a Region
Chapter 5. Entire Functions
Chapter 6. Analytic Continuation
Chapter 7. Singularities
Chapter 8. Harmonic Functions
Chapter 9. Families of Functions
Chapter 10. Convexity Theorems
In the pages that follow there are: A. A revised and enlarged version of Problems in analysis (PIA) . (All typographical, stylistic, and mathematical errors in PIA and known to the writer have been corrected.) B. A new section COMPLEX ANALYSIS containing problems distributed among many of the principal topics in the theory of functions of a complex variable. C. A total of 878 problems and their solutions. D. An enlarged Index/Glossary and an enlarged Symbol List. Notational and terminological conventions are to be found for the most part under Conventions at the beginnings of the chapters. Spe cial items not included in Conventions are completely explained in the Index/Glossary. The audience to which the current book is addressed differs little from the audience for PIA. The background of the reader is assumed to include a knowledge of the basic principles and theorems in real and complex analysis as those subjects are currently viewed. The aim of the problems is to sharpen and deepenthe understanding of the mechanisms that underlie modern analysis. I thank Springer-Verlag for its interest in and support of this project. State University of New York at Buffalo B. R. G. v Contents The symbol alb under Pages below indicates that the Problems for the section begin on page a and the corresponding Solutions begin on page b. Thus 3/139 on the line for Set Algebra indicates that the Problems in Set Algebra begin on page 3 and the corresponding Solutions begin on page 139.---Summary provided by publisher
9788184896275
Mathematics
QA301