Complex Analysis

This is a complete solution guide to all exercises from Chapters 1 to 20 in Rudin's Real and Complex Analysis. The features of this book are as follows: It covers all the 397 exercises from Chapters 1 to 20 with detailed and complete solutions. As a matter of fact, my solutions show every detail, every step and every theorem that I applied.There are 40 illustrations for explaining the mathematical concepts or ideas used behind the questions or theorems.Sections in each chapter are added so as to increase the readability of the exercises.Different colors are used frequently in order to highlight or explain problems, lemmas, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only)Necessary lemmas with proofs are provided because some questions require additional mathematical concepts which are not covered by Rudin.Many useful or relevant references are provided to some questions for your future research.

This is a complete solution guide to all exercises from Chapters 10 to 20 in Rudin's Real and Complex Analysis. The features of this book are as follows: It covers all the 221 exercises from Chapters 10 to 20 with detailed and complete solutions. As a matter of fact, my solutions show every detail, every step and every theorem that I applied.There are 29 illustrations for explaining the mathematical concepts or ideas used behind the questions or theorems.Sections in each chapter are added so as to increase the readability of the exercises.Different colors are used frequently in order to highlight or explain problems, lemmas, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only)Necessary lemmas with proofs are provided because some questions require additional mathematical concepts which are not covered by Rudin.Many useful or relevant references are provided to some questions for your future research.

This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices.

With its emphasis on the argument principle in analysis and topology, this book represents a different approach to the teaching of complex analysis. The three-part treatment provides geometrical insig

複分析是研究復函數，特別是亞純函數和複解析函數的數學理論。複分析的應用領域較爲廣泛，在其它數學分支和物理學中也起著重要的作用。包括數論、應用數學、流體力學、熱力學和電動力學。

This user-friendly textbook introduces complex analysis at the beginning graduate or advanced undergraduate level. Unlike other textbooks, it follows Weierstrass' approach, stressing the importance of power series expansions instead of starting with the Cauchy integral formula, an approach that illuminates many important concepts. This view allows readers to quickly obtain and understand many fundamental results of complex analysis, such as the maximum principle, Liouville's theorem, and Schwarz's lemma. The book covers all the essential material on complex analysis, and includes several elegant proofs that were recently discovered. It includes the zipper algorithm for computing conformal maps, as well as a constructive proof of the Riemann mapping theorem, and culminates in a complete proof of the uniformization theorem. Aimed at students with some undergraduate background in real analysis, though not Lebesgue integration, this classroom-tested textbook will teach the skills and intui

This textbook is intended for a one semester course in complex analysis for upper level undergraduates in mathematics. Applications, primary motivations for this text, are presented hand-in-hand with

This book features papers presented during a special session on algebra, functional analysis, complex analysis, and pluripotential theory. Research articles focus on topics such as slow convergence, s

This volume conveys some of the surprises, puzzles and success stories in high-dimensional and complex data analysis and related fields. Its peer-reviewed contributions showcase recent advances in var

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences.Traditi

The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayas

This book discusses a variety of topics in mathematics and engineering as well as their applications, clearly explaining the mathematical concepts in the simplest possible way and illustrating them wi

Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex a

This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Ste

Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension

This volume conveys some of the surprises, puzzles and success stories in high-dimensional and complex data analysis and related fields. Its peer-reviewed contributions showcase recent advances in var

This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics for a complete list of titl

The aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in c

The aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in c

This book develops an understanding of sophisticated tools by using them. Complex variable theory is developed. The first three chapters and selected topics make a nice course. This course should appe

This book systematizes recent research work on variable-structure control. It is self-contained, presenting necessary mathematical preliminaries so that the theoretical developments can be easily unde

This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of th

Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book contains survey and expository articles by leading experts in their corresponding fi